Essay Eight Part Two: Why Opposing Forces Aren't 'Contradictions'


Technical Preliminaries


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As is the case with all my Essays, nothing here should be read as an attack either on Historical Materialism [HM] -- a theory I fully accept --, or, indeed, on revolutionary socialism. I remain as committed to the self-emancipation of the working class and the dictatorship of the proletariat as I was when I first became a revolutionary thirty-five years ago.


The difference between Dialectical Materialism [DM] and HM, as I see it, is explained here.


In what follows, I have taken the results of Essay Eight Part One -- Change Through 'Internal Contradiction' -- for granted.


It is also worth pointing out that a good 50% of my case against DM has been relegated to the End Notes. Indeed, in this particular Essay, most of the supporting evidence is to be found there. This has been done to allow the main body of the Essay to flow a little more smoothly. This means that if readers want fully to appreciate my case against DM, they will need to consult this material. In many cases, I have added numerous qualifications, clarifications, and considerably more detail to what I have to say in the main body. In addition, I have raised several objections (some obvious, many not -- and some that will have occurred to the reader) to my own arguments, which I have then answered. [I explain why I have adopted this tactic in Essay One.]


If readers skip this material, then my answers to any qualms or objections they might have will be missed, as will my expanded comments and clarifications.


[Since I have been debating this theory with comrades for well over thirty years, I have heard all the objections there are! (Many of the more recent debates have been listed here.)]


Furthermore, phrases like "ruling-class theory", "ruling-class view of reality", "ruling-class ideology" (etc.) used at this site (i.e., in connection with Traditional Philosophy and DM), aren't meant to suggest that all or even most members of various ruling-classes actually invented these ways of thinking or of seeing the world (although some of them did -- for example, Heraclitus, Plato, Cicero, and Marcus Aurelius). They are intended to highlight theories (or "ruling ideas") that are conducive to, or which rationalise, the interests of the various ruling-classes history has inflicted on humanity, whoever invents them. Up until recently this dogmatic approach to knowledge had almost invariably been promoted by thinkers who either relied on ruling-class patronage, or who, in one capacity or another, helped run the system for the elite.**


However, that question will become the central topic of Parts Two and Three of Essay Twelve (when they are published); until then, the reader is directed here, here, and here for more details.


[**Exactly how this applies to DM will, of course, be explained in the other Essays published at this site (especially here, here, and here). In addition to the three links in the previous paragraph, I have summarised the argument -- but this time for absolute beginners -- here.]


Several readers have complained about the number of links I have added to these Essays because they say it makes them very difficult to read. Of course, DM-supporters can hardly lodge that complaint since they believe everything is interconnected, and that must surely apply even to Essays that attempt to debunk that very idea. However, to those who find such links do make these Essays difficult to read I say this: ignore them -- unless you want to access further supporting evidence and argument for a particular point, or a certain topic fires your interest.


Others wonder why I have linked to familiar subjects and issues that are part of common knowledge (such as the names of recent Presidents of the USA, UK Prime Ministers, the names of rivers and mountains, the titles of popular films, or certain words that are in common usage). I have done so for the following reason: my Essays are read all over the world and by people from all 'walks of life', so I can't assume that topics which are part of common knowledge in 'the west' are equally well-known across the planet -- or, indeed, by those who haven't had the benefit of the sort of education that is generally available in the 'advanced economies', or any at all. Many of my readers also struggle with English, so any help I can give them I will continue to provide.


Finally on this specific topic, several of the aforementioned links connect to web-pages that regularly change their URLs, or which vanish from the Internet altogether. While I try to update them when it becomes apparent that they have changed or have disappeared I can't possibly keep on top of this all the time. I would greatly appreciate it, therefore, if readers informed me of any dead links they happen to notice.


In general, links to 'Haloscan' no longer seem to work, so readers needn't tell me about them! Links to RevForum, RevLeft, Socialist Unity and The North Star also appear to have died.




As of May 2024, this Essay is just over 143,500 words long; a much shorter summary of some its main ideas can be accessed here.


The material presented below does not represent my final view of any of the issues raised; it is merely 'work in progress'.


[Latest Update: 25/05/24.]


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(1) Forces And Contradictions


(a) Introduction


(b) Gravity Is Reassuringly Undialectical


(2) Is This An Apt Analogy?


(a) Is "Contradictory Force" Merely A 'Dialectical' Figure Of Speech'?


(b) Are 'Contradictions' Simply Mathematical Models?


(c) Are 'Contradictions' Properties Of Totalities?


(3) What Exactly Do Forces 'Contradict'?


(a) Different Types Of Force Couples


(b) AA-, And RR-Forces


(c) Interlude One: The Classical Problem Of Forces


(d) Interlude Two: Several Annoying Technicalities


(e) First Attempts At Clarification


(f) Interlude Three: Hamlet Without The Prince


(g) Interlude Four: Limit Or No Limit -- That Is The Question


(h) AR-Forces


(i) Interlude Five: 'Opposites'


(j) Interlude Six: Magnetic And Other Natural Forces


(4) A Contradictory Theory?


(a) Literal Forces In Opposition


(b) The Revenge Of The Non-Existent


(c) Interlude Seven: Further Complications


(d) Prevention And Its Discontents


(e) Interlude Eight: Tom Weston


(f) A Balanced Account Of Prevention?


(g) S&M?


(h) Hole To Let -- Previous Occupant Self-Destructed


(i) Interlude Nine: Objections Neutralised


(j) Too Many Forces Spoil The Broth


(5) Real Material 'Contradictions'?


(a) Sinking In Concrete


(b) Interlude Ten: Contradictions, Contradictions Everywhere!


(c) Rees, Ollman And 'Concrete Forces'


(d) The Impertinent Explanation


(e) Conflict Resolution


(f) Where The Shoe Pinches


(g) Not What The System Ordered


(h) An Apparent Contradiction, At Last!


(i) Interlude Eleven: Everyday Contradictions


(j) Opposite Tendencies I


(k) Opposite Tendencies II


(l) Interlude Twelve: Opposites, Again?


(m) Interlude Thirteen: Ordinary Language


(n) Interlude Fourteen: Contradictions In Das Kapital?


(o) Heilbroner To The Rescue?


(p) Is The Supposed 'Contradiction Between The Proletariat And The Capitalist Class' Even 'Dialectical'?


(q) Last Chance Saloon


(6) True Contradictions?


(7) Last Rites


(a) Dialectics In ICU


(b) Back To The Drawing-Board?


(c) 'Internally Contradictory'


(d) Dialectics And The Revival Of Teleology


(e) Coup De Grace


(f) For Dialecticians, Truth Is The [W]hole -- Alas, It's Six Foot Deep


(8) Notes


(9) Appendix A: Kant On 'Real Negation'


(10) Appendix B: Plato's Allegory Of The Cave


(11) Appendix C: DM-Fans Struggle To Explain Use Value And Exchange Value


(12) References



Summary Of My Main Objections To Dialectical Materialism


Abbreviations Used At This Site


Return To The Main Index Page


Contact Me


Forces And Contradictions




In this Second Part of Essay Eight I intend to substantiate a claim advanced in Part One, which was that it isn't possible to equate 'contradictions' with 'opposing forces', either literally or figuratively. Hence, the aim is to sever the link that most dialecticians believe exists between opposing forces and 'dialectical contradictions'.


In Part Three, I will pose and then answer the question: What sense, if any, can be made of the term "dialectical contradiction"?


[Spoiler Alert: none whatsoever.]


[As with other Essays at this site, much of the material below has been deliberately restricted to the use of DM-terminology, the employment of which doesn't imply I accept its validity, or that it even makes any sense. It is only being used in order to assist in its demise.]


Be this as it may, Marxist dialecticians nevertheless continue to assert that 'dialectical contradictions' (in nature or society) may be understood as, or modelled by, the inter-relationship between "opposing forces". These forces allegedly condition one another, operating either in equilibrium or in disequilibrium, depending on the prevailing circumstances -- and, indeed, on exactly who is telling the tale. But, they also admit that this view of forces is only valid if it is backed-up in each case by a careful scientific and theoretical analysis of all the relevant issues, the results having been thoroughly and repeatedly tested in practice.


For example, here is Engels:


"Motion is the mode of existence of matter…. All rest, all equilibrium, is only relative, only has meaning in relation to one or another form of motion…. Matter without motion is just as inconceivable as motion without matter…. Each separate movement strives toward equilibrium, and the total motion puts an end to the equilibrium...." [Engels (1976), pp.74-77.]


"So long as we consider things at rest and lifeless, each one by itself…we do not run up against any contradictions in them…. But the position is quite different as soon as we consider things in their motion, their change, their life, their reciprocal influence. Then we immediately become involved in contradictions. Motion itself is a contradiction…. [T]here is a contradiction objectively present in things and processes themselves, a contradiction is moreover an actual force...." [Ibid., pp.152-53.]


"Processes which in their nature are antagonistic, contain internal contradiction; transformation of one extreme into its opposite…. [This is] the negation of the negation…. [which is a] law of development of nature, history and thought; a law which…holds good in the animal an the vegetable kingdoms, in geology, in mathematics, in history and in philosophy…. [D]ialectics is nothing more than the science of the general laws of motion and development of nature, human society and thought." [Ibid., pp.179-80.]


"The great basic thought that the world is not to be comprehended as a complex of ready-made things, but as a complex of processes, in which the things apparently stable…go through an uninterrupted change of coming into being and passing away…. [T]he transformation of energy, which has demonstrated to us that all the so-called forces operative in the first instance in inorganic nature -- mechanical force and its complement, so-called potential energy, heat, radiation (light, or radiant heat), electricity, magnetism and chemical energy -- are different forms of manifestation of universal motion…. [W]e have now arrived at the point where we can demonstrate the interconnection between the processes in nature not only in particular spheres but also the interconnection of these particular spheres on the whole…by means of the facts provided by empirical natural science itself." [Engels (1888), pp.609-11.]


"All motion is bound up with some change of place…. The whole of nature accessible to us forms a system, an interconnected totality of bodies…. [These] react one on another, and it is precisely this mutual reaction that constitutes motion…. When two bodies act on each other…they either attract each other or they repel each other…in short, the old polar opposites of attraction and repulsion…. It is expressly to be noted that attraction and repulsion are not regarded here as so-called 'forces', but as simple forms of motion...." [Engels (1954), pp.70-71.]


"All motion consists in the interplay of attraction and repulsion. Motion, however, is only possible when each individual attraction is compensated by a corresponding repulsion somewhere else…. Hence, all attraction and all repulsions in the universe must mutually balance one another…. Dialectics has proved from the results of our experience of nature so far that all polar opposites in general are determined by the mutual action of the two opposite poles on each other, that the separation and opposition of these poles exist only within their mutual connection and union...." [Ibid., p.72. Bold added.]


"All natural processes are two-sided, they are based on the relation of at least two operative parts, action and reaction. The notion of force, however, owing to its origin from the action of the human organism on the external world…implies that only one part is active, the other part being passive…[and appearing] as a resistance...." [Ibid., p.82.]


"Dialectics…prevails throughout nature…. [T]he motion through opposites which asserts itself everywhere in nature, and which by the continual conflict of the opposites…determines the life of nature...." [Ibid., p.211. Bold added.]


"[A]ttraction is a necessary property of matter, but not repulsion. But attraction and repulsion are as inseparable as positive and negative, and hence from dialectics itself it can already be predicted that the true theory of matter must assign a place to repulsion as to attraction, and that a theory of matter based on mere attraction is false…. Equilibrium is inseparable from motion…. All equilibrium is only relative and temporary…. Motion of the heavenly bodies [is an] approximate equilibrium of attraction and repulsion in motion." [Ibid., pp.243-46. Bold emphasis alone added.]


This is how Bukharin made the point:


"[T]he world consists of forces, acting many ways, opposing each other. These forces are balanced for a moment in exceptional cases only. We then have a state of 'rest', i.e., their actual 'conflict' is concealed. But if we change only one of these forces, immediately the 'internal contradictions' will be revealed, equilibrium will be disturbed, and if a new equilibrium is again established, it will be on a new basis, i.e., with a new combination of forces, etc. It follows that the 'conflict,' the 'contradiction,' i.e., the antagonism of forces acting in various directions, determines the motion of the system…." [Bukharin (1925), p.74. Bold added.]


And here are Lenin's thoughts:


"The identity of opposites…is the recognition…of the contradictory, mutually exclusive, opposite tendencies in all phenomena and processes of nature…. Development is the 'struggle' of opposites." [Lenin (1961), pp.357-58. Bold emphasis alone added.]


Here, too, is Stalin:


"Dialectics comes from the Greek dialego, to discourse, to debate. In ancient times dialectics was the art of arriving at the truth by disclosing the contradictions in the argument of an opponent and overcoming these contradictions. There were philosophers in ancient times who believed that the disclosure of contradictions in thought and the clash of opposite opinions was the best method of arriving at the truth. This dialectical method of thought, later extended to the phenomena of nature, developed into the dialectical method of apprehending nature, which regards the phenomena of nature as being in constant movement and undergoing constant change, and the development of nature as the result of the development of the contradictions in nature, as the result of the interaction of opposed forces in nature." [Stalin (1976b), p.836, quoted from here. Bold emphasis alone added.]


Veteran communist philosopher, Maurice Cornforth, argued as follows:


"If we consider the real, complex movements and interconnections of real complex things, then we find that contradictory tendencies can and do exist in them. For example, if the forces operating in a body combine tendencies of attraction and of repulsion, that is a real contradiction…. [C]ontradiction is the driving force of change…. [O]nly the presence of contradictions in a process…provides the internal conditions making change necessary…. The real universe is…full of contradictions -- the contradictions of attraction and repulsion studied by physics…." [Cornforth (1976), pp.92-95. Bold added.]


The author of TAR, John Rees, had this to say:


"The conservatism of Hegel's system is thus buried in his notion of contradiction. Contradictions in Hegel are merely intellectual contradictions to be resolved by merely intellectual methods…. The dialectic is therefore only a pseudo-dialectic; its contradictions are never those of opposed material forces capable of doing real damage or of effecting real progress…. Marx was, however, obliged to transform completely the terms of the dialectic when he altered its starting point from abstract concepts to real material forces…. The contradictions are no longer simply between concepts but between real, material forces…. Marx and Engels's dialectic is utterly different from Hegel's. It starts from real, material, empirically verifiable contradictions." [Rees (1998), pp.67-69, 83. Bold added.]


Here is leading Trotskyist theorist, the late George Novack:


"The unified process of development is the universality of the dialectic, which maintains that everything is linked together and interactive, in continuous motion and change, and that this change is the outcome of the conflict of opposing forces within nature as well as everything to be found in it." [Quoted in Green Left, 20/10/1993. I owe this reference to Petersen (1994), p.156. Bold emphasis added.]


Woods and Grant expressed themselves as follows:


"Dialectics explains that change and motion involve contradiction and can only take place through contradictions.... Dialectics is the logic of contradiction.... So fundamental is this idea to dialectics that Marx and Engels considered motion to be the most basic characteristic of matter.... [Referring to a quote from Aristotle] [t]his is not the mechanical conception of motion as something imparted to an inert mass by an external 'force' but an entirely different notion of matter as self-moving....


"The essential point of dialectical thought is not that it is based on the idea of change and motion but that it views motion and change as phenomena based on contradiction.... Contradiction is an essential feature of all being. It lies at the heart of matter itself. It is the source of all motion, change, life and development. The dialectical law which expresses this idea is the unity and interpenetration of opposites.... The universal phenomena of the unity of opposites is, in reality, the motor-force of all motion and development in nature. It is the reason why it is not necessary to introduce the concept of external impulse to explain movement and change -- the fundamental weakness of all mechanistic theories. Movement, which itself involves a contradiction, is only possible as a result of the conflicting tendencies and inner tensions which lie at the heart of all forms of matter....


"The opposing tendencies can exist in a state of uneasy equilibrium for long periods of time, until some change, even a small quantitative change, destroys the equilibrium and gives rise to a critical state which can produce a qualitative transformation. In 1936, Bohr compared the structure of the nucleus to a drop of liquid, for example, a raindrop hanging from a leaf. Here the force of gravity struggles with that of surface tension striving to keep the water molecules together. The addition of just a few more molecules to the liquid renders it unstable. The enlarged droplet begins to shudder, the surface tension is no longer able to hold the mass to the leaf and the whole thing falls.


"Attraction and Repulsion


"This is an extension of the law of the unity and interpenetration of opposites. It is a law which permeates the whole of nature, from the smallest phenomena to the largest. At the base of the atom are immense forces of attraction and repulsion.... Engels points out the universal role of attraction and repulsion:


'All motion consists in the interplay of attraction and repulsion. Motion, however, is only possible when each individual attraction is compensated by a corresponding repulsion somewhere else. Otherwise in time one side would get the preponderance over the other and then motion would finally cease. Hence all attractions and all repulsions in the universe must mutually balance one another. Thus the law of the indestructibility and uncreatability of motion is expressed in the form that each movement of attraction in the universe must have as its complement an equivalent movement of repulsion and vice versa; or, as ancient philosophy -- long before the natural-scientific formulation of the law of conservation of force or energy -- expressed it: the sum of all attractions in the universe is equal to the sum of all repulsions.'


"In Engels' day, the prevailing idea of motion was derived from classical mechanics, where motion is imparted from an external force which overcomes the force of inertia. Engels was quite scathing about the very expression 'force,' which he considered one-sided and insufficient to describe the real processes of nature. 'All natural processes,' he wrote, 'are two-sided, they are based on the relation of at least two operative parts, action and reaction. The notion of force, however, owing to its origin from the action of the human organism on the external world, and further from terrestrial mechanics, implies that only one part is active, operative, the other part being passive, receptive.'


"Engels was far in advance of his time in being highly critical of this notion, which had already been attacked by Hegel. In his History of Philosophy, Hegel remarks that 'It is better (to say) that a magnet has a soul (as Thales expresses it) than that it has an attractive force; force is a kind of property that, separate from matter, is put forward as a kind of predicate -- while soul, on the other hand, is this movement itself, identical with the nature of matter.' This remark of Hegel, approvingly quoted by Engels, contains a profound idea -- that motion and energy are inherent to matter. Matter is self-moving and self-organising." [Woods and Grant (1995), pp.43-45, 47, 68, 71-72. Their reference is to Engels (1955), pp.95-96, 110. Quotation marks altered to conform with the conventions adopted at this site. Bold emphases added. Several paragraphs merged.]


It is interesting to note in passing that Woods and Grant naively record Engels's approving reference to Hegel's depiction of magnets as having 'souls' while failing to notice its mystical implications. How could that notion -- i.e., 'having a soul' -- be given a 'materialist spin' aimed at putting Hegel's theory 'back on its feet'/'the right way up'? Presumably a soul is a soul, upside down or not.


Here, too, are Levins and Lewontin:


"What characterises the dialectical world, in all its aspects, as we have described it is that it is constantly in motion. Constants become variables, causes become effects, and systems develop, destroying the conditions that gave rise to them. Even elements that appear to be stable are in a dynamic equilibrium of forces that can suddenly become unbalanced, as when a grey lump of metal of a critical size becomes a fireball brighter than a thousand suns....


"This appearance of opposing forces has given rise to the most debated and difficult, yet the most central, concept in dialectical thought, the principle of contradiction.... For us, contradiction is not only epistemic and political, but ontological in the broadest sense. Contradictions between forces are everywhere in nature, not only in human social institutions.... [O]pposing forces lie at the basis of the evolving physical and biological world. Things change because of the action of opposing forces on them, and things are the way they are because of the temporary balance of opposing forces....


"The dialectical view insists that persistence and equilibrium are not the natural state of things but require explanation, which must be sought in the actions of the opposing forces.... The opposing forces are seen as contradictory in the sense that each taken separately would have opposite effects, and their joint action may be different from the results of either acting alone.... However, the principle that all things are internally heterogeneous directs our attention to the opposing processes at work within the object.... Thus systems are either self-negating (state A leads to some state not-A) or depend for their persistence on self-negating processes.


"We see contradiction first of all as self-negation. From this perspective it is not too different from logical contradiction. In formal logic process is usually replaced by static set-structural relations, and the dynamic of 'A leads to B' is replaced by 'A implies B'. But all real reasoning is takes place in time, and the classical logical paradoxes can be seen as A leads to not-A leads to A, and so on.... As against the alienated world view that objects are isolated until proven otherwise, for us the simplest assumption is that things are connected...." [Levins and Lewontin (1985), pp.279-87. Bold emphases alone added. Spelling altered to conform with UK English. Several paragraphs merged.]


Quotations like those given above (and in Note 1) can be multiplied almost indefinitely.1


Admittedly, such passages are often hedged about with numerous qualifications -- again, depending both on the context and the author in question -- but the overall message is reasonably clear.2


Nevertheless, my concern here isn't so much with whether these passages are consistent with one another, or even whether any attempt has (ever) been made to substantiate the sweeping generalisations they make with anything like adequate evidence -- or, indeed, any at all --, but with whether the claim that forces can be used to model, illustrate or explain 'dialectical contradictions' makes any sense at all.3


Gravity Is Reassuringly Undialectical


However, as we are about to find out, the identification of forces with contradictions is about misconceived an idea as anything else we have so far encountered in the DM-Grimoire -- that is, where any sense can be made of it.4


First of all, there here are several obvious 'difficulties' with the whole idea. For example, if the forces in a system are in 'conflict' -- and are thus 'contradictory' -- there would presumably have to be at least two of them, with both operational and both in opposition to one another (actually or potentially), for that to be the case. But, when we consider one of the most important and universal examples of motion in the universe -- i.e., the orbital trajectory of bodies in a gravitational field -- we find that in Classical Physics, at least, this sort of motion is governed by the operation of at most one force, which deflects the otherwise (assumed) rectilinear path of the body in question toward the centre of mass of the system it is affected by or is orbiting. So, if Classical Physics is to be believed, it isn't easy to see how such forces could be viewed as 'contradictions'.5


Admittedly, the picture just painted is highly simplified, for even in such circumstances there could be several forces operating on an orbiting body -- the resultant motion will therefore be a function of the vector sum of all the forces acting in, or on, the system. The point at issue here is that relative to the centre of mass of the orbiting body, motion isn't the result of two different sorts of forces -- those of attraction and repulsion -- but a consequence of just one (resultant) force. Hence, orbital motion (at least) is produced by the action of only one (resultant) force (in Classical Physics), and, plainly, if there is only one force, there can be no 'contradiction'. Now, since orbital motion implicates the overwhelming bulk of motion in the entire universe, this means that most of the latter can't be the result of any sort of 'contradiction'.


Furthermore, any secondary motion (resulting from the effect of other forces operating in the system), which happens to be superimposed on the primary action, only serves to complicate the above picture, it doesn't alter it. This extra activity might also be the result of other attractive -- but, not repulsive -- forces in Classical Physics (once more), which clearly affect the said resultant. While they might influence that resultant, they don't turn it into two or more resultants. [This topic, along with several other options, is examined again in more detail here.]


Nevertheless, it could be argued that the motion of such bodies around others is determined by the operation of the two forces of attraction that pass between them: body, A, attracts body, B, and B does likewise with A.


Even so, it is difficult to see how two attractive forces could be regarded as opposites or as 'contradictories' -- nor yet how they are supposed to be 'struggling' with each other. Anyway, Engels himself argues that oppositional forces are those of attraction and repulsion (even though he prefers their translation into different forms of motion), despite the fact that with respect to the vast amount of the bulk motion in the universe they seem to have little or no part to play. Not only that, but the motion of, say, planet, A, around, say, star, B, is caused by forces originating in B, not A. While, the forces originating in A may affect B, they don't affect A itself, or its motion around B.


It could be argued once more that the interconnected and reciprocal chain of effects in play between A and B show that such forces are dialectically-linked. Hence, on this view, B would affect A's motion while A reciprocates; this in turn alters B's motion, which must then affect A's movement, and so on. But, even then, these attractive forces don't confront each other as oppositional or as 'contradictory'. At best, such forces affect the motion of the two bodies in tandem, which motion in turn then affects any other forces in play, and so on. In fact, they appear to augment one another. On that basis, if we insist on anthropomorphising nature in this way, shouldn't we say (with more justification, too) that such forces aren't contradictory, they are in fact tautological?


[On that, see Note 38, below. See also Note 6b.]


Moreover, these attractive forces don't turn into one another, and they certainly don't imply each other, in the way that the proletariat is supposed to imply the capitalist class, where we are also told that the one can't exist without the other (although I have thrown that claim itself into considerable doubt here). So, whatever else they are, these forces can't be 'dialectical opposites'. Either that, or the DM-classics were seriously mistaken.


And, even if we take two such forces into account, it is their combination (in a resultant force) which causes, or which changes, the said motion.


Notwithstanding this, Thomas Weston has recently made a valiant attempt to find a 'second force' (or cause) in such cases -- which he locates in...'inertia'!


"In the classical mechanics pioneered by Newton, elliptical motion of a body will result if it is attracted to another 'central' body by a force inversely proportional to the square of the distance between them, provided that the body has an initial velocity that is not too large or too small, and not directly toward or directly away from the central body. This situation involves only a single force on the body, which, in the case of a planet orbiting the Sun, is the force of gravity. Gravity is not the only cause of this motion, however.


"An elliptical orbit is the result of two causes, which produce two tendencies of motion. One tendency results from the force directed toward the central body, which makes the body turn toward that central body. The second tendency is that of the body to continue in a straight line at a constant speed. This tendency is usually called 'inertia'. Inertia is not a force, since forces cause change in speed or direction, and inertia is the tendency not to change speed or direction. Inertia is a causal principle, as Newton recognised, calling it an 'innate force of matter'. He expressed this principle in his first law of motion, while forces are described in the second law. In elliptical motion, these two causes, gravity and inertia, are united by the physical fact that the mass responsible for inertia is proportional to the mass that gives rise to gravity. This fact is an important element in recognising the dialectical contradiction in elliptical motion." [Weston (2012), pp.6-7. Bold emphasis alone added.]


One moment Weston tells us that inertia isn't a force, the next he quotes Newton to the effect that it is (or, to be more precise, it is "a force of matter")! However, nowhere does Weston explain how gravity and inertia can "struggle" with each other (whether or not they are, or they cause, opposing "tendencies"), or how they could possibly turn into each other -- which the DM-classics tell us they must "inevitably" do. Nor yet how this set-up is even a 'contradiction' to begin with! As is the case with other DM-fans, Weston simply helps himself to that word with no attempt to justify it.


Indeed, as Weston admits, Hegel himself argued that the orbital motion of a planet is governed by the operation of only one force:


"We must not therefore speak of forces. If we want to speak of force, then there is but one force, and its moments do not, as two forces, pull in different directions." [Hegel (2004), p.65. Italic emphasis in the original. Bold added.]


As noted earlier, it is difficult to see how a 'dialectical contradiction' can be cobbled together from only one force.


Another serious difficulty arising from Weston's attempt to shoehorn Marx's comments into this ill-fitting dialectical boot is the inconsistent way he uses the word "tendency". One minute "tendencies" aren't causes, but are caused by something else (in the first of the above passages, where it seems that an elliptical orbit "produce[s] two tendencies of motion"), next they are causes:


"Tendency A, if strong enough, will cause the opposite tendency B to be less fully realised than if tendency A were absent, and conversely." [Weston (2012), p.17. I examine variations on this theme later on in this Essay.]


However, we have already had occasion to note that tendencies not only aren't, they can't be, causes. They are the result of causes.


Finally, Weston only mentions the TOR once (p.7, ftn.17), but even then he fails to notice that one of the components of the 'contradiction' here has been edited out of the picture; 'the force of gravity' has been replaced by motion along a geodesic. According to the TOR, we no longer have even one force operating here, we have no gravitational forces at all!


[TOR = Theory Of Relativity.]


In which case, post-Classical Physics offers even less assistance to DM-theorists in their endeavour to find a physical correlate for these 'contradictions' in nature. According to the TOR, all such motion is either a function of the topology of Spacetime (gravitational 'force' having been edited out of the picture), or it is the result of the body in question being situated in a tensor, vector, or scalar field, in as many dimensions of phase space as are deemed necessary and appropriate.6


As one of the standard textbooks on gravitation points out:


"Whatever aspect of gravity one measures, and however one measures it, one is studying the geometry of space-time." [Misner, et al (1973), p.400. Bold emphasis added. (This links to a PDF.)]


One history of the concept of force also points out:


"In Newton's theory the symbol F in F = ma refers to the cause of the acceleration of the body. Force, then, is an external agent that acts on matter with an inertial mass m, causing it to accelerate at the rate a. In the GTR [General Theory of relativity -- RL], however, there is no external force. Indeed, Einstein was able to derive Newton's equation F = ma from purely geometric considerations. He saw the possibility that all 'external' forces may be only apparent -- that the 'effect' of other matter may be representable by a generalization of the geometry of space-time that describes the motions." [Stinner (1994), p.84. Bold emphases added. (This links to a PDF.)]



Video One: Why Gravity Isn't A Force


Even in Classical Hamiltonian Mechanics, such forces have been edited out of the picture, replaced by dynamical considerations -- indeed, along lines later suggested by Engels himself.


Once again, if there are no such forces, there can be no DM-'contradictions', so conceived.


[On this, see Goldstein, et al (2002), pp.34-36, and Jammer (1999), pp.158-264.]


And, that isn't just the case with respect to gravity, as physicist, Max Jammer, notes:


"[The eliminability of force] not confined to the force of gravitation. The question of whether forces of any kind do exist, or do not and are only conventions, ha[s] become the subject of heated debates.... In quantum chromodynamics, gauge theories, and the so-called Standard Model the notion of 'force' is treated only as an exchange of momentum and therefore replaced by the ontologically less demanding concept of 'interaction' between particles, which manifests itself by the exchange of different particles that mediate this interaction...." [Jammer (1999), p.v. Paragraphs merged; links and bold emphasis added.]6a


Even Woods and Grant acknowledge this fact:


"Gravity is not a 'force,' but a relation between real objects. To a man falling off a high building, it seems that the ground is 'rushing towards him.' From the standpoint of relativity, that observation is not wrong. Only if we adopt the mechanistic and one-sided concept of 'force' do we view this process as the earth's gravity pulling the man downwards, instead of seeing that it is precisely the interaction of two bodies upon each other." [Woods and Grant (1995), p.156.]


However, and despite what those two say, it is reasonably clear that a mere "relation" between two bodies is incapable of making either of them move -- unless there were a 'force' of some sort operating between them, or, indeed, something else consequent on that relation, such as a time-based trajectory along a "world-line", perhaps(?) to bring it about.6b


Unfortunately, this means that most (if not all!) of the bulk motion in the universe can't be accounted for by DM (that is, if such motion, or, change of motion, is the result of 'contradictions' interpreted as opposing forces). Again: if there is only one force present -- or perhaps even none at all! -- there can't be any 'dialectical contradictions', to begin with.


Admittedly, Engels made a weak attempt to solve the orbital 'problem' by inventing a repulsive force, which he implausibly identified with "heat" (for example, Engels (1954), pp.73-80).7


[I haven't reproduced those passages here since they are far too long. The reader is invited to check for herself what Engels has to say to see if I have either misrepresented him or have missed something.]


Nevertheless, it is far from clear what Engels was driving at in that section. If he meant to say that heat operates as a repulsive force then that would have been a desperate and unconvincing dodge. Not only do cold bodies have satellites (e.g., Neptune), hot bodies swallow matter up all the time. However, it is possible that Engels simply copied this idea off several theorists working in the previous century. [Hesse (1961), Williams (1980).]


Admittedly, Engels considered other repulsive forces that could operate in a planetary system, but his ideas weren't just speculative and fanciful, they were manifestly ad hoc. I can find no evidence that anyone else -- DM-fan or otherwise -- has followed up on, or has developed any of these ideas in the intervening years.


For example, Engels appealed to the original repulsive properties of the "individual particles of the gaseous sphere" from which the Solar System was formed (as a result of "contraction"), to account for its origin by means of an "interplay of attraction and repulsion." [Ibid., pp.73-74.]


It would be difficult to find a better example than this of how the 'dialectical method' has been imposed on nature, not deduced from the phenomena. And we can assert that with some confidence. Even if this 'theory' weren't so obviously fanciful, it certainly couldn't have been deduced from the phenomena since the alleged incidents took place billions of years ago. Admittedly, there might have been theoretical considerations that recommended these ideas to Engels as a tentative 'explanation' of how the Solar System could have formed -- although even that is questionable since Engels explicitly based his theorising on the old Kant-Laplace model, itself nearly a century old in his day. But, even granting all this, Engels's account is superficial, impressionistic and lacks both mathematical and evidential support. It was clearly motivated by his desire to find some force -- any force -- to counterbalance gravity just because DM requires it, not because the phenomena dictate it -- rather like Thomas Weston, in fact. This is a classic example of Engels using the concepts he inherited from Hegel as a dogmatic "form of representation", and, as we will see, a thoroughly confused one into the bargain.


Of course, scientists employ formal devices like this all the time, but Engels turned this particular example into a non-sensical metaphysical thesis.


[The difference between Metaphysics and Science will be discussed in Essay Thirteen Part Two. On Metaphysics and DM, see Essay Twelve Part One.]


Indeed, Einstein himself wasn't above inventing forces to suit his theory (the same was also the case with Newton cf., Cohen (1970) and Jammer (1999), pp.116-57), introducing "the cosmological constant" to account for the fact that the Universe hasn't collapsed in on itself, an idea which has now morphed into Dark Energy. [Cf., Lerner (1992), pp.131-32.] There are countless examples of moves like this in the history of science. Thomas Kuhn called them "paradigms" if or when they gained some traction. [On that, see Kuhn (1970, 1996), and Sharrock and Read (2002).]


Incidentally, an appeal to so-called 'centrifugal forces' ("fictional forces" found in Classical Physics) won't save Engels's theory either, since they don't 'exist'. If anything they are the result of misleading shorthand for the way that rectilinear, tangential motion will resume if a force responsible for centripetal acceleration ceases to operate for whatever reason, subjectively experienced in certain rotating systems.


John Molyneux also weighed in with the following comment:


"If anything (a grain of sand, a mountain, a tree, a fish, a human, a society) gives the appearance of stability and permanence it is because it constitutes a particular moment in a longer process of change. That moment constitutes a particular balance between forces within it working for and against change -- a unity of opposites; much as the earth's, or any planet's, orbit around the sun represents a balance between the force of gravity pulling it into the sun and the momentum which would send it flying off into space." [Molyneux (2012), pp.44-45. Bold added.]


Once again, if the TOR is correct, there is no force of gravity.


Even supposing there were such a force, in Molyneux's scheme-of-things it isn't balanced by an opposing force, just "momentum", which can in no way be interpreted as a, or even the, 'dialectical opposite' of the force of gravity. [The significance of that particular comment (i.e., why there has to be a unique opposite for each object or process -- something Hegel and Lenin called its "other") is explained here.] But, even if this attempt to impose dialectics on nature could be made to work, or was in any way plausible, and "momentum" was a/the 'dialectical opposite' of the force of gravity, the following aspect of Molyneux's theory would still fail to work:


"That moment constitutes a particular balance between forces within it working for and against change -- a unity of opposites...." [Ibid.]


What are the opposing forces internal to the Earth that make it orbit the Sun? Or, the internal forces in the Sun that make the Earth orbit it? Molyneux is surprisingly silent on this issue.


Of course, it could be replied that these opposites are internal to the Sun-Earth pair, or perhaps even the Solar System itself. But, as we have seen, there are no opposing forces there either! Nor are there any relevant united 'opposites'. And, even if there were, which of them is providing:


"a particular balance between forces within it working for and against change...." [Ibid.]


Is gravity the cause of change, or is it opposing it? Is "momentum" opposing change, or creating it? Is the 'dialectical union' of these two doing one or the other?


[See also my earlier comments about a Thomas Weston's recent attempt to recruit inertia, but not momentum, to the cause.]


Moreover, are we really supposed to believe that gravity "struggles" with momentum? Or that they turn into one another (as the DM-classics tell us they should)? In what way does momentum imply gravity, which it should do if they form a UO (rather like the proletariat is said to imply the capitalist class, and vice versa)?


As usual, in books and articles on DM, we are presented with what are in effect less than half-formed thoughts and off-the-cuff musings, which don't make sense even in their own terms.


Is This An Apt Analogy?


Is "Contradictory Force" Merely A 'Dialectical' Figure Of Speech?


In view of the above, it might be wise to interpret "opposing forces" exclusively as 'figurative contradictions' -- or, maybe, the other way round, interpreting 'dialectical contradictions' solely as 'figurative forces'. Either one or both of these might then form part of an analogical, or perhaps even metaphorical (but non-literal), depiction of nature and society. Alternatively, forces could be described as 'contradictions' as a sort of shorthand, which would then enable the modelling of different types of accelerated motion. Naturally, that approach would allow the word "force" to be edited out of the picture as a physical entity in its own right. Indeed, Engels seems to have had that in mind in the passage quoted below, where he argues that attraction and repulsion shouldn't be regarded as forces, but as simple forms of motion. This major theoretical retreat perhaps recommended to him by his admission that the concept of "force" was originally derived from ancient animistic/mystical theories of nature, hence its use in DM would smack of anthropomorphism:8


"All motion is bound up with some change of place…. The whole of nature accessible to us forms a system, an interconnected totality of bodies…. [These] react one on another, and it is precisely this mutual reaction that constitutes motion…. When two bodies act on each other…they either attract each other or they repel each other…in short, the old polar opposites of attraction and repulsion…. It is expressly to be noted that attraction and repulsion are not regarded here as so-called 'forces', but as simple forms of motion...." [Engels (1954), pp.70-71. Bold emphasis added.]


"All natural processes are two-sided, they are based on the relation of at least two operative parts, action and reaction. The notion of force, however, owing to its origin from the action of the human organism on the external world…implies that only one part is active, the other part being passive…[and appears] as a resistance." [Ibid., p.82. Bold emphasis added.]


However, the above revision had two untoward consequences Engels appears not to have noticed:


(1) It makes his version of DM look even more positivistic that it might already seem -- at least as Engels presents it in DN. If an appeal to forces in nature is no more than a shorthand for the relative motion of bodies, then, plainly, forces will have no real counterpart in nature (since, of course, they have just been edited out of the picture!). Forces would then be little more than "useful fictions", introduced in order to account for the phenomena, instrumentally -- rather like the epicycles of Ptolemaic Cosmology. This would make the identification of forces with 'contradictions' even more problematic (as will be demonstrated below). Once again: if there are no forces, there can be no DM-'contradictions'.


[DN = Dialectics of Nature, i.e., Engels (1954); UO = Unity of Opposites.]


(2) Given this re-write of the word "force", the supposed 'contradictory relationship' between bodies would become little more than a re-description of their relative motion. [Woods and Grant also seem to be thinking along those lines, as we saw earlier.]


Unfortunately, in that case, there would be no interconnection between any of these moving bodies, which appears to be an essential factor required by other DM-principles -- for instance, where we are told that everything is "interconnected". The alternative put forward by Engels clearly means that causal interactions of this sort are in fact external, not mediated by forces, and thus can't be internally inter-conditioned. In which case, the 'unity-in-opposition' between objects and processes in the Totality has been broken; the thesis that change is the result of 'internal contradictions' would then be left without any sort of internal, mediating factors. [This confusion was analysed in much more detail in Part One.]


Not even the relative motion between bodies travelling in opposite directions could supply a credible dialectical connection in this case -- should an interaction result from this. Without question, this would fail to capture the "internal relations" that DM-theorists claim must exist between such bodies. Once more, objects behaving like this wouldn't be internally interrelated (as part or parts of a UO, the one wouldn't imply the existence of the other, as they should if there were a dialectical relation at work, unlike the relation that is supposed to exist between the proletariat and the capitalist class), since the connection, or mediation, between moving bodies is now missing. In that case, any subsequent interaction would appear to be difficult to account for dialectically, which would be, to state the obvious, bad news for DM-fans.9


As already noted, with events and processes sealed-off from each other DM would begin to resemble CAR and 'crude materialism' all the more. Indeed, if this is how DM is supposed to be interpreted, it would differ from 'crude mechanical materialism' in name alone.


[CAR = Cartesian Reductionism; follow the above link for more details.]


Of course, even if Engels's version of DM could account for motion along a certain line of action -- but in diametrically opposed directions --, it would be of little help because most of the bulk motion in the universe isn't of this sort; it is either orbital motion under the action of a central force, or it is movement along a geodesic (depending on which version of modern Physics one accepts). In fact, as we will see, matter in general moves in complex ways which are difficult, if not impossible, to depict in such crude oppositional terms.


Like it or not, DM-theorists need real material forces acting between bodies so that their "Totality" has the holistic, or mediated, integrity we are told it possesses. A theoretical fiction like this is no use at all. If DM is to work, forces must exist, and any reference made to them as 'contradictions' must be concrete and literal, which in turn means that interacting bodies, or even these forces themselves, are 'internally-related' to each other.10


Naturally, this exposes an ambiguity brought out by these two questions:


(i) Are forces related to each other 'dialectically' -- so that they are 'dialectical opposites' of one another, and their relation is what forms the 'contradiction' here? Or.


(ii) Are the bodies and process involved dialectically related to one another?


So, is the 'contradiction' here:


(a) Between the bodies and processes themselves?


(b) Between the forces operating in the system? Or,


(c) Both?


That ambiguity will be explored as this Essay unfolds. Readers are advised to keep it in mind.


Anyway, the figurative reading of forces as 'contradictions' runs counter to the claim advanced by dialecticians that what they are offering is an 'objective' account of nature. It isn't easy to see how figurative language is capable of filling the gaps in an explanation of the relationship between objects and processes in the material world -- at least, no more than, say, the following can account for Juliet's beauty:


"But, soft! what light through yonder window breaks? It is the east, and Juliet is the sun." [Romeo and Juliet, Act Two, Scene Two.]


Or, indeed, no more than would describing a man as a "pig" imply he has a curly tail, four legs and was a convenient source of bacon.


Despite this, in view of the above difficulties -- and in addition to those that will be examined below --, interpreting forces figuratively might prove to be the only viable way that contradictions could be 'interpreted' as 'forces', even if it compromises DM's avowedly 'objective' picture of reality.11


Of course, if this view of the nature of forces were to be adopted by dialecticians, it would be difficult to distinguish their theory from a 'poetic' version of Instrumentalism or Conventionalism.


On the other hand, it is difficult to see how 'figurative forces' could account for anything. What sort of explanation would it be to say that contradictions -- already suspiciously figurative themselves -- can be modelled by forces, which are themselves just figures of speech? Once more, describing a man as, say, a "pig" might perhaps account for his crude behaviour (but not because his anatomy or physiology is literally pig anatomy or physiology), but the utility even of that metaphor would be virtually nil if it were now admitted that the word "man" was figurative, too. Unlike iterated negation, multiple tropes don't undo each other.


Nevertheless, even if this proved to be an acceptable resolution of Engels's problem, it would still fail to provide DM-theorists with a viable way out of this impasse. Taken literally or figuratively, the equation of DM-'contradictions' with forces in nature or society can't work.


That is so for several reasons --, to which I now turn.


'Contradictions' As Mathematical Models?


The first of these is connected with the way that forces are already represented. for example, in Mathematics and Physics, which doesn't appear to be an even remotely appropriate way of depicting DM-contradictions as literal forces. Consider the following:


(a) Forces often operate according to an inverse square law. It is difficult to see how the same could be true of contradictions. Presumably, two objects, states of affairs, or processes contradict each other in nature or society or they don't.12 Not much sense can be made, one presumes(!), of the idea that a contradiction could operate with, say, only 25% of its former intensity (or whatever the appropriate descriptor is here) if the distance between its oppositional elements is doubled. Do bosses really become more conciliatory if workers walk away from them? Or if the local trade union offices are moved to a new location ten miles further away? Does wealth cause less conflict if the rich stash their money to the Cayman Islands? Do appearances 'contradict' reality any the more -- or less -- if someone used a microscope, or pressed their face against the surface of an object?13


Indeed, little sense can be made either of the idea that there is a literal separation distance between components of DM-'contradictions'; for instance, that there is, or could be, a separation distance between Capital and Labour, or that there might be a literal gap between the forces and relations of production, or even between an object and itself as it moves in a 'contradictory' sort of way. What could it possibly mean to suggest, for example, that the "contradiction between use value and exchange value" changes if these two terms (or the commodities to which they are supposed to apply) are moved further apart? Clearly, these two 'entities' can't be separated (except perhaps in thought), since they aren't the sorts of thing that could be physically moved away from, or even closer to, each other -- but even if they could, they would still be just as contradictory as they were before they had been moved (one presumes?). And yet, no force in nature has its local or remote magnitude unaffected by such changes.


Admittedly, dialecticians speak about the "contradictions" in the capitalist system "intensifying", but that isn't because the 'separation distance' between the relevant classes has decreased. Whatever DM-theorists think they mean by "intensification" here (which seems be that the alleged "contradictions" become more obvious, intractable, or crisis-ridden), they certainly don't mean it in the same way that physicists mean it when they talk about, say, the strength of a force field intensifying. Nor has there ever been any mathematics applied in such DM-goings-on. So, while a scientist, for example, might be dispatched to measure the intensity of forces in the earth's crust prior to an earthquake (as part of a genuine scientific research programme), no one, it seems, has ever been asked to do the same with these "intensifying" 'dialectical contradictions'. They (or at least their 'strength') appear to be permanently locked in subjective space, stubbornly resistant to scientific investigation.


Be this as it may, what sense can be made of the other 'contradictions' alleged to exist in nature? For instance, can a moving object be more 'contradictory' than it used to beat any point along line of action? Increasingly here and not here? Or increasing and not increasing at the same time? Perhaps an object can be In more than two places at once, as it accelerates? Maybe an electron can be more of a particle and a wave, at the same time? Is it possible for 'appearances' to 'contradict' underlying 'essences' more today than last week? Anyone who thinks they can, please email me the numbers, along with the details of the experiment(s) you performed or the measurements you took in order to ascertain them.


(b) Forces in nature can be (and are) represented by vectors, the use of which is governed by well-understood rules. As such, for example, they may be inclined at various angles to one another, added, subtracted and multiplied (to give inner, vector or scalar triple products, and the like), by means of which diverse quantities such as areas, volumes, field densities, boundary fluxes (etc.), may be calculated. In addition, vectors may be parallel or orthogonal to one another, or to previously defined axes, just as they can be decomposed into their components and projected onto a given direction, plane or surface. They can also be used to identify and classify the mathematical properties of various manifolds. Unit vectors can be defined in a given vector space, providing it with a base and spanning set. Modulii can be ascertained for any given vector, and so-called "Eigenvectors" can also be determined. Furthermore, matrices may be employed to represent vectors more efficiently, their determinants and inverses ascertained (where they exist). The ordinary and partial derivatives of vectors can also be calculated, and they can be integrated (as part of line, surface or volume integrals), too, and so on.


It is difficult to see how any of the above (and many more besides) could possibly be the case with a single DM-'contradiction', interpreted literally or figuratively as a force. What, for example, is the angle between the 'contradictions' mentioned on the opening pages of TAR:


"[S]ince the Second World War there have been 149 wars which have left more than 23 million dead…. On an average yearly basis, the numbers killed in wars during this period have been more than double the deaths in the nineteenth century and seven times greater than in the eighteenth century…. Regression, by any criterion. Yet it is the very same development of human productivity that gives rise both to the possibility of life and to its destruction…. Everywhere we look another paradox appears. How can it be, for instance, that in the richest capitalist society in the world, the United States, real weekly incomes have fallen steadily since 1973?… How is it that in Britain, where the economy, despite the ravages of recession, produces more than it has ever done…a full quarter of the population live below the poverty line? The contradictions are no less striking if we shift our gaze from economics to politics. The introduction of the market to Russia and Eastern Europe was supposed to bring stability and prosperity but has actually produced the opposite." [Rees (1998), pp.1-2. Paragraphs merged.]


And, while we are at it, what is the cross product of the following 'contradictions' (mentioned in Socialist Worker)?


"Elvis's career illuminated a contradiction at the heart of capitalism. Capitalism needs to generate profits in order to survive. But to suck profit out of workers it also needs an ideology to ensure that workers know their place in society...." [Ian Birchall, Socialist Worker, 14/08/2007.]


"However, there are contradictions in the role of prison officers. It is summed up by Cardiff prisoners chanting 'you're breaking the law' to the strikers.... Prison officers' work, upholding law and order, frequently pushes them to accept the most right wing ideas and actions of the system. One of their main jobs is to control prisoners –- and throughout the prison system, many officers have a proven record of racism and violence. Some of the contradictions can be seen in the strike. In Liverpool the POA shop steward Steve Baines responded to the high court injunction by telling fellow strikers, 'Tell them to shove it up their arse, we're sitting it out.' Yet when prisoners in the jail protested against their treatment, the POA members rushed back in to control the situation and end a roof top protest." [Simon Basketter, Socialist Worker, 01/09/2007. Quotation marks altered to conform with the conventions adopted at this site. Paragraphs merged.]13a


Is it possible to find the inner product of the 'contradiction' between freedom and necessity? Is there an eigenvector applicable to the 'contradiction' between 'appearance' and 'underlying essence'? Is there any way of specifying the extent to which bosses and workers -- Capital and Labour -- contradict one another, individually or as a class? If so, what is the modulus of the 'contradiction' between boss NN and worker MM -- or, between the classes to which they belong? Is the 'contradiction' between ice and water orthogonal to…, well, what?


But, what of the div, curl and grad of the 'contradiction' between a grain of barley and the plant that grows from it? Can we ascertain the Jacobian for the contradictory relationship between wealth and poverty? Is the 'contradiction', between "John" and his "manhood" normal to a given direction or manifold?


In her otherwise excellent book, Lindsey German had this to say:


"The Working class has to have a party to overcome the contradiction between its potential revolutionary role and its actual situation. To overcome this contradiction requires a conscious struggle by an organised minority…." [German (1996), p.87.]


If contradictions were indeed literal forces, we would be able to ascertain, say, the i, j and k components of "the contradiction between [the] potential revolutionary role [of the working-class] and its actual situation", differentiate it/them, and find out how quickly this link was changing, and in what direction.14 The fact that we can't do this -- and no sane Marxist has ever even so much as suggested this was a possibility -- implies that in practice not even DM-fans think this analogy is at all apt, or, indeed, is all that literal.


Plainly, if 'contradictions' could be interpreted literally as forces, it would be possible to construct a vector algebra depicting them in nature and society. Do we possess such a 'Vector Algebra of Revolution'? Has anyone ever bothered to construct one?


Given the title of his book, the author of TAR was mysteriously silent about this.14a


It could be objected that social contradictions were never meant to be interpreted in this crude and inappropriate manner, as vectors (etc.). Maybe not, but this section of the Essay is trying to make some sort of sense of the equation of forces with contradictions, and forces certainly can be represented by vectors. If it isn't possible to represent social forces in this way, then all well and good. But, in that case, we are still no nearer understanding what these 'social contradictions' are, or in what way they can be described as, or be illustrated by, forces. In fact, we are now further away!


Also in doubt is exactly how something that actually exists (i.e., the current state of the working class) can 'contradict' in a 'dialectical' sort of way (involving forces) something that does not exist (i.e., the proletariat's potential revolutionary role, as Lindsey German characterised it). We have already seen that dialecticians use the word "contradiction" almost ad nauseam in inappropriate circumstances to depict things that seem quirky, odd, paradoxical, contrary to expectations, and so on -- almost as the mood takes them. [On that, see, for instance, here and here.]


"The Working class has to have a party to overcome the contradiction between its potential revolutionary role and its actual situation. To overcome this contradiction requires a conscious struggle by an organised minority…." [German, op cit.]


What Lindsey might have had in mind in the above passage is that there is what seems to be a contradiction in revolutionary theory, which depicts the proletariat as the revolutionary class, but it does so in the face of the undeniable fact that workers are often quiescent or compliant (or relatively so) for long periods. But, this is no more a contradiction than it would be if, say, we heard that a heavy object near to the surface of the earth didn't actually fall to the ground. As soon as we learnt that this heavy object was held in place by pillars, cables or magnets, the phenomenon would puzzle us no more.


Three questions worth posing in relation to this are the following:


(i) Do the above factors struggle with each other?


(ii) Do they change into one another (as the DM-classics assert they should)? And,


(iii) Do they imply one another (like, say, the proletariat implies the bourgeoisie -- although I have thrown even that inference into considerable doubt here)?


The answer is surely in the negative in each case. That being so, whatever else it is, what Lindsey mentioned isn't a 'dialectical contradiction'.


It could be replied that there is a struggle going on in the working class. Maybe so, but there isn't one going on between "its potential revolutionary role and its actual situation". One of these at least is an abstraction which can't struggle with anything. And are they changing into one another?


Another moral here is that no law in Physics is 'true' on its own; each one is hedged about by all manner of ceteris paribus (i.e., "all things being equal") clauses. [On this, see Cartwright (1983). However, there is  a forceful rebuttal to this way of seeing things here. See also Earman, et al (2002), and van Brakel (2000), pp.151-69. Naturally, it would be out of place to pursue that topic any further in this Essay; it will be discussed in more detail in Essay Thirteen Part Two, when it is published.]


In that case, and analogously, as soon as we know what is holding the working class back, the above puzzle also disappears.


Hence, Lindsey German's worry about overcoming this 'contradiction' can now be shelved -- since there isn't one.


Naturally, that doesn't mean that socialists should just let things drift, fail to intervene, or, indeed, sit back and wait for workers to organise themselves, but since further consideration of this topic would take us into areas involving HM, no more will be said about it here (for reasons set out in Essay One).


Properties Of Totalities?


The second reason why this is an inappropriate way to depict 'contradictions' is in fact connected with a possible response that could be made to the objections outlined above: it could be argued that it is the inter-relationship between contradictory forces that explains change, and hence it is only within a network of forces situated in a Totality of some sort that their contradictory inter-play becomes clear. Indeed, it could be maintained that the above interpretation of contradictions (which seems to picture them isolated from their surroundings) completely misconstrues their role in DM, as well as their operation in nature and society.


The above volunteered objection was in fact considered in Part One of this Essay -- but from a slightly different direction (no pun intended) -- where it was pointed out that there are serious ambiguities in DM on this issue. That is because dialecticians are unclear whether 'contradictions':


(a) Are internal to objects and processes, causing them to change as a result of an internal dynamic,


(b) Arise externally between objects as they form part of a mediated system, group of systems and processes,


(c) Merely result from our description of objects and processes as 'contradictory', this perhaps arising from our partial or relative knowledge of reality, etc.,


(d) Derive from a combination of all three


Or, indeed, whether they,


(e) Emerge because of some other factor about which we are currently unaware.


This confusion is further compounded by the fact that in the hands of DM-theorists the meaning of "internal" oscillates erratically between "spatially internal" and "logically internal".


And, as we also saw in Part One, while each of the above options faces serious difficulties of its own, in the end they all fail to explain change because they merely re-describe it, and they do so in a thoroughly obscure manner. That is why they fall apart so readily when examined closely (as we will see is also the case with the equation of forces and 'contradictions' in what follows).


In response, it could be argued that the problem with the analysis of dialectical systems promoted in these Essays is that it attempts to 'objectify' contradictions (i.e., it endeavours to make objects out of them). Hence, it could be countered that in Materialist Dialectics it isn't 'objects' that are subject to contradictions -- or which contain them, or which constitute them --, but systems, or totalities, in change that reveal their inner contradictions, and which motivate further development. In that case, it could be maintained that contradictions are properties of systems, or totalities, in the process of change, not 'objects' as such.


In reply to these volunteered DM-responses, it is worth asking where this leaves forces if contradictions are no longer to be viewed as 'objects' or as 'object-like'. Forces presumably have a physical form of some sort. They aren't just relations, are they? Furthermore, this response makes a mockery of many things the DM-classicists themselves say about change. Here is Lenin, for example:


"Dialectical logic demands that we go further…. [It] requires that an object should be taken in development, in 'self-movement' (as Hegel sometimes puts it)…." [Lenin (1921), p.90. Bold emphases in the original. Italic emphasis added.]


[Numerous similar-looking quotations were added to Part One of this Essay.]


It could be objected that this misrepresents Lenin, since he went on to argue as follows:


"The gist of his [Bukharin's -- RL] theoretical mistake in this case is substitution of eclecticism for the dialectical interplay of politics and economics (which we find in Marxism). His theoretical attitude is: 'on the one hand, and on the other', 'the one and the other'. That is eclecticism. Dialectics requires an all-round consideration of relationships in their concrete development but not a patchwork of bits and pieces. I have shown this to be so on the example of politics and economics....


"A tumbler is assuredly both a glass cylinder and a drinking vessel. But there are more than these two properties, qualities or facets to it; there are an infinite number of them, an infinite number of 'mediacies' and inter-relationships with the rest of the world.... Formal logic, which is as far as schools go (and should go, with suitable abridgements for the lower forms), deals with formal definitions, draws on what is most common, or glaring, and stops there. When two or more different definitions are taken and combined at random (a glass cylinder and a drinking vessel), the result is an eclectic definition which is indicative of different facets of the object, and nothing more.


"Dialectical logic demands that we should go further. Firstly, if we are to have a true knowledge of an object we must look at and examine all its facets, its connections and 'mediacies'. That is something we cannot ever hope to achieve completely, but the rule of comprehensiveness is a safeguard against mistakes and rigidity. Secondly, dialectical logic requires that an object should be taken in development, in change, in 'self-movement' (as Hegel sometimes puts it). This is not immediately obvious in respect of such an object as a tumbler, but it, too, is in flux, and this holds especially true for its purpose, use and connection with the surrounding world. Thirdly, a full 'definition' of an object must include the whole of human experience, both as a criterion of truth and a practical indicator of its connection with human wants. Fourthly, dialectical logic holds that 'truth is always concrete, never abstract', as the late Plekhanov liked to say after Hegel. (Let me add in parenthesis for the benefit of young Party members that you cannot hope to become a real, intelligent Communist without making a study -- and I mean study -- of all of Plekhanov's philosophical writings, because nothing better has been written on Marxism anywhere in the world.)" [Ibid. pp.90-93. Bold emphases alone added; quotation marks altered to conform with the conventions adopted at this site. Several paragraphs merged.]


From this it is clear that Lenin in fact argued that an understanding of the inter-relation between an object and the rest of the world was essential to comprehending that object's contradictory development. [I have discussed this topic in much more detail here and here.]


Or so it could be argued.


[This response creates problems of its own, which will be discussed presently.]


But, even if forces were just relations, it is far from easy to see what it is that could possibly physically relate objects and processes in nature and society in this way -- that is, over and above the gratuitous insertion of a few Hegelian 'concepts' (of dubious provenance and even more questionable content).


Indeed, in all this, it seems that the idea that objects change because of an 'inner dynamic' has been lost sight of again. If objects change only because of a set of external forces -- albeit, which forces might also be internal to a system of some sort, mediated, or not, by the yet-to-be-explained 'influence' of the "Totality" --, this can only mean that "external" has now become the new "internal". In that case, "internal contradictions" have now in effect become factors that an object merely experiences as part of its external relations with other objects and processes (which are, in turn, internal to the "Totality"). But, once more: what is the point of arguing that change is "internally-motivated" if external mediation is the only show in town, and forces are merely "relations"?


[As we will see in Essay Four Part Two (when it is published), these "relations" are supposed to be 'logical' (in a quasi-Hegelian sort of sense), but they are no less bogus for all that. Until then, readers are redirected here.]


Before we proceed, my I remind readers of something that was pointed out several sections ago?


So, is the 'contradiction' here:


(a) Between the bodies and processes themselves?


(b) Between the forces operating in the system? Or,


(c) Both?


That ambiguity will be explored as this Essay unfolds. Readers are advised to keep it in mind.


We are now about to find out why.


In addition, the proffered DM-response outlined a few paragraphs back fails to resolve the problems also mentioned earlier.


First of all, as we will also see in Essay Eleven Part One, there is good reason to question the nature of the nebulous DM-"Totality" -- or, to be more honest, there would be if we knew what 'it' was, and there was some sign that dialecticians themselves knew what 'it' was! Its re-appearance here can only hinder comprehension.


Secondly, even if a clear account of the "Totality" were forthcoming, this way of depicting forces would still fail to work. If contradictions are properties of totalities -- as opposed to their parts -- then those parts couldn't change, since, on this account, contradictions wouldn't belong to them, but to the whole, taken as a whole. In that case, while the whole might change, it would do so only as a result of the rearrangement of its changeless parts. Given this way of thinking, the "Totality" (or, indeed, any sub-system of the "Totality") would be:


(a) Composed of infinitely small changeless elementary particles, or,


(b) Composed of infinitely complex further sub-systems, which enjoy no connections among themselves. [The reader is referred back to Part One for a more detailed explanation of this point.]


Again, it could be objected that a Totality is constituted by its own internal contradictory relations and processes. That is precisely what a Totality is -- a contradictory, differentiated unity. The account given above seems to want to separate the parts from the whole.


However, that reply still won't do, for on that basis it would now seem that it is part and whole which are contradictory (and in a manner that has yet to be explained with any clarity). And yet, such parts can't be contradictory in the same way that wholes are. That is because, on this account, parts mutually condition one another; this is, presumably, the nature of their mediated 'unity in contradiction'. However, the "Totality" is related to nothing else that could condition it (one also supposes, should we ever be told what the Totality is!). So, if the "Totality" is a contradictory whole, then it would appear to be so in a new and so-far-unexplained sense. The 'parts' of a 'dialectical contradiction' are said to imply one another, being a 'reflection' of each other's 'essence' in development, such that one couldn't exist without the other (just as the proletariat both implies and couldn't exist without the bourgeoisie, for example). Not only does the whole here not imply any one of its parts, it could exist without many its parts. Does the universe itself really imply Venus, or the Crab Nebula? The universe could surely have existed without Venus or the Crab Nebula. If so, whatever else is true of the relation between part and whole here, it can't be "contradictory" in the required DM-sense of that word.


In fact, as seems obvious from what little DM-theorists themselves have said about the "Totality", it looks like 'it' must be an Unconditioned Absolute. It certainly can't be conditioned from the 'outside', otherwise it wouldn't be the Whole (one presumes!). If, on the other hand, it were conditioned from the 'outside', an infinite 'exgress' (or inflation -- an infinite exgress is the opposite of an infinite regress, sometimes called an "explosion") would be implied. That is because we should now want to know if and how this 'external' object or process (about which we know even less) was itself conditioned, and by what -- and so on, forever. But we have been here already.


And, it seems these disconcerting observations must apply otherwise, for the "Totality" to be contradictory, it would have to 'contradict' its parts. [Ex hypothesi it would have to do this anyway, since there is nothing else for it to condition.] Moreover these parts must then contradict each other in turn in the same way, after all.


[The opposite supposition will be considered presently.]


But, if we ignore the above 'problems' and the "Totality" is composed solely of its parts and their inter-relations (unless, of course, we assume the Totality is "more than the sum of its parts" -- that Wholist cliché was exposed as yet another DM-dead-end in Essay Eleven Part Two), the contradiction between the "Totality" and its parts must be:


(i) The same as the contradiction between each of the aforementioned parts, or,


(ii) More than the contradiction between its parts (since, as we have just seen, dialecticians believe that the whole is more than the sum of its parts).15


As far as (i) is concerned, it seems that the "Totality" must drop out of the picture as a sort of shorthand for the sum total of 'its' parts in contradictory change and development, becoming a mere fiction, only this time a useless one.16


On the other hand, if (ii) were the case, we would be owed an explanation of the alleged 'contradiction' between this 'more' and that 'less' -- i.e., between this 'more-of-a-Totality' and its 'lesser parts'. But, as things stand, we have no idea whether this new 'contradictory' relation between whole and part is the same as that which operates between the parts, or is different.


[Anyone impatient with all this 'nit-picking' should re-direct their complaints to their local Dialectical Magus. Such 'pedantry' is forced upon us because even now, after more than 200 years, we still have no idea what these 'forces' are, how they can possibly 'contradict' one another, or even what the mysterious "Totality" is. The first two of these allegations will be substantiated as this Essay unfolds; the third was considered in detail in Essay Eleven Part One.]


However, and independently of the above 'difficulties', this 'theory' still faces other serious problems. If the 'contradiction' between the whole and its parts is the same as (but no more than) that which exists between the parts, then manifestly the whole wouldn't then be more than the sum of the parts (in at least this respect), since the whole would in that case be the entire 'contradictory' ensemble, all of whose elements (whole and part) operate alike. But, this would be contrary to the DM-hypothesis that wholes (whether these are wholes made of 'contradictory' parts or not) are more than the sum of their parts, whose natures (including the nature of their "internal contradictions") are said to be determined entirely by, while not being reducible to, the nature of their parts and the interconnection between these parts. Conversely, if the 'contradiction' between the whole and its parts weren't the same as that between the parts, then we would still have an unexplained type of 'contradiction' -- that which exists between a mysterious whole that is "more than the sum of the parts" and those parts themselves.17


Anyway, the idea that the whole 'contradicts' the parts in the same way that the parts 'contradict' each other doesn't appear to be a viable option for DM-theorists. The parts relate to each other by some form of "mediation", so we are told; but how can the part-whole relation be one of "mediation"? The mutually 'contradictory' nature of the parts in development constitutes the whole; if now the whole has its own 'contradictory' relation with the parts over and above this (if, as we are told, this whole is more than the sum of its parts), then this new 'contradictory' relation can't be one of part on part. But, if not, then what is it?


Hence, as noted in Part One of this Essay, it seems that a literal interpretation of DM-'contradictions' as forces lapses either into some form of CAR, or it inflates alarmingly into HEX (or, indeed, into Absolute Idealism). Conversely, if the identification of forces with contradictions is merely figurative, then DM would be indistinguishable from, say, metaphysical poetry.


[HEX = Hegelian Expansionism; CAR = Cartesian Reductionism. Follow those links for more details.]


Notwithstanding this, in order to examine this issue more thoroughly, it might be useful to suppose that some sort of solution to all of the above 'difficulties' can be found -- by someone, at some point, somehow.


However, even if we assumed this the analogy drawn between forces and contradictions will still fail to work.


The substantiation of that allegation brings us to the third reason for questioning the connection between forces and 'contradictions'.


This option is connected with a point made earlier that the reader was asked to keep in mind.


So, is the 'contradiction' here:


(a) Between the bodies and processes themselves?


(b) Between the forces operating in the system? Or,


(c) Both?


Contradictory To What?


Different Types Of Force Couples


In a physical system there may be several different combinations of interacting attractive and repulsive forces. If we abbreviate "attractive" and "repulsive" to "A" and "R", respectively, there appear to be only three types of combinations of just two of these: AA-, AR-, and RR-forces.18


Of course, this assumes that these relations are symmetrical -- i.e., that AR = RA, which seems reasonable enough. Another simplifying assumption is that these forces are in binary systems; that is, this discussion concentrates exclusively on force-couples. It is reasonably clear, I take it, that this simplification doesn't materially affect the conclusions drawn. Anyway, further complications will be introduced as this Essay unfolds. Naturally, a comprehensive, scientific (or even philosophical) account of the concept of force would have to include modern ideas about gravity, the strong nuclear, weak and electroweak forces, etc.


As I noted earlier, forces have now been edited out of the picture in favour either of exchange particles or the geometry of space-time -- here The first option is illustrated in this simplified video:



Video Two -- Exchange Particles And

Apparent 'Forces'


And here is a video of the second option:



Video Three -- Visual Representation Of Motion Governed

By The Geometry Of Space-Time


[I will return to discuss one or two issues raised in Video Three later on in this Essay.]


However, it is possible that as science develops, reference to forces (even in school Physics) will progressively disappear [cf., Jammer (1999), pp.iv-vi (partially quoted earlier)]. In that eventuality, if DM-theorists continue to promote the idea that 'forces' give their 'contradictions' some sort of materialist/physical grounding, their theory would thereby become 'unscientific' by default. Either that, or they will have to abandon all talk of the 'objective' nature of forces and join with Engels in regarding them as shorthand for relative motion. Of course, in that case, forces wouldn't just be "useful fictions", they would be useless fictions.


On the other hand, should that scientific development (i.e., the editing out of all forces from nature) fail to materialise, it would be interesting to see how DM-theorists might try to harmonise their attraction/repulsion scenario with successful attempts to unify the four fundamental forces in a Grand Unification Theory (or even in Superstring/M Theory, etc.) -- and perhaps into one over-arching 'force'. It might finally kill-off informed talk in DM-circles about the existence of 'contradictory' forces in nature.


Clearly, if there is only one force, it can hardly 'contradict' itself.


Nevertheless, many of the quotations given earlier and in Note 1 clearly imply that in DM only AR-forces are 'contradictory'. This category of force couples will be examined later on. However, AA-, and RR-forces weren't explicitly ruled out, and in a thoroughgoing analysis of every conceivable option available to DM-theorists, they will also need to be addressed. Hence, it is to them that I now turn.


AA- And RR-Forces


Unfortunately, and upfront, it is difficult to see how an AA-force could be interpreted as a unity of opposites, let alone as 'contradictory'. They are the same type of force, so they can hardly be opposites. But, such forces abound in nature. For example, as noted earlier, the centre of gravity of any conglomeration of matter in the universe is the result of countless such AA-forces. Plainly, in systems like this, kinematic (or, rather, dynamic) changes are caused by non-opposites. So, when, say, a planet is in the process of formation, particles begin to gravitate together under the operation of forces of mutual attraction --, i.e., these aforementioned non-opposites.19


[This is, of course, to adopt the vocabulary of Classical Physics. However, no inference should be drawn from this about the present author's views concerning the 'ontological' status of forces. As noted elsewhere, this terminology is only being employed here in order to expose the confusions that abound in DM. It is up to scientists to tell us what the world contains, not Philosophers -- or even yours truly --, and definitely not Mystics like Hegel.]


Nevertheless, with respect to the above comments, it is assumed that R-forces prevent the collapse of accumulated matter into a 'singularity' under the action of local AA-forces.


[If the gravitational field is strong enough, this should happen -- a singularity should form, at least in theory. [On this see Curiel (2019).] However, physicists get around this fatal flaw in their theory with a handful of ad hoc mathematical dodges. That alone suggests these theories are at least incomplete. This reminds one of the additional epicycles that were required to make Ptolemaic Astronomy 'consistent'.]


Clearly, this just complicates the point without altering it. In such circumstances we would have an ARA-system-of-forces, which would be even more difficult to interpret as 'contradictory'. As pointed out below, the meaning of the word "opposite" would have to be altered so that systems of forces could then have any number of 'opposites', components or contributory forces. If so, these artificial 'contradictions' -- "artificial" since they would be the product of an arbitrary choice of words --, won't have been based on 'objective' factors, but on linguistic tinkering.


Moreover, if the DM-theory of change is to survive, there has to be only one 'opposite', and that 'opposite' has to be dialectically-, not accidentally-, related to its own 'opposite', or "other", too. [On that, see here.]


Finally, and once again, given the classical picture, motion itself is actually altered by the operation of a single resultant force. This is even more difficult to square with the idea that forces are 'contradictions'. [More on that later, too.]


Similarly, it isn't easy to see how RR-forces could be interpreted as 'contradictory' -- or even as opposites --, either, and yet these are also found throughout nature. For example, intra-atomic forces of repulsion prevent atomic nuclei from approaching one another.20


Even in DM-terns it is difficult to see how such forces could be opposites. As we noted above, 'dialectical opposites' are not only supposed to imply one another, each can't exist without the other. But, which A-force implies another A-force; which one of these can only exist if the other does? Which R-force implies another R-force; which one can only exist if the other does?


One objection to the above immediately springs to mind: it ignores the fact that such forces operate in the manner they do because they work in opposition to one another -- that is, they do so in a way that brings them (or the system to which they belong) into, or out of, equilibrium. However, that response in fact concerns forces acting as AR-couples, which will be examined presently. It can't therefore assist us in our attempt to analyse/understand AA-, and RR-forces.


Despite this, even if it were true that A-forces are opposites of each other, in order for them still to be regarded as 'contradictory', they couldn't also be regarded as the opposite of R-forces -- unless, that is, these A-forces are now allowed to have two sorts of "opposites": (a) other A-, and (b) other R-forces. But, in that case, this would make a mockery of the notion that there are "polar opposites" at work in natural (or even social) systems of forces (implicated either in change or in equilibria, and in connection with 'contradictions'):


"All motion is bound up with some change of place…. The whole of nature accessible to us forms a system, an interconnected totality of bodies…. [These] react one on another, and it is precisely this mutual reaction that constitutes motion…. When two bodies act on each other…they either attract each other or they repel each other…in short, the old polar opposites of attraction and repulsion…." [Engels (1954), pp.70-71. Bold emphasis added.]


It is difficult to see how a particular A-force could be the "polar opposite" of another A-force while at the same time being the polar opposite of an R-force -- i.e., it isn't easy to see how A-, and R-forces could have two "polar opposites" without altering the meaning of the phrase "polar opposite". Even then, if the meaning of "polar opposite" were modified to neutralise this 'difficulty', it would succeed in so doing only because of yet more linguistic tinkering. In that case, any 'truths' that suddenly sprang into existence as a result would plainly be a by-product of yet another example of terminological juggling, not because of the way the world happened to be -- which would in turn mean that dialectics had been read into nature, not read from it.21


[However, there are dialecticians who claim that objects and processes not only can, they do possess many "opposites"; for example Gollobin (1986), p.122 (but even he says they are "paired").]


Of course, this whole metaphysic originated in the defective 'logic' Hegel concocted, who posited a unique opposite (an "other", as he called it) for each and every item implicated in change. He did so in order to forestall the criticism that if everything changes into 'what-it-is-not' (i.e., its 'opposite'), then, since everything else in the universe is 'what-it-is-not' in relation to any given object or process, every object/process could or would change into anything-else-whatsoever. [On that, see here.]


In which case, instead of growing into barley plants, a barley seed, for instance, could turn into a volcano, an unexploded bomb, Stalin's moustache or your left hand, and much else besides -- since all of these are 'what-a-seed-is-not'.


[However, in Part Three of this Essay we will see that in the end Hegel had to abandon the idea that objects and processes were somehow linked to a logical(?), or unique, 'opposite', or "other". In Essay Seven Part Three it will be shown that this concession fatally damages Hegel's attempt to respond to Hume's criticisms of rationalist theories of causation (reposted below).]


But, if objects and processes are allowed to have many (and possibly an infinite number of) 'opposites' -- all of which they could change into --, that would completely undermine what little is left of Hegel's already tattered system, which, as we have just seen, postulates that everything is paired with its own unique "other". Naturally, if that were the case, it would mean that the Empire State Building, for example, could change into, say, a T Rex, and the Pacific Ocean could morph into a crate of Tennessee Whiskey, and much else besides. Since things like this don't happen, so far as we know, we must conclude that, either:


(i) Hegel was right: objects and processes have only one unique "other" that is either:


(a) 'Dialectically'-, or logically-'internal' to that object or process, which would in turn mean that no object or process could turn into this unique 'other', since the latter already exists, or,


(b1) 'External' to that object or process, meaning that the cause of change can't be internal to objects and processes, or, perhaps even,


(b2) 'External' to that object or process, which object or process turns into that 'other', meaning that change can't have been caused by that 'other' (since it isn't 'dialectically'-related to it) -- and the whole point of accepting this dogma will now have vanished;


Or even:


(ii) Objects, processes and forces have only one opposite, not many.21a


Nevertheless, it could be argued once again that in this context the word "opposite" really means "oppositional". That change of emphasis now highlights the active inter-relation that exists between forces rather than their passive interconnection, which is something the above discussion seems to have ignored. Hence, it would seem perfectly natural to speak of RR-, or AA-forces as contradictory in this respect --, i.e., in the sense that all and only those forces that are oppositional (i.e., which engage in, or are part of, some sort of "struggle") should be classed as contradictory.


Or, so it might be objected.


However, this latest revision seems to be inconsistent with the claims made in several of the passages quoted earlier. They appear to suggest that only certain forces were to be regarded as inseparable from matter. Others indicate that forces are merely the consequence of the complex inter-play between quanta of energy (or of motion). For example, Engels claimed that:


"The whole of nature accessible to us forms a system, an interconnected totality of bodies…. [These] react one on another, and it is precisely this mutual reaction that constitutes motion…. When two bodies act on each other…they either attract each other or they repel each other…in short, the old polar opposites of attraction and repulsion…. It is expressly to be noted that attraction and repulsion are not regarded here as so-called 'forces', but as simple forms of motion." [Engels (1954), pp.70-71. Bold emphasis added.]


Once again, this seems to lose sight of internally-connected oppositionality, since Engels appears to edit out of the picture the dialectical interrelation between forces, replacing it, or them, with mere "forms of motion".


Now, "forms of motion" aren't in any obvious way interconnected -- that is, if the relevant forces are edited out of the picture. But, DM requires bodies in motion to be inter-related; that is why intermediary forces seemed to be so useful -- no, strike that, so crucially important -- to its theorists. Forces and 'contradictions' were clearly supposed to assume just such a role -- i.e., forming part of the 'connective tissue' of reality, as it were. If they are now re-classified as little more than "useful fictions" -- i.e., as relative "forms of motion" --,  there would seem to be nothing physical left in nature to act either as the bearer of, or as the mediator between, these interconnections. Without a material substrate (pictured as just such forces), 'contradictions' could only operate on bodies or processes magically --, or, perhaps supernaturally --, it would seem.


Ignoring these serious difficulties again -- at least for the present -- perhaps the above objection can be summarised in the following way:


F1: All and only those forces that are oppositional -- or are implicated in struggle -- are contradictory.


But, if F1 were true, motion itself couldn't be regarded as the product of 'contradictory forces' -- unless we confine our attention solely to accelerated motion -- since, ex hypothesi, no net forces operate in cases where there is no acceleration (in post-Aristotelian Physics, that is). Even then, accelerated motion (under gravity, say) is subject to only one force (or, rather, one resultant force) in classical Physics, and none at all in relativistic Physics.


At best, therefore, taking the classical view, most of the accelerated motion in the universe (which covers, as far as we know, all of the bulk, non-rectilinear movement in nature) is the product of only one force (or resultant force). Given F1, it is hard to see how such motion could be viewed as part of a 'contradictory' Totality, if the 'classical view' were correct. So, if F1 does indeed express what DM-theorists mean, then most (perhaps all) of the motion in nature can't have been induced, caused, changed or sustained by a set of DM-'contradictions'.


With that observation much of classical DM falls apart.22


It could be objected to this that, as a matter of fact, all motion in the universe is the result of a disequilibrium between oppositional forces; that is precisely what a resultant force is. In that case, therefore, bodies would move (or their state of motion would change) because of just such an imbalance between forces. Hence, for example, the planets -- which traverse in what are apparently steady orbits around the Sun -- actually have their trajectories determined by resultant forces internal to the Solar System, the Galaxy, and, indeed, beyond, all of which are induced by complex inter-relating systems of forces.


Or, so it could be argued, once more.


This objection will be considered in more detail later, but for present purposes it is sufficient to point out that it is difficult to see how such forces could be regarded as oppositional. Presumably, these forces don't affect each other; they operate on, or they merely change, whatever motion is already present in the system. At best, then, such forces would only oppose the impressed motion already apparent, which motion would itself have been the result of still other forces operating earlier, or elsewhere, in the system. This can be seen from the fact that if the moving bodies in question hadn't been in the said 'force field', these forces would have had nothing on which they could act. In 'empty space', plainly, we would see no new motion.23 Forces without bodies to operate on don't interfere with each other, as far as we know -- unless they are themselves regarded as particulate in some way, or are carried by particles, which would, of course, mean they weren't forces, they were bodies, to begin with.24


Readers are again reminded of something they were earlier advised to keep in mind (which is connected with the above remarks):


So, is the 'contradiction' here:


(a) Between the bodies and processes themselves?


(b) Between the forces operating in the system? Or,


(c) Both?


That ambiguity will be explored as this Essay unfolds. Readers are advised to keep it in mind.


Interlude One: The Classical Problem Of Forces


This is, of course, just one aspect of the classical 'ontological problem' concerning the precise nature of forces, and it is partly why it is so difficult to understand them. Indeed, the detection of forces seems to depend only on the effects they have on bodies, or on instruments -- or, rather, a 'force' seems to be little more than the way scientists either depict or measure certain relationships between bodies, as Engels, in an uncharacteristically sober mood, pointed out (on that, see Note 4) -- or, indeed, on other 'fields'.


However, if forces are now seen as particulate (that is, if certain particles are viewed as the 'bearers' of forces -- on that, see Video Three), the problem simply reappears at a lower level, and we would be no further forward -- which is a conundrum that Leibniz was, I think, among the first to recognise. [On that, see here, here, here and here.]


So, it would seem that an interaction between forces could only take place if they were viewed as particulate in some way -- that is, if they registered some sort of resistance to one another (i.e., if they are impenetrable to a greater or lesser extent).


On the other hand, if they aren't particulate, it is hard to see how they could interact at all, let alone 'contradict' each other. Continuous media have no rigidity and no impenetrability that enables them to exert forces of any sort (except, of course, as part of a figurative extension to particulate interaction, after all).


[This has been questioned in Smith (2007). My response that article will be posted in Note 30 in the next few weeks.]


But, there are well-known classical problems associated with the idea that forces are particulate (they have been outlined here) -- not the least of which is the observation that if forces were particulate then they could only interact if they exerted still other forces (contact forces, cohesive forces, forces of reaction, and so on, which hold them together or lend to them some sort of coherence), so that they could act on other particulates and hence resist disintegration -- which considerations would, plainly, initiate an infinite regress. That is, in order to account for the ability of particles to resist one another, we would need to appeal to yet more forces internal to a given body to stop, say, one of them penetrating the other, or prevent distortions tearing them apart when two or more collide. But, if the forces internal to bodies are particulate, too -- as it seems they must be, given this view -- that would require further forces to account for the internal coherence of these new, smaller, 'force-particles', and so on...


Alternatively, if these 'internal forces' were in fact continuous (i.e., non-particulate), they would be incapable of sustaining their inner coherence -- once again, since they would have no rigidity, etc., etc.


In the end nothing would be accounted for since at each level there would be nothing to provide the required resistance or coherence.


So, it seems that reducing the interaction between forces to that between bodies explains nothing. It also implies that particles can't 'contradict' one another without exerting non-particulate forces on each other -- which would mean, once again, that such entities are incapable of exerting forces, having no rigidity to do so, etc., etc.


[It is important to add that I am not arguing that there can be no interactions -- as Kline and Matheson (1987), for example, maintains -- just that we have as yet no idea how they can happen! I have said more about this in Note 30.]


Unfortunately, even exchange particles (in Quantum Field Theory) would succeed in exerting forces only if there were still further reaction forces internal to these bodies -- that is, if they were bodies. However, as noted earlier (but in more detail in Essay Seven Part One), many physicists now speak of such 'particles' as perturbations in 'the field':


"We learn in school that the basic building blocks of matter are particles. In fact, we often continue to teach this in universities where we explain that quarks and electrons form the lego-bricks from which all matter is made. According to our best laws of physics, the fundamental building blocks of Nature are not discrete particles at all. Instead they are continuous fluid-like substances, spread throughout all of space. We call these objects fields. The most familiar examples of fields are the electric and magnetic field. The ripples in these fields give rise to what we call light or, more generally, electromagnetic waves.


"If you look closely enough at electromagnetic waves, you'll find that they are made out of particles called photons. The ripples of the electric and magnetic fields get turned into particles when we include the effects of quantum mechanics. But this same process is at play for all other particles that we know of. There exists, spread thinly throughout space, something called an electron field. Ripples of the electron field get tied up into a bundle of energy by quantum mechanics. And this bundle of energy is what we call an electron. Similarly, there is a quark field, and a gluon field, and Higgs boson field. Every particle your body --- indeed, every particle in the Universe --- is a tiny ripple of the underlying field, moulded into a particle by the machinery of quantum mechanics." [Quoted from here; accessed 13/12/2017. Several paragraphs merged. Italic emphases in the original.]


However, this poses serious problems of its own. The forces exerted in the above manner (inside exchange particles or, indeed, other particles they act upon) must themselves be the result of rigidity, cohesion, and contact (etc.), if they are capable of stopping the force carrier particle passing right through the target particle without acting on it. Of course, as noted above, physicists these days appeal to fields, energy gradients, Feynman diagrams and the like, and reject such 'mechanistic' notions like those rehearsed in the previous couple of paragraphs, but if fields and particles are both continuous, the above problems will simply re-emerge at this new level. On the other hand, if they are particulate, after all, this merry-go-round just takes another spin across the metaphysical dance floor.


So, the neat picture painted in and by Video Three, where, for example, repulsive forces are explained by an analogy drawn between two individuals stood or sat in two separate but closely aligned boats (on a lake). If one individual throws a heavy ball to the other individual, both boats will move apart, and it will seem that there is a repulsive force acting between the two boats/individuals (as momentum is conserved). But that only works if the first individual's body is rigid enough to allow the ball to be thrown in the first place, and the second individual's body is rigid enough to stop the ball passing straight through their body unopposed. If they are both rigid enough then that will be because of forces internal to those two bodies, which can't also be explained in the same particulate terms without an infinite regress being initiated. So, if forces are communicated by carrier particles, nothing will have been explained. On the other hand if forces aren't particulate, but are continuous, then nothing would actually happen (for reasons explored in the previous few paragraphs).


Of course, it could be objected once more that the above approach adopts an out-dated 'mechanistic' view of interaction and is, as a result, completely misguided. However, the modern 'mathematical' approach has clearly abandoned the possibility of giving a causal, or even physical account of forces -- or, at least, an explanation that doesn't itself depend on a figurative use of the sort of verbs we find in the vernacular that allow a physical explanation to be given why things happen in the everyday world (such as "push", "move", "resist", "hit", "collide", "deflect", "interact", and the like).


So, if a particle is viewed as the carrier of a force, and that force can be given no physical content, for want of a better word, but is still deemed capable of making things happen, deflecting other particles from their line of action (etc.), then the above verbs must themselves lose contact with the meaning of typographically identical everyday verbs when they are used to talk about macro-phenomena.


Now, there is no problem with that providing we are aware of it and don't make the mistake of interpreting the technical use of such verbs literally, understanding them in their everyday sense.


Even so, a 'mathematical account' like this would thereby merely be descriptive, not explanatory. Differential Equations, Hamiltonians, vectors, tensors and abstract spaces can't make anything move, or alter the path of a single particle. To be sure, we can describe these phenomena using mathematical language and symbols, thus enabling us to 'balance the books of nature', as it were. But, the downside is that mathematical models can't explain why anything actually happens in the physical world.


[Of course, this depends on what one means by "explanation". I will say more about that in Essay Thirteen Part Two. However, for more recent qualms in this area, see Note 30. Cf., also my comments over at Wikipedia, here (at the foot of the page) and here. Readers shouldn't conclude at this point that I am questioning the existence of 'The Field'. What I am doing is questioning whether it can account for anything physical, or explain why anything actually happens in the universe. On that, see the discussion between myself and Paul Cockshott, here, and another between myself and a comrade who posted under the name "Lynx", here. (Unfortunately those links are now dead!)]


This, perhaps, helps explain Engels's own suspicion of forces. Ontologically, they appear to be deeply mysterious, if not animistic. He isn't alone. [Other relevant aspects of the nature of forces have been discussed here.]


Clued-in physicists already appear to be aware of this problem (i.e., that this presents them with serious difficulties connected with the language they use). Here, for example, is the late David Peat:


"It hasn't been a great couple of years for theoretical physics. Books such as Lee Smolin's The Trouble with Physics and Peter Woit's Not Even Wrong embody the frustration felt across the field that string theory, the brightest hope for formulating a theory that would explain the universe in one beautiful equation, has been getting nowhere. It's quite a comedown from the late 1980s and 1990s, when a grand unified theory seemed just around the corner and physicists believed they would soon, to use Stephen Hawking's words, 'know the mind of God'. New Scientist even ran an article called 'The end of physics'.


"So what went wrong? Why are physicists finding it so hard to make that final step? I believe part of the answer was hinted at by the great physicist Niels Bohr, when he wrote: 'It is wrong to think that the task of physics is to find out about nature. Physics concerns what we can say about nature.'


"At first sight that seems strange. What has language got to do with it? After all, we see physics as about solving equations relating to facts about the world -- predicting a comet's path, or working out how fast heat flows along an iron bar. The language we choose to convey question or answer is not supposed to fundamentally affect the nature of the result. Nonetheless, that assumption started to unravel one night in the spring of 1925, when the young Werner Heisenberg worked out the basic equations of what became known as quantum mechanics. One of the immediate consequences of these equations was that they did not permit us to know with total accuracy both the position and the velocity of an electron: there would always be a degree of irreducible uncertainty in these two values.


"Heisenberg needed an explanation for this. He reasoned thus: suppose a very delicate (hypothetical) microscope is used to observe the electron, one so refined that it uses only a single photon of energy to make its measurement. First it measures the electron's position, then it uses a second photon to measure the speed, or velocity. But in making this latter observation, the second photon has imparted a little kick to the electron and in the process has shifted its position. Try to measure the position again and we disturb the velocity. Uncertainty arises, Heisenberg argued, because every time we observe the universe we disturb its intrinsic properties.


"However, when Heisenberg showed his results to Bohr, his mentor, he had the ground cut from under his feet. Bohr argued that Heisenberg had made the unwarranted assumption that an electron is like a billiard ball in that it has a 'position' and possesses a 'speed'. These are classical notions, said Bohr, and do not make sense at the quantum level. The electron does not necessarily have an intrinsic position or speed, or even a particular path. Rather, when we try to make measurements, quantum nature replies in a way we interpret using these familiar concepts.


"This is where language comes in. While Heisenberg argued that 'the meaning of quantum theory is in the equations', Bohr pointed out that physicists still have to stand around the blackboard and discuss them in German, French or English. Whatever the language, it contains deep assumptions about space, time and causality -- assumptions that do not apply to the quantum world. Hence, wrote Bohr, 'we are suspended in language such that we don't know what is up and what is down'. Trying to talk about quantum reality generates only confusion and paradox.


"Unfortunately Bohr's arguments are often put aside today as some physicists discuss ever more elaborate mathematics, believing their theories to truly reflect subatomic reality. I remember a conversation with string theorist Michael Green a few years after he and John Schwartz published a paper in 1984 that was instrumental in making string theory mainstream. Green remarked that when Einstein was formulating the theory of relativity he had thought deeply about the philosophical problems involved, such as the nature of the categories of space and time. Many of the great physicists of Einstein's generation read deeply in philosophy. In contrast, Green felt, string theorists had come up with a mathematical formulation that did not have the same deep underpinning and philosophical inevitability. Although superstrings were for a time an exciting new approach, they did not break conceptual boundaries in the way that the findings of Bohr, Heisenberg and Einstein had done.


"The American quantum theorist David Bohm embraced Bohr's views on language, believing that at the root of Green's problem is the structure of the languages we speak. European languages, he noted, perfectly mirror the classical world of Newtonian physics. When we say 'the cat chases the mouse' we are dealing with well-defined objects (nouns), which are connected via verbs. Likewise, classical physics deals with objects that are well located in space and time, which interact via forces and fields. But if the world doesn't work the way our language does, advances are inevitably hindered.


"Bohm pointed out that quantum effects are much more process-based, so to describe them accurately requires a process-based language rich in verbs, and in which nouns play only a secondary role.... Physics as we know it is about equations and quantitative measurement. But what these numbers and symbols really mean is a different, more subtle matter. In interpreting the equations we must remember the limitations language places on how we can think about the world...." [Peat (2008), pp.41-43. Bold emphases and several links added; quotation marks altered to conform with the conventions adopted at this site. Several paragraphs merged.]


Now, I don't want to suggest for one moment that I agree with the above comments about the nature of language (or even about the nature of scientific language), but the above passage certainly shows that at least some leading scientists are aware there is a problem here.


[To be sure, Peat agrees with Bohm's suggestion that we need to learn from Native American languages, which seem to have rather odd grammars; but it is to be wondered how a culture that has produced no advanced science or technology has much to teach one that has, least of all about physics. Thus isn't to disparage Native American culture -- far from it -- it is merely to point out that no such culture could be expected to compete with one that is so much more technologically advanced. On this, also see Essay Eleven Part One.]




So, classically, forces seem to work only on bodies by altering their motion. In which case, the supposed opposition isn't between bodies, nor is it between bodies and forces, nor yet between forces and forces -- it is between forces and the motion already in the system. But, this picture is difficult to square with the idea that there is a UO at work here -- nor does it seem to tally with the claim that dialectically polar opposites ultimately induce all motion and change. That is because (once again) forces don't oppose each other; they oppose or augment whatever motion is already present in the system, howsoever it was caused.


In short, given this 'revised' view, the term "contradiction" wouldn't apply to opposing or opposed forces (i.e., to forces that oppose one another), nor to bodies; on the contrary, 'contradictions' would now connect forces with whatever movement is already present. But, as yet, no DM-theorist has given any clear sense to the idea that a force could 'contradict' the impressed motion in a system. And rightly so; there are no opposites here for a single DM-'contradiction' to latch onto. How could a force be the 'opposite' of movement -- i.e., the 'opposite' of a change of place?


It could be objected that as a matter of fact forces in nature oppose (in the sense of change) motion. Indeed, it could be argued that dialecticians are concerned with forces as they actually operate in nature and society (as opposed to those abstracted from it); such opposites objectively exist and can't be analysed away.


That much won't be disputed here (even if its wording might). But, in what way can this set-up be said to involve the interconnection of opposites required by the theory? And, what sense can be given to the idea that motion in one direction is the opposite of any force that affects it? Certainly these aren't unified opposites (i.e., opposites on the same type, so they are 'dialectically'/'logically' connected -- that is, the existence of one implies the existence of the other, in the Hegelian sense of that word, which, as we have seen, is a DM-requirement). So, whatever else it is, this can't be a 'dialectical' interaction. That is because movement itself doesn't imply the existence of the force that is supposedly opposing it, nor does the force imply the existence of the motion it is opposing. They can both exist without the other (unlike, say, the proletariat and the bourgeoisie, which supposedly imply one another). If this were a 'dialectical' interaction, they would imply one another and neither could exist without the other.


At best, the forces involved might tend to produce an opposite motion (or change of motion, perhaps) to that which already exists -- or even none at all. But, to describe force and motion as "opposites" would appear to make about as much sense as claiming that "left" was the opposite of "television", even if as a matter of fact someone moved a television to the left. Their actual linkage in reality has nothing to do with whether it is sensible to describe such items as unified opposites, or even as oppositional. These terms are categorically different -- as are "force" and "motion". Hence, it isn't a question of whether or not DM-theorists are dealing with 'objective' facts; it is why the above counter-claim can only be 'justified' by mis-describing the phenomena.25


Interlude Two: Several Annoying Technicalities


Admittedly, when viewed as vectors, velocities, accelerations and forces can, in some circumstances, be represented as 'opposites', but this is given within vector algebra and follows from certain definitions. However, unless we are prepared to admit all the absurdities outlined earlier (arguing, for instance, that vectors 'struggle' among themselves), this approach can't lend any support to DM. That is quite apart from the fact that these forces don't imply one another in a dialectical-sort-of-way, which they should do if they were 'interpenetrated' opposites' -- for example, again, in the way that we are told that capitalist relations of production imply the existence of the proletariat, and vice versa. But, if these forces aren't 'internally related' then the dialectical theory of change simply falls apart.


Anyway, if vector, v, has an opposite, -v, that vector could be a billion miles away or it could be co-terminal with v. Either way, these two don't 'struggle' with one another, nor do they turn into each other (which is what they should do if the DM-classics are to be believed). Again, whatever else they are, such vectors aren't 'dialectical'.


In addition, as will be argued in Interlude Six, mathematics can in no way be regarded as an abstraction from reality. And, of course, as noted earlier, most vectors aren't opposites, anyway. Many augment, while others operate at various angles to, one another.


[In fact, this topic is connected with 'real negation', a concept introduced into Philosophy by Immanuel Kant. I will have much more to say about this in Appendix A. Other related issues will be examined in Essay Thirteen Part Two, when it is published. Finally, this topic is also connected with the fact that, where there is more than one force at work in a system, change in motion is caused by a resultant force, discussed in more detail here.]


As already noted, when forces are represented as vectors they can produce accelerations that appear to 'oppose' the motion already in the system. Ignoring for the present the fact that the use of such language is arguably anthropomorphic (or, at best, metaphorical), in such cases we would be establishing connections between objects, events, and processes drawn from the same category (i.e., vectors connected with movement), which clearly makes sense. In this way, forces could be replaced with relative accelerations by means of Newton's Second Law, etc. But, even then, an acceleration in an opposite direction doesn't oppose the original velocity; an acceleration (in vector algebra, which is what we are speaking of here!) just is a description of that changing velocity, it doesn't produce that velocity or create it. A force is supposed to do that (in Newtonian Physics). Even in the physical universe, accelerations aren't 'disembodied beings' that inhabit the world, throwing their weight about, bullying velocities to do their bidding. They just are changing velocities --, no more, no less. Period. And velocities, in like manner, simply represent a rate of change of displacement. Even in DM-terms, the idea that they might 'contradict' one another seems rather odd (to say the least); that is because no accelerating body implies the existence of the velocity in any other body, and both can surely exist without the other -- unlike, once more, the connection between the capitalist class and the proletariat, which do imply one another, or so we are told.


However, in vector algebra no sense can be made of the addition (or subtraction) of force and velocity vectors, unless it is mediated by the Second Law (etc.), once more. Even then, the relation between acceleration and velocity vectors has to be established by well-known equations. The various physical quantities represented by these equations can only be connected by means of such translations, which set up analogies between categorically different items, but in a dimensionally consistent manner. That is one reason why no mathematical or physical sense can be given to 'equations' like the following:


(1) F = -v (sic)


(2) a = kv (sic)


[Where "F" stands for "force", "v" for "final velocity", "a" for "acceleration", and "k" is a constant of proportionality.]


Equations like these would be regarded as dimensionally incoherent (unless further dimensions were built into the 'constant' -- but now variable --, k). Compare them with the next series of examples:


(3) s = ut + ½at2


(4) a = -ω2r


(5) F = -m2


[Where "r" represents radial displacement, "u" is the initial velocity, "t" is time, "ω" is angular velocity, "m" represents mass, "F" centripetal force, and "a" centripetal acceleration in (4), but linear acceleration in (3).]


In Classical Physics, by means of translational or analogical equations like these -- or, perhaps to make the same point more clearly --, by the use of algebraic rules that enable inferences involving physical quantities to be drawn in which forces appear as part of a "norm of representation", we can 'convert' forces into accelerations, compare magnitudes, and thus account for change in motion.


Unfortunately, this is of little help to DM-enthusiasts, since the translation of forces into relative accelerations means that forces are, indeed, "useful fictions", once more, which would simply re-introduce all the difficulties noted earlier (and again, below).


[This isn't a problem for the account presented here, for reasons expressed in the previous paragraph but one.]


However, even if the above comments were rejected for some reason, this would still lend scant support to dialecticians, for such representations aren't oppositional; they don't slug it out on the page, screen or whiteboard. And, manifestly, they don't turn into one another (as we are told they should by the DM-classics).


Hence, if two ('opposite') forces (for instance, F and G, inclined at θo to the x axis in R2) are in equilibrium and are resolved (into their i and j components), and then equated as follows:


|F| cosθ - |G| cosθ = 0,


|F| sinθ - |G| sinθ = 0,


no one would suppose (it is to be hoped!) that these symbols are locked in a life-or-death 'struggle', and will one day change into each other.


Naturally, the above conclusions aren't affected in any way if these forces aren't in equilibrium:


|F| cosθ - |G| cosθ > 0


|F| cosθ - |G| cosθ < 0




|F| sinθ - |G| sinθ > 0


|F| sinθ - |G| sinθ < 0


And, it would be little use arguing that while it is true that the above expressions may be lifeless (and thus incapable of struggling and then turning into each other), what they represent in the real world not only can they actually do struggle and then turn into each other. It would be little use because the above considerations were aimed at undermining the idea that the vector calculus is 'dialectical'. The allegedly 'dialectical' nature of forces 'in reality' represented by the above symbols is an entirely separate issue, which has been systematically demolished throughout the rest of this Essay, as well as here. However, it would be interesting to see if there are any DM-fans out there who can explain how these forces manage to struggle with, and then turn into, each other (as they should if the DM classics are to be believed). Exactly how do F and G above turn into one another?


[On the allegedly 'dialectical' nature of 'Higher Mathematics' and the Calculus in general, see here.]


Incidentally, some readers may be puzzled by the use of the word "analogical" in an earlier paragraph. The use of that word is connected with:


(i) The history of the development of mathematical language associated with this area of Physics and Applied Mathematics, and,


(ii) The way we make sense of such equations.


More specifically, a significant change in terminology (or at least what it signifies) arose out of:


(iii) The reservations expressed by Ancient Greek mathematicians concerning the relationship between the so-called "incommensurables" (i.e., physical quantities from different categories for which no common noun or predicate could be found that allowed them to be 'co-measured'), and then with,


(iv) How these problems were resolved by European mathematicians in the High Middle Ages.


Following on the growth and development of market economies in mid-, to late-feudal society, the artificial barriers between these categories were progressively eroded as new grammars ('concepts') were introduced by merchants and traders to help them account for the exchange of quantities drawn from just such different categories. Since they had to be co-measured (to balance the books!), the language and mathematics involved were adjusted accordingly.


Hence, these new concepts were introduced by mathematicians, merchants, and bankers so that what had been regarded as incommensurable quantities could be compared analogically -- enabling, for example, the calculation of the exchange value of a widely diverse range of commodities. As a spin-off, these conceptual innovations -- when they were also incorporated into the physics of the day -- allowed theorists to move beyond an earlier 'commonsense' approach to motion encapsulated in Aristotelian Physics, thus enabling the foundations of modern mechanics to be laid down in the period between the 13th and the 18th centuries.


This emphasis on the analogical nature of modern algebraic forms depicting motion follows on from an approach to mathematical development that sees it as conditioned by contingent historico-economic factors predicated on material and social relations. This view of mathematical innovation also helps undermine the idea that mathematics is concerned with, or is derived from, some form of 'abstraction' -- which further undercuts theories predicated on the belief that there is an Ideal World anterior to, but more real than, the world we see around us. Since this Ideal World may only be accessed by thought, it then appeared to make sense that mathematics was solely based on thought, too. In which case, it was then but a short step to conclude that mathematics is founded exclusively on thought processes, on 'abstraction' -- and much later still, on logic itself.


To many, this appeared to put mathematics/mathematicians in direct touch with the 'Divine', and hence with a range of pure concepts originally called into existence by 'God', a doctrine explicit in Plato. In fact, the universe itself was regarded as a reflection of 'Divine Thought', which, of course, implied that 'God' was a Mathematician and the world was a mathematical object of some sort -- which is a paradigm that currently dominates Modern Physics (indeed, as we will see in Note 30), and that includes the ideas of physicists who even claim to be agnostics or atheists.


Here area just few recent examples of the genre:


"All science proceeds from the assumption that the cosmos is ordered in an intelligible way. Beneath the bewildering richness of natural phenomena there lies an elegant mathematical unity. How astonishing that the human mind is attuned to this hidden subtest of nature!" [Physics Professor, Paul Davies, quoted in the flyleaf to Livio (2009), and quoted at the publisher's website (expand the 'Praise' section). Bold added.]


"Philosophy is written in that great book which ever lies before our eyes (I mean the universe) but we cannot understand it if we do not first learn the language and grasp the characters in which it is written. It is written in the language of mathematics, and the characters are triangles, circles and other geometrical figures, without which it is humanly impossible to comprehend a single word of it, and without which one wanders in vain through a dark labyrinth." [Galileo, quoted in Livio (2009), pp.76-77. Bold added.]


"The Higgs Boson was predicted with the same tool as the planet Neptune and the radio wave: with mathematics. Galileo famously stated that our Universe is a 'grand book' written in the language of mathematics. So why does our universe seem so mathematical, and what does it mean? In my new book 'Our Mathematical Universe', I argue that it means that our universe isn't just described by math, but that it is math in the sense that we're all parts of a giant mathematical object, which in turn is part of a multiverse so huge that it makes the other multiverses debated in recent years seem puny in comparison." [Max Tegmark, excerpted from Tegmark (2015). Quotation marks altered to conform with the conventions adopted at this site. Bold emphasis and link added.]


"In [Plato's] famous cave analogy, he likened us to people who'd lived their entire lives shackled in a cave, facing a blank wall, watching the shadows cast by things passing behind them and eventually coming to mistakenly believe that these shadows were the full reality. Plato argued that what we humans call our everyday reality is similarly just a limited and distorted representation of the true reality, and we must free ourselves from our mental shackles to begin comprehending it. If my life as a physicist has taught me anything at all, it's that Plato was right: modern physics has made abundantly clear that the ultimate nature of reality isn't what it seems.... Our external physical reality is a mathematical structure." [Tegmark (2015), pp.8, 254. See also Tegmark (2008). Paragraphs merged; bold added. I have added a lengthy passage from Plato (1997b) to Appendix B, where the allegory of the cave first saw the light of day (no pun intended).]


One wonders why Tegmark trusts a single experiment or observation in physics or any of the other sciences (which he seems to take for granted in the rest of his book, and which he also appears to think aren't illusory) if it is all just a 'shadow', or based on 'subjective experience' --, and that includes anything written by mathematicians. Does he have direct access to this hidden world that the rest of us don't? Is he able to apprehend mathematical theorems that somehow bypass the senses? If not, then just as soon as anything mathematical has been committed to paper, or typed onto a screen, it too must be a 'shadow', and hence can't reflect 'reality'.


Anyone who thinks this misrepresents Tegmark need only read Chapter Nine of his book (Tegmark (2015)), where the author tries to sell the reader a downmarket, revamped view of the world first aired by John Locke and David Hume, but he doesn't once consider how to construct "external reality" out of what he calls "internal reality". Now, I have no wish to praise Immanuel Kant, but Tegmark's amateur metaphysics would put epistemology back to where it was before the Critique of Pure Reason rolled off the presses (this links to a PDF).


[I have covered this topic extensively here. Readers are directed there for more details.]


Something like this, but which comes across as less extreme, seems to be motivating Greene (1999, 2004) and Penrose (1989, 1995, 2004); it also appears to be (partially) exercising Smolin (2006) and Woit (2006). For example, here is Roger Penrose:


"But are mathematical notions things that really inhabit a 'world' of their own? If so, we seem to have found our ultimate reality to have its home within that highly abstract world. Some people have difficulties with accepting Plato's mathematical world as being in any sense 'real', and would gain no comfort from the view that physical reality itself is constructed merely from abstract notions. My own position on this matter is that we should certainly take Plato's world as providing a kind of 'reality' to mathematical notions..., but I might baulk at actually attempting to identify physical reality with the abstract reality of Plato's world.... [Penrose then commits himself to the 'three world' theory, somewhat similar to Karl Popper's view (this links to a PDF), that there are mathematical, physical and 'mental' components to 'the world' -- RL.] I like to think that, in a sense, the Platonic world may be the most primitive of the three, since mathematics is a kind of necessity, virtually conjuring its very self into existence through logic alone." [Penrose (2004), p.1029. Italic emphasis in the original; bold emphases and link added.]


Earlier in the same book Penrose argued as follows (with respect to mathematical models):


"If the model itself is to be assigned any kind of 'existence', then this existence is located within the Platonic world of mathematical forms. Of course, one might take a contrary viewpoint: namely that the model is itself to have existence only within our various minds, rather than to take Plato's world to be in any sense absolute and 'real'. Yet, there is something important to be gained in regarding mathematical structures as having a reality of their own. For our individual minds are notoriously imprecise, unreliable, and inconsistent in their judgements. The precision, reliability, and consistency that are required by our scientific theories demand something beyond any one of our individual (untrustworthy) minds. In mathematics, we find a far greater robustness than can be located in any particular mind. Does this not point to something outside ourselves, with a reality that lies beyond what each individual can achieve?...


"Mathematics itself indeed seems to have a robustness that goes far beyond what any individual mathematician is capable of perceiving. Those who work in this subject, whether they are actively engaged in mathematical research or just using results that have been obtained by others, usually feel that they are merely explorers in a world that lies far beyond themselves -- a world which possesses an objectivity that transcends mere opinion, be that opinion their own or the surmise of others, no matter how expert those others might be." [Ibid., pp.12-13. Bold emphases added.]


Clearly, Penrose is a moderate compared to Tegmark, for whom the world is an illusion of some sort, and only mathematical structures/objects are really 'real'.


By way of contrast, the approach adopted at this site also helps neutralise yet another core DM-thesis: i.e., that scientific development somehow depends on the ability of theorists to 'abstract' concepts, or general terms, into existence.


Abstractionism has already been destructively analysed here and here. There is a detailed discussion of these issues in Hadden (1988, 1994), upon which much of the above was based. Hadden's pioneering work is only prevented from being Marxist classic by the absence of a clear account of the nature of language and the logic of analogical reasoning. However, in view of the fact that the logic of analogy hasn't advanced much since Aristotle's day (although it has proliferated in detail, extensively), this is hardly Hadden's fault. On what has been achieved in this area, see White (2010). White's book is in fact a pioneering study, only slightly spoiled by the author's attempt to divert his many clear insights into trying to make sense of talk about 'God'.


[Hadden's conclusions are themselves a development of ideas originally found in Borkenau (1987), Fleck (1979) and Grossmann (1987). Cf., also Sohn-Rethel (1978). Clagett (1959) contains many of the original medieval sources. See also Zilsel (2000), and the more detailed historical study, Kaye (1998).]


In that case, the admission that forces can be edited out of the picture (so that relative acceleration and motion can be viewed as opposites) might succeed in winning this particular battle, but only at the cost of losing the war. Once again, that is because it would imply the universe was much more CAR-like than DM-theorists are prepared to admit. On this account, any reference to a DM-UO would be little more than a confused way of alluding to relative acceleration and relative velocity. The connection between events could only then be explained in one or more of the following two ways:


(a) An appeal to the topology of spacetime, or:


(b) A detailed analysis of the vector and scalar fields in which the said processes were embedded.


[CAR = Cartesian Reductionism/Reductionist, depending on the context; UO = Unity of Opposites.]


In either case, the connection between events and processes wouldn't be governed by any sort of physical mediation (or, indeed, with the rest of the Totality) -- which is what DM requires, since, on this view, a moving body would have no 'internal connection' with any other moving body.


At least an appeal to forces had the merit of appearing to provide some sort of mediating link between bodies in motion, required by DM. They at least appear to be capable of connecting moving bodies in some sort of 'dialectical' relationship. Of course, that is only because the literal interpretation of forces depends on the acceptance of what is in effect an animistic view of nature.


In which case, any attempt to edit forces out of the picture would result in the disappearance of the dialectical 'connective-tissue' of reality (as it were); and with that DM would become indistinguishable from mechanical materialism (i.e., a version of CAR itself), which its theorists sought to replace or surpass.


As noted earlier, DM-theorists require forces to be part of the ontological fabric of the universe, which is why they become defensive, if not highly agitated and emotional when the existence of forces is questioned. Even after what Engels said about forces has been brought to their attention, they totally ignore the fact that he had already questioned their nature. In which case, DM-fans pick and choose which parts of Engels's work they finally decide to accept.


So, in order for DM even to seem to be able to work, its theorists require the existence of a world populated by anthropomorphic concepts (or what they supposedly 'reflect') -- in this case, forces --, which were themselves a result of the fetishisation of the products of social interaction as if they were real objects and processes in nature. This is, of course, just another toxic spin-off of their supposed 'inversion' of Hegelian 'logic'.


[Why that is so is explained here, here, here and here.]


Hence, whether or not DM-fans acknowledge it, the language they use suggests that objects and processes in nature are quasi-intelligent, engaged in what can only be described as some sort of mystical conversation, or shouting match, with other objects and processes, as they 'contradict' and 'negate' one another.


[DN = Dialectics of Nature, i.e., Engels (1954).]


As has already been pointed out, in parts of DN Engels pictured motion in dynamic terms, portraying it as no more than the transfer of energy. [Engels (1954), pp.69-102.] That seems to connect these rather sketchy ideas with more recent theories of motion, modelled by vector and scalar fields -- maybe with the Laws of Thermodynamics. Or perhaps even with concepts employed in the study of non-Euclidean Spacetime, where talk is no longer of forces --, which theories began to be constructed late on in Engels's life and completed a generation or so after he died. Unfortunately for DM-fans, such a re-write would mean that familiar DM-concepts (such as "contradiction", "polar opposite", "UO", "internal relation", etc.) would become as obsolete as "natural place", "substantial form", "accident" and "substance" are now --, notions that once featured prominently in ancient scientific and metaphysical theories.


Indeed, it is difficult to imagine how, say, an energy gradient (depicted as a scalar field) could be interpreted as 'contradictory' in any way at all, even though gradients like this often feature in modern theories of motion. Well, no more perhaps than, say, a ladder should be regarded as contradictory if someone fell off it.


Far worse: it is even more difficult see how states of affairs involving vector and scalar fields, the geodesics of Spacetime -- or even the 'strings' of M-theory -- could form part of a material universe. If everything in nature is just a complex array of energy gradients, vector fields and differential curvatures in Spacetime (which, as we have just seen, many Physicists now suppose) -- spruced up with a few probability density functions -- there would seem to be no place left for anything that even looks remotely material. Given the 'modern', mathematical picture of reality, matter itself becomes a "useless fiction", too, explanatory of nothing at all. Small wonder then that Lenin was highly suspicious of the Idealism implicit in the Physics of his day (even if he had no answer to it). The situation has only grown worse in the years since.


[On that, see Essay Thirteen Part One. I hasten to add -- but it should be obvious by now -- that I don't accept this 'mathematical picture of reality'; or, to be more accurate, I view it as thoroughly metaphysical if interpreted along realist/Platonic lines. (No pun intended!)]


Quite apart from this, the 'ontological status' of 'energy' itself is highly problematic -- and that situation is unlikely to change. [On that, see here.] Energetics is thus no friend of DM/'Materialist Dialectics'.


[I have said more about this topic in Essay Seven Part One, here. Independently of that, I regularly ask Physicists who post, for example, on Quora what energy actually is. I either receive no answer, or they admit they don't really know -- see, for example, here and here (in the comments section).]


Of course, in DM-writings, clear definitions of matter are as rare as hens' teeth -- as we will see in Essay Thirteen Part One. Indeed, when pressed, DM-fans think matter is just an 'abstraction'!




Only those who feel confident that they can give a clear sense to the claim that forces and motion are ('dialectical') opposites will be in any position to reject an objection from earlier with anything more substantive than a simple wave of the hand. Moreover, as we will see, forces often augment motion, they don't always "oppose" it; indeed, most of the bulk motion in the universe is of this sort, as was pointed out earlier.26


However, even if it were possible to give a clear sense to the idea that forces and motion are 'dialectical' opposites, that would still be bad news for DM-fans. That is because any other oppositional force in the system couldn't also be the opposite of the original pairing between this force and that change in movement. And, that in turn would mean that systems of opposing forces couldn't function (in DM) as is currently supposed. In that case, it wouldn't be forces that opposed one another (as had originally been claimed); in such a set-up, forces would oppose motion already present (not other forces), and the idea that change is the result of systematically inter-related forces would have to be abandoned.


Readers are again reminded of something they were asked to keep in mind from earlier:


So, is the 'contradiction' here:


(a) Between the bodies and processes themselves?


(b) Between the forces operating in the system? Or,


(c) Both?


That ambiguity will be explored as this Essay unfolds. Readers are advised to keep it in mind.


As should now seem obvious, each constituent part of a complex array of forces like this would have to be viewed as the opposite of every other. Given such an ensemble, moving bodies would have countless 'opposites' (i.e., any other forces or moving bodies in the system).27 This would put a strain on the meaning of the word "opposite", once more, rendering it meaningless -- in which condition it would remain until its meaning had been clarified, or, indeed, modified so that it would now allow several elements to be regarded as the "opposite" of any one or more of the rest. Under such circumstances, as we have already seen, the notion of a polar opposite would lose its key role in DM. In fact, it would become meaningless if everything possessed countless "polar opposites". [This is quite apart from the fact that this would undermine the DM-theory of change, given the fact that none of these forces would imply the others, and each could exist without the rest -- which shouldn't be the case with DM-'opposites'.]


Not only that, as we have also seen several times, ad hoc linguistic tinkering like this implies that this theory/method would apply to nature and society only because of yet another bout of subjectively applied terminological juggling.


Unfortunately, this jellyfish-of-a-theory can't be squeezed anywhere without some of it slipping through our fingers somewhere else. On this interpretation, what had been touted all along as a grand theory capable of explaining change because it took serious account of the 'contradictory' nature of reality, interpreted as the result of the interplay between opposite forces, now amounts to little more than a few vague ideas about the relation between a force and the motion already in a system compounded by the realisation that the DM-Totality is a mediated system of forces only because the definition of a "polar opposite" had conveniently been 'adjusted'. If this is what DM-theorists mean when they come out with their impressive sounding 'dialectical' ideas, then it would seem that their theory can only be rescued from oblivion if reality were Ideal. As we will see in Essay Twelve, that is a direct consequence of making the 'truth' of DM-theses dependent on ad hoc linguistic 'tinkering'.


However, even if the above objections were misguided in some way, in DM-terms none of this theory makes any sense, since not one of these opposites (i.e., force and motion) turns into the other, as the DM-classics tell us they should:


"The law of the interpenetration of opposites.... [M]utual penetration of polar opposites and transformation into each other when carried to extremes...." [Engels  (1954), pp.17, 62. Bold emphasis added.]


"Already in Rousseau, therefore, we find not only a line of thought which corresponds exactly to the one developed in Marx's Capital, but also, in details, a whole series of the same dialectical turns of speech as Marx used: processes which in their nature are antagonistic, contain a contradiction; transformation of one extreme into its opposite; and finally, as the kernel of the whole thing, the negation of the negation. [Engels (1976), p.179. Bold emphasis added.]


"Hegel brilliantly divined the dialectics of things (phenomena, the world, nature) in the dialectics of concepts…. This aphorism should be expressed more popularly, without the word dialectics: approximately as follows: In the alternation, reciprocal dependence of all notions, in the identity of their opposites, in the transitions of one notion into another, in the eternal change, movement of notions, Hegel brilliantly divined precisely this relation of things to nature…. [W]hat constitutes dialectics?…. [M]utual dependence of notions all without exception…. Every notion occurs in a certain relation, in a certain connection with all the others." [Lenin (1961), pp.196-97. Bold emphasis added.]


"[Among the elements of dialectics are the following:] [I]nternally contradictory tendencies…in [a thing]…as the sum and unity of opposites…. [This involves] not only the unity of opposites, but the transitions of every determination, quality, feature, side, property into every other [into its opposite?]…. [Ibid., pp.221-22. Last set of parentheses in the original; bold emphasis added.]


"And so every phenomenon, by the action of those same forces which condition its existence, sooner or later, but inevitably, is transformed into its own opposite…." [Plekhanov (1956), p.77.]


"Why is it that '...the human mind should take these opposites not as dead, rigid, but as living, conditional, mobile, transforming themselves into one another'? Because that is just how things are in objective reality. The fact is that the unity or identity of opposites in objective things is not dead or rigid, but is living, conditional, mobile, temporary and relative; in given conditions, every contradictory aspect transforms itself into its opposite....

"In speaking of the identity of opposites in given conditions, what we are referring to is real and concrete opposites and the real and concrete transformations of opposites into one another....

"All processes have a beginning and an end, all processes transform themselves into their opposites. The constancy of all processes is relative, but the mutability manifested in the transformation of one process into another is absolute."  [Mao (1937), pp.340-42. Bold emphases added.]


[Dozens of other quotations that make the same points have been posted here.]


Consider any given force and the motion it supposed opposes: Clearly, that force doesn't change into that movement, nor does that movement change into that force.


[Incidentally, that disposes of Weston's attempt to interpret the second force in a gravitational field as 'inertia' -- Weston (2012), p.7. It could be objected that modern physics interprets force as an exchange of momentum; so force and movement are connected, contrary to the above claims. But, there are no forces in modern physics; just an exchange of momentum. So force and movement can't be connected if one half of this pair doesn't actually exist.]


Someone could further object that they do indeed change into one another -- perhaps via an exchange of energy, or as part of equal and opposite reactions, etc., etc.


But, if that were so, another problem would immediately assert itself. If force, F, were to turn into new movement, N, then the second of these two would follow the first -- i.e., F first, N second. But, F would create N at a later time, otherwise it couldn't turn into it. [Recall that, according to the DM-classics, objects and processes turn into that with which they 'struggle'.] Plainly, if N already exists, F can't turn into it. On the other hand, F and N can't 'struggle' with one another for the two of them can't exist simultaneously in order for one to turn into the other. If, on the other hand, F were to change as a result of some (as yet) unspecified factor, say U*, then U*, not N, would be the opposite of F, and F would turn into U*, not N! The same is the case, vice versa. And the same applies if we substitute "inertia" for "momentum", or "movement".


Alternatively, consider force, R, and episodic movement, M, the first supposedly opposing, or 'contradicting', the second -- perhaps R is the reaction force of a body that has just collided with another moving body. It could be argued that in this case, the motion, M, of the second body is what produces the reaction, R, and that reaction then alters M in response.


[It is worth recalling that we are here considering the relation between a force and the motion already in the system, not the relation of a force with a body. That is because we are trying to make sense of the idea that forces contradict the motion already in the system. We will return to consider the relation between forces and bodies below.]


To that end, let us imagine two bodies, A and B, are in collision. Let the motion of both be MA1 and MB1, respectively before the collision, and MA2 and MB2 after. Further, let the reaction force produced in each body be RA and RB, respectively. Hence, in this scenario, MA1 produces RB, and MB1 produces RA. In turn RA then induces MB2, and RB induces MA2. But, according to the DM-classics, an object or process turns into that with which it 'struggles', its 'dialectical opposite'. So, since MA1 turns into MA2 it must have 'struggled' with it. The same must apply to MB1 and MB2. But, this can't happen since neither of MA2 and MB2 yet exist for MA1 and MB1 in order to 'struggle' with anything! If they did, MA1 and MB1 couldn't change into them, since they already exist! On the other hand, if MA2 and MB2 don't exist, then there will be nothing with which MA1 and MB1 could 'struggle' and hence change. That can only mean that, according to this moribund theory, MA1 and MB1 can't change!


[At least, not in the above way.]


On the other hand, if RA 'struggles' with MB1, then, according to the DM-classics, it must change into it. The same applies to RB and MA1. But, MB1 changes into MB2, not RA, and MA1 changes into MA2, not RB.


Once more, we hit the same brick wall. [No pun intended.]


Even worse, there is an equal and opposite reaction force in A and B, namely, RC and RD -- both produced by RA and RB, respectively. This means that: RC = -RA and RD = -RB. Exactly how these are now supposed to fit into this 'dialectical' interaction is even less clear.


DM-fans are invited to play around with the above as much as they like, the result won't change. [No pun intended.]


Howsoever we try to re-package this ill-considered 'theory', none of it seems to make any sense.


If a force 'contradicted' a moving body (and not any motion in the system), then this force would change in to the body and the body would change into this force -- if the DM classics are to be believed.


[The above are just specific examples of a more general, but fatal, defect that sits right at the heart of the DM-'theory' of change, exposed in detail in Essay Seven Part Three. Nevertheless, this point can and will be generalised in order to show that no two or more forces could 'contradict' one another in the way that dialecticians imagine.]


Nevertheless, in order to examine every possible alternative available to DM-fans, I propose to analyse this particular option in even more detail. To that end, I will offer an alternative clarification of what it might mean.


First Attempts At Clarification


Perhaps then the following re-write might succeed in repairing the holes in the above interpretation of DM at the same time as preventing the theory that UOs operate everywhere in nature from being completely undermined:


F2: A UO involves the opposition between a force, P1, and the impressed motion that another force, or set of forces, Q, has produced (or would have produced) in a body, B, had P1 never existed. The resultant motion of B is the final outcome of this struggle.


[UO = Unity of Opposites.]


F2 links the operation of one force (P1) with that of another set of forces (Q). However, it is difficult to distinguish what F2 says about these two factors from the vector resultant of two forces if we subjected this system to the usual mathematical analysis. If so, the word "struggle" would amount to little more than an anthropomorphic re-write of the functional relations that exist within the vector calculus, only now applied to just one force, the resultant. In that case, if and when P1 and Q interact, they will produce just one resultant force, R, and it is this force which would induce the recorded change in motion.28


But, if that is so, a contradiction between forces can't arise here: if there is only one force operating in the system, there can be no contradiction (if we adopt this interpretation). In that case, F2 threatens to undermine this interpretation of DM, killing it for want of forces.29


Interlude Three: Hamlet Without The Prince


This section of the Essay might be dismissed as just the latest unsympathetic reading of yet another artificially modified DM-proposition.


Maybe so, but the reader will find that dialecticians themselves consistently fail to examine their own theory in anything like the detail attempted here, despite the fact that DM is supposed to represent the best, if not the very epitome, of scientific and philosophical thought. The present Essay, in contrast, has endeavoured to set-out in more detail than has ever been attempted anywhere else before the implications of this area of DM. As such, it ventures into entirely unexplored territory. Hence, it is impossible to say whether or not this misrepresents DM -- indeed, dialecticians themselves would be hard-pressed to decide among themselves whether or not this is the case. For one thing, they can't even decide what matter is! [As Essay Thirteen Part One shows, their 'materialism' is rather like Hamlet without the Prince!]


In addition, it is worth pointing out yet again that F2 was motivated by the idea that forces contradict impressed motion. As we have just seen, because change in motion is the consequence of just one resultant force (when analysed classically), the alleged 'contradiction' between two forces simply disappears.


F2: A UO involves the opposition between a force, P1, and the impressed motion that another force, or set of forces, Q, has produced (or would have produced) in a body, B, had P1 never existed. The resultant motion of B is the final outcome of this struggle.


It would take an especially alert, or eagle-eyed, dialectician, therefore, to be able to spot 'contradictory' forces in a system where there is only one force responsible for the said change in motion!


Worse still, F2 postulates a 'contradiction' between a force and the motion that is (or might be) produced as the counterfactual result of the action of other forces, but since some or all of the latter's effects won't have been actualised (having been prevented from doing so by P1), the alleged 'contradiction' here contains only one real term.


Even the most committed of DM-fans might find it difficult to visualise (let alone explain) a 'contradiction' between something that is real and something that isn't (in that either it never existed or it was prevented from existing): i.e., the motion that would have occurred if the impeding force, P1, hadn't acted.


It could be objected that these other forces don't vanish; they are still there, as is the resultant. If they were to vanish, so would the resultant. That response will be examined later in the Essay.




This suggests we should reconsider an option left unexplored earlier, where it was argued that forces are the only legitimate candidates to be placed in such oppositional couples, not the motion they change or induce, or the bodies upon which they act -- contrary to what Engels seems to have believed when he tried to replace forces with relative motion. To that end it might prove useful to see whether F2 can be modified to provide support for the idea that the forces involved contradict each other before they combine to create the resultant, R.


On this revised view, forces are 'contradictory' only of other forces, and not of bodies or of any motion in the system. The following might, therefore, bring out more clearly this latest alternative:


F3: Given a body, B, and a system of forces, V, comprising n vectors, v1-vn, operating on B, a resultant force vector, R, represents the outcome of the struggle between these contradictory force vectors. In this scenario, R needn't be fixed, but could itself be subject to countless changes as B moves under the influence of V, which would also change accordingly.


One immediate problem with this is that the specification of the forces belonging to V depends on the choice of co-ordinate system and inertial frame.30 This shows that even if F3 were acceptable, the representation of forces as 'contradictions' is perhaps more convention-sensitive than it is reality-driven -- which would mean, of course, that 'dialectical contradictions' are no more 'objective' than, say, latitude and longitude.


However, even if this latest difficulty is put to one side, it is still worth asking whether any sense can be made of F3.


As noted above, F3 seems to bring us back full circle to the idea that forces -- not bodies, or the motion of bodies -- are mutually 'contradictory'. And yet, as we have seen, it isn't possible to depict AA-, and RR-forces as 'contradictory', unless their effects are involved in some way.


On the other hand, as we have noted several times, if force is just a convenient shorthand for relative motion, it would mean that this part of DM is more consistent with a CAR-like picture of reality -- because the elements of the "Totality" would now be externally-, not internally-related to one another.


[CAR = Cartesian Reductionism.]


To repeat: it isn't easy to see how the motion of one body could be internally-related to that of others without re-introducing the idea that bodies exercise some sort of an effect on one another independently of how they are moving. While this relative motion might subsequently affect their movement, it still wouldn't internally-link such bodies. And yet, this is precisely the difficulty that exercised Traditional Philosophers in relation to the classical metaphysical problem of the nature of forces; DM has simply reproduced this conundrum in an even more obscure form. If relative motion were an internal, or 'logical' link, of the sort required by DM, then the movement of one body in one direction would imply the movement of another body in a different (or even the same) direction. The existence of the one would imply the existence of the other; they would 'interpenetrate' one another, such that one couldn't exist without the other (just like the bourgeoisie couldn't exist without the proletariat, and these two classes imply each other, for example -- although, once more, I have thrown that inference into considerable doubt here). But, unless DM-theorists have been keeping the salient details to themselves, that isn't the case with relative motion. So, the relative motion of bodies can't be a 'dialectical' relation, whatever else it is. The same comment also applies to forces. They don't imply one another, and can exist without each other.31


Ignoring this fatal defect for now, perhaps the unwelcome slide into CAR can be forestalled by means of the following re-wording of F3:


F4: Given a system of forces, V, comprising n vectors, v1-vn, a resultant force vector, R, represents the outcome of the struggle between these n force vectors.


F5: This ensemble is only contradictory within a Totality of inter-related processes that mutually condition one another.


F5 is clearly one aspect of the thesis that the whole determines the nature of its parts, and vice versa. Hence, F4 and F5 appear to restore the dialectical unity that earlier paragraphs seem to have sundered.


Unfortunately, this just brings us back full circle to a consideration of the relationship between the "Totality" and its parts. That is because F5 introduces its own pernicious version of HEX, for it seems impossible (on this account) to determine whether or not anything is 'contradictory' unless the nature of the whole had already been ascertained. But, since the latter is always changing, no element in this 'cosmic wild-goose chase' will ever be hunted down and trapped, as it were. [We encountered different versions of this fatal defect in DM-epistemology in other Essays at this site; see, for example here, here and here. Readers are directed there for more details. Much of what follows takes the conclusions drawn there for granted.]


The most relevant aspect of this latest quandary centres on the idea (entertained by several dialecticians) that the growth of scientific understanding means that the 'contradictions' that now plague our knowledge of the world will somehow diminish (or would somehow be 'resolved') as science progressed. Presumably, this implies that, in the limit (i.e., in an ideal state where humanity possesses (at least in theory) the Absolute Truth about everything), there will be, or should be, no contradictions at all in or between scientific theories, or between theories and 'reality'. The problem with this is that, according to DM-theorists, in order for a scientific theory to be true it must faithfully 'reflect' the world. But the state of knowledge in this hypothetical Ideal Limit can only mean that the world itself can't contain any contradictions, otherwise they would be reflected in theory, even in the limit, which possibility has just been discounted. In turn, this implies that even if humanity never actually reaches this blessed state (i.e., Absolute Knowledge), we can, in the here-and-now, draw this safe conclusion: the Absolute Truth is that not only is the world not contradictory, the motion of bodies and the operation of forces isn't either.32


In fact, the above must be true now, for if it weren't now true that there were few, or even that there are no 'contradictions' at all in the ultimate future state of knowledge of the "Totality", then either (a) The DM-view of the limit of knowledge (where most if not all contradictions have been resolved) must be false, or (b) The belief that humanity is converging on that limit must itself be erroneous, since there is no such limit. As we have just seen, that outcome is actually implied by the DM-theory of knowledge itself -- that reality is a largely, or is a completely, contradiction-free zone.33


Interlude Four: Limit Or No Limit -- That Is The Question


So, either:


(i) There is no limit toward which knowledge is converging, or,


(ii) As knowledge advances external reality alters accordingly, or even,


(iii) It is now true to say that, in the limit, the world contains no contradictions whatsoever.


Plainly, unless we are Idealists, (ii) can't be the case. We aren't to suppose (it is to be hoped!) that our understanding of the world alters the 'objective contradictions' that allegedly give life to or which power the whole of reality -- so that as knowledge increases 'objective contradictions' slowly disappear. Of course, many of the latter might vanish in a socialist society (so we are told), but not those in the natural world. Does anyone who believes that motion is  contradictory, for instance, think that anything humans can do, or will or come to understand, will alter this supposed fact -- which would, of course, mean that meaning that motion isn't objectively contradictory?


But if not, then as (iii) indicates, it must now be true that absolute knowledge of the world (even if we never attain to it) implies that nature isn't contradictory -- complete knowledge of reality will have removed all the contradictions from our thought, or our theories about it. It doesn't matter if we never reach this blessed state, the possibility of complete knowledge means that nature itself must be a contradiction-free zone. [However, on that see here.]


Of course, it might be incorrect to conclude that dialecticians believe that as science advances all contradictions will be resolved -- even though it isn't easy to see how they could consistently deny it. Faced with each new contradiction -- if they are committed to the view that science can only advance if it overcomes or resolves contradictions in our knowledge -- dialecticians must believe they can be resolved, if we but knew more about the world. Otherwise they will have to admit that science can't advance beyond a certain point. But they deny that, too. In that case, they must either believe that:


(iv) There is no limit to scientific advance, or that,


(v) There is a limit (because there are irresolvable contradictions in nature and hence in our theories about it).


But, if they also believe that there is scientific advance has no limit, then they must also believe both of the following:


(vi) There is no limit to scientific advance, and,


(vii) There is a limit to scientific advance.


[(vi) follows from the asymptote metaphor to which Engels referred, and which Lenin and subsequent DM-theorists have lent their credence. On that, see the quotations listed below.]


But, the combination of (vi) and (vii) is itself a contradiction, and it lies right at the heart of DM (if this line of reasoning is sound).


Of course, this means that DM itself can only advance if this contradiction is resolved. But, since DM-theorists don't even recognise this blatant contradiction in their own theory, that must mean DM can't advance!


Hence, either:


(viii) DM can't advance, or,


(ix) Dialecticians must hold that all contradictions are resolvable.


But, and once more, if (ix) is the case, by the above argument, there can be no objective 'contradictions' in reality.


So, in terms of DM's own theory, it would seem that nature can't be fundamentally contradictory!


Again, the only apparent way of avoiding this fatal result is either to:


(a) Deny science can only advance by resolving all contradictions, or,


(b) Deny that Absolute Truth 'exists'.


However, the rejection of option (i) from earlier  (i.e., "There is no limit toward which knowledge is converging") would mean that there is a (non-Absolute) limit to knowledge, after all. In which case, plainly, the DM-thesis that human knowledge is unlimited would have to be abandoned, and along with that would go the idea that knowledge is converging on it. In addition, the belief that there is an 'objective' reality (out there) for us to know (even if we never fully attain to it) would have to be jettisoned, too.


It would also leave dialecticians with no way of deciding which of the allegedly irresolvable contradictions their theory throws up is:


(c) An 'objective' feature of reality, or is,


(d) A by-product of their own imperfect, or even defective, theory -- which could be resolved if only we had more knowledge.


These observations of course assume that the universe might be 'infinite' (a view held by many DM-theorists) and constantly changing. But, neither of those factors affects the idea that there must now be a set of truths (possibly infinite) about reality toward which human knowledge is asymptotically converging (even if that set itself grows over time) -- that is, if Engels and Lenin were correct when they said the following:


"'Fundamentally, we can know only the infinite.' In fact all real exhaustive knowledge consists solely in raising the individual thing in thought from individuality into particularity and from this into universality, in seeking and establishing the infinite in the finite, the eternal in the transitory…. All true knowledge of nature is knowledge of the eternal, the infinite, and essentially absolute…. The cognition of the infinite…can only take place in an infinite asymptotic progress." [Engels (1954), pp.233-35.]


"The identity of thinking and being, to use Hegelian language, everywhere coincides with your example of the circle and the polygon. Or the two of them (sic), the concept of a thing and its reality, run side by side like two asymptotes, always approaching each other but never meeting. This difference between the two is the very difference which prevents the concept from being directly and immediately reality and reality from being immediately its own concept. Because a concept has the essential nature of the concept (sic) and does not therefore prima facie directly coincide with reality, from which it had to be abstracted in the first place, it is nevertheless more than a fiction, unless you declare that all the results of thought are fictions because reality corresponds to them only very circuitously, and even then approaching it only asymptotically." [Engels to Schmidt (12/3/1895), in Marx and Engels (1975b), p.457.]


"Cognition is the eternal, endless approximation of thought to the object." [Lenin (1961), p.195.]


"Thought proceeding from the concrete to the abstract -– provided it is correct (NB)… -- does not get away from the truth but comes closer to it. The abstraction of matter, the law of nature, the abstraction of value, etc., in short all scientific (correct, serious, not absurd) abstractions reflect nature more deeply, truly and completely." [Ibid., p.171. Emphases in the original.]


Of course, if there is no such set of truths, no such limit, then Engels's metaphor is defective and Lenin was mistaken, since, once again, there would be no such thing as 'objective truth' (if the latter is defined as the limit toward which human knowledge is heading).


However, in this regard, Woods and Grant quote a revealing passage from DN:


"The fact that our subjective thought and the objective world are subject to the same laws, and that consequently too in the final analysis they can't be in contradiction to one another in their results, but must coincide, governs absolutely our whole theoretical thought. It is the unconscious and unconditional premise for theoretical thought." [Woods and Grant (1995), p.349; quoting this source. Bold added.]


Admittedly, the above passage wasn't included in the 'official'/final version of AD, but it does tend to suggest that Engels believed either that:


(e) Despite appearances to the contrary, the 'objective' world is actually free from contradiction, or,


(f) In the end there will be no contradiction between our thoughts about reality and reality itself (the first of which alternatives -- (e), it must be admitted, is impossible to distinguish from the second -- (f)), or even that,


(g) In the limit there will be no contradictions at all in any of our theories.


So, to take just one example (and assuming Engels is to be believed): if any randomly-selected dialectician were to conclude that motion is 'contradictory', then that subjective thought can't itself contradict 'objective' reality -- or 'objective' theory itself, one presumes, even if that blessed end state is never actually attained. So, if knowledge is to advance, even this 'contradiction' (i.e., the subjective thought that motion is 'contradictory') must itself be resolved, and thus removed. It, too, is a 'contradiction' that should be resolved if and when know more, or when we finally attain 'objective knowledge' of the world.


[But, of course, as we saw in Essay Five, it isn't even a contradiction!]


Naturally, that doesn't commit Engels to the view that reality is, in the limit, a contradiction-free zone, but if science can only advance by resolving contradictions in our subjective theories (so that they become progressively more 'objective'), the conclusion (given above) seems inescapable: In the limit, human knowledge of the world must picture nature as progressively, if not totally, free from contradictions.


However, in the absence of any clear indication from Engels that he genuinely believed what the above passage says, little more can be asserted here with any confidence.


It is a reasonably safe bet that because the DM-classics are silent on this topic, modern-day dialecticians won't even be able to decide among themselves about this -- that is, without their being branded 'Revisionists', perhaps sparking yet another dialectical dog fight, and then more debilitating splits.




Again, if this is what dialecticians mean by 'contradictory forces',34 then nothing may be so described until everything has been so described. [Once more, I am taking for granted the conclusions mentioned earlier. If readers find this latest assertion hard to accept, they should consult the full argument presented in the other Essays listed.] And yet, this reverses the dialectical story, for, as we have just seen, some DM-theorists appear to believe that things only look 'contradictory' because we don't possess the Big Picture -- i.e., an 'Absolute View' of reality --, and that if humanity ever were to attain to such an all-encompassing vantage point, 'contradictions' would disappear (or largely disappear -- the story gets a little vague at this point). In contrast, the idea seems to be that we may only depict forces in nature as absolutely 'contradictory' after The Epistemological Trumpet has finally been blown on 'dialectical' Judgement Day -- when humanity at last hits the asymptotic buffers to which Engels referred. The problem here is that this may only be done when all (or most) 'contradictions' have been resolved!


Paradoxically, this in turn appears to mean that, 'objectively', these 'contradiction' both exist and do not exist -- or, maybe even, we do and we don't know whether they do or they don't!


So, one horn of this dilemma seems to suggest that 'dialectical contradictions' don't really exist (because they are merely the artefacts of 'relative knowledge'), and hence if they don't, they can hardly play any part in change and development. The other horn of this dilemma appears to suggest that we are now in no position to assert that 'dialectical contradictions' do in fact exist (since we aren't in possession of 'Absolute Knowledge'). In which case, because we aren't in possession of the full picture, we can't claim to know whether 'dialectical contradictions' actually cause change! Either way, yet another core DM-thesis self-destructs!35


At any rate, and to return to the main theme, if AA-, and RR-forces are mutually oppositional, change would still be caused by resultant forces. But, as we saw in Essay Seven, it is far is easier and more natural to interpret this scenario as 'tautological', not 'contradictory' -- that is, if we insist on viewing nature in such figurative, anthropomorphic or animistic terms.


Of course, if we resist such a capitulation to mystical primitivism, as indeed we ought, then both descriptors (i.e., "contradictory" and "tautological") should rightly be fed into the 'obsolete-concept-shredder'. [More on that here.]


Perhaps, then, it would be wise to draw a veil over this self-imposed dialectical impasse, and turn to a much more likely source of these DM-'contradictions'. To that end I will return to F4 and F5, but consider them from a more promising angle -- as AR-force couples.


F4: Given a system of forces, V, comprising n vectors, v1-vn, a resultant force vector, R, represents the outcome of the struggle between these n force vectors.


F5: This ensemble is only contradictory within a Totality of inter-related processes that mutually condition one another.




In the previous section, it became clear that little sense can be made of the equation of 'dialectical contradictions' with  AA-, or RR-forces, and this turned out to have nothing to do with the difficulty of seeing whether or not such force-couples contained 'opposites' -- which they manifestly do not. An A-force isn't the opposite of another A-force; the same is true with respect to two R-forces.


However, a prima facie case could be made for regarding AR-force couples as the polar opposites to which DM-theorists refer in order to depict 'contradictions' as they supposedly operate in DM and HM.


Unfortunately, as we will see, this slender straw once clutched soon turns into a dead weight, sinking this doomed 'theory'. Quite apart from the considerations outlined above, no clear sense can be made of the idea that AR-forces can be co-opted to model 'contradictions', anywhere, any way, anyhow.36



Figure One: Hey, Comrades! Grab This --

It's A 'Dialectical Straw', Honest It Is!


An initial serious difficulty confronts this idea: AR-couples don't appear to operate in nature in quite the manner this handy prefix seems to suggest: i.e., as AR-forces.


Consider a straightforward case: the accumulation of matter that formed the stars, planets and their moons (etc.) over billions of years. There, R-forces (operating at the nuclear level) apparently prevent(ed) (for a time) the catastrophic collapse of these growing masses into 'singularities' by balancing-out the A-forces that presumably set the whole thing in motion.


The problem with these R-forces is that, while they look as though they oppose any other A-forces in the system, they aren't their polar opposites (in the way that, say, the North and South poles of a magnet are said to be) -- that is, they aren't opposite manifestations of the same type of force. So, the inter-atomic forces preventing the above collapse aren't the same type of force as the gravitational forces that initiated the process.37 While a case might be made for depicting North and South poles of a magnet as polar opposite magnetic forces (but on that, see below), gravitational and nuclear forces aren't 'interpenetrated' opposites of the same type, and so can't, it seems, 'contradict' each other in the 'dialectical' sense required. For example, neither force turns into the other, contrary to what the DM-classics tell us they should.


Maybe we need to learn more about 'dialectical opposites'?


Interlude Five: Opposites


So, even though, for example, male and female, dead and alive are said to be 'opposites', a male dog isn't the opposite of a female flower, and a dead cat isn't the opposite of a live wire. Such contrasts can only work as opposites if they apply to, or implicate, the same substantival (or, at least, if they involve a use of the same common noun). Hence, on this view, a male dog will be the opposite of a female dog, a dead cat the opposite of live cat, and so on. Logical  connections of this sort are essential if objects and processes are to count in DM as 'interpenetrated opposites'.


Or, so the story goes.


[On substantivals, see here.]


Naturally, this undermines much of what dialecticians themselves say about UOs; but since this ground was covered extensively in Essay Seven Parts One and Three, no more will be said about it here.


Having said that, a hot oven isn't the DM-'opposite' of a cold can of beer, in which case it is difficult to see how, in DM-terms, they can interact, with the one heating the other up. But who doesn't know a hot oven can heat up all manner of things, including cold cans of beer? Who doesn't know that cold hands can be warmed by a hot fire, even if they aren't 'dialectical opposites', and even if they don't imply one another or turn into each other (which they would have to do if they were 'dialectical opposites')? And yet, if we were to accept what we read in Hegel's work and the DM-classics -- that only 'dialectical opposites' can interact -- then you couldn't warm your cold hands on anything other than another pair of warm hands! You couldn't cool a hot can of beer with anything other than a cold can of beer.


[The argument presented here continues in Interlude Twelve.]




At this point, readers are reminded of something they were asked to keep in mind as this Essay unfolds:


Is the 'contradiction' here:


(a) Between the bodies and processes themselves?


(b) Between the forces operating in the system? Or,


(c) Both?


However, even if A-, and R-forces were opposites of the same type, they manifestly alter the motion of bodies; they don't directly confront each other as opposing forces, and hence don't 'struggle' with one another. Admittedly, they can be represented as 'oppositional' in a vector calculus, but we have already seen that even this formal translation is of little use to DM-supporters -- and that is partly because the relevant forces disappear, only to be replaced by a single resultant force that is the cause of all the subsequent action.


It could be argued that these initial difficulties can be neutralised if emphasis is placed once more on the oppositional nature of AR-forces as a way of explaining change.


Unfortunately, this detour is no more successful than it was when it was considered above in relation to AA-, and RR-forces. AR-forces don't imply one another such that one can't exist without the other (unlike, say, the proletariat and the bourgeoisie, which are supposed to imply one another). In which case, whatever else they are, they can't be 'dialectical opposites'. They don't 'interpenetrate' each other.


Even if this further difficulty is shelved for now, it would still be difficult to see how AR-forces could be interpreted literally (or figuratively) as 'contradictions' (especially in HM). That is because of the way in which they can combine and augment one another.


For example, consider two forces operating in diametrically opposite directions tangentially placed around a rotating body (and hence not acting in the same line). These two forces -- although 'opposites' at their point of action -- exercise a combined, augmenting effect on the angular acceleration of that body, thus ceasing to be oppositional in any plausible sense of that word.38


This is a familiar feature of force vectors. In some instances, they seem to 'oppose', in others they appear to 'augment' one another, while in still others they look like they do both at once.39 , 40


Interlude Six -- Magnetic And Other Natural Forces


Engels himself regarded the two poles of a magnet as a clear example of the unity of AR-opposites in nature (another idea he borrowed from Hegel and other German Idealists, and which has been parroted down the ages by countless 'highly original' DM-echo-chambers).


[AR = Attraction-Repulsion.]


Here is Hegel:


"Positive and negative are supposed to express an absolute difference. The two however are at bottom the same: the name of either might be transferred to the other. Thus, for example, debts and assets are not two particular, self-subsisting species of property. What is negative to the debtor is positive to the creditor. A way to the east is also a way to the west. Positive and negative are therefore intrinsically conditioned by one another, and are only in relation to each other. The north pole of the magnet cannot be without the south pole, and vice versa. If we cut a magnet in two, we have not a north pole in one piece, and a south pole in the other. Similar, in electricity, the positive and the negative are not two diverse and independent fluids. In opposition, the different is not confronted by an other, but by its other." [Hegel (1975), §119, p.173. There are somewhat similar comments in Hegel (2004), §312, p.165. (This links to a Scribd page which features a photographic reproduction of this book.) Clearly, Hegel lifted these ideas from Kant and his theory of 'real negation'. On that, see Appendix A.]


And here Engels:


"Dialectics has proved from the results of our experience of nature so far that all polar opposites in general are determined by the mutual action of the two opposite poles on one another, that the separation and opposition of these poles exists only within their unity and inter-connection, and, conversely, that their inter-connection exists only in their separation and their unity only in their opposition. This once established, there can be no question of a final cancelling out of repulsion and attraction, or of a final partition between the one form of motion in one half of matter and the other form in the other half, consequently there can be no question of mutual penetration or of absolute separation of the two poles. It would be equivalent to demanding in the first case that the north and south poles of a magnet should mutually cancel themselves out or, in the second case, that dividing a magnet in the middle between the two poles should produce on one side a north half without a south pole, and on the other side a south half without a north pole. Although, however, the impermissibility of such assumptions follows at once from the dialectical nature of polar opposites, nevertheless, thanks to the prevailing metaphysical mode of thought of natural scientists, the second assumption at least plays a certain part in physical theory." [Engels (1954), p.72.]


The alleged 'unity' in this case clearly revolves around the presumed fact that the North and South poles of a magnet can't exist independently of each other, or, indeed, without one another; their 'opposite' nature is shown by the affect they have on magnetically susceptible bodies and upon each other.


[Of course, if the legendary magnetic monopole is ever discovered (as it seems it might have been!), this classic DM-example will go the way of other defunct ideas --, like, say, the crystalline spheres.]


However, upon closer examination, it is clear that the relationship between the poles of a magnet is in fact an example of AA-, or RR-, but not AR-opposites. That is because in this case, non-opposites -- i.e., alike poles --, repel each other (i.e., two Norths or two Souths). On the other hand, opposites attract -- i.e., a North and a South. Consequently, in the way that these poles inter-relate, magnets are thus AA-, or RR-type forces. A moment's thought will also confirm this: since when do magnets attract and repel one another at the same time?


In that case, it now turns out that the magnet is hardly a paradigm example of an AR-force -- united in opposition --, as DM-lore would have us believe.


Mysteriously, DM-theorists en masse have failed to notice this obvious flaw in one of their key examples!


So much for the claim that DM-theses have been read from -- but not imposed on -- the facts.


The same comments apply to electrical, and thus also to sub-atomic, phenomena in general -- like charges repel, unlike charges attract. This means that much of the (sub-atomic) dialectical 'evidence' in, say, Woods and Grant (1995), is seriously misguided. How on earth do electrons and protons 'struggle' if they attract one another? [There will be more on this in Essay Seven Part Two (when it is published).]


It could be objected that while it might be true that two unlike poles are examples of AA-forces, their continued motion toward one another will be prevented at some point by structural forces within the magnets themselves, and these couples will operate as AR-forces. In that case, R-forces operating between approaching atoms of the material from which the magnets are made will prevent these opposite poles closing in on one another, counteracting the A-forces that brought them together. This implies that the relation between the poles of a magnet is in fact that of an AR-couple,


Or, so an objector might claim.


Even so, this means that, as magnetic opposites, the poles themselves still fail to be AR-UOs. To be sure, other forces might come into play, but this doesn't affect that salient point. In which case, these new forces and those magnetic forces wouldn't be opposites of the same Aristotelian/Hegelian type (as noted above).


Despite this, the above objection would reduce the oppositional relationship between forces originating in these magnets to the effect that these poles have on motion (since, manifestly, these opposite forces don't affect each other, just the relative motion induced by each force). Hence, once more, the two poles aren't inter-related to each other directly as opposite AR-forces; they would simply oppose any motion that either or both of them had induced in the system. We have already had occasion to dismiss this option as inimical to DM.


In which case, the inter-atomic forces governing the operation of AA-, RR-, or even AR-couples, actually oppose, limit or augment whatever motion is already present in the system -- or, they restrict the freedom of bodies to move once set in motion. But, they still don't seem to oppose -- i.e., 'contradict' -- each other as force upon force.


Again, this is probably one reason why Engels toyed with a positivistic re-interpretation of forces (in DN, as pointed out above, in Note 4), since no physical sense can be given to any such relation between forces (as was also noted earlier) -- that is, over and above seeing any such relation as an obscure way of attempting to represent the relative motion between bodies.


Of course, it could be argued that the force field of each pole does in fact affect that of the other; hence, the above claims are incorrect. But, these force fields are merely the expression of the motion of, or the motion induced in, measuring instruments (or, indeed, patterns created by scattered iron filings) placed near the said poles, so the above claims aren't incorrect. Such forces are, as Engels argued, a shorthand for relative motion.



Figure Two: Force Fields And Iron Filings


On the other hand, if by "force field" we mean the mathematical structures postulated by scientific theory, they can't affect one another, for they aren't physical. They certainly affect the theorists in question, those who do the calculations and draw the diagrams. [This was discussed in more detail in Interlude Two, and will be again, below.]


Anyway, as we have just seen, the nature of the UO here clearly depends on what is meant by the terms "opposite" and "unity". North and South poles aren't united in the sense that they are one (as DM-theorists would be the first to point out), they are connected in the sense that they 'depend' on each other. But, this 'dependence' is causal, not logical; magnetic properties are the result of the vector configuration of the 'motion' and 'spin' of certain electrons. There is nothing in nature that logically forces this physical interrelation on these poles (as, for example, the capitalist class supposedly 'implies' the proletariat). Indeed, the idea that such a configuration represents a 'dialectical'-UO is misconceived, since the 'forces' involved are the consequence of a vector field, which is no more 'contradictory' than your front and back are. And, as we have also already seen, it isn't easy to see how vectors can be regarded as 'contradictions' (or, indeed, as UOs).


Moreover, in ferromagnetic substances, the magnetic field is built up by the cooperative alignment of individual magnetic moments (perhaps illustrating the fundamentally cooperative nature of reality once again, created by those helpful 'dialectical tautologies' we met elsewhere in this Essay).


Certainly, given Engels's use of the term "force" (whether interpreted realistically -- or positivistically as a "useful fiction"), this is a rather poor example of a DM-UO, anyway; it is consequent upon a particular sort of mathematical analysis (i.e., it is based on the alignment of electrons, which orients the vector field that arranges the direction of the magnetic field). Calling this a UO would be to substitute an obscure metaphor for a clear mathematical description, for no extra explanatory gain.


Of course, there is no UO here anyway, since the field in question is the result of one sort of cause, the electron, which is a single charged elementary particle (or wave?) that isn't itself a UO. (That DM-busting fact has already been commented upon here.) Do these arrows form a UO? But this is how we picture vectors (especially those associated with a magnetic field).



Figure Three: A 'Dialectical Tautology'?



Figure Four: Where's Waldo? Where's The UO?


Naturally, deflationary conclusions like these will satisfy few DM-fans since it depends on a non-standard view of the nature of mathematical 'objects' (i.e., vectors, matrices, manifolds, dimensions, abstract spaces, etc.). Hence, in response it could be argued that mathematics in fact represents what is really out there in the world, since it has been abstracted from nature by human beings as a result of their practical activity and social development. This means that mathematics presents us with an abstract reflection of reality.


[Chapter 16 of Woods and Grant (1995) contains a classic (but nonetheless confused) version of this idea. Because of its influence, I will be devoting a special Essay to this book, which will be posted at this site (as Essay Seven Part Two) in the next year or so.]


However, this interpretation of mathematics is seriously mistaken. Mathematics can't be a description of the world (nor an 'abstraction' from it) for reasons rehearsed in Essays Three Parts One and Two and Thirteen Part One (as well as earlier). Mathematics is based on systems of concepts that aren't causally inter-linked. The concepts that mathematicians construct do not exercise any sort of causal influence on material bodies; nor do they 'correspond' to anything in reality that could conceivably so behave, unlike material bodies and processes that can and do. [On that, see here and here.]


Mathematical propositions and theorems yield neither an abstract nor a concrete picture of reality. That is because they aren't pictures to begin with, nor could they be. They express rules for the manipulation of certain symbols that licence inferences we make about objects and events in nature and society (or, indeed, in formal systems). At best, they set up complex analogies that assist in our understanding of processes in the material world.


The development of Field Theory since Maxwell's day doesn't alter this picture in any way. Vector and scalar fields are mathematical structures that not only enable scientists to model nature, they assist in the derivation and interpretation of the empirical consequences of their hypotheses. To imagine otherwise (i.e., to suppose that mathematics is an abstract description or picture of the world) would reduce its structures to absurdity. For example, it would imply that, say, a vector field -- in reality -- is actually composed of a set of infinitely thin and infinitely strong wire-like curves, or curve segments (of mysterious composition and provenance), and which aren't actually made of anything. Or, that a scalar field is actually an invisible array of real numbers 'floating' in (abstract?) space -- or, worse still, that it is an infinite n-dimensional set of dimensionless connected, dense but disjoint points (which can't themselves exist physically -- they have no shape (circular, spherical, or otherwise), or they wouldn't be points, just volume intervals) --, and so on.


We might picture, say, a mathematical point as a infinitely small dot if that helps us make appropriate inferences, but, as we have just seen, a dot has a shape (circular to normal vision, irregular under a microscope); but no mathematical point has a shape, circumference, radius, or even centre. What then can a mathematical point possibly share with anything in the universe? What could mathematical points, lines or surfaces be abstracted from, or be a generalisation of, if they share absolutely nothing with the material points, lines, or surfaces they supposedly represent? Of course, at this point (no pun intended), abstractionists go rather quiet. They have in fact nothing with which to work.


Here is a comment I left on Quora recently (slightly edited):


Clearly, mathematical points have no shape, circumference, diameter or radius -- and they aren't even circular or have a centre! They aren't containers, either, so no other point can 'occupy' them. Otherwise they'd be volume intervals, not points.


We sometimes say lines are 'made of points', but that can't be so or they'd fall apart rather quickly (and they would be rather bumpy, like a string of pearls), since there is no 'mathematical' force to hold those points together. Lines are also perfectly strong and rigid, they neither age nor begin to fray at the edges -- and yet they can be easily cut/intersected by other lines and planes, as well as bent into any shape we please by a suitable homeomorphism. But even then the original line is still there in 'mathematical space', 'unbent', so that someone else can use it as many times as they like and for whatever mathematical purpose they choose, as can any number of other mathematicians and they can all do that at the same time. They don't need to form a queue.


Lines are supposed to intersect other lines at a 'common point', but if neither line is made of points, they can't have 'common points', can they? How then do they intersect?

And if planes aren't made of points, either -- otherwise we could ask the same questions as those above about lines --, how can a line intersect a plane at a 'common point'? Furthermore, planes can't be made of lines (or they'd be like an array of really thin knitting needles with nothing to 'hold them together'), and if that is so, planes can't intersect at a 'common line', either.


Furthermore, there are no 'perfect circles', since there are no mathematical circles to begin with. If there were, we might well ask where they exist, and what their size or thickness is -- or even what they are made of. Are they solid, or do they have a big hole in the middle, like a rarefied polo mint, with an extremely thin non-minty rim?


The same goes for rectangles, squares, cubes, cones, ellipses, spheres, ellipsoids, paraboloids…


As Philip, the original answerer, rightly says, we mathematicians deal with 'objects’ that not only do not exist, they can't exist, and not just in real life -- but, anywhere. They soon exhibit contradictory properties when we think otherwise or we confuse them with physical objects. But are they even 'non-physical' objects, or, indeed, 'objects' of any sort? If they were 'non-physical', how could they be perfectly rigid, for example? Is a line comprised of 'non-physical' points? And how does that hold together? What exactly are 'non-physical points', anyway? They, too, have no shape, circumference, or centre. They, too, aren't containers, otherwise they'd be 'non-physical volume intervals'! If that is so, no other 'non-physical point' can occupy them, either.


Much of traditional analytic and differential geometry, as well as topology, will need to be re-written if we are to free them of such crude ideas, and, indeed, avoid such awkward questions.


The traditional approach to mathematical 'objects' and 'processes' thus confuses mathematics with physical science -- and physicists return the compliment with interest by treating the universe as a mathematical object in its own right. Hence all those 'worm holes', 'parallel' universes, 'branched' time zones, 'warped spacetime', 'branes' -- and, of course, the 'paradoxes' of 'time travel'. No wonder physicists face insuperable problems explaining 'force', 'energy', 'space' and 'time' -- not to mention all those particles that seem to be wave and particle all in one go, can be in two places at once and can 'pop into existence' whenever they feel the urge.


And such problems don't stop there; the 'paradoxes' of number theory (and, indeed, set theory) also arise from viewing even these as if they were physical objects of some sort.


Of course, this means that there are no viable versions of mathematical Platonism, which theory positively invites awkward questions and 'difficulties' such as these.


And that also goes for 'bargain basement' Platonism — i.e., 'mathematical realism'.


Added on edit: You can see this confusion spreading through many of the comments in this thread as Quorans, for example, try to work out the 'pressure' exerted by a mathematical sphere (!!) (as if such objects are subject to gravity, or any other force!), or when they make comments about the size (!!) of a mathematical point. If it had any size, it wouldn't be a mathematical point, for goodness sake, whatever else it was. They are still conflating mathematical objects with physical objects, hence their puzzlement, the 'contradictions' this generates, and all those inexplicable 'infinities' that so 'effortlessly' emerge from nowhere.


Furthermore, if abstractionism were true, no two mathematicians would or could agree with each other. Indeed, if abstractionism were true, they could dispense with all those useless definitions, theorems, lemmas and proofs, and just brain scan one another.


[On Maxwell, cf., Buchwald (1985); on mathematics as it features in Physics, see Morrison (2000), pp.62-108. In addition, the last chapter of Harré and Madden (1976) is also relevant. Other literature related to this topic has been listed here. In addition to the links posted above, more will be said about the nature of mathematics and 'mathematical objects' in later Essays -- for example, here; see also here.]


But, even if it were conceded that DM-theorists are correct about the nature of mathematics, it would still fail to explain how, for example, the arrows from earlier could possibly be part of a UO. Again: this is how mathematicians represent vectors. So, even if mathematical objects and structures were 'abstractions from reality', or they 'reflected' what exists in the physical world, it still behoves DM-fans to explain exactly how these arrows would be a UO:



Figure Five: Still A 'Dialectical Tautology'?


Indeed, it would be as ridiculous to regard the above alignment as a UO as it would be to regard a column of ants as a UO if they were all marching in the same direction.



Figure Six: Anti-Dialectics?




Cases like those considered before Interlude Six illustrate a well known fact that forces aren't rigidly fixed as permanent opposites, nor are they always oppositional, even when they are classified as opposites. Hence, it isn't easy to see how viewing forces only as polar oppositional pairs could accommodate this particular property of natural forces.


In that case, this is unwelcome news, for little sense can be given in DM to the idea that opposites can switch in this way.41


That could be regarded as a serious interpretive error -- given the fact that change is central to DM. But, the point being made here is specifically targeted at the DM-notion that all change is a consequence of the interplay between polar opposites. Clearly, if these alleged polar opposites can combine in some way to augment one another, the term "opposite" can't fail to lose its dialectical bite. If change can occur as a result of 'opposites' that don't work as 'opposites' (still less as "polar" opposites) then this particular dialectical 'law' stands in some danger of violating a dialectical equivalent of the metaphysical Trades Description Act.


If this picture is now extended to take in HM, and if, for example, we consider the operation of "opposing" forces in the class war, it isn't easy to see how, say, one social force could switch around in the way that forces operating in nature manifestly can. Is it possible, therefore, for the capitalist class to swap sides in the class struggle (as a class force -- not as individual members of that class) to augment workers' battles in the latter's interests and on their terms? Admittedly, the detailed structure of -- and processes within -- the class war are complex; elements from each side may detach themselves (or be detached), and can work against their own (misperceived) class interests (on a temporary or even semi-permanent basis), but this isn't something upon which revolutionaries can or should depend -- still less ought they to trust in the outcome. If they were to do this, it would clearly encourage reformism and centrism (let alone invite defeat). Even at the margin (where whole class forces aren't involved), switches are sporadic.


But, such things occur all the time in nature. Hence, this crude analogy relating opposite forces to 'contradictions' lifted from DM is useless, at best, when it is imported into, and then applied in, HM.


Again, it could be objected here that this is a gross distortion since the above phenomena are actually consistent with DM. Dialecticians themselves reject the idea that there are fixed and unchanging forces in nature. Hence, the recognition that forces can change and operate in 'opposite directions' is one of DM's strengths, not one of its weaknesses.


Or, so it could be maintained.


However, this volunteered response succeeds in achieving one thing: it helps focus on what has been a recurring problem throughout this site: DM is so vague and equivocal that it is impossible to say with any clarity what its consequences amount to, or even if it has any. The claim that 'contradictions' in nature must be understood as opposing forces has, under close examination, turned out to mean that such forces might not actually oppose each other -- indeed, according to Engels, the concept of a force could simply be a convenient shorthand for the complex relative motion of bodies. Now, it seems that even this is incorrect, for oppositional forces may actually augment one another, but only if they aren't viewed as shorthand for the relative motion of bodies. And, to cap it all, we have just discovered that they can't even be 'dialectical opposites'!


It is therefore impossible to decide which of these DM-type forces are genuine opposites (or, indeed, which are polar opposites, if any are), or even distinguish any that are from those that aren't. But, if every force can work in any manner whatsoever, then it becomes deeply mysterious why only some are depicted as opposites. And, what has become of the AR-typology Engels regarded as fundamental?


Given such vague and ambiguous terminology, little meaning may be given to a single DM-concept in this area; still less to the idea that DM force 'laws' operate anywhere in nature.


Imagine a Chemist, say, who identified an element as having just so many protons in its nucleus, except it didn't really have that number of protons, and these alleged protons weren't really protons, and the element rarely if ever had a nucleus, and anyway it wasn't an element to begin with! Suppose further that this chemist claimed that she knew what she was talking about (even if no one else did) because she was an expert player of the 'Nixon Card', and thus skilled in the art of "grasping contradictions", which unfortunate lack of 'flexibility' and slavish adherence to 'formal concepts' prevents her critics from seeing the truth as she sees it.


Few, I think, would take her seriously. The same judgement should, I think, be reserved for DM-theorists, too.


Unfortunately, such discursive and theoretical 'contradictions' are grist to the DM-mill, but this isn't something about which dialecticians should feel proud. For if Capitalists, say, (as a social force) can indeed operate in such a contradictory manner, who is to say whether a revolution is necessary to overthrow them? Perhaps -- as result of a 'dialectical inversion' -- the class enemy could become the strongest ally of the working class? In such a topsy-turvy 'dialectical universe' anything might happen. Capitalism might be reformed away; Imperialists could assist in the abolition of poverty; the Nazi's might one day help create 'racial' harmony; and the Ku Klux Klan could wind up supporting Black Lives Matter. Who knows? The ruling-class might even overthrow itself42


If it is a central postulate of the theory that 'contradictions' are oppositional forces, and that these can change in 'contradictory' ways to become 'non-oppositional', then reformism, centrism, class collaboration (and the prospect of having the Fascists (etc.) as allies) can't be ruled out. On the other hand, if these possibilities are to be rejected (as surely they must), then the importation of such 'contradictory' DM-ideas into HM must be resisted no less emphatically.


In fact, as we will see in Essay Nine Part Two, this is indeed how class collaborationists have argued: the supposedly 'contradictory' nature of the Guomindang, for example, 'allowed' the CCP to 'justify' the formation of an alliances with them. DM also supplied the, shall we say, flexible theoretical atmosphere that 'allowed' the Stalinist regime to enter into a pact with the Nazis, and then help rationalise this treachery before the communist movement world-wide. As we will also see, this contradictory theory can be, and has been, used to defend whatever is expedient, and its opposite in the next breath and often by the very same dialectician.


Of course, it could be countered that forces operate in history in more complex ways than those we find in nature, so the above analogy with natural forces (and the KKK, etc.) is inapt -- especially if it is applied in the crude manner just illustrated. Unfortunately, if this rebuttal were itself successful then it would be misleading to describe natural and social forces as 'contradictory', for if the analogy between forces and 'contradictions' is inapt, it is inapt. End of story. Of course, that admission would amount to the abandonment of this unhelpful analogy in its entirety: that 'contradictions' may be depicted as oppositional forces anywhere at all.43


Nevertheless, even if all of the above points turn out to be completely misguided, there are other far more fundamental reasons for ruling-out the identification of opposing forces with 'contradictions'.


It is to these that I now turn.


A Contradictory Theory?


'Literal Forces' In Opposition


Most of the above criticisms were aimed at demonstrating that the analogy between forces and 'contradictions' was seriously misguided. Despite this, it could be argued that this doesn't affect the view that the identification of forces with 'contradictions' is in fact literal, not figurative.


Nevertheless, it is worth remarking that despite its centrally-important role in DM, and as far as can be ascertained, the precise details of the literal connection between forces and 'contradictions' have never been worked-out by a single dialectician!


One reason for this might be that they consider this identification to be so obvious that the specifics either don't matter or they are deemed to be trivial. On the other hand, it could turn out to be the case that nothing could have been said in this respect, which would more obviously explain this protracted, deafening silence. Indeed, as will soon become clear, this in fact seems to be the case: this omission isn't the least bit surprising, for the imagined connection between forces and 'contradictions' turns out to be entirely illusory.


In order to substantiate this latest allegation it might help if we back-tracked a little. Part of the argument in favour of the identification of forces and contradictions at first appeared to depend on an analogy drawn between literal contradictions and conflict (which view, as we will see in Essay Twelve (summary here), is a throw-back to ancient and animistic theories about the origin of all forms of conflict, locating them in the activities the 'gods' or other invisible, personified forces at work 'behind the scenes', or 'beneath appearances').


Mere contradictions are clearly verbal wrangles, which can indeed look oppositional. When one person asserts p, and another person denies it (or asserts not p, where "p" stands for a spoken token indicative sentence), then at the level of discourse at least some sort of opposition appears to be implied (but on that, see here). So, analogously, it seems that a 'contradiction' in nature signals the existence of real material opposition -- but, alas, only to those who are happy to fetishise social relations as if they represented real relations in nature itself.


DM-theorists view real, material 'contradictions' as their primary concern; verbal wrangles are clearly only of peripheral interest. Having said that, many dialecticians refer back to the origin of 'the dialectic' in the verbal wrangles recorded in Plato's dialogues. Here are just a few:


"In his Phänomenologie des Geistes [Hegel] compares human life with dialogue, in the sense that under the pressure of experience our views gradually change, as happens to the opinions of disputants participating in a discussion of a profound intellectual nature. Comparing the course of development of consciousness with the progress of such a discussion, Hegel designated it by the word dialectics, or dialectical motion. This word had already been used by Plato, but it was Hegel who gave it its especially profound and important meaning." [Plekhanov (1917), p.601. Bold emphases alone added.]


"Dialectics comes from the Greek dialego, to discourse, to debate. In ancient times dialectics was the art of arriving at the truth by disclosing the contradictions in the argument of an opponent and overcoming these contradictions. There were philosophers in ancient times who believed that the disclosure of contradictions in thought and the clash of opposite opinions was the best method of arriving at the truth. This dialectical method of thought, later extended to the phenomena of nature, developed into the dialectical method of apprehending nature, which regards the phenomena of nature as being in constant movement and undergoing constant change, and the development of nature as the result of the development of the contradictions in nature, as the result of the interaction of opposed forces in nature...." [Stalin (1976b), p.836. Bold emphasis added.]


"Let us inquire into the sources of dialectics in antiquity. Why was it that in antiquity man had already come upon the foundations of the dialectical method of thinking? 1. The old philosophers of nature, Heraclitus, Anaximander, etc., investigated the emergence and decline of the world. They thus had to arrive at the concept of the universal change and the universal motion of all things. I refer to Heraclitus especially. 2. Social relations, meditation on the form of the State, on religion, etc., stimulated the consideration of all things as changeful and self-contradictory. (This applies especially to Socrates, Plato, etc.) The immediate stimulus was that in public life contradictory viewpoints clashed one with another. Public life in Athens was a very lively affair. In the market-place discussions were constantly taking place concerning what is good and what is evil, how the State should be constituted, etc. One said A, another Not-A. This was true of all things in public and private life. From this there ultimately developed an art of conversation, and this art of conversation became the source of the art of dialectics. Dialectics was originally called the art of discourse because it grew out of discourse." [Thalheimer (1936), pp.98-99. Bold emphasis added.]


"This consideration enables us to understand the original meaning of the term 'dialectics.' The word is derived from the Greek dialego, meaning to discuss or debate. It was considered that to discuss a question from all sides, and from all angles, allowing different one-sided points of view to oppose and contradict each other during the debate, was the best method of arriving at the truth. Such was the dialectics employed, for example, by Socrates. When anyone claimed to have a formula which answered some questions once and for all, Socrates would enter into discussion with him and, by forcing him to consider the question from different angles, would compel him to contradict himself and so to admit that his formula was false. By this method Socrates considered that it was possible to arrive at more adequate ideas about things." [Cornforth (1976), pp.60-61. Bold emphases alone added.]


"Elaborated first by the Greek philosophers (dialego – I debate), dialectics remained something of an intellectual curiosity, a philosophical cul-de-sac, particularly when religious beliefs dominated." [Quoted from here. Bold emphasis added.]


"Dialectics is derived from the Greek word 'dialego' which means to discourse or debate. Many of the old Greek philosophers were dialecticians like, Aristotle and Plato. Heraclitus formulated masterpieces of dialectic. Plato used the 'dialectical method' in his dialogues, whereas Aristotle, the most encyclopaedic intellect among these philosophers, investigated the most essential forms of dialectical thought." [Quoted from here. Quotation marks altered to conform with the conventions adopted at this site. Minor typo corrected. Bold emphasis added.]


"Dialectics was initially a particular kind of dialogue invented in Ancient Greece in which two or more people holding different points of view about a subject seek to establish the truth of the matter by dialogue with reasoned arguments.... Today dialectics denotes a mode of cognition which recognizes the most general laws of motion, contradiction and new development. In ancient times dialectics was the art of arriving at the truth by exposing the contradictions in arguments of opponents and overcoming these contradictions. They thought that the clash of opinions was the best method of eventually getting to the truth." [Quoted from here. Paragraphs merged. Bold emphasis added.]


"The word dialectics refers to a method of intellectual discussion by dialogue. It is a term of logic. The meaning of dialectics is the conflict between two mutually opposite forces or tendencies. According to the Greek philosopher Aristotle (384-322 BC) it referred to the art of deputation by question and answer." [Quoted from here. Bold emphasis added]


Even so, the theory that there are contradictions, even 'dialectical contradictions', in nature and society is still analogical, for we were certainly aware that contradictions involve verbal wrangles well before we were informed (by Hegel) that there were any such in nature and society. In that case, Hegel's argument must have proceeded from the social to the natural world, which is indeed what the history of the subject reveals: Hegelian dialectics didn't exist in pre-historic times (nor even before the 18th century), even though people have been arguing and contradicting one another for tens of thousands of years.43a Hence, social interaction has plainly been projected analogically onto nature, and DM-theorists have manifestly relied on an analogy drawn between the way human beings argue (or fight) and the way conflict seems to occur in the natural and social world. Unfortunately, this makes the literal interpretation of forces as 'contradictions' unavoidably dependent on analogical and figurative language, leaving perplexed non-believers with absolutely no clue what literal meaning, if any, could possibly be attributed to this way of picturing conflict. Even to this day, we are still in the dark about the material grounding that DM-theorists assume exists.


We certainly have a much clearer grasp of the use of contradictions in language, and arguably also in logic, but we have none at all when it comes to those that allegedly occur in nature -- or, indeed, in society --, as we will see.


Having said that, there is this minimal consideration in favour of the application of DM to society: 'contradictions' in capitalism, for example, are based on the presumed fact that certain concepts (or what they supposedly 'reflect') are dialectically linked. For instance, the capitalist class not only implies the working class (the proletariat), the one can't exist without the other (although I have thrown that clichéd inference into considerable doubt here) -- hence, they are said to be 'dialectically-united opposites', interpenetrating one another (or so the story goes). But, as we have discovered, there is nothing in the natural world that enjoys this sort of 'logical' inter-connection -- as we have already seen, not even the opposite poles of a magnet, or positive and negative poles in atomic theory and electrodynamics can be viewed this way. In that case, the application of DM to the non-social world is, at best, figurative and non-literal, which, as we have found out in the first half of this Essay, won't wash either.


Nevertheless, this would at least account for the figurative way that 'dialectical contradictions' continually surface in DM (and which are seriously overused in HM), and why dialecticians regularly conflate their social and material forms with each other.44


Once more, even if we ignore this problem, one thing is clear: for DM-theorists verbal contradictions represent perhaps the least significant category of opposition. Changes in nature and society are (for them) the result of much more fundamental 'contradictions' than those occasioned by the mere gainsaying of another person's words. In many cases, of course, discursive contradictions might turn out be a 'reflection' of more basic conflicts in the real world, and it is the latter that are of interest to DM-theorists.


However, when this 'neat' picture is examined a little more closely much of it falls apart.


The Revenge Of The Non-Existent


As has already been noted, DM-theorists have so far failed to offer a clear account of the precise nature of the connection between 'contradictions' and opposing forces that their theory requires. In that case, once again, one will have to be provided for them.45


Presumably, when DM-theorists claim that 'contradictions' are represented in nature by opposing forces they have something like the following in mind (if they but knew it):45a


F6: Let force, P1, oppose force, P2, in configuration, C1, in nature.


F7: Here, opposition amounts to the following: the normal effects produced by P1 in C1 (had P2 not been present) are the opposite of the effects P2 would have produced in C1 (had P1 similarly not been operative).


F8: Let P1's normal effects in C1 be elements of an event set, E1, and those of P2 be elements of an event set, E2. For the purposes of simplicity let E1 and E2 be disjoint.


F9: By F7, E1 and E2 contain only opposites, such that elements of E1 and E2 taken pair-wise respectively from each set form oppositional couples.46


[Here, the content of C1 could include any other local or remote forces and/or processes operating in the system; alternatively, the forces themselves may even be 'edited out' on the lines envisaged by Engels (as a sort of shorthand for relative motion, etc.). In addition, all the internal "mediations" between these forces and/or events in the Totality (T) may also be incorporated into the picture at any point. Other 'dialectical' caveats could, of course, be stirred into the mix, as deemed necessary or appropriate.]


It is worth emphasising at this point that P1 or P2 must operate 'independently' in C1.47 This seems to be an essential assumption so that sets E1 and E2 may be determinate themselves.


[Admittedly, this qualification runs foul of the idea that everything in the Totality (T) is interrelated, but we can avoid that untoward consequence by modifying the stated condition to "relative independence". Naturally, this would mean that several other comments in this part of the Essay (originally aimed at trying to make this aspect of dialectics clear for the very first time ever) would become rather vague by default. However, as will readily be appreciated, a 'theory' like this -- beset as it is on all sides by an internally-generated fog, further aggravated by its supporters lobbing metaphysical smoke bombs in its general direction -- will always resist attempts to dispel the Stygian gloom in which it seems permanently engulfed. Anyway, this 'independence' needn't suggest a CAR-like scenario since it could form part of the 'dialectical development' of new forces and processes as C1 and the rest of T develop. Naturally, this simplifying assumption could be modified at a later stage, as the need arises.]


The first problem with the above account centres on the term "opposites", in F9. Something a little more precise than merely an "opposite" seems to be required here in order for DL to surpass FL in its ability to account for change, etc.48


F9: By F7, E1 and E2 contain only opposites, such that elements of E1 and E2 taken pair-wise respectively from each set form oppositional couples.


Unfortunately, the difficulty here lies in seeing whether even this minimal condition is actually implied by F6-F9, and whether the rather weak concept of an "opposite" is capable of bearing all the weight usually put on it. These can't be 'dialectical opposites', anyway, since they don't imply one another. They can surely exist independently of each other (unlike, say, the proletariat and the bourgeoisie, or so we have been told), and hence they aren't 'interpenetrated opposites'.


[I have resisted representing E1 and E2 propositionally since I want to concentrate on real material opposites, rather than their linguistic correlates. Nevertheless, it is worth recalling, once again, that in FL two contradictory propositions can't both be true and can't both be false at once. One implication of this condition is that the claim that two allegedly contradictory states of affairs could both exist at the same time (expressed by two supposedly true 'contradictory' propositions) must rest on either a mis-description or an un-discharged ambiguity --, or even, of course, on the projection of logical categories onto nature. This topic will be analysed in more detail in a later subsection -- as it has also been in Essay Five -- and will be further examined in Interlude Eleven and Essay Eight Part Three.]


However, quite independently of these latest 'difficulties', far more problematic is the fact that given F6-F9, it would be impossible to say what the 'contradictory' state-of-affairs here is meant to be, whether or not it is actually 'dialectical'.


That is because F6-F9 imply that E1 and E2 do not in fact obtain together, for if just one of P1 or P2 is operative, then only one of E1 or E2 will be instantiated.


Clearly, in such circumstances there could be no 'contradiction' -- even if we were accommodating enough to accept the vague DM-'definition' of a 'dialectical contradiction' -- since, at least one 'half' of the alleged contradiction wouldn't actually exist for it to contradict anything, having been prevented from acting by the operation of either one of P1 or P2!49


Interlude Seven -- Further Complications


Of course, this conclusion (i.e., that at least one 'half' of the alleged contradiction wouldn't actually exist for it to contradict anything, having been prevented from occurring by the operation of either one of P1 or P2) itself depends on the peculiar Hegelian doctrine that contradictions can somehow exist. If that thesis is abandoned, DM falls apart, anyway.


F6: Let force, P1, oppose force, P2, in configuration, C1, in nature.


F7: Here, opposition amounts to the following: the normal effects produced by P1 in C1 (had P2 not been present) are the opposite of the effects P2 would have produced in C1 (had P1 similarly not been operative).


F8: Let P1's normal effects in C1 be elements of an event set, E1, and those of P2 be elements of an event set, E2. For the purposes of simplicity let E1 and E2 be disjoint.


F9: By F7, E1 and E2 contain only opposites, such that elements of E1 and E2 taken pair-wise, respectively, from each set form oppositional couples.


However, it could be objected that the disjunction of the effects of P1 and P2 (as in "E1 or E2") completely distorts the picture. Indeed, it could be maintained that what is missing here is an account of how P2 interacts with E1, which would itself be dialectical. [One variation on this theme will be considered presently, others later on -- for example, in Interlude Nine.]


Indeed, what hasn't been taken account of in this Essay is that alterations induced in E1 by these interactions would mean that the idea that change comes about through contradictions -- modelled by material forces -- could still gain some sort of purchase.


Hence, it could be argued that the contradiction between P1 and P2 alters E1 so that it becomes, say, E1a. In that case, we would have real terms here for the 'contradiction' to reflect, which in turn means we would have here a concrete example of change through 'internal contradiction'.


Or, so it could be argued.


But, plainly, this would only be the case because a decision had already been taken to describe these forces as "contradictory", when it hasn't yet been established whether this is an accurate, or even an appropriate, way to depict the relationship between them.


Nevertheless, and ignoring even that rejoinder for now, and as has been underlined already, what actually happens here is that the resultant of these two forces actually causes the said change. If so, and once more, calling this a change motivated by a 'dialectical tautology' would be far more accurate. [That particular option among others will be examined again below.]


Moreover, even if the DM-objection volunteered above were valid -- whereby the interaction between P1 and P2 alters E1 so that it becomes E1a -- it would still be of little use to dialecticians. That is because, in this case, E1 itself will have been altered externally, and so change here wouldn't have been the result of E1's own 'internal contradictions'. That is because, as we have seen many times, these items don't imply one another, so they can't be 'internally-connected', in the way that the proletariat is supposedly internally related to the capital class, so that the one can't exist without the other since they supposedly imply one another. So, whatever else it is, this can't be an example of dialectical change through 'internal contradiction'.


Worse still, if this is to be the model for all DM-change, then no change at all would be 'internally-generated'. We saw this problem recur throughout Part One of this Essay, where no matter how we tried to re-package this theory, the result was always the same: if everything is "self-moving" (according to Lenin and several other DM-theorists quoted in Part One), then the universe must be populated by:


(i) Eternally changeless simples, or by,


(ii) Non-interacting systems.


On the other hand, if systems of forces actually change the objects internal to the system to which they belong, then, plainly, those objects can't be "self-moving". The volunteered response above simply reproduces this fatal defect in a more abstract form.


["System" and "simples" were defined in Part One.]


Anyway, this volunteered DM-response will be tackled later in this Essay -- and in more detail below, in Interlude Nine.


Since this Essay was originally written, a superficial attempt has in fact been published which at least endeavoured to specify the precise nature of the link between oppositional forces (or, to be more honest, oppositional "tendencies") and 'dialectical contradictions' -- i.e., Weston (2012).


Here are two different translation of Marx's words and what I have said about them in Essay Nine Part One:


Tom Weston refers his readers to this passage from Das Kapital (I have quoted it as it appears in Weston's article first, and then as it has been rendered in MECW):


"We saw that the process of exchange of commodities includes relations that contradict and exclude one another. The development of the commodity does not overcome [aufhebt] these contradictions, but creates a form within which they can move themselves. This is in general the method through which real [wirkliche] contradictions solve [losen] themselves. It is a contradiction, for example, for one body to continuously fall into another, and just as constantly fly away from it. The ellipse is one of the forms of movement in which this contradiction is actualised [verwirklicht] just as much as it is solved [lost]." [Quoted in Weston (2012), pp.5-6. This links to a PDF; italic emphases in the original.]


"We saw in a former chapter that the exchange of commodities implies contradictory and mutually exclusive conditions. The differentiation of commodities into commodities and money does not sweep away these inconsistencies, but develops a modus vivendi, a form in which they can exist side by side. This is generally the way in which real contradictions are reconciled. For instance, it is a contradiction to depict one body as constantly falling towards another, and as, at the same time, constantly flying away from it. The ellipse is a form of motion which, while allowing this contradiction to go on, at the same time reconciles it." [Marx (1996), p.113. This links to a PDF; italic emphases in the original.]


Weston takes exception to several of the translated phrases in the second of the above two passages, such as "it is a contradiction to depict one body as constantly falling towards another", on the grounds that:


"[T]he phrase 'it is a contradiction to depict' conveys an idea directly opposite to the assertions of the German text. The contradiction is not only in the depiction of elliptical motion; it is in the motion itself. This is the clear sense of the German text's assertions that the contradictions are 'real [wirklich]', are 'actualised [verwirklicht]', and that the sides of the contradiction are the two tendencies of motion that are mentioned, not their depictions." [Weston (2012), p.28. Italic emphases in the original.]


Weston must mean "not merely their depictions" in the last sentence above since it would seem reasonably clear that if a 'contradiction' is 'real' then its depiction can't fail to be contradictory, too.


Be that as it may, for this and other reasons, Weston clearly prefers the first translation to the second.


The following is also a passage we have already had occasion to quote in part -- concerning the above obscure throw-away comment in Das Kapital concerning the elliptical motion of planets around the Sun:


"As we saw above, an opposition is a contradiction if negativity is present, that is, if the two sides interfere with each other.... Although tendencies can interfere with each other in numerous ways, I suggest the following criterion is a sufficient condition for negativity of, or interference between, opposing tendencies A and B:


Tendency A, if strong enough, with cause the opposite tendency B to be less fully realised than if tendency A were absent, and conversely.  


"This criterion is satisfied by both tendencies that Marx finds in the ellipse case. The tendency of a planet to fly away from the Sun will only result in its actually flying away (a parabolic or a hyperbolic orbit [in that case, these wouldn't be orbits, just trajectories -- RL]) if the tangential velocity is large enough to overcome the counter-tendency produced by gravity. On the other side, the tendency of the planet to fall into the Sun will only result in the planet actually hitting the Sun if the tangential tendency is small compared with the gravitational tendency. Thus unless one of the tendencies is too weak to constrain the other, each tendency prevents the realisation of the other. At least one will not be fully realised, although both may be partially realised." [Weston (2012), pp.17-18. Italic emphasis in the original.]


I will return to this passage again later on in this Essay, in a section where I plan to discuss these and other possibilities in much greater detail. For present purposes it is sufficient to note that:


(a) Just like other DM-theorists, Weston simply helps himself to the word "contradiction" with no attempt to justify its use in such contexts -- that is, over and above stipulating that these phenomena are to be so described. Plainly, this is little other than an attempt to foist this concept on nature (in defiance of what DM-fans tell us they never do);


(b) We have already seen that "tendencies" aren't in any way causal, and can only be called forces by those with an agenda;


(c) Weston has plainly appealed to "tendencies" as an artificial way of trying to link these phenomena, since "force" won't work here, nor will "inertia" (his other favoured word);


(d) Even if the DM-use of "contradiction" were justifiable, how can "less fully realised" be viewed as the equivalent of "dialectical contradiction"? Weston failed to say. Finally,


(e) Do these "tendencies" turn into each other? And how exactly do they "struggle" with one another? But they should do both if the DM-classics are to be believed.


(f) As we saw in Essay Nine Part One, Marx told us he was merely "coquetting" with Hegelianisms like this in Das Kapital. In which case, in conjunction with the points made above (and below), very little, if no weight at all, can be placed on Marx's words.


So, whatever else it is, this relation isn't 'dialectical'.


It is also worth pointing out that Newton's First Law (which appears to be integral to Weston's attempt to defend this neo-Hegelian world-view) says nothing about "tendencies":


"Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon." [Quoted from here. Accessed 04/07/2016.]


Moreover, the Classical Law of Gravity also fails to mention "tendencies":


"Newton's Universal Law of Gravitation states that any two objects exert a gravitational force of attraction on each other. The direction of the force is along the line joining the objects.... The magnitude of the force is proportional to the product of the gravitational masses of the objects, and inversely proportional to the square of the distance between them." [Quoted from here. Accessed 04/07/2016.]


"Newton's Law of gravitation: every particle attracts any other particle with a gravitational force whose magnitude is given by


F = G m1m2


"Here m1 and m2 are the masses of the particles, r is the distance between them, and G is the gravitational constant." [Halliday, et al (1993), p.412. Link added.]


Which means that Weston's theory actually depends on a series of Persuasive Definitions, or, perhaps, Persuasive Re-descriptions. This is the only way it can even be made to seem to work.


[I have said more about Weston's 'argument', here, here, here, here and here.]




Later on, I will examine the question whether E1 and E2 (from earlier), even though 'opposites', can legitimately be described as 'contradictory'. In what follows, I will simply assume that they are.50


Prevention And Its Discontents


Despite this, it could be claimed that the following propositions are all that DM-theorists really require:


F10: P1 prevents E2, and P2 prevents E1.


F11: Anything that prevents something else happening contradicts it.50a


F12: Therefore, P1 and P2 contradict each other's effects.


If so, then plainly P1 and P2 don't actually contradict one another, just each other's effects. In that case, it is far from clear whether or not DM-theorists (who are keen to maintain the orthodox view that forces contradict each other) will want to embrace F10-F12 too enthusiastically. It is also worth repeating an earlier, fatal objection to this attempt to do CPR on this dying theory: when, for example, P1 prevents E2, it can't be contradicting it in dialectical sense of that word, since these two factors don't imply one another, and both can exist without the other (unlike the bourgeoisie and proletariat, which do imply one another, so we are told). Hence, whatever else this is, it, too, can't be a 'dialectical contradiction'. That is the same fatal objection to this entire way of viewing 'dialectical contradictions' we have met several times in this Essay. Nevertheless, I will once again ignore it so that other defects of this theory may be highlighted. However, I will introduce it again from time-to-to-time to remind the reader that this is, rather like that Monty Python parrot, an ex-theory, it has gone to meet its maker:



Video Four: DM -- As Dead As This Parrot?


Interlude Eight -- Tom Weston


F11: Anything that prevents something else happening contradicts it.


This appears to be a line adopted in Weston (2012):


"Hegel distinguished contradiction from opposition by the category of negativity, which means, roughly, conflict of the opposite sides: 'Opposites...contain contradiction in so far as they relate to each other negatively in the same respect or are both mutually canceling...and indifferent to each other.' It is the negativity of a contradiction that is responsible for its key role in dialectical theory, that contradiction causes motion: 'The sides of a manifold only become active and lively against each other when they are driven to the peak of contradiction, and contradiction contains the negativity, which is the indwelling pulse of self-movement and liveliness.'... (p.12)


"For  Marx as for Hegel, the main difference between opposition and contradiction is negativity, the internal activity of a contradiction.... (p.13)


["Negativity is an abstraction of conflict, not of the absence of something.... (Footnote p.13)]


"As we saw above, an opposition is a contradiction if negativity is present, that is, if the two sides interfere with each other. From Marx's brief comments, he appears to have thought that it is obvious that falling into a body and flying away from it are contradictory tendencies, but we can reinforce his conclusion. Although tendencies can interfere with each other in numerous ways, I suggest that the following criterion is a sufficient condition for negativity of, or interference between, opposing tendencies A and B:


Tendency A, if strong enough, will cause the opposite tendency B to be less fully realised than if tendency A were absent, and conversely.


(α) "This criterion is satisfied by both tendencies that Marx finds in the ellipse case. The tendency of a planet to fly away from the Sun will only result in its actually flying away (a parabolic or hyperbolic orbit) if the tangential velocity is large enough to overcome the counter-tendency produced by gravity. On the other side, the tendency of the planet to fall into the Sun will only result in the planet actually hitting the Sun if the tangential tendency is small compared with the gravitational tendency. Thus unless one of the tendencies is too weak to constrain the other, each tendency prevents the realisation of the other. At least one will not be fully realised, although both may be partially realised.... (pp.17-18)


"A reasonable interpretation of increased intensity or sharpness of a contradiction is an increase in the mutual interference of the two sides. As the contradiction undergoes the fullest possible development and nears resolution, this interference is increased to such an extent that the two sides cannot coexist any longer, and one must defeat the other, either by destroying it or by weakening it so completely that it can no longer interfere with the victorious side.... (p.24)


(β) "In that case, the inertial tendency will prevent the full realisation of the gravitational tendency -- falling into the central body -- and the gravitational tendency will prevent the full realisation of the inertial tendency, the tendency to fly off to infinity. Thus the two tendencies interfere with each other, and represent a contradiction." (p.34) [Weston (2012), pp.12-34. Italic emphases in the original.]


Weston here appeals to a handful of rather obscure ideas connected with "negativity" the latter of which we are told is "an abstraction of conflict" and "interference" (whatever that means!). This suggests that Weston's analysis doesn't rely on 'one side' of a contradiction preventing the 'other' from operating, but merely "interfering" with it. In other words, it is clear that for Weston the two sides of the 'contradiction' in such cases must co-exist.


If so, it should be possible to adapt what was said earlier (except, of course, Weston has dropped the use of "force", replacing it with "tendency"), as follows: 


W1: Let force/"tendency", P1, oppose/interfere with force/"tendency", P2, in configuration, C1, in nature.


W2: Here, opposition amounts to the following: the normal effects produced by P1 in C1 (had P2 not been present) are the opposite of the effects P2 would have produced in C1 (had P1 similarly not been operative).


W3: Let P1's normal effects in C1 be elements of an event set, E1 (comprised of sub-events, E1a- E1n), and those of P2 be elements of an event set, E2 (comprised of sub-events, E2a- E2n). For the purposes of simplicity let E1 and E2 be disjoint.


W4: By W2, E1 and E2 contain only opposites, such that elements of E1 and E2 taken pair-wise respectively from each set form oppositional couples.


From what Weston says in paragraphs (α) and (β) above "opposite" can be given a Weston-style spin so that it means something like "the opposite result of...", or maybe "prevent the full realisation of...", one or more events. This means that one or more of E1a- E1n and E2a- E2n will be prevented from occurring. This seems to be the only way of interpreting the following sentence:


"[T]he inertial tendency will prevent the full realisation of the gravitational tendency -- falling into the central body -- and the gravitational tendency will prevent the full realisation of the inertial tendency, the tendency to fly off to infinity." [Ibid.]


So, P1 might prevent, say, event, E2i, while P2 will prevent, say, event, E1j. In which case:


W5: P1 and P2 contradict one or more of each other's effects.


But, if these effects don't happen, or don't take place (even on Weston's recognition), then they can't exist to be contradicted by anything, let alone by a force/"tendency". More to the point, these two forces/"tendencies" don't actually 'contradict' one another, just each others effects. As noted earlier (edited):


In that case, it is far from clear whether or not DM-theorists (who are keen to maintain the orthodox view that forces contradict each other) will want to embrace [the above] too enthusiastically.


No surprise, we hit the same brick wall!


[I will return this side-argument again later, after a few peripheral 'difficulties' have been ironed out.]


To continue: the above passage seems to imply that the aforementioned planet will orbit the Sun when the "tendencies" involved have balanced one another out:


"As we saw above, an opposition is a contradiction if negativity is present, that is, if the two sides interfere with each other. From Marx's brief comments, he appears to have thought that it is obvious that falling into a body and flying away from it are contradictory tendencies, but we can reinforce his conclusion. Although tendencies can interfere with each other in numerous ways, I suggest that the following criterion is a sufficient condition for negativity of, or interference between, opposing tendencies A and B:


Tendency A, if strong enough, will cause the opposite tendency B to be less fully realised than if tendency A were absent, and conversely.


"This criterion is satisfied by both tendencies that Marx finds in the ellipse case. The tendency of a planet to fly away from the Sun will only result in its actually flying away (a parabolic or hyperbolic orbit) if the tangential velocity is large enough to overcome the counter-tendency produced by gravity. On the other side, the tendency of the planet to fall into the Sun will only result in the planet actually hitting the Sun if the tangential tendency is small compared with the gravitational tendency. Thus unless one of the tendencies is too weak to constrain the other, each tendency prevents the realisation of the other. At least one will not be fully realised, although both may be partially realised.... (pp.17-18)


"In that case, the inertial tendency will prevent the full realisation of the gravitational tendency -- falling into the central body -- and the gravitational tendency will prevent the full realisation of the inertial tendency, the tendency to fly off to infinity. Thus the two tendencies interfere with each other, and represent a contradiction." (p.34)


So, it looks like the "tendency" to fly off at a tangent is balanced by the "tendency" to fall into the Sun, and when that happens the planet will enter into an orbital trajectory.


I take up this notion (i.e., "balancing"), and several other related issues below (here, here, and here), and in more detail in Interlude Nine, where I consider several variations on Weston's theory. [See also here.]


Independently of this, we have already had occasion to note that Hegel's invention of 'negativity' was thoroughly misconceived since it was based on


(i) An egregious mis-interpretation of the LOI (where we also saw that contradiction has nothing to do with cancellation), and,


(ii) Kant's introduction of the concept of "real negation", which has been debunked in Appendix A.


[LOI = Law of Identity.]


Finally, it is far from clear that the two "tendencies" Weston has recruited to his cause are 'dialectical opposites' of one another in the required manner; they don't seem to imply one another in any sense of that word, which they would have to do in order to qualify as 'internally-connected' opposites. In what way does a "tendency" to fall into a planet imply a "tendency" to continue to move in the same line of action -- in the way that one class under capitalism (the bourgeoisie) is said to imply the existence of the other (the proletariat), such that one can't exist without the other -- or so we have been told? Weston omits consideration of this core Hegelian principle, and it isn't hard to see why: that omission hides the fact that this isn't by any measure a 'dialectical relation' and hence it can't be a 'dialectical contradiction', either, whatever else it is. [On that, see here.]


[I will offer a different reading of this passage in Essay Nine Part One -- and one that absolves Marx of any involvement in this 'Hegelian' farce (which, as we have just seen, turns out not to be Hegelian, after all!).]


But, what about the "fully realised" aspect of Weston's argument?


"Tendency A, if strong enough, will cause the opposite tendency B to be less fully realised than if tendency A were absent, and conversely." [Ibid.]


This has already been covered: If a 'tendency' is "less fully realised" then some of its effects won't follow or take place, as we have found out. We have also seen that, whatever else it is, this can't be a 'dialectical' interaction since these 'tendencies' don't imply one another. In which case, Weston's entire analysis is devoid of rational support, at any level -- even in DM-terms!




So despite this, in order to examine every possible way of reviving this moribund theory, I will concede for the purposes of argument that E1 and E2 are 'contradictories' after all. However, it now appears from the above considerations, and from F10-F12, that not only does E1 'contradict' E2, but also that P1 'contradicts' E2, and P2 'contradicts' E1, as well. I shall return to consider these added complications, below.


F10: P1 prevents E2, and P2 prevents E1.


F11: Anything that prevents something else happening contradicts it.


F12: Therefore, P1 and P2 contradict each other's effects.


But, there now appears to be no good reason to accept F11, and every reason to reject it. Consider the following scenario -- aimed at showing why F11 is unacceptable (even given the truth of other DM-theses):


F13: NN saved child MM from drowning.


F14: NN prevented the drowning.


F15: So, NN contradicted the drowning (by F11).


The problem here lies not so much with the non-standard use of language found in the above sentences, but with the fact that if a drowning (or if anything) is prevented from happening then it never actually took place. In that case, if the said incident didn't happen it can't have been 'contradicted' by any of the forces or events doing the preventing -- since there would be no 'it' for anything to contradict. Unless we are prepared to envisage forces 'contradicting' things that don't exist, or we allow them to 'contradict' unrealised possibilities -- or even 'contradict' ideas (perhaps those in NN's mind above) --, the word "contradiction" can gain no grip here, even in DM-terms.


It might also become problematic explaining how something that exists can 'struggle' with something that doesn't.


It might prove even more problematic explaining how this 'contradiction' is dialectical, since what an individual does or doesn't do in no way implies what they hoped to prevent, in this case, the drowning. The two can certainly exist without one another (unlike the proletariat and the capitalist class, or, so we have been told). If so, whatever else this is, it can't be dialectical'.


It could be objected that if NN formed the intention to prevent a drowning that intention implies there is a drowning to prevent. In fact all that is implied here is that NN believed someone was drowning and intended to save that individual. It certainly doesn't imply that there is someone who is drowning since NN could be mistaken, delusional, or a publicity seeker.


Even more problematic, did what NN attempt turn into the drowning? But that is what the DM-classics tell us must happen if this is to be counted as a dialectical relation. That is, if these are 'dialectical opposites' locked in struggle, they must change into each other!


Again, whatever else it is, this can't be dialectical'.


One obvious fall-back position for dialecticians to occupy in response to the above would be to argue that the action mentioned in F13 halted a series of events that would have led to the said drowning. In that case, that intervention contradicted that series of events. This objection will be looked at more closely in Interlude Nine -- and again presently, below.


However, in case this latest counter-example is considered prejudicial, or contentious (in that it doesn't deal with real forces, or with the sort of forces over which DM-theorists are exercised), then perhaps the following considerations might prove to be more acceptable. To that end, let us begin with this rather obvious assumption:


F16: Any process or series of events that is prevented from occurring does not exist (or take place).51


It is clear that while F16 is a truism, it seems to ignore protracted or extended events and processes, so it might not be acceptable as a clarification of the 'contradictions' that are of interest to DM-theorists. Consider, then, the following emendations:


F17: Event, E, consists of a set of inter-connected sub-events, E1-En.


F18: E1-En form a complex of material interactions (of a sufficiently mediated and contradictory nature) within T.


F19: Let P2 prevent some or all of E1-En from taking place.


F20: Therefore, some or all of E do not exist, will never exist, or do not take place.


["T" stands for "The Totality".]


It is quite plain from this that because of the operation of P2, certain events failed to materialise. But, that simply generalises the point made in relation to the drowning example considered earlier. Even if it were assumed that the vague notion of a 'contradiction' employed by DM-theorists is viable, it would still be difficult to see how anything could 'contradict' something else if the latter doesn't exist or never occurred. Hence, in the example above, if P2 halted certain unspecified elements of the series of events -- perhaps, Ei-En --, which would have led to the said drowning had they not been prevented, then those prevented events never happened (nor did the drowning), and hence didn't exist, and so can't have been 'contradicted'.


That objection also appears to be fatal to DM since it appears to tell us that, if anything, forces actually prevent 'contradictions' from arising!


Of course, all this is independent of the fact that even if it could be shown that this was a 'contradiction', it couldn't be a 'dialectical contradiction' since the factors involved -- i.e., the actions aimed at preventing the drowning and the events that led up to the drowning -- do not imply one another, and can (surely) exist without one another, unlike, say, the proletariat and the bourgeoisie, so we have been told. Nor do they turn into each other.


As we have seen time and again, this is a recurring problem which has sunk every such attempt to breath life into this corpse of a theory. [Apologies for that mixed metaphor!]


Therefore, far from forces being DM-friendly, they appear to be among its very worst enemies.


In that case, if this fatal weakness is to be neutralised, a new and more consistent account of the relationship between 'contradictions' and forces must, as a matter of some urgency, be found.52


A More Balanced Account Of Prevention?


In order to construct a more viable account, we need to reconsider a difficulty we met earlier that was temporarily put to one side: the claim that forces -- not forces and effects, or simply effects, but forces -- forces are directly contradictory to one another. Consider then the following scenario:


F21: P1 contradicts P2 in so far as it prevents P2 acting, and/or vice versa.


Again, this perhaps puts too much weight on the term "prevent"; it might prompt F21 to self-destruct just as fast as F17-F20 did, for if one of these forces fails to operate (it having been prevented), no 'contradiction' would be implied.


[Whether or not the actual act of prevention is what constitutes the 'contradiction' here will be considered below, here and in Interlude Nine.]


But, perhaps that conclusion is just a little too hasty. For example, both of the above forces could still exist even if one ceased to operate in an F21-style configuration, and no problem need arise because of that since no reference has been made to the non-existent effects of either one of them.


This means that even though one of P1 or P2 might have been prevented from acting, they could both still exist in some form or other. If so, F21 might appear to be the viable option that dialecticians require. One further advantage here would be that F21 connects forces directly with 'contradictions', rather than linking 'contradictions' to the effects of forces. Could this be the lifeline DM requires?


Alas, upon closer examination, this lifeline soon turns into a noose.



Figure Seven -- A DM-'Lifeline' Unsurprisingly

Turns Into A Noose


The fatal consequences this option presents DM-theorists become apparent when we attempt to unravel what it means for a force to be 'prevented' from operating.


Despite disclaimers, it seems that if a force no longer operates, it no longer exists. Perhaps the problem lies not so much with the precise physical form that forces take (which, even to this day, is still mysterious; on that, see Interlude One), but with the fact that the word "operate" is ambiguous. Consider the following examples of forces that are capable of being rendered inoperative:


F22: The electromagnetic force ceased to operate when worker NN threw the switch.


F23: An aerofoil produces the lift necessary to keep an aeroplane in the air provided that there is sufficient relative velocity between that aerofoil and the ambient medium to prevent the force of gravity from operating normally, pulling the aircraft to the ground.


[In order to avoid unnecessary complexity, I have left F23 in a more colloquial form -- for instance, by my use of "pulling".]


In F22, the relevant force simply ceased to exist (or it was converted (or reverted) back into another force, 'potential' force, or some form of energy, etc.) when the switch was thrown. But, in F23, a second force (lift) 'opposes' the effects of the first force (gravity) -- which, of course, still exists (perhaps as part of the resultant force in the system).


Can F21 now be interpreted along lines similar to those suggested in F23? This way of viewing the relation between P1 and P2 would see them both as still existing, even while they counterbalance each other. In which case, it might prove helpful to re-write F21 in the following manner:


F24: P1 contradicts P2 only if it counterbalances P2.53


[F21: P1 contradicts P2 in so far as it prevents P2 acting, and/or vice versa.]


Now, F24 doesn't appear to face any of the existential problems that F21 encountered since the relevant forces co-exist, counterbalancing each other. Perhaps then we have here the clear statement that DM-theorists require?


Alas not.


A new difficulty arises just as soon as we ask why only counterbalancing forces should be considered 'contradictory'. This is relevant since F24 simply restricts our attention to situations where there is an equilibrium between forces, and ignores dis-equilibria.54 But surely, it is largely as a result of the latter that change occurs (certainly changes of the sort that interest dialecticians) -- meaning that 'contradictions' should be connected with dis-equilibria, rather than equilibria. If so, F24 must be re-written in the following way:


F25: P1 contradicts P2 whether it counterbalances P2 or not.


Unfortunately, F25 can't now provide the clarity that was missing from previous attempts to illuminate this part of DM. That is because F25 fails to distinguish between equilibria and dis-equilibria. F24 seemed to express a clear definition of 'contradictory' forces, but in order to make it applicable to the real world, F25 had to be recruited in support, completely undermining F24. F25 informs us that forces are 'contradictory' whether or not F24 is true. Worse still, F25 could be true even when F24 is false:


F24: P1 contradicts P2 only if it counterbalances P2.


F25: P1 contradicts P2 whether it counterbalances P2 or not.


Hence, if the following were true, F24 would be false:


F26: P1 contradicts P2 even though it doesn't counterbalance P2.


Now, anyone reading these three sentences (and taking them for an accurate exposition of this area of DM) would rightly complain that nothing had actually been explained, since there is nothing about the relationship between the forces mentioned that indicates what the overall theory is committed to.


In response, others could argue that this latest problem is not only spurious, it is solely the result of a use of the phrase "only if" in F24. Its removal should eliminate the difficulty.


Unfortunately, the removal of the "only if" in F24 would plunge the theory back into all the existential problems it had been introduced to eradicate. This can be seen if we try to re-word F24 in the following manner:


F27: P1 contradicts P2 if it counterbalances P2.


Although F27 might look acceptable, it is merely a sufficient condition; hence, it does not rule out the following:


F28: P1 contradicts P2 in so far as it prevents P2 acting, and/or vice versa.54a


[F21: P1 contradicts P2 in so far as it prevents P2 acting, and/or vice versa.]


[F22: The electromagnetic force ceased to operate when worker NN threw the switch.]


But, F28 is just a resurrected version of F21, which we found didn't rule out F22, and thus non-existent forces. What was required here instead was a description of 'contradictory' forces that doesn't imply that one of the forces operating ceased to exist as a result of the action of any other force in the system. Furthermore, we also required an account that doesn't rely on forces merely 'contradicting' the effects of other forces -- because of the serious difficulties that that particular alternative encountered earlier.


That is why an appeal had to be made to forces that counterbalance one another, since (clearly) they must exist to do this -- hence, the "only if" had to be introduced, making this a necessary condition. But, as we discovered, this more restrictive version ruled out forces that didn't counterbalance one another, which DM seems to need; reintroducing these at a later stage simply ruined this neat picture.


Unfortunately, F24 and F26 seem to divorce 'contradictions' from equilibria, since the presence or absence of the latter is in no way affected by the former.


F24: P1 contradicts P2 only if it counterbalances P2.


F26: P1 contradicts P2 even though it does not counterbalance P2.


This means that if F24 and F26 reflect the real nature of things, then 'contradictions' are in fact unrelated to the balancing effects of forces. As paradoxical as this might seem, DM-theorists should deny the truth of the conjunction of F24 and F26 if they want to maintain their belief that there is some sort of a connection between forces, 'contradictions', equilibria and disequilibria in nature and society. Alas, in order to account for the 'contradictory' nature of reality, DM-theorists can't actually afford to do this. For, as soon as F24 and F26 are adopted, DM ceases to be explanatory; but the minute these two are rejected, this attempt to render comprehensible the nature of DM-forces collapses.


Nevertheless, that annoying conclusion might appear to some to be a little too hasty and contrived. And yet, with so little in the writings of DM-theorists to guide us, how is it possible for anyone to decide whether or not the above attempt to understand DM is misleading or prejudicial? Indeed, how could dialecticians themselves arrive at a clear decision on this score without some form of theoretical innovation, an option that has so far been complete anathema to the 'Orthodox' DM-community, who are only too happy to wave the 'Revisionism' (or even the 'pedantry') card at anyone who has the temerity to try to 'think outside the box' on this and other 'difficulties' this theory faces?


Nevertheless, if we adhere to the requirement that 'contradictions' are capable of explaining change -- when pictured as opposing forces (that is, if we give 'contradictions' some sort of physical bite) --, then this theory must self-destruct by the above argument. That is because the theory maintains that forces are 'contradictory' whether what its theorists claim about them is true or not -- if that is, indeed, what DM-theorists claim or what this theory actually implies.


Naturally, all this is independent of the far more fundamental question whether the theory that 'contradictory' forces are capable of counterbalancing each other can itself be explained without referring to the sort of 'prevented', or 'non-existent', effects we met earlier. If it can't, this latest detour would prove to be just another dead end, since 'prevented' effects don't exist to be contradicted. On the other hand, if this theory can be explained without referring to such effects, then it would be difficult to decide what impact it could possibly have on the real world. How could such forces be described as "material" if they have no effect on anything material --, except, perhaps, on those seemingly insubstantial 'non-existent' effects?


Of course, all this is independent of the fatal defect mentioned earlier; that these forces and effects do not imply one another (unlike the proletariat and the bourgeoisie), so they can't be 'dialectical contradictions', whatever else they are. For example, gravity doesn't imply the existence of the lift created by a wing (or anything else that can provide it). Gravity existed for billions of years, and wings for maybe a couple of hundred million (in winged insects, or plants that use the air to spread seeds, etc., flying dinosaurs and birds). Of course, if there were no gravity, then such things wouldn't have evolved, but then again, if there were no gravity, there would be no universe. Clearly, gravity can exist without such flying devices, so the relation between the force provided by a wing and gravity can't be 'dialectical'. Even if they were 'opposite' in some-as-yet-unspecified way, they don't 'interpenetrate' each other, and can't be 'dialectical'.


Well, this is another dialectical hole out of which DM-fans can dig themselves. I am merely content to remind them that it is a hole, it is very deep, and it is one they have dug for themselves.



Figure Eight: DM-Fan Ignores Sound Advice


Yet More S&M?


Maybe even this is being a little too hasty. Perhaps we should begin again.


To that end, it might help if we re-examined a passage from Cornforth's book, quoted in Part One of this Essay:


"The unity of opposites in a contradiction is characterised by a definite relation of superiority-inferiority, or of domination, between the opposites. For example, in a physical unity of attraction and repulsion, certain elements of attraction or repulsion may be dominant in relation to others. The unity is such that one side dominates the other -- or, in certain cases, they may be equal.


"Any qualitative state of a process corresponds to a definite relation of domination. Thus, the solid, liquid and gaseous states of bodies correspond to different domination-relationships in the unity of attraction and repulsion characteristic of the molecules of bodies.... Domination relationships are obviously, by their very nature, impermanent and apt to change, even though in some cases they remain unchanged for a long time. If the relationship takes the form of equality or balance, such balance is by nature unstable, for their is a struggle of opposites within it which is apt to lead to the domination of one over the other....


"The outcome of the working out of contradictions is, then, a change in the domination relation characteristic of the initial unity of opposites. Such a change constitutes a change in the nature of a thing, a change from one state to another, a change from one thing to another, a change entailing not merely some external alteration but a change in the internal character and laws of motion of a thing." [Cornforth (1976), pp.97-98. Some paragraphs merged.]


[This is in fact a differently worded version of Weston's argument, where forces/"tendencies" 'interfere' to a greater or lesser extent with one another -- Weston (2012). I have examined Weston's alternative elsewhere in this Essay.]


Now, the above argument might appear to work when applied to human social systems, where agents (individually or in groups) are capable of 'upsetting' any number of 'balanced' configurations, and who don't need too much in the way of external motivation to do that (although, in order for Cornforth to be able to say even that much with any clarity, he found he had no use for the obscure words Hegel employed). However, when this theory is applied to nature as a whole, it can't work. Consider, therefore, the following:


F29: Let FD be a set of force 'elements' in a 'dominant' relation to FS, which is a 'submissive' set of forces (i.e.,  FD > FS), and let both operate in system, S, however that is defined or characterised.


F30: For this relation to change so that a qualitative transformation occurs in the overall system, S, one or both of FD and FS will have to change first.


F31: If the change occurs in FD it will have to do so because of the latter's own 'internal contradictions', otherwise the theory must fail at the first hurdle. [The same applies to FS, or, indeed, to both taken severally or collectively.]


F32: But, if that is so, then the same analysis will now apply one more level down, as it were: whatever causes FD to change will have to be the result of further dominance/submissive relations inside, or internal to, FD itself. In turn, the pre-conditions noted in F31 will also apply at, or to, these 'lower level' relations; they must change because of their own 'internal contradictions'.


F33: Either this continues forever, or it will halt at some point.


F34: If it halts at some point, then there must be fundamental units that don't change because of their 'internal contradictions', and the theory will fail at this point. [In fact, these fundamental units can have no effect on each other for reasons set-out in detail in Part One of this Essay.]


F35: If this process continues forever, then there would be nothing to condition anything internal to anything else, just more and more layers, tailing off to infinity (i.e., to "who knows where?"). DM would thus have its own "bad infinity". [We saw that this was a non-viable alternative, anyway, in Part One, as well as here.]


F36: All this is independent of whether or not an external cause (or causes) initiated these internal changes in FD or FS. While the latter may be influenced by external causes (according to Cornforth), external causes can't bring about the internal, qualitative changes required (again, according to Cornforth). The latter must be internally-generated in the last analysis.


It looks, therefore, like this 'theory' can't be rescued if this line is adopted.


Hole To Let -- Previous Occupant Self-Destructed


Howsoever we try, there seems to be no way of rescuing this self-destructing theory -- killed-off by its own internal obscurities.


In short: if a force prevents something from happening, that force can't contradict it; once prevented, the latter doesn't exist. Moreover, when an effect of that force has been prevented, it can't contradict any other effect that hasn't existed.55


Interlude Nine: Objections Neutralised


However, some may still object and claim that if a force prevents something coming into being, or happening, it must have contradicted it.


Let us say, therefore, that:


Ω1: If event, Ei, at time, t, belonging to process, Δ (normally comprising sub-events, E1-En), is prevented from becoming Ei+1, at t+1 by force, P, then Ei will have been contradicted by P. [t+1 > t]


[Here, "event" can be interpreted as widely, or as narrowly, as is required so that it is compatible with plausible/acceptable 'dialectical' theories of "causation", or of "mediations", and their effects. I have had to use Greek letters "Ω" and "Δ" here since I have run out of viable Latin capital letter options I haven't already employed! I originally used the letter "T" (now replaced by "Ω"), but decided that it might be confused with the "T"s I have also used to stand for time and for the "Totality".]


Hence, it could be argued that in this sense it is clear that forces prevent the effects of other forces from being realised by contradicting certain events, stopping them from occurring.


But, even then, forces still fail to 'contradict' one another as force-on-force, they merely prevent the events, or effects, induced by other forces from happening. So, this alternative can't help us understand how forces actually 'contradict' each other.


Nevertheless, we need to examine this objection a little more closely so that every conceivable possibility has been explored.


Consider then the following:


Ω2: Let there be an event set, E, consisting of sub-events, E1-En, which would all take place, or would all have taken place, had force, P, not stopped things at the Ei-th stage.


Ω3: Had these events proceeded as 'normal', Ei would have been followed by Ei+1, but as things turned out, Ei+1 failed to occur because P prevented it.


Ω4: Hence, P contradicted Ei+1.


However, since Ei+1 never existed or occurred, it can't have been 'contradicted' by P -- unless, once more, we assume that a force can 'contradict' non-existent objects, events or processes. Moreover, since P didn't prevent Ei itself, it can't have 'contradicted' it, either.


And, as we have seen several times, P and Ei+1 don't imply one another and both can (and do) exist without one another (indeed, as we have just seen). Hence, whatever else it is, this can't be a 'dialectical relation/contradiction'.


We hit the same brick wall once again.


Consider now this variant on Ω3:


Ω5: P contradicted Ei by stopping it producing Ei+1.


But, this is no good either. That is because events aren't like eggs that produce other egg producers (i.e., chickens!). If so, events themselves can hardly be prevented from producing other events if they don't produce them in the first place.


In that case, perhaps the following revision will do:


Ω6: P contradicted Ei by stopping Ei+1 following on from Ei.


But, again, the alleged 'contradiction' amounts to the prevention of something that doesn't now exist (and never did). If forces can only 'contradict' something by preventing or stopping non-existent objects, process, or events from taking place, then all the above objections still have their place.


It could be argued that if the chain of events above is replaced by a series of causes and their effects, the contradiction will become clear -- perhaps along the following lines:


Ω7: Let there be an event set, E, consisting of sub-events, E1-En, which would all take place, or would all have taken place, had force, P, not stopped things at the Ei-th stage.


Ω8: In the 'normal course of events', let each event, Ei, cause the next event, Ei+1.


Ω9: However, Ei+1 failed to occur because P prevented Ei causing it.


Ω10: Hence, P contradicted Ei.


This looks more promising, but there remain several problems with it:


(i) Once again, if this were so, then DM-fans will have to drop their claim that forces contradict each other;


(ii) Force, P, and event, Ei, aren't 'internally related' -- how can a force be 'internally related' to an event? So, to repeat, whatever else this is, it can't be a 'dialectical contradiction' (we saw something similar to this obstruct Weston's attempt to recruit Marx to this mystical view of nature, just as we have seen it neutralise other, alternative rescue attempts);


(iii) Even if it were a legitimate example of a 'dialectical contradiction', P and event, Ei, would have to turn into one another, if the DM-classics are to be believed.


Consider, therefore, a more concrete example: Imagine a fire that had been started in a forest by a match inadvertently dropped on some tinder dry grass. All things being equal, the resulting and growing conflagration will be maintained by the following factors, at least: (a) The organic material in the grass, (b) The energy released by this fire, and (c) The oxygen in the surrounding air. Imagine further that someone hits the burning grass with a fire broom before the conflagration has a chance to grow, putting it out. Plainly the force of the blow from the broom deprived the nascent conflagration of enough oxygen to keep it going and so quelled the blaze. In that case, one cause (the supply of oxygen) was prevented by the force of the broom from further causing a series of damaging events or effects. But, does the blow from the broom turn into the oxygen? Or, into the organic material comprising this tinder dry grass? What if that fire were extinguished by a rain storm? Would such a fire turn into a rain storm? And yet it ought to do all of these if the DM-classics are to be believed.


[Anyone interested can read the doomed attempts of one comrade to defend the DM-theory of change in the face of objections like this, here.]


However, the biggest problem with the above DM-volunteered response lies in the dearth of details, and the difficulty of filling them in on behalf of DM-fans who don't seem to be too bothered to do so!


Consider a different example: a match used to light a trail of gunpowder. The match sets off a series of chemical reactions that pass along that trail, each of which causes the next reaction in line. Call this series of events, or causes, C1-Cn. Let us further imagine that some force (say, a violent thunder storm, S, which either blows the trail of gunpowder away, or which drenches it in a downpour) stops this series at the Ci-th stage, preventing the next cause/event, Ci+1, from happening. In that case, should we not say that S contradicted Ci?


However, problems (i)-(iii) above still apply in this case (as they also do in relation to the forest fire example considered earlier, when the details are filled in) -- which would involve, for example, a thunder storm turning into a chemical reaction in the gunpowder, and vice versa, if the DM-classics are to be believed!


In fact, the idea that causes necessitate their effects (whether or not the latter are themselves causes in their own right), upon which the above depends, is itself predicated upon an anthropomorphic view of nature. Since I have considered this topic in more detail in Essay Thirteen Part Three, I will say no more about it here.


Exactly why this view of causation depends on necessitation is connected with the points raised in Essay Seven Part Three (concerning Kant and Hegel's response to Hume's criticisms of rationalist theories of causation). There, it was demonstrated that in order to defuse Hume's attack, Hegel had to find a dialectical-logical, and therefore necessary, link between a cause and its effects:


Hume had argued that there is no logical or conceptual connection between cause and effect. This struck right at the heart of Rationalism, and Hegel was keen to show that Hume and the Empiricists were radically mistaken. Kant had already attempted to answer Hume, but his solution pushed necessitating causation off into the Noumenon, about which we can know nothing. That approach was totally unacceptable to Hegel, so he looked for a logical connection between cause and effect; he found it in (1) Spinoza's claim that determination is also negation (which, Hegel rendered "Every determination is negation" -- by the way, neither Spinoza nor Hegel even so much as attempted to justify this 'principle' -- more about that in Essay Twelve; on this, see Melamed (2015)), and in (2) His argument that the LOI "stated negatively" implies the LOC (which, unfortunately for Hegel, it doesn't).


[LOI = Law of Identity; LOC = Law of Non-contradiction.]


Based on this, Hegel was 'able' to argue that for any concept A, "determinate negation" implies it is also not-A, and then not-not-A. [I am, of course, simplifying greatly here! I have reproduced Hegel's argument below for those who think I might have misrepresented him.]

This then 'allowed' Hegel to conclude that every concept has development built into it as A transforms into not-A, and then into not-not-A. This move provided him with the logical/conceptual link he sought in causation. Hence, when A changes it doesn't just do so accidentally into this or that; what it changes into is not-A, which is logically connected with A and is thus a rational consequence of the overall development of reality. This led him to postulate that for every concept A, there must also be its paired "other" (as he called it), not-A, its 'internal' and hence its unique 'opposite'. Hegel was forced to derive this consequence since, plainly, everything (else) in the universe is also not-A, which would mean that A could change into anything whatsoever if he hadn't introduced this limiting factor, this unique "other".


From these moves was born the "unity of opposites". So, the link between cause and effect was now given by a 'logical' unity, and causation and change were the result of the interaction between these logically-linked "opposites".


Plainly, this paired, unique opposite, not-A, was essential to Hegel's theory, otherwise, he could provide his readers with no explanation why A should be followed by a unique not-A as opposed to just any old not-A -- say, B, or, indeed, something else, C, for example -- all of which would also be not-A.


So, since B and C (and an indefinite number of other objects and processes) are all manifestly not-A, Hegel had to find some way of eliminating these, and all the rest, as candidates for the development of A, otherwise he would have had no effective answer to Hume.


[Hume, of course, wouldn't have denied that A changes into "what it is not", into not-A, he would merely have pointed out that this can't provide the conceptual link that rationalists require unless all the other (potentially infinite) not-As could be ruled out in some way. He concluded that it is only a habit of the mind that prompts us to expect A to change into what we have always, or what we have in general, experienced before. There is no logical link, however, between A and what it develops into since there is no contradiction in supposing A to change into B or C, or, indeed, something else. (In saying this the reader shouldn't conclude that I agree with Hume, or that Hume's reply is successful!)]


Hence, as an integral part of his reply, Hegel introduced this unique "other" with which each object and process was conceptually linked -- a unique "other" that was 'internally' connected to A --, something he claimed could be derived by 'determinate negation' from A.


[How he in fact derived this "other" will be examined in Essay Twelve Part Five, but a DM-'explanation' -- and my criticism of it -- can be found in Essay Eight Part Three.]


This special not-A was now the unique "other" of A. Without it Hegel's reply to Hume falls flat.


Engels, Lenin, Mao, and Plekhanov (and a host of other Marxist dialecticians) bought into this spurious 'logic' (several of them possibly unaware of the above 'rationale'; although, as far as I can see, of the DM-classicists, only Lenin seems to be explicitly aware of it!), and attempted to give it a 'materialist make-over'. And, that is why this Hegelian theory (albeit "put back on its feet") is integral to classical DM. It supplied Engels, Lenin and Mao (and all the rest) with a materialist answer to Hume.


[There are in fact far better ways than this to neutralise Hume's criticisms, as well as those of more recent Humeans, which do not thereby make change impossible. More details will be given in Essay Three Part Five. Until then, the reader is directed to Hacker (2007), and Essay Thirteen Part Three.]


Here is Lenin's open acknowledgement and endorsement of this theory:


"'This harmony is precisely absolute Becoming change, -- not becoming other, now this and then another. The essential thing is that each different thing [tone], each particular, is different from another, not abstractly so from any other, but from its other. Each particular only is, insofar as its other is implicitly contained in its Notion....' Quite right and important: the 'other' as its other, development into its opposite." [Lenin (1961), p.260. Lenin is here commenting on Hegel (1995a), pp.278-98; this particular quotation coming from p.285. Bold emphasis added; quotation marks altered to conform with the conventions adopted at this site.]


"But the Other is essentially not the empty negative or Nothing which is commonly taken as the result of dialectics, it is the Other of the first, the negative of the immediate; it is thus determined as mediated, -- and altogether contains the determination of the first. The first is thus essentially contained and preserved in the Other. -- To hold fast the positive in its negative, and the content of the presupposition in the result, is the most important part of rational cognition; also only the simplest reflection is needed to furnish conviction of the absolute truth and necessity of this requirement, while with regard to the examples of proofs, the whole of Logic consists of these." [Lenin (1961), p.225, quoting Hegel (1999), pp.833-34, §1795. Emphases in the original.]


Lenin wrote in the margin:


"This is very important for understanding dialectics." [Lenin (1961), p.225.]


To which he added:


"Marxists criticised (at the beginning of the twentieth century) the Kantians and Humists [Humeans -- RL] more in the manner of Feuerbach (and Büchner) than of Hegel." [Ibid., p.179.]


This shows that Lenin understood this to be a reply to Hume, and that it was integral to comprehending dialectics.


It is worth quoting the entire passage from Hegel's Logic (much of which Lenin approvingly copied into the above Notebooks -- pp.225-28):


"Now this is the very standpoint indicated above from which a universal first, considered in and for itself, shows itself to be the other of itself. Taken quite generally, this determination can be taken to mean that what is at first immediate now appears as mediated, related to an other, or that the universal appears as a particular. Hence the second term that has thereby come into being is the negative of the first, and if we anticipate the subsequent progress, the first negative. The immediate, from this negative side, has been extinguished in the other, but the other is essentially not the empty negative, the nothing, that is taken to be the usual result of dialectic; rather is it the other of the first, the negative of the immediate; it is therefore determined as the mediated -- contains in general the determination of the first within itself. Consequently the first is essentially preserved and retained even in the other. To hold fast to the positive in its negative, in the content of the presupposition, in the result, this is the most important feature in rational cognition; at the same time only the simplest reflection is needed to convince one of the absolute truth and necessity of this requirement and so far as examples of the proof of this are concerned, the whole of logic consists of such.


"Accordingly, what we now have before us is the mediated, which to begin with, or, if it is likewise taken immediately, is also a simple determination; for as the first has been extinguished in it, only the second is present. Now since the first also is contained in the second, and the latter is the truth of the former, this unity can be expressed as a proposition in which the immediate is put as subject, and the mediated as its predicate; for example, the finite is infinite, one is many, the individual is the universal. However, the inadequate form of such propositions is at once obvious. In treating of the judgment it has been shown that its form in general, and most of all the immediate form of the positive judgment, is incapable of holding within its grasp speculative determinations and truth. The direct supplement to it, the negative judgment, would at least have to be added as well. In the judgment the first, as subject, has the illusory show of a self-dependent subsistence, whereas it is sublated in its predicate as in its other; this negation is indeed contained in the content of the above propositions, but their positive form contradicts the content; consequently what is contained in them is not posited -- which would be precisely the purpose of employing a proposition.


"The second determination, the negative or mediated, is at the same time also the mediating determination. It may be taken in the first instance as a simple determination, but in its truth it is a relation or relationship; for it is the negative, but the negative of the positive, and includes the positive within itself. It is therefore the other, but not the other of something to which it is indifferent -- in that case it would not be an other, nor a relation or relationship -- rather it is the other in its own self, the other of an other; therefore it includes its own other within it and is consequently as contradiction, the posited dialectic of itself. Because the first or the immediate is implicitly the Notion, and consequently is also only implicitly the negative, the dialectical moment with it consists in positing in it the difference that it implicitly contains. The second, on the contrary, is itself the determinate moment, the difference or relationship; therefore with it the dialectical moment consists in positing the unity that is contained in it. If then the negative, the determinate, relationship, judgment, and all the determinations falling under this second moment do not at once appear on their own account as contradiction and as dialectical, this is solely the fault of a thinking that does not bring its thoughts together. For the material, the opposed determinations in one relation, is already posited and at hand for thought. But formal thinking makes identity its law, and allows the contradictory content before it to sink into the sphere of ordinary conception, into space and time, in which the contradictories are held asunder in juxtaposition and temporal succession and so come before consciousness without reciprocal contact. On this point, formal thinking lays down for its principle that contradiction is unthinkable; but as a matter of fact the thinking of contradiction is the essential moment of the Notion. Formal thinking does in fact think contradiction, only it at once looks away from it, and in saying that it is unthinkable it merely passes over from it into abstract negation." [Hegel (1999), pp.833-35, §§1795-1798. Bold emphases alone added. I have used the on-line version here, correcting a few minor typos.]


The most relevant and important part of which is this:


"It is therefore the other, but not the other of something to which it is indifferent -- in that case it would not be an other, nor a relation or relationship -- rather it is the other in its own self, the other of an other; therefore it includes its own other within it and is consequently as contradiction, the posited dialectic of itself." [Ibid. Bold emphases alone added.]


This "reflection", as Hegel elsewhere calls it, of the "other in its own self", a unique "other", provides the logical link his theory required. Any other "other" would be "indifferent", and not the logical reflection he sought. It is from this that 'dialectical contradictions' arise, as Hegel notes. Hence, Lenin was absolutely right, this "other" is essential for "understanding" dialectics -- except he forgot to mention that dialectics is in fact rendered incomprehensible and unworkable as a result!


Hegel underlined this point (but perhaps less obscurely) in the Shorter Logic:


"Instead of speaking by the maxim of Excluded Middle (which is the maxim of abstract understanding) we should rather say: Everything is opposite. Neither in heaven nor in Earth, neither in the world of mind nor of nature, is there anywhere such an abstract 'either-or' as the understanding maintains. Whatever exists is concrete, with difference and opposition in itself. The finitude of things will then lie in the want of correspondence between their immediate being, and what they essentially are. Thus, in inorganic nature, the acid is implicitly at the same time the base: in other words, its only being consists in its relation to its other. Hence also the acid is not something that persists quietly in the contrast: it is always in effort to realise what it potentially is." [Hegel (1975), p.174; Essence as Ground of Existence, §119. Bold emphases added.]


[The problems these rather odd ideas in fact create for Hegel have been highlighted here.]


Hence, any attempt to (1) Eliminate the idea that change results from a 'struggle of opposites', or (2) Deny that objects and processes change into these 'opposites', or even (3) Reject the idea that these 'opposites' are 'internally'-related as one "other" to another specific "other", will leave DM-fans with no answer to Hume, and thus with no viable theory of change.


[For Hegel's comments on Hume, see Hegel (1995b), pp.369-75.]


In which case, Hegel's theory (coupled with the part-whole dialectic) was at least a theory of causation, change and of the supposed logical development of history; so the above dialecticians were absolutely right (as they saw things) to incorporate it into DM. It allowed them to argue that, among other things, history isn't accidental -- i.e., it isn't just 'one thing after another' -- it has an inner logic to it. Hence, Hegel's 'logical' theory enabled them to argue, for example, that capitalism must give way to the dictatorship of the proletariat, and to nothing else. Hume's criticisms -- or, rather, more recent incarnations of them (which, combined with contemporary versions of Adam Smith's economic theory (Smith was, of course, a close friend and collaborator of Hume's) in essence feature in much of modern economic theory and large swathes of contemporary philosophy, and thus in criticisms of Marx's economic and political theory) -- are a direct threat to this idea. If these bourgeois critics are right, we can't predict what the class struggle will produce. Or, rather, if Hume is right, the course of history is contingent, not necessary, not "rational" -- and there is no 'inner logic' to capitalism.


[This dependency on Hegel's theory of causation and change also supplies us with an explanation for the implicit teleology and determinism apparent in DM, providing its acolytes with hope in a hopeless world. More on this in Essays Nine Part Two and Fourteen Part Two. The mystical and rationalist foundations of this approach to change are outlined here, here, here and here.]


As far as I can tell, other than Lenin, very few dialecticians have discussed (or have even noticed!) this aspect of their own theory. The only authors that I am aware of who take this aspect of DM into consideration are Ruben (1979), Lawler (1982), and Fisk (1973, 1979). I will examine Fisk's arguments, which are the most sophisticated I have so far seen (on this topic), in other Essays published at this site. Lawler's analysis is the subject of Essay Eight Part Three. [However, since writing this I have also come across some of Charles Bettelheim's comments that suggest he, too, understood this point.]


Incidentally, this puts paid to the idea that there can be such things as 'external contradictions' (a notion beloved of STDs and MISTs). If there were any of these oddities, they couldn't be 'logically' connected as 'one-other-linked-with-another-unique-other' required by Hegel's theory. For Hegel, upside down or the 'right way up', this would fragment the rational order of reality, introducing contingency where once there had been 'logico-conceptual' or 'necessary' development. Hence, any DM-fan reckless enough to introduce 'external contradictions' into his or her system/theory would in effect be 're-Hume-ing' Hegel, not putting him 'back on his feet'! In which case, it is no surprise to find that 'external contradictions' were unknown to Hegel, Marx, Engels, Lenin and Plekhanov.


[STD = Stalinist Dialectician; MIST = Maoist Dialectician.]


[I have analysed several other fatal defects implicit in the idea that there can be 'external' and/or 'internal contradictions' (in nature or society) in Essay Eleven Part Two, here and here. See also here, where I develop the above argument in response to a 'Marxist-Leninist' who seems not to know his own theory.]


Nevertheless, as we have seen, it is precisely this which makes the entire theory unworkable, as points (i)-(iii) above have shown.


How this is connected with my reply to the earlier proffered response will now be explained. Here is that response again:


Ω7: Let there be an event set, E, consisting of sub-events, E1-En, which would all take place, or would all have taken place, had force, P, not stopped things at the Ei-th stage.


Ω8: In the 'normal course of events', let each event, Ei, cause the next event, Ei+1.


Ω9: However, Ei+1 failed to occur because P prevented Ei causing it.


Ω10: Hence, P contradicted Ei.


The first point worth making is that for this to be a 'dialectical contradiction', P and Ei must be "internally-connected opposites"; indeed, P must be the "other" of Ei. But, P and Ei are of logically different categories, so they can't be "internally-related opposites". In which case, the above response falls at the first hurdle! Moreover, P and Ei don't imply one another (and each can exist without the other, unlike the proletariat and the bourgeoisie, so we are told), in which case, they can't be 'dialectical opposites', to begin with.


[That depends, of course, on what dialecticians mean by "internally-related opposite" -- but we have already seen they oscillate erratically between a spatial and a logical interpretation of that notion.]


Moreover, as we witnessed in detail here, if, in the normal course of things, Ei is to cause, or to change into, Ei+1, these two must also be opposites (which means that P can't be the 'dialectical opposite' of either of them, after all!), and they must 'struggle' with each (i.e., Ei must struggle with Ei+1 ), if the DM-classics are to be believed. But, they can't struggle with one another since Ei+1 doesn't exist yet! [Unless, of course, we suppose it exists before it exists!]


On the other hand, if Ei+1 already exists, so that Ei can 'struggle' with it, and thus cause, or change into, Ei+1, Ei can't in fact do that since Ei+1 already exists! In which case, Ei would no longer be the cause of Ei+1, and so P couldn't have prevented it from causing Ei+1, meaning, clearly, that this supposed contradiction simply vanishes! The same applies to the supposed relation between S and Ci mentioned earlier.  


Either way, if DM were 'true', change here would be impossible.


Of course, there is an obvious clause missing from Ω7-Ω10 above -- namely, Ω11:


Ω7: Let there be an event set, E, consisting of sub-events, E1-En, which would all take place, or would all have taken place, had force, P, not stopped things at the Ei-th stage.


Ω8: In the 'normal course of events', let each event, Ei, cause the next event, Ei+1.


Ω9: However, Ei+1 failed to occur because P prevented Ei causing it.


Ω10: Hence, P contradicted Ei.


Ω11: Instead of Ei+1 following Ei, because of the operation of P, Ei was followed by alternative event set, W, comprised of sub-events, W1-Wn.


Ω11 must be the case otherwise, at the Ei-th stage we would have to suppose that Ei was no longer part of the 'causal structure of the world', and hence ceases to have an effect on anything around it.


Consider again the concrete scenario examined earlier:


Imagine a fire that had been started in a forest by a match inadvertently dropped on some tinder dry grass. All things being equal, the resulting and growing conflagration will be maintained by the following factors, at least: (a) The organic material in the grass, (b) The energy released by this fire, and (c) The oxygen in the surrounding air. Imagine further that someone hits the burning grass with a fire broom before the conflagration has a chance to grow, putting it out. Plainly the force of the blow from the broom deprived the nascent conflagration of enough oxygen to keep it going and so quelled the blaze. In that case, one cause (the supply of oxygen) was prevented by the force of the broom from further causing a series of damaging events or effects.


No one supposes that if this fire is put out, the grass that was burning, and is now out, disappears from the world or ceases to have a causal effect on anything else ever again. It, too, will initiate or take part in another series of events, depicted schematically perhaps by Ω11:


Ω11: Instead of Ei+1 following Ei, because of the operation of P, Ei was followed by alternative event set, W, comprised of sub-events, W1-Wn.


But, if that is so, Ei will now be the dialectical opposite of W1, its new 'unique other' (since, as we have seen, dialectical objects/processes turn into their opposites, into that with which they have 'struggled', their 'unique other'), which would mean that Ei's earlier 'unique other' -- Ei+1 -- will have been deposed, making a mockery of Hegel's argument that each object or process has a 'unique other'.


[But we have already shown that this entire theory is a defective, anyway.]


Even so, what hasn't yet been made clear is how this is connected with my reply to the proffered response outlined earlier. Given the fact that causes, E1-En, aren't accidentally linked in the DM-scheme-of-things, but are connected by a 'necessary law' (or 'law of necessity') of some sort, Ei itself isn't just plain-and-simple-Ei. In fact, in DM, each one of causes, E1-En, is identified by what it is not -- its 'other'. [This was the whole point of "determinate negation" in Hegel's theory, as we saw above.]


[NON = Negation of the Negation.]


So, Ei isn't just Ei, it is also not-Ei (since, by 'determinate negation', Ei is 'identical' with what it is not -- why that is so is explained here, but more concisely here), which is also Ei+1. That is, Ei+1 is also not-Ei, its Hegelian 'other'. But, by the NON, Ei is also not-not-Ei -- and hence Ei is not-itself, and thus not-itself by 'reflection' -- this is in fact what supposedly causes Ei to develop, according to Hegel -- the lack of identity between itself and its 'concept'. This is 'reflected' in what it subsequently becomes -- Ei+1.


This means that Ei is identical with Ei+1 in an identity-in-difference sort of way, and this is what links these two together, 'logically', in an Hegelian sort of way. So, Ei is not now just Ei, it is Ei-that-causes-Ei+1 (except, perhaps, this needs translating back into something a little more Hegelian -- maybe along these lines).


These 'dialectical' moves now provide the necessary link between a cause and its effect(s) in Hegel's scheme of things -- or between a cause and whatever comes next in this (necessary) causal sequence, or chain. Since Hegel imagined he had 'proved' this 'logically', he clearly didn't feel it needed any confirmation from experience or supporting evidence. So, even if it isn't possible to observe these 'necessary' links -- how could they be observed? -- they nevertheless must exist (if we are prepared to buy into this Idealist fantasy).


Denial of this is what provides superficial plausibility to Hume's attack on rationalist theories of causation --, this theory nevertheless tells us these 'necessary' links are there since Hegel had presumably shown they exist of necessity -- a perfect, a priori 'answer' to Hume (and, indeed, Kant).


And that is why P 'contradicts' Ei: P isn't now just affecting Ei, it is changing it from Ei-that-causes-Ei+1 into Ei-that-causes-W1 (or, indeed, Ei-that-doesn't-cause-Ei+1):


Ω11: Instead of Ei+1 following Ei, because of the operation of P, Ei was followed by alternative event set, W, comprised of sub-events, W1-Wn.


So, the following now seems correct:


Ω12: It isn't the case that it is Ei-that-causes-Ei+1,


which is, of course, the contradictory of:


Ω13: It is the case that it is Ei-that-causes-Ei+1.


[I am well aware that this is unsatisfactory as it stands, since P can't 'contradict' Ei by altering it in the above manner, but this is the only way I can make sense of the idea that P could conceivably 'contradict' Ei. If anyone can make clearer sense of it in any other way, please enlighten me.]


But, if there are no necessary links here (and we have seen why there can't be any -- in Essays Seven Part Three and Twelve Part One), then P can't affect Ei in this way, since, in that eventuality, it isn't the case that it is Ei-that-causes-Ei+1. And that is because there is no such defining condition for Ei, and hence no such thing as is represented by Ei-that-causes-Ei+1, to begin with, as we have just seen.


In short, because of the incoherencies of 'determinate negation', this entire way of viewing 'contradictions' falls apart.


[But, the real problems lie much deeper than even this, as we will see in a later Essay.]


Of course, in an Ideal 'Hegelian Universe' this 'theory' might be made to work somehow. However, I will pass no comment on that bare possibility here; but, as we will see in Essay Twelve Parts Five and Six, this 'theory' in the end collapses faster than a portfolio of Enron shares.


However, in the real world, where we are told that change results from a 'struggle' between opposites, and where everything supposedly changes into its opposite, this theory can't work, as indeed we have seen.


In which case, P can't 'contradict' anything at all.


At this point, it could be objected that this entire approach to 'events' and 'forces' is totally misguided since it atomises them, putting them in rigid categories, compartmentalising and thus fragmenting the flowing nature of reality. In contrast, dialectics deals with the unified, fluid and organic nature of the world, which means it depicts interactions like those above in a totally different, albeit contradictory, light. Hence, the analysis in this Essay is completely misguided.


Or, so it might be maintained.


Unless and until DM-apologists tell us with some clarity what it is they do intend, or what, for example, the "fluid nature of reality" actually amounts to (that is, over and above the phrase "fluid nature of reality" looking like an inappropriate metaphor -- or, indeed, what this odd metaphor about 'fluidity' could possibly mean), that objection is itself devoid of content (since it contains several empty terms). [Anyway, it has been neutralised here.]


Independently of that, in what way does the phrase "fluid nature of reality" help explain how any of the forces involved in change are 'internally-related'? For example, how are force, P, and event, Ei from earlier 'dialectical opposites'; how can a force be 'internally related' to an event? How are a rain storm and a forest fire (also from earlier) 'dialectically' linked if the first extinguishes the second? They don't imply one another (like the proletariat and the capitalist class imply one another, so we are told); rain storms happen all the time with no forest fire anywhere in sight -- and vice versa. But there can be no proletariat without there also being the capitalist class (again, so we are told). Furthermore, rain storms don't turn into forest fires (nor vice versa), which they should do if the DM-classics are to be believed.


So, whatever else it is this, supposed "fluid nature of reality" isn't 'dialectical'.


[The allegedly 'fluid nature of reality' will be examined in more detail in a later re-write of Essay Eight Part Three. It is reasonably clear that this metaphor derives from Heraclitus's dogmatic 'theory' that 'everything flows'. However, we have already seen that Heraclitus based that 'universally valid' conclusion solely on what he thought was the case when someone steps into a river! And, he got those details wrong, too! That is quite apart from the fact that there are countless trillion particles in each microgram of matter that don't change (unless acted upon externally).]


Once again, faced with the above, there is a simple solution staring us in the face: dialecticians should tell us what, if anything, they do mean by their use of obscure, incoherent Hermetic language/metaphors like this.




Alternatively, if forces affect one another externally (as seems to be the case), then, clearly, change can't be the result of 'internal contradictions'. On the other hand, if forces have an internal influence on one another (in some as-yet-unspecified way), and they change as a result of their own 'internal contradictions', then either they are composed of simple units that don't change, or they are infinitely complex, and nothing internal to them can condition anything else 'internally', for there would be no such thing.


[The above points were established in Part One.]


Too Many Forces Spoil The Broth -- Or Is It Too Few?


It could be objected that these spurious results have been cherry-picked, tailored, and skewed to fit a pre-determined conclusion -- the motivation behind which is which is clearly to malign DM, come what may; the choice of F24 (repeated below) being a prime example of this 'anti-dialectical' mind set.


In that case, a much better way of representing the oppositional and contradictory nature forces might prove to be the following -- in fact, with suitable changes in wording, this is the line taken in Weston (2012), for example:


F37: Contradictory forces are those that enter into opposition in such a way that they (dialectically) partially or totally cancel each other out.


[F24: P1 contradicts P2 only if it counterbalances P2.]


This means that the 'contradictory' relation between two or more forces would operate along a sort of continuum, or sliding scale -- as it were -- with no fixed relation between them. The arguments presented above clearly make the link between 'contradictory' forces an "either-or", all-or-nothing sort of affair.


Or so a counter-argument might go.56


At this point, an example from mechanics might help illustrate the complex relationship that is intended here: un-damped Simple Harmonic Motion. [SHM -- that link requires JAVA; try here if you have no JAVA installed (scroll down the page!).]


Consider a particle set in motion under the operation of two forces, such that its acceleration is proportional to its displacement from the point of equilibrium, and directed toward that point. Since the acceleration of this particle changes in proportion to its position, the net force operating on it must also change accordingly. This is due to the fact that the resultant force in this system is the vector sum of these two distinct but changing forces, which at the equilibrium point counterbalance one another, but at any other point they either augment or partially 'nullify' each other, depending on the physics of the situation. Because these two forces work in opposite directions and cause the impressed acceleration (achieving this by their -- let us say for now -- 'dialectical interaction') we appear to have here an example of F37-type motion.


F37: Contradictory forces are those that enter into opposition in such a way that they (dialectically) partially or totally cancel each other out.


[F24: P1 contradicts P2 only if it counterbalances P2.]


In this highly simplified picture of just one type of motion, the forces present in the system appear to 'contradict' one another in complex but changing ways, as DM seems to require. But, if this scenario actually does illustrate F24-, or F37-type 'contradictions', several untoward consequences also seem to follow from it:


(1) Clearly, this analogy means that 'contradictions' (just like forces) operate on a continuum. Hence, at any point along the path of the above particle (other than the equilibrium point), the net force operating isn't equal to the net force at any other point (in the same cycle). So, at a specific displacement, the modulus of the net force might be, say, only 1% of its maximum, at another it might be 99% of that maximum -- while at a symmetrical location on the other side of the point of equilibrium, the same would be true but in an opposite sense. Even so, it isn't easy to see how such a picture may be made to fit seamlessly into the DM-view of 'contradictions'; and as we saw above, such a model would have unacceptable consequences for HM (involving, for example, the Nazis fighting racism!).


(2) This trope depends on forces being viewed as basic units of reality, as opposed to the product of the relations between bodies in motion.


[Recall, Option (2) appears to be one that Engels himself rejected when he spoke of relative velocities replacing forces. However, if the term "force" is just a shorthand for relative motion (or if it depends on the presence of a "field"), then, as we have also seen, the 'dialectical unity of nature' would be thrown into question. On that basis, the links between bodies and processes would be external, whereas DM requires them to be 'internal', with the existence of forces providing the 'connective tissue' of reality, as it were. However, if forces themselves depend on bodies in relative motion, then reality would be discrete, not continuous.]


But, DM-theorists have yet to tell us what the physical nature of a single force is. Physicists themselves have ceased to use this word (except as a sort of shorthand, as noted earlier). If forces have no physical nature, can they really be part of nature? How could such 'useful fictions' feature in a materialist account of the universe?


(3) This neat picture, tailor-made to be consistent with F37, obscures the complexity found in nature. Even so, it isn't easy to see how such a tidy model could cope with systems of forces, which, given this view, indicate that several things must be 'contradicted' all at once by countless others, or, indeed, which suggest that bodies and/or processes could have innumerable 'contradictories'. That would, of course, divorce DM-type 'contradictions' completely from both FL-contradictions and Hegelian 'contradictions'. While this might not be totally unacceptable to some, it would mean that the former sort of contradiction would be even more tenuously linked to the latter (or, for that matter, with contradictions that supposedly feature in everyday life). In that case, the meaning of the word "contradiction", as it is used in DM, would be even more obscure than it already is. In addition, it would imply that any object or process in nature had more than one opposite at any point in time. The word "opposite" would thereby cease to have any clear meaning. But, we have been here several times already.


Despite these niggling problems, it might be felt that F37 suitably modified could still capture essential features of the 'contradictory' nature of forces.


In order to investigate this alternative further, let us suppose that the two forces operating in the above scenario are aligned so that the angle between them is 180°, once more.57


F38: Let the first force be F1, and the second, F2.


F39: At t1, let F1 + F2 < 0.


F40: At t2, let F1 + F2 = 0.


F41: At t3, let F1 + F2 > 0. [t3 > t2 > t1.]


[F24: P1 contradicts P2 only if it counterbalances P2.


F37: Contradictory forces are those that enter into opposition in such a way that they (dialectically) partially or totally cancel each other out.]


F39 and F41 imply that there is a net force operating in the system in either direction; F40 expresses the background condition to F24, where no net force exists.


But, as we saw earlier, we face immediate problems with this way of depicting forces -- those encountered above in relation to the inappropriate analogy drawn between 'contradictions' and mathematical objects/structures like these -- i.e., forces represented by vectors.


Ignoring that 'problem', too, it is worth pointing out once more that F40 in fact implies that there are no forces operating in the system (unless we regard the zero vector as a force by default), and F39 and F41 both mean that there is only one force -- the resultant -- at work. On that basis, F37 would collapse for want of forces. As we have seen, no contradiction seems possible if only one force -- the resultant -- is present in the system. Still less if no forces are at work (as is the case in F40).


F39: At t1, let F1 + F2 < 0.


F40: At t2, let F1 + F2 = 0.


F41: At t3, let F1 + F2 > 0. [t3 > t2 > t1.]


F37: Contradictory forces are those that enter into opposition in such a way that they (dialectically) partially or totally cancel each other out.


It could be objected that in the above both of the original forces (F1 and F2) still exist, since it is they that create the zero vector and/or any resultant force(s) in the system (as they do in F39 and F41).


The problem with this reply is that it is difficult to see how the two original forces may also be said to exist alongside this third force -- the resultant --, whether the latter is zero or not. If they do exist in this way, we would plainly have three forces at work here, not two.


That would, of course, create energy out of nowhere.58


To be sure, our ability to calculate resultants involves us in applying some mathematics to the relevant components, but that doesn't itself mean nature does the calculating. If it did, that would clearly imply nature was Mind, or the product of Mind! No one, it is to be hoped(!), thinks that in nature there are three forces here where once there were only two. And yet, it is this third force that does all the work.


It could be objected that there is no third force at work here, no resultant. That is just how we express the relation between two genuine forces (or their components) in the system. Resultants are therefore just mathematical fictions. The problem with that response is that resultant forces can be measured and what happens to the bodies involved can be predicted from the magnitude and direction of that resultant. If we can reject resultant forces so easily, then what are we to say to those who reject forces altogether, even though they can also be measured and their effects predicted? Aren't forces in general just mathematical fictions that we can edit out of nature in favour of the relative motion of bodies, just as Engels concluded?


Rid the world of resultant forces and all forces threaten to follow them into oblivion.


Now, if an F37-type model is in fact applicable in HM, we ought to conclude that the 'contradiction' between Capital and Labour (or that between the forces and relations of production), say, produces a resultant third social force, the nature of which has to this day remained not just completely obscure, but totally unacknowledged. Based on this model, since all motion in the Capitalist system is produced by this mysterious "third force", its identification by revolutionaries is, to say the least, of the utmost importance!59


It might be felt that this view of forces is simplistic in the extreme. In HM, social forces are far too complex to be represented as vectors, which means that the criticisms aired above are once again exposed as completely misguided.


In response, it is worth recalling that the analyses that have been developed in this Essay have been forced upon us (no pun intended) because DM-theorists have so far failed to say what they mean (if anything) when they equate 'dialectical contradictions' with opposing forces. Dialecticians seem quite happy to assert that these 'contradictory' forces operate everywhere in the universe, even though that has been done in the absence of any clear or detailed account having been presented of the supposed relationship at work here. This means, of course, that erstwhile critics of this Essay are objecting when they are almost totally in the dark about their own theory!


Is this not yet another example of them foisting dialectics on nature and society?


[It is worth reminding the reader here that the existence of forces in HM isn't being questioned by the present author (nor will it be), merely the assumption that they can be equated with, or modelled by, 'contradictions'. But see also Note 61, below.]


Apart from simply conforming to tradition -- as was argued here -- DM-theorists appear to use the phrase "contradictory forces" in order to provide their theory with a scientific-looking façade, linking it with a genuine and successful science like Physics. Otherwise, why do this?


If that seemingly impertinent allegation is correct, it would be disingenuous of DM-supporters to complain that the analogy given above (i.e., using SHM to illustrate changing forces) doesn't apply to social forces. If the word "force" wasn't meant to be taken in its usual scientific sense (as a vector), the analogy would, indeed, be inapt. But, in that case, the exact meaning of the word "force" (as it appears in DM) would be even more obscure. If "force" isn't being employed in the way that physicists use it, what other scientific way is there?


Anyway, as far as the complexity of social forces is concerned, the counter-argument (mentioned above) itself fails to address the problem of the identification of forces with 'contradictions' in nature and society. If it is impossible to give a clear sense to an avowedly simplified picture of forces as 'contradictions' (i.e., as they seem to operate in nature), a more complex one applied elsewhere stands no chance.


As has been pointed on many occasions at this site, if dialecticians object to any of the comments made in this Essay, there is a simple remedy: they should say clearly, and in detail, for the first time ever what they mean when they equate forces, or the relations between them, with 'contradictions'.


Moreover, forces appear to be 'contradictory' when and only when they produce a third resultant force. This might provide DM-fans with a certain amount of aesthetic satisfaction (in that this picture is triadic), but it would in fact sink the theory faster than a lead-lined diving suit sinks a diver. That is because change would then be a result not of contradictory forces, but of resultant forces.


And, as we have seen already, it is just as easy to describe such a set-up as 'tautologious' as it is to picture it as 'contradictory' -- even though both options should rightly be fed into the 'mystical-concept-crusher' as irredeemably anthropomorphic. Moreover, we have already seen that whatever else they are these forces aren't involved in a 'dialectical contradiction' with one another since none of them imply the existence of the other in a force couple, or configuration of forces -- again, unlike the alleged 'dialectical contradiction' between the proletariat and the capitalist class (so we have been told).


Howsoever we twist and turn, the equation of forces with 'contradictions' seems to be as misconceived as anything could be. When interpreted metaphorically it turns out to be inappropriate (if not paradoxical and animistic); when interpreted literally it crumbles into incoherence and confusion, even in DM-terms.


In order to avoid these difficulties we need to return to an alternative that was considered briefly, earlier -- one that could provide DM-theorists with a successful way of interpreting forces as 'contradictions'. However, before this alternative is re-examined in more detail, it is necessary to counter an objection that should by now have occurred to the reader:


This entire analysis is abstract and fails to consider "real material forces".59a1


Real 'Contradictions'?


Sinking In Concrete


As noted above, considerations like those aired above would stretch the patience of most dialecticians. Indeed, they would probably be the first to point out that this Essay fails to consider real material, empirically verifiable contradictions, and by this they generally (but not exclusively) mean the 'contradictions' that feature in HM, in the class war and that help account for the dynamic in history.


First of all it is worth reminding ourselves that many of the examples considered earlier were in fact typically concrete, and undeniably material! What else is gravity, for instance?


Nevertheless, if no sense can be made of 'contradictory forces' in nature (as we have seen), then that automatically throws into question their role in HM.


Now, as is easy to demonstrate, revolutionaries seriously overuse the word "contradiction" in their endeavour to depict not just capitalism, but the class war in general. In fact, comrades seldom bother to justify their almost neurotically profligate application of this word to everything and anything they just happen to be discussing or analysing.59b


Interlude Ten: Contradictions, Contradictions Everywhere!


Here are just a few examples of the profligate use "contradiction": 1, 2, 3, 4, 5 -- with a particularly crass list posted here (which link will take the reader to a site called Dialectics For Kids, so it can perhaps be forgiven somewhat for its sub-sophomoric over-simplifications). Several more cases in point were itemised earlier. Readers should also check out the handful of egregious examples on offer in that rather poor film, Half Nelson, a movie not unconnected with the aforementioned site; indeed, the director of that film is the son of the owner of Dialectics for Kids!


Updates: December 2011 and October 2013: See also my recent debate with Mike Rosen (in the 'Comments' section at the bottom; organise these "Newest First"). [Unfortunately, these comments are no longer available!] See also here, again in the comments section at the bottom.


Here is another recent example:


"The current debate over stem cells provides a very good illustration of the contradictions inherent within capitalism. On the one hand it is capable of generating amazing new technologies. However, the amount of money flowing into stem cell research is still miniscule compared to that being used for developing new ways to kill people. A recent report concluded that while stem cell research was pioneered in this country, lack of funding was compromising the ability of British scientists to keep things moving forward in this area. Meanwhile, as the leader of the richest country on earth talks about the sanctity of a ball of cells, in Iraq the most sophisticated weapon systems are being used to murder real, living human beings." [Parrington (2007), p.9. Paragraphs merged; bold emphasis added.]


In fact, this illustrates the by-now-familiar fact that dialecticians like Parrington are only too ready to confuse 'contradictions' with unacceptable, paradoxical, irrational or unexpected events, as I alleged in Essay Five.


Even in DM-terms this makes no sense: Does either 'half' of the above 'contradiction' struggle with the other? Does one of them turn into the other (which they should do, if the dialectical classics are to be believed)? Is George W Bush, or the rest of his class, about to 'develop' into a bunch of under-funded scientists or new equipment, and vice versa? Does the one imply the other, such that the first can't exist without the second? Hardly.


If not, where is the 'dialectical contradiction' here?


Update, October 31/10/2021:


Not to be outdone, here is David Harvey, who thinks there are seventeen basic contradictions in capitalism; here they are:


"The direct provision of adequate use values for all (housing, education, food security etc.) takes precedence over their provision through a profit-maximising market system that concentrates exchange values in a few private hands and allocates goods on the basis of ability to pay.

"A means of exchange is created that facilitates the circulation of goods and services but limits or excludes the capacity of private individuals to accumulate money as a form of social power.


"The opposition between private property and state power is displaced as far as possible by common rights regimes -- with particular emphasis upon human knowledge and the land as the most crucial commons we have -- the creation, management and protection of which lie in the hands of popular assemblies and associations.


"The opposition between private property and state power is displaced as far as possible by common rights regimes -- with particular emphasis upon human knowledge and the land as the most crucial commons we have -- the creation, management and protection of which lie in the hands of popular assemblies and associations.


"The appropriation of social power by private persons is not only inhibited by economic and social barriers but becomes universally frowned upon as a pathological deviancy.


"The class opposition between capital and labour is dissolved into associated producers freely deciding on what, how and when they will produce in collaboration with other associations regarding the fulfilment of common social needs.


"Associated populations assess and communicate their mutual social needs to each other to furnish the basis for their production decisions (in the short run, realisation considerations dominate production decisions).


"New technologies and organisational forms are created that lighten the load of all forms of social labour, dissolve unnecessary distinctions in technical divisions of labour, liberate time for free individual and collective activities, and diminish the ecological footprint of human activities.


"Technical divisions of labour are reduced through the use of automation, robotisation and artificial intelligence. Those residual technical divisions of labour deemed essential are dissociated from social divisions of labour as far as possible. administrative, leadership and policing functions should be rotated among individuals within the population at large. We are liberated from the rule of experts.


"Monopoly and centralised power over the use of the means of production is vested in popular associations through which the decentralised competitive capacities of individuals and social groups are mobilised to produce differentiations in technical, social, cultural and lifestyle innovations.


"The greatest possible diversification exists in ways of living and being, of social relations and relations to nature, and of cultural habits and beliefs within territorial associations, communes and collectives. Free and uninhibited but orderly geographical movement of individuals within territories and between communes is guaranteed. Representatives of the associations regularly come together to assess, plan and undertake common tasks and deal with common problems at different scales: bioregional, continental and global.


"All inequalities in material provision are abolished other than those entailed in the principle of from each according to his, her or their capacities and to each according to his, her, or their needs.


"The distinction between necessary labour done for distant others and work undertaken in the reproduction of self, household and commune is gradually erased such that social labour becomes embedded in household and communal work and household and communal work becomes the primary form of unalienated and non-monetised social labour.


"Everyone should have equal entitlements to education, health care, housing, food security, basic goods and open access to transportation to ensure the material basis for freedom from want and for freedom of action and movement.


"The economy converges on zero growth (though with room for uneven geographical developments) in a world in which the greatest possible development of both individual and collective human capacities and powers and the perpetual search for novelty prevail as social norms to displace the mania for perpetual compound growth.


"The appropriation and production of natural forces for human needs should proceed apace but with the maximum regard for the protection of ecosystems, maximum attention paid to the recycling of nutrients, energy and physical matter to the sites from whence they came, and an overwhelming sense of re-enchantment with the beauty of the natural world, of which we are a part and to which we can and do contribute through our works.


"Unalienated human beings and unalienated creative personas emerge armed with a new and confident sense of self and collective being. Born out of the experience of freely contracted intimate social relations and empathy for different modes of living and producing, a world will emerge where everyone is considered equally worthy of dignity and respect, even as conflict rages over the appropriate definition of the good life. This social world will continuously evolve through permanent and ongoing revolutions in human capacities and powers. The perpetual search for novelty continues." [Harvey (2014), pp.294-97; I have quoted the above from here. Spelling altered to agree with UK English.]


Does Harvey even attempt to derive any of the items in the above pairs from the other in the same pair? Do any of the items in any pair imply the other? Is it the case that each one can't exit without the other? Do they struggle with and then turn into each other? But they ought to do both since that is what the DM-classics insist they should.


Readers can check, but Harvey just asserts that the above are contradictions; he nowhere makes any move to show they are even 'dialectical', let alone that they are any other sort of contradiction. But that is par for the course on Planet Dialectics.




Indeed, this word/concept seems to operate almost as a code word, even a shibboleth, the use of which signals to others of like mind that the one employing it belongs to the same 'speech community' with its own distinctive jargon, thus defining an 'in-group' that excludes those belonging to the 'out-group', rather than genuinely applying in each and every case -- or in any case -- or, indeed, in a way that means anything at all.


[Why DM-fans do this will be revealed in Essays Nine Part Two and Fourteen Part Two (when it is published).]


But, perhaps this, too, is a little unfair?


In order to substantiate the above allegations it might be wise to consider a few (generally agreed upon) examples of "real material contradictions" in capitalism that supposedly underpin and drive social development.60


Rees, OLLMAN And 'Concrete Forces'


[TAR = The Algebra of Revolution (i.e., Rees (1998); HM = Historical Materialism.]


TAR, for example, opens with several apposite and well-observed examples of the irrational and destructive nature of Capitalism. As John Rees correctly points out, while life expectancy, for instance, has increased dramatically over the last hundred years or so (even in the poorest regions of the planet), other factors have grown alongside these developments that counteract or undermine them:


"[S]ince the Second World War there have been 149 wars which have left more than 23 million dead…. On an average yearly basis, the numbers killed in wars during this period have been more than double the deaths in the nineteenth century and seven times greater than in the eighteenth century…. Regression, by any criterion. Yet it is the very same development of human productivity that gives rise both to the possibility of life and to its destruction…. Everywhere we look another paradox appears. How can it be, for instance, that in the richest capitalist society in the world, the United States, real weekly incomes have fallen steadily since 1973?… How is it that in Britain, where the economy, despite the ravages of recession, produces more than it has ever done…a full quarter of the population live below the poverty line? The contradictions are no less striking if we shift our gaze from economics to politics. The introduction of the market to Russia and Eastern Europe was supposed to bring stability and prosperity but has actually produced the opposite." [Rees (1998), pp.1-2. Paragraphs merged; bold emphasis added.]60a0


Bertell Ollman had something similar to say:


"Like virtually everyone else in his day, Marx was astounded by the scope and rapidity of the changes that were occurring all around him, but also by their contradictory nature. The enormous growth in the production of wealth, for example, came along with an increase in the worst forms of poverty; progress in science and technology that had a potential for making work much easier only succeeded in speeding up the pace of work and lengthening the working day; even the increase of personal freedom due to the abolition of various feudal ties came on the back of an even greater decrease in freedom due to the unforgiving conditions in which people were forced under pain of starvation to live and work (or what Marx was later to call the 'violence of things'). Meanwhile, more and more of the world was becoming privatized, commodified, fetishised, exploitable and exploited, and alienated as 'all that is solid melts into air.'" [Ollman (2005); quoted from here. Spelling modified to agree with UK English; bold emphasis added.]


First of all, it should be emphasised that in what follows the validity of the above criticisms of Capitalism won't be questioned -- nor will the explanation given by Rees or Ollman for these and other intolerable features of the political, economic and social system that still dominates this planet. The sole aim here is to ascertain what if anything they (or any one else, for that matter) mean by calling unacceptable developments like these "contradictions", or why they and other dialecticians insist on linking that word with material forces in nature and society.


Second, I have chosen the above passages since few DM-fans belonging to other wings of Marxism (be they Stalinists, Maoists, anti-Leninists, Orthodox Trotskyists, Libertarian Marxists, or Academic Marxists) would disagree that the things the above two call "contradictions" are indeed contradictions. While they will certainly disagree over some of their causes, or even over what to do to remedy them, they will all characterise them in the same way as 'dialectical contradictions'.


In what follows, I will focus mainly on Rees's comments.


The Impertinent Explanation


Of course, a trite and impertinent answer to the question "Why do DM-theorists use 'contradiction' in the way they do?" would be to point out that they use this word simply because it is part of the 'Marxist tradition', adherence to which helps define a dialectical 'in group', as noted earlier. It is reasonably clear that the use of this word is only part of 'Materialist Dialectics' because of contingent features of the lives of Marx and Engels -- i.e., those related to (i) when and where they were born, (ii) which class they found themselves members of, (iii) how they were educated, and (iv) who they studied -- specifically, Hegel.


Hence, as fate would have it, the world-view adopted by the above two was conditioned by their own "social being" -- to use Marx's term.


In fact, had Hegel died of Cholera (or whatever it was that finally killed him) 45 years earlier than he actually did, does anyone really think we would be using this term -- "contradiction" -- in the way DM-theorists do, or would even be bothering with 'dialectics'?60a


Be this as it may, because of the towering authority that Marx and Engels have assumed ever since, all subsequent dialecticians have been constrained to think and reason along similar lines. They have to use the obscure vocabulary bequeathed to them or risk being be accused of 'Revisionism', branded 'anti-Marxist', and maybe suffer expulsion, political isolation, or even worse.


[Or, of course, face the same sort of ritual abuse with which I am constantly regaled. Not that I am complaining; I expect it, and would be puzzled had there been none of it.]


In short, it is quite clear that theorists (like Rees and Ollman) use obscure Hegelian concepts and jargonised expressions because prominent comrades have always done so, and they are merely conforming to tradition.


Naturally, the impertinent nature of this 'trite' explanation won't win over many dialecticians -- but since a less impertinent one stands no chance either, there is little to lose advancing it here.


In that case, there is a pressing need to try to find a better reason why hard-nosed materialists should want to anthropomorphise nature and society in this manner, using terms drawn from Hermetic Mysticism -- such as "contradiction" -- in what is supposed to be a materialist theory.


Unfortunately, as we will soon find out, there isn't a better explanation why confirmed materialists have allowed themselves to be conned into accepting the use of Hermetic jargon like this, or for employing it quite so indiscriminately, as we have seen.


We have also seen that each and every attempt to render viable the analogy between forces and 'contradictions' fall apart; hence, it should come as no surprise to see the very same thing happen when we examine the use of "contradiction" in HM, below.


[Spoiler Alert: The result will be that, apart from the ideological and political motivations mentioned in the next paragraph, the impertinent reason mentioned above turns out to be the only viable one left standing.]


[The political setting to the use of "contradiction" is examined in detail in Essay Nine Part Two, and more generally in Essay Twelve (summary here), where I also examine the social and class background of the originators of this theory in order to link it with the reason why DM-theorists were, and still are, pre-disposed to adopt such an ancient, decrepit and class-compromised world-view -- alongside their use of "contradiction". Indeed, as hinted above, there are political and ideological reasons over and above the impertinent explanation offered here for its use. They are also explored in Essay Nine Part Two, specifically here.]


Conflict Resolution


The underlying cause of the many absurdities caused by capitalism is, as TAR rightly points out, the complex, changing interplay between the "material productive forces of society" and the associated "relations of production". [Rees (1998), p.2, quoting Marx.] That account of the driving force of capitalism (but, interpreted humanistically, in terms of the class struggle), I fully accept.


However, this brings us no closer to understanding what it is about opposing (social) forces that merits calling them "contradictions". Why turn a clear employment of an ordinary word drawn from the vernacular into an obscure concept in a doctrine peppered with other impenetrable jargon lifted from mystical Idealism (i.e., phrases such as "determinate negation", "identity of opposites", "negation of the negation", "mediate", and the like), the use of which completely undermines our ability to explain change, anyway?


In HM, we can certainly make sense of the term "force" -- and even of words like "opposing" and "struggle" --; but what is there to gain by calling these "contradictions"?61


Some might regard this as a harmless use of a certain word, but, as we will see in Essay Twelve (summary here), in this case there is no such thing, just as there is no such thing as a neutral use of the word "oppression". We will also see in Essay Nine Part Two that this particular word 'allows' DM-fans to impose contradictory tactics, strategies and theories on the party faithful in order to 'justify', among other things, class collaboration, substitutionism, splits, expulsions, and even mass murder, all predicated on the idea that if reality is contradictory, the Party should be, too. Indeed, as Lenin noted:


"The splitting of a single whole and the cognition of its contradictory the essence (one of the 'essentials,' one of the principal, if not the principal, characteristics or features) of dialectics.... The struggle of mutually exclusive opposites is absolute, just as development and motion are absolute...." [Lenin (1961), pp.357-58. Quotation marks altered to conform with the conventions adopted at this site. Paragraphs merged.]


"Splitting" is therefore an "essential" part of this theory, and "struggle" is an "absolute". That must also involve the relations between comrades. An emphasis on intra-party strife and splitting thus sits right at the heart of Dialectical Marxism!


In which case, we needn't sit around waiting for the ruling-class to divide us, we are already experts!


[An excellent example of the use of this theory to 'justify' a regressive political dogma (which would be condemned if anyone else were to do it) is the way that Trotsky used dialectics to justify the revolutionary defence of the former USSR on the basis of its 'contradictory' nature as a 'degenerated workers' state', in which workers exercised no power and were systematically oppressed and exploited for their pains -- and hence also the murderous invasion of Finland. Another is the way that Ted Grant, for instance, used 'Materialist Dialectics' to 'justify' his confused and contradictory theory of 'Proletarian Bonapartism' (sic), which then 'allowed' him to rationalise the substitution of the Maoist ruling-clique for the Chinese working class -- a topic I have debated here. (This link is unfortunately now dead!)]


So, these mystical concepts aren't 'innocent bystanders', as it were; their use has helped turn Dialectical Marxism into a spectacularly unsuccessful long-term disaster.


[Notice the use of "helped" here. DM is just one of the reasons for the protracted failure of Dialectical Marxism.]


Where The Shoe Pinches


Nevertheless, the relevant part of the argument in TAR appears to be the following:


F42: Capitalism seems to offer unprecedented possibilities for human development.


F43: But, in reality Capitalism delivers only partial or faltering progress.


F44: Alongside this progress we have witnessed major regression.


F45: Thus, Capitalism actually delivers a mixture of progress and regression.


For Rees, the "contradiction" appears to be based on the fact that Capitalism holds out certain possibilities, which it either can't fully deliver, or can't provide at all; almost invariably the opposite of what it promises (to the majority of ordinary working people, one presumes) is what actually unfolds.


Rees clearly believes that the involvement of opposites is important here: instead of peace we find war; in the place of prosperity we find poverty (where it need not be); the growth in human need isn't catered for by the incessant search for profit; the waste of human potential conflicts with the increased capacity society has for augmenting and satisfying its members needs, and so on. So, it looks like 'contradictions' arise either from the incongruity that exists between what might be expected of Capitalism (by those who don't understand its nature, presumably) and what it actually delivers. Or, perhaps this arises from the yawning gap that exists between its potential to satisfy human need and its obvious inability to do so. In that case, forces and structures brought into existence by Capitalism seem capable of freeing humanity from want and oppression also appear to be inextricably linked with structures and forces that only succeed in intensifying or spreading both.


However, these by-now-familiar observations still leave the supposed link between forces and 'contradictions' entirely unclear. In order to clarify Rees's point we perhaps need to consider various plausible interpretations of what he might have meant.


There appear to be several distinct possibilities:


F46: Capitalism offers A, but delivers only not A.


F47: Capitalism offers A, but delivers both A and not A.


F48: Capitalism offers A, but delivers only B, where A and B are opposites.


F49: Capitalism offers A, but delivers A and B, where A and B are opposites.


F50: Capitalism offers A, but delivers C instead, where C is a paradoxical outcome.


F51: Capitalism offers A, but delivers A and not A as well as B and C.


[The denotation of these capital letters will be revealed as the argument unfolds.]


Doubtless there are many other combinations that could be imagined along similar lines, but they would, I think, merely be elaborations on these six possibilities. I propose, therefore, to examine each of them in turn, beginning, naturally, with the first.


Not What The System Ordered


The first option was:


F46: Capitalism offers A, but delivers only not A.


[F46a: Capitalism offers abundance, but delivers only scarcity (i.e., 'not-abundance').]61ao


But, F46/F46a presents us with a scenario we have met already; it resembles several earlier unsuccessful attempts to solve this overall problem. As we discovered, whatever forces there are in the system that actually produce not A, no contradiction can arise between A and not A because A itself does not exist, since only not A will have been actualised in place of A. Nor can any forces which are at work in the system contradict what they themselves actually produce (viz., not A in this case) --, especially if whatever they 'offer' (i.e., A) doesn't exist.


F46 and F46a are, therefore, of no use in our search to find a viable way of equating forces and 'contradictions' in HM.


[But do these factors struggle with and then turn into one another? Does abundance struggle with turn into scarcity, and vice versa? But they would have to do both if these were 'dialectical opposites' (according to the DM-classics). Once again: whatever else this is, it isn't a DM-'contradiction'.]


An Apparent Contradiction, At Last!


The second alternative went as follows:


F47: Capitalism offers A, but delivers both A and not A.


This seems to be a little more promising since A and not A certainly looks like a genuine contradiction. However, because F47 appears to depict contradictory outcomes it can't illuminate the alleged contradictory connection between forces in nature and society that exist prior to their emergence. That is because F47 is manifestly not about the forces themselves, but about their results.


So, even here, we don't seem to have contradictory forces.61a


It could be objected that there are forces in capitalism that produce just such opposites, and those forces can, therefore, be described as contradictory. For example, competition forces individual capitalists to accumulate capital, but this accumulation has a tendency to reduce the rate of profit for the whole capitalist class. So, here we have one tendency imposed on individual units in the system (in order to maintain or increase their own share of surplus value), which, when actualised, produces the opposite result for the entire class. The search for increased profit only succeeds in eroding it in the long term.


Maybe so, but in what way is this a 'contradiction'?


It would be if this were the case:


Q1: Individual capitalists search for increased profits and they don't.


Or, this:


Q2: Profit both rises and doesn't rise at the same time and in the same respect.


But, no sane Marxist would argue any of these.


Of course, DM-fans might be using the word "contradiction" in a new and as-yet-unexplained sense. If so, what is it? [On that, see here.]


It is worth emphasising at this point that I am not objecting to a new use of "contradiction". [However, on this, see Interlude Fourteen.] DM-fans can use words as they see fit (not that they need my permission!). But, when they do, they can't also claim to be using such words with their old meaning in place -- and hence, with respect to "contradiction", they can't also use it to justify claims about, say, the 'contradictory' nature of the former Soviet Union, either -- where this word is now being used in a more ordinary, familiar sense. And, if that is so, this new use of "contradiction" will bear no relation to its use in FL and ordinary language, which in turn means that DL in effect fails to 'surpass' FL and 'banal common sense'. [I go into this in much more detail here. See also here, and here.]


Not that ordinary language is the same as 'common sense', anyway.


DM-fans can't have it both ways. If their use of this word is indeed new, then 'dialectical contradictions' (whatever they are) can't be a 'superior form' of logical contradiction, as Hegel and all subsequent dialecticians appear to many to have claimed.


[Although, there are Hegel scholars who deny this is what Hegel actually intended -- for example, Hahn (2007).]


[FL = Formal Logic; DL = Dialectical Logic.]


But, far more importantly, do these forces, whatever they are, struggle with and then change into each other, which is what the DM-classics tell us they must do?


Call these forces, F1 and F2, respectively. But, if these two forces do struggle with one another they must surely coexist. If so, F1 can't change into F2 since it already exists! If it didn't, no struggle could take place.


[This general objection to the 'dialectical theory of change' has been expanded upon in extensive detail in Essay Seven Part Three, where I have responded to several objections, some obvious, some not so obvious.]


But, independently of that, it is clear that we are once again talking about the effects of these forces not the forces themselves. Those forces are described as 'contradictory' because their effects are contrary to expectations, not that they actually contradict one another.


In fact, what we have here is one economic factor (the accumulation of capital) that somehow produces the opposite effect to what might be expected, not two forces doing this with one of them predominating.


But, by no stretch of the imagination can this be the option we are looking for in our attempt to find out what Rees meant. There aren't even two forces at work here!


Nevertheless, this section is aimed at considering the last few remaining options available to DM-theorists to make their ideas comprehensible, so F47 won't be abandoned just yet.


However, as noted above, F47 corresponds to a relation depicted abstractly in an earlier section (i.e., that between E1 and E2, in F6 to F9, reproduced below) -- but interpreted here concretely (albeit schematically).


In which case, it looks like we might at last have found a genuine interpretation of E1 and E2 that is undeniably 'contradictory'.


F6: Let force, P1, oppose force, P2, in configuration, C1, in nature.


F7: Here, opposition amounts to the following: the normal effects produced by P1 in C1 (had P2 not been present) are the opposite of the effects P2 would have produced in C1 (had P1 similarly not been operative).


F8: Let P1's normal effects in C1 be elements of an event set, E1, and those of P2 be elements of an event set, E2. For the purposes of simplicity let E1 and E2 be disjoint.


F9: By F7, E1 and E2 contain only opposites, such that elements of E1 and E2 taken pair-wise, respectively, from each set form oppositional couples.


Unfortunately, this appearance is illusory since the conjunction of A and not A can't be considered contradictory until it is clear what interpretation is to be given to the schematic letter "A".


At this point, it is worth recalling that we are searching for a literal interpretation of the term "contradiction" that will allow DL to surpass FL -- not a metaphorical or analogical use of this word -- still less one that possesses a secondary or derivative sense (or even one that carries the 'special' DM-sense that has yet to be explained with any clarity). As should seem obvious, this search is of the utmost importance if we are to rescue from oblivion the idea that forces and 'contradictions' may be equated objectively -- and not, for instance, poetically, or even in some other fanciful sense.


Clearly, there are several different ways of reading the expression "A and not A"; some of these will be contradictions, others not.


In what follows, I shall utilise a further example taken from TAR (quoted above), which seems (at least to many DM-theorists) to be a genuine contradiction (i.e., that which supposedly exists between wealth and poverty). In that case, this might involve interpreting "A" as "wealth", and "not A" as "not wealth" (it clearly can't be "not poverty"!). In that case, "A and not A" would cash out as "wealth and not wealth".62


Unfortunately, the problem with this way of interpreting "A and not A" is that it actually creates a phrase, not a clause, indicative sentence or proposition.63 As such, it can't be a literal contradiction.


[The vast majority of DM-fans will fail to appreciate this point since their knowledge of logic is woefully defective. That, of course, hasn't stopped them pontificating on the subject as if they were all latter-day Aristotles.]


The only apparent way to situate the schematic noun phrase -- "A and not A" -- in a propositional context would be to interpret it a little more loosely -- perhaps along the following lines:


F52: Capitalism produces wealth and not wealth.64


As such, F52 is a paraphrase of:


F52a: Capitalism produces wealth and Capitalism produces not wealth.


Or perhaps even:


F53: Capitalism produces wealth for some and not wealth for others.65


Again, F53 itself is short for:


F53a: Capitalism produces wealth for some and Capitalism produces not wealth for others.


None of these look at all promising; they are not only stylistic monstrosities, their import is rather unclear. Anyway, F53 and F53a aren't contradictory -- that is, no more than, say, a tap would be contradictory if it supplied water for some but not for others, or any more than the claim that "opposing forces are contradictory" would itself be 'contradictory' if it convinced some but not others. No one would think they had been contradicted if they asserted that a certain factory, say, produced several batches of defective Widgets, and someone else clamed it also produced some that weren't defective.66


Anyway, F52a is far too vague as it stands -- it is certainly no more of a 'contradiction' than F53 and F53a were, and probably for the same reason. If sentences like these have no clear meaning they can't possibly assist in any attempt to clarify DM. Hence, a further widening of the interpretation of "A and not A" is called for if we are to gain a clearer understanding of the implications of F47. Perhaps the following will do?


F54: Capitalism produces capitalists who are wealthy and workers who aren't wealthy.


F47: Capitalism offers A, but delivers both A and not A.


[F53: Capitalism produces wealth for some and not wealth for others.


F53a: Capitalism produces wealth for some and Capitalism produces not wealth for others.]


As was the case with F53 and F53a, F54 isn't even a contradiction. Again, anyone asserting the first clause of F54 who was then confronted with the second wouldn't feel that they had been contradicted. That is plainly because the first clause is about Capitalists, while the second is about workers. To be contradictory F55 would have to be:


F55: Capitalism produces worker, W1 (or Capitalist, C1), who is both wealthy and not wealthy at the same time and in the same respect.


But, quite apart from the fact that no one would assent to, or even want to assert F55, it possesses no clear sense. The situation would be no better if it were re-written as:


F55a: Capitalism produces a set of workers, W (or Capitalists, C), who are both wealthy and not wealthy at the same time and in the same respect.


It is reasonably certain that Rees meant neither F55 nor F55a.


[If he had intended either, it would be entirely unclear what he could possibly have meant by one or both of them.]


At best, F55 and F55a might be re-interpreted in a comparative sort of way, as follows:


F55b: Capitalism produces a set of workers, W, that is both wealthy (in comparison to a set of peasants, P) and not wealthy (in comparison to a set of Capitalists, C), at the same time and in the same respect.


But, F55b is no more contradictory than this would be:


F55c: John Rees wrote a book that is both long (when compared with an average weekday print copy of The Guardian) and not long (when compared with Das Kapital).


The observation that TAR is both long compared to The Guardian and short compared to Das Kapital is not, one imagines, what most DM-theorists mean by "contradiction". If it were, their theory would plainly be based on logico-linguistic naivety, or linguistic incompetence, but little else.


Consequently, it looks like F47 can't be shoe-horned into this particular dialectical boot after all.


More problematic, however, is the following question: is either one of these options going to turn into the other?


In the above example, is W going to turn into C, and C into W? Indeed, is wealth going to turn into poverty? But, if these were 'genuine' 'dialectical opposites' or 'contradictions', they most surely should. In which case, whatever else it is, this can't be a 'dialectical contradiction'.66a


Further attempts to interpret "A and not A" can be extended almost indefinitely. DM-enthusiasts are welcome to play around with them as much as they like, the end result will be no different. There are no literally true contradictions that can be manufactured out of "A and not A" -- where these relate to the same person, persons, groups, forces, etc., in the same respect, at the same time. And as we have seen, this can't even be a 'dialectical contradiction'!


In addition to the reasons given above: that is because, if a putative 'contradiction' were held true, it would thereby cease to be a literal contradiction. As was established in in Essay Five, if such a 'contradiction' were encountered in everyday life, it would normally be viewed either as figurative or based on an undischarged ambiguity of some sort. There is no way around that socio-linguistic convention this side of altering the meaning of the word "contradiction". [On this, see also Interlude Eleven, below.] And, even that would be of little help to DM-theorists since that would 'solve' this 'problem' by means of yet more subjective, question-begging, linguistic reform, thereby imposing this part of DM on the facts.67


And as we have just seen, this can't even be a 'dialectical contradiction'!


Interlude Eleven: Everyday Contradictions


Linguistic tinkering like this merely creates 'contradictions' by fiat when what is required is an example of a real material contradiction -- not a reified linguistic expression for one, hastily cobbled-together simply to save the theory.


Nevertheless, some might argue that the claim advanced earlier (i.e., that contradictions would normally be regarded as figurative or ambiguous, if held 'true') is controversial -- and yet it is based on how we would respond now when faced with a contradiction in ordinary life. So, this claim is controversial only in the sense that some have thought to controvert it.


[There is a partial explanation of the background to this approach (based on Wittgenstein's work), here.]


Naturally, this means that the earlier observation isn't a consequence of the present author having been 'corrupted' by Analytic Philosophy. On the contrary, it is informed by the way workers themselves speak, and how anyone not suffering from 'dialectics' talks when they operate in the real world. Indeed, it is based on the way DM-theorists themselves would have to speak in order to make themselves understood in everyday life, let alone when they try to communicate with the working class.


Nevertheless, the following comments will test the patience of any dialecticians who have made it this far. They will no doubt regard the examples of contradictions given below as discursive, not dialectical, contradictions. That worry will be laid to rest in Essay Eight Part Three, where examples of just such 'contradictions' (i.e., those advanced by DM-theorists themselves) will be considered. The only point of the following argument is to illustrate how we might proceed if anyone were to utter (and try to mean) a contradiction in everyday life.


In that case, in order to illustrate how we would now handle such 'contradictions', consider how worker, NN, would respond if she were faced with the following scenario:


C1: Boss BB: "NN, you are being paid £9.50 an hour and not being paid £9.50 an hour."


[Of course, no one who isn't the worse for drink, drugs or mental confusion speaks like this, but other than the examples considered here it isn't easy to cite instances where ordinary human beings (again, not in the grip a some theory or under the influence of Zen Buddhism) utter 'true contradictions', or, indeed, intend to utter them and genuinely mean them.]


At first sight, C1 would in all likelihood be interpreted as a joke of some sort, a slip of the tongue, or a mistake. If the boss insisted that none of these were the case, then the only way to proceed would be to ask what on earth this boss meant by the sentence quoted in C1. In the event, the explication of the use of that sentence might involve interpreting the word "paid" in one of three ways:


(1) It might indicate what NN was going to earn, regardless of whether or not she will ever receive the money. Hence, in a round-about sort of way, the sentence quoted in C1 could be alluding to the effect of taxation and other deductions on NN's pay. It might even refer to the boss's intention to pay the worker in 'kind'. Or:


(2) It could mean that although the money had been earned, it wouldn't actually be paid to NN for some reason. So, it might be withheld as a part of the boss's attempt to victimise her for helping to lead a successful strike, for example. Or:


(3) It could mean that although NN will be paid at the stated rate, the true value of her contribution to production can't be measured in cash terms. Hence, it might suggest that BB intends to reward NN with more than mere money (or maybe with none at all) -- but, with his/her 'highest esteem', etc. A clue to this way of viewing the sentence quoted in C1 would be the inflection in the boss's voice -- a note of sarcasm, perhaps.


[Of course, there might be other ways of interpreting C1, but the above seem the most obvious to me.]


However, 'contradictions' like this would never be regarded as literally true, for as soon as NN was actually paid the said money the second half of the sentence quoted in C1 would become false -- which means that the conjunction of a falsehood with a truth (in C1) could never become literally true (short of altering the meaning of the words employed, or, indeed, of those used to assert that it is true -- or, without altering the meaning of "literal", of course). We wouldn't be able to make sense of anyone who thought that this sort of eventuality could arise (save in the ways indicated above, etc.). Certainly, without the alternatives outlined in (1)-(3) -- or, perhaps, expressed by several other possible interpretations --, no worker (or anyone else, for that matter) would be able to understand the sentence quoted in C1.


C1: Boss BB: "NN, you are being paid £9.50 an hour and not being paid £9.50 an hour."


This brings us back to a difficulty DM-theorists must always face if they persist in regarding 'contradictions' as true, or they continue to use the word "contradiction" in the loose and indiscriminate way to which they have become accustomed -- where one minute they sort of half mean the word in its ordinary-, or even its FL-sense, the next they sort of half mean it in this new, and as-yet-unexplained, DL-sense. When we bring this word back to its ordinary meaning, any propositions that contain it -- if they are still to be regarded as true -- could only ever be understood in a non-standard way, and then disambiguated along lines suggested earlier.


Exactly why we should want to do that was made clear by Marx himself:


"The philosophers have only to dissolve their language into the ordinary language, from which it is abstracted, in order to recognise it, as the distorted language of the actual world, and to realise that neither thoughts nor language in themselves form a realm of their own, that they are only manifestations of actual life." [Marx and Engels (1970), p.118. Bold emphases added.]


If, on the other hand, the word "contradiction" is meant to be taken in a special or technical (but as-yet-unspecified) sense, DM-theorists risk being misunderstood at every turn -- with their words failing to communicate anything determinate, especially if they hope to depict the sorts of situations in the material world that are familiar to ordinary people and workers. Furthermore, to make the same point once more, that risk will remain in place unless and until DM-apologists make it clear (and for the first time ever) what they mean by their odd use of this word in such contexts.


This means that in practice, when faced with sentences like C1, DM-theorists would interpret the alleged "contradictions" they express in a standard way, in line with the vast majority of ordinary human beings -- and hence paraphrase them away. Despite their commitment to dialectics, few DM-fans would understand the words attributed to the fictional boss in C1 literally. In fact, only the most useless trade union organiser in history would allow such a boss to get away with the nonsense reported in C1. Representing and defending the material interests of the working-class certainly doesn't mean that we let bosses off the hook by adopting, or accepting, ways of speaking that have been invented by ruling-class hacks, mystics and Idealists.


C1: Boss BB: "NN, you are being paid £9.50 an hour and not being paid £9.50 an hour."


However, socialists, who are normally alert to the dangers of class collaboration when they surface elsewhere, seem only too happy to allow ordinary language to suffer from ideological contamination of this sort when it comes to philosophy.


Even if the word "contradiction" were intended to be taken literally, DM-theorists themselves wouldn't be able to say what in nature or society a 'true contradiction' would, or could, depict without helping themselves to yet more figurative language.


If (per impossible) they could do this, then the word "literal" would have to be taken non-literally!


In Essay Five, we saw every attempt to unravel the confusions that plague Engels's (brief) account of motion fail. It turned out that it was impossible to make sense of what Engels thought he might have meant by what he actually said -- that is, if we attempt to take his words literally.


So, it is no big surprise to find that DM-theorists have remained consistently unclear and equivocal about core DM-theories like this for well over a hundred years. There is in fact nothing that anyone could say, or could have said, to make the incomprehensible comprehensible. Just like the mysteries of Transubstantiation and the Incarnation of Christ, DM-propositions resist all attempts at clarification. Indeed, as David Stove argued:


"If a statement 'p' is impossible to understand if taken literally, it will also be impossible to understand the statement 'So-and-so believes that p', taken literally. If you could understand the statement that knowledge is literally a poached egg, then you could understand the statement that Smith literally believes that knowledge is a poached egg; but since you can't understand the former, you can't understand the latter either." [Stove (1991), p.28.]


[Readers should, however, check out the warning I have also posted about Stove, here.]


At present, unless DM-theorists come up with the goods, it is impossible to understand a single thing they say about these mysterious 'dialectical contradictions', and hence it is equally impossible to understand anyone who swears that DM-theorists themselves understand them.


[This is on a par with Wittgenstein's aside: the negation of nonsense is also nonsense.]


When I have made this point to DM-fans in 'debate', they tend to respond with something like the following:


"Just because you can't make sense of this use of 'contradiction' doesn't mean it makes no sense. Your failings can't be attributed to our theory!"


To which I invariably reply:


 "I agree. But in that case, help me out. What do you mean by your odd use of 'contradiction', for example?"


That is usually met with silence, abuse or further attempts at deflection. But in the nearly 35 years I have been arguing with DM-fans, not one of them has been able to help me out. Not that I ever expected it, any more than I expect Christians to explain with any clarity, or even candour, the nature of their Trinity to me.


At this point, DM-apologists might be tempted to complain about the continual use of contradictions drawn from FL to make points against their use of "dialectical contradiction". The obvious response to this is (once again) to request a clear explanation of what a 'dialectical contradiction' itself could possibly be so that those advancing this complaint could themselves convince critics that they do mean something (anything?) by that phrase, as opposed to their having used an empty string of words for well over a hundred years -- just because it is traditional to do so.


Until then, the volunteered complaint (recorded at the beginning of the previous paragraph) would itself be devoid of meaning since it contains a term that is, so far, meaningless -- i.e., "dialectical contradiction". DM-theorists might just as well use "schmontradiction" for all the good it does.


Finally, the claim that there are 'literally true contradictions' (advanced by philosophers like Graham Priest) will be examined in a later Essay. [However, it is a moot point whether the examples and paradoxes he considers are, or ever could be called "dialectical". Strike that; they aren't.]


Until then the reader is directed toward the following: Goldstein (1992, 2004), Slater (2002, 2007b, 2007c), and this review, by Hartry Field.


[Field has now published a book on the paradoxes, where he is able to show that the Dialetheic and Paraconsistent Logic Priest favours can't even handle the paradoxes of truth, which had in fact been one of the main motivators for this branch of non-standard logic -- i.e., Field (2008), pp.36-92.]


[An entire sub-section on 'dialectical contradictions' that used to appear here has now been moved to form Essay Eight Part Three.]




Opposite Tendencies I


In that case, perhaps F48 is the reading we are searching for?


F48: Capitalism offers A, but delivers only B, where A and B are opposites.


Unfortunately, as we have seen several times already, since A doesn't exist -- Capitalism not having delivered it --, it can't 'contradict' B. This means that F48 isn't a viable reading of Rees's intentions, either. Even if B 'contradicted' any forces and/or processes already present in the system, that would just return us to where we were when we considered several earlier examples, such as this one (but substituting the word "society" for "nature"):


F6a: Let force, P1, oppose force, P2, in configuration, C1, in society.


F7: Here, opposition amounts to the following: the normal effects produced by P1 in C1 (had P2 not been present) are the opposite of the effects P2 would have produced in C1 (had P1 similarly not been operative).


F8: Let P1's normal effects in C1 be elements of an event set, E1, and those of P2 be elements of an event set, E2. For the purposes of simplicity let E1 and E2 be disjoint.


F9: By F7, E1 and E2 contain only opposites, such that elements of E1 and E2 taken pair-wise, respectively, from each set form oppositional couples. 


It seems this is yet another dialectical dead-end, for here we have even more non-existents 'contradicted' by existents.


Opposite Tendencies II


Does, therefore, F49 provide DM with a lifeline?


F49: Capitalism offers A, but delivers A and B, where A and B are opposites.


This looks a little more promising -- but looks can be deceptive.


If we now read "A" as "wealth" and "B" as "poverty" once more, we would appear to have the following:


F63: Capitalism offers wealth, but delivers wealth and poverty, where wealth and poverty are opposites.68


Interlude Twelve: Opposites, Again?


[This follows on from Interlude Five. and depends on the conclusions reached there.]


But, are opposites always contradictory? At this moment I am sat in front of my computer looking at the house opposite. Is my house therefore in some sort of 'struggle' with that house? Or, indeed, am I 'struggling' with it?


Unfair? Perhaps so. Dialecticians will be the first to point out that the opposites they regard as contradictory are those that are involved in a dialectical union of some sort (i.e., as UOs). Since my house and the one opposite aren't so linked (and neither am I), they aren't therefore in 'struggle', nor could they be.


Well, how do we know? Clearly we don't. Nature often surprises us. Anyway, isn't everything interconnected in DM?


Be this as it may, consider the opposite sides of an equilateral triangle (and one that has been carefully drawn on paper, so this isn't an abstract example). Such a triangle has two opposite sides; do they 'contradict' one another? Are they both battling against the third side, or with each other? Here, these sides are physically-, and logically-, or 'internally'-, linked. Even so, they steadfastly refuse to contradict one another. If we now extend this example to cover more complex manifolds, these 'difficulties' only multiply.


But, once again it could be argued that these counter-examples aren't relevant since the items involved aren't dialectically-logically linked.


It seems then that only certain logical connections in reality are allowed to be, or to constitute, a DM-UO, which means that objects and processes that are merely physically-, or even those which are formally-, connected can't be so described.


However, on a purely empirical basis, since no house has yet been observed to be engaged in a life-and-death struggle with another property across the way, can they be ruled-out conclusively as UOs? Who can say? And yet, who has ever actually witnessed a set of use values slugging it out with a set of exchange values? Or seen 'appearances' locked in a bitter tussle with 'underlying essences'? Or even witnessed a billiard ball struggling with itself as it rolls along. But, which DM-fan would now want to disagree with Engels (who claimed that motion like this is contradictory) simply on the basis that it is impossible to observe this alleged contradiction? If not, empirical niceties (i.e., observation) like this can't be crucially important in such cases.


We are still in the dark, therefore.


Some might object to the banal examples covered in this Essay. But Hegelian opposites look pretty banal themselves (and so do those that litter most DM-texts -- for example: magnets, males and females, up and down, seeds that negate plants, etc.) -- and they don't work, either, even in their own terms.


Oddly enough, and by sheer coincidence (I'm sure), 'dialectical opposites' turn out to be (by-and-large) the kind of 'opposites' dreamt-up by Idealist Philosophers thousands of years ago (and, indeed, more recently). Now, since this doctrine is a central tenet of Hermeticism, that should be enough to malign it in the eyes of anyone concerned to remain consistent with atheistic materialism:


"For everything must be the product of opposition and contrariety, and it cannot be otherwise." [Copenhaver (1995), p.38. Bold emphasis added.]


[In fact, pointing out that DM has appropriated the ideas of previous generations of mystics has absolutely no effect on dialecticians; why that is so will be revealed in Essay Nine Part Two.]


To test this claim, readers should now try to spot the difference (over and above a handful of superficial, stylistic variations) between the following two passages:


"CHAPTER X POLARITY 'Everything is dual; everything has poles; everything has its pair of opposites; like and unlike are the same; opposites are identical in nature, but different in degree; extremes meet; all truths are but half-truths; all paradoxes may be reconciled.' -- The Kybalion.


"The great Fourth Hermetic Principle -- the Principle of Polarity -- embodies the truth that all manifested things have 'two sides'; 'two aspects'; 'two poles'; a 'pair of opposites,' with manifold degrees between the two extremes. The old paradoxes, which have ever perplexed the mind of men, are explained by an understanding of this Principle. Man has always recognized something akin to this Principle, and has endeavoured to express it by such sayings, maxims and aphorisms as the following: 'Everything is and isn't, at the same time'; 'all truths are but half-truths'; 'every truth is half-false'; 'there are two sides to everything'; 'there is a reverse side to every shield,' etc., etc. The Hermetic Teachings are to the effect that the difference between things seemingly diametrically opposed to each is merely a matter of degree. It teaches that 'the pairs of opposites may be reconciled,' and that 'thesis and antithesis are identical in nature, but different in degree'; and that the ''universal reconciliation of opposites' is effected by a recognition of this Principle of Polarity. The teachers claim that illustrations of this Principle may be had on every hand, and from an examination into the real nature of anything


"Light and Darkness are poles of the same thing, with many degrees between them. The musical scale is the same-starting with 'C' you moved upward until you reach another 'C,' and so on, the differences between the two ends of the board being the same, with many degrees between the two extremes. The scale of colour is the same -- higher and lower vibrations being the only difference between high violet and low red. Large and Small are relative. So are Noise and Quiet; Hard and Soft follow the rule. Likewise Sharp and Dull. Positive and Negative are two poles of the same thing, with countless degrees between them....


"CHAPTER IX VIBRATION 'Nothing rests; everything moves; everything vibrates.' -- The Kybalion.


"The great Third Hermetic Principle-the Principle of Vibration-embodies the truth that Motion is manifest in everything in the Universe-that nothing is at rest-that everything moves, vibrates, and circles. This Hermetic Principle was recognized by some of the early Greek philosophers who embodied it in their systems. But, then, for centuries it was lost sight of by the thinkers outside of the Hermetic ranks. But in the Nineteenth Century physical science re-discovered the truth and the Twentieth Century scientific discoveries have added additional proof of the correctness and truth of this centuries-old Hermetic doctrine.


"The Hermetic Teachings are that not only is everything in constant movement and vibration, but that the 'differences' between the various manifestations of the universal power are due entirely to the varying rate and mode of vibrations. Not only this, but that even THE ALL, in itself, manifests a constant vibration of such an infinite degree of intensity and rapid motion that it may be practically considered as at rest, the teachers directing the attention of the students to the fact that even on the physical plane a rapidly moving object (such as a revolving wheel) seems to be at rest. The Teachings are to the effect that Spirit is at one end of the Pole of Vibration, the other Pole being certain extremely gross forms of Matter. Between these two poles are millions upon millions of different rates and modes of vibration.


"Modern Science has proven that all that we call Matter and Energy are but 'modes of vibratory motion,' and some of the more advanced scientists are rapidly moving toward the positions of the occultists who hold that the phenomena of Mind are likewise modes of vibration or motion. Let us see what science has to say regarding the question of vibrations in matter and energy.


"In the first place, science teaches that all matter manifests, in some degree, the vibrations arising from temperature or heat. Be an object cold or hot-both being but degrees of the same things-it manifests certain heat vibrations, and in that sense is in motion and vibration. Then all particles of Matter are in circular movement, from corpuscle to suns. The planets revolve around suns, and many of them turn on their axes. The suns move around greater central points, and these are believed to move around still greater, and so on, ad infinitum. The molecules of which the particular kinds of Matter are composed are in a state of constant vibration and movement around each other and against each other. The molecules are composed of Atoms, which, likewise, are in a state of constant movement and vibration. The atoms are composed of Corpuscles, sometimes called 'electrons,' 'ions,' etc., which also are in a state of rapid motion, revolving around each other, and which manifest a very rapid state and mode of vibration. And, so we see that all forms of Matter manifest Vibration, in accordance with the Hermetic Principle of Vibration." [Anonymous (2005), pp.59-62, 55-58. The first has been posted here; the second here. Spelling altered to conform with UK English. For more quotations along the same lines (taken from other mystical systems/theorists), see here and here.]


Compare the above with this:


"The Unity and Interpenetration of Opposites


"Everywhere we look in nature, we see the dynamic co-existence of opposing tendencies. This creative tension is what gives life and motion. That was already understood by Heraclitus (c. 500 B.C.) two and a half thousand years ago. It is even present in embryo in certain Oriental religions, as in the idea of the ying (sic) and yang in China, and in Buddhism. Dialectics appears here in a mystified form, which nonetheless reflects an intuition of the workings of nature. The Hindu religion contains the germ of a dialectical idea, when it poses the three phases of creation (Brahma), maintenance or order (Vishnu) and destruction or disorder (Shiva). In his interesting book on the mathematics of chaos, Ian Stewart points out that the difference between the gods Shiva, 'the Untamed,' and Vishnu is not the antagonism between good and evil, but that the two principles of harmony and discord together underlie the whole of existence....


"In Heraclitus, all this was in the nature of an inspired guess. Now this hypothesis has been confirmed by a huge amount of examples. The unity of opposites lies at the heart of the atom, and the entire universe is made up of molecules, atoms, and subatomic particles. The matter was very well put by R. P. Feynman: 'All things, even ourselves, are made of fine-grained, enormously strongly interacting plus and minus parts, all neatly balanced out....'


"The question is: how does it happen that a plus and a minus are 'neatly balanced out?' This is a contradictory idea! In elementary mathematics, a plus and a minus do not 'balance out.' They negate each other. Modern physics has uncovered the tremendous forces which lie at the heart of the atom. Why do the contradictory forces of electrons and protons not cancel each other out? Why do atoms not merely fly apart? The current explanation refers to the 'strong force' which holds the atom together. But the fact remains that the unity of opposites lies at the basis of all reality.


"Within the nucleus of an atom, there are two opposing forces, attraction and repulsion. On the one hand, there are electrical repulsions which, if unrestrained, would violently tear the nucleus apart. On the other hand, there are powerful forces of attraction which bind the nuclear particles to each other. This force of attraction, however, has its limits, beyond which it is unable to hold things together. The forces of attraction, unlike repulsion, have a very short reach. In a small nucleus they can keep the forces of disruption in check. But in a large nucleus, the forces of repulsion can't be easily dominated....


"Nature seems to work in pairs. We have the 'strong' and the 'weak' forces at the subatomic level; attraction and repulsion; north and south in magnetism; positive and negative in electricity; matter and anti-matter; male and female in biology; odd and even in mathematics; even the concept of 'left and right handedness' in relation to the spin of subatomic particles. There is a certain symmetry, in which contradictory tendencies, to quote Feynman, 'balance themselves out,' or, to use the more poetical expression of Heraclitus, 'agree with each other by differing like the opposing tensions of the strings and bow of a musical instrument.' There are two kinds of matter, which can be called positive and negative. Like kinds repel and unlike attract....


"Moreover, everything is in a permanent relation with other things. Even over vast distances, we are affected by light, radiation, gravity. Undetected by our senses, there is a process of interaction, which causes a continual series of changes. Ultra-violet light is able to 'evaporate' electrons from metal surfaces in much the same way as the sun’s rays evaporate water from the ocean. Banesh Hoffmann states: 'It is still a strange and awe-inspiring thought, that you and I are thus rhythmically exchanging particles with one another, and with the earth and the beasts of the earth, and the sun and the moon and the stars, to the uttermost galaxy....'


"The phenomenon of oppositeness exists in physics, where, for example, every particle has its anti-particle (electron and positron, proton and anti-proton, etc.). These are not merely different, but opposites in the most literal sense of the word, being identical in every respect, except one: they have opposite electrical charges -- positive and negative. Incidentally, it is a matter of indifference which one is characterised as negative and which positive. The important thing is the relationship between them....


"This universal phenomenon of the unity of opposites is, in reality, the motor-force of all motion and development in nature. It is the reason why it is not necessary to introduce the concept of external impulse to explain movement and change -- the fundamental weakness of all mechanistic theories. Movement, which itself involves a contradiction, is only possible as a result of the conflicting tendencies and inner tensions which lie at the heart of all forms of matter.


"The opposing tendencies can exist in a state of uneasy equilibrium for long periods of time, until some change, even a small quantitative change, destroys the equilibrium and gives rise to a critical state which can produce a qualitative transformation. In 1936, Bohr compared the structure of the nucleus to a drop of liquid, for example, a raindrop hanging from a leaf. Here the force of gravity struggles with that of surface tension striving to keep the water molecules together. The addition of just a few more molecules to the liquid renders it unstable. The enlarged droplet begins to shudder, the surface tension is no longer able to hold the mass to the leaf and the whole thing falls." [Woods and Grant (1995), pp.64-68; quoted from here.]


"'Everything Flows'


"Everything is in a constant state of motion, from neutrinos to super-clusters. The earth itself is constantly moving, rotating around the sun once a year, and rotating on its own axis once a day. The sun, in turn, revolves on its axis once in 26 days and, together with all the other stars in our galaxy, travels once around the galaxy in 230 million years. It is probable that still larger structures (clusters of galaxies) also have some kind of overall rotational motion. This seems to be a characteristic of matter right down to the atomic level, where the atoms which make up molecules rotate about each other at varying rates. Inside the atom, electrons rotate around the nucleus at enormous speeds....


"The essential point of dialectical thought is not that it is based on the idea of change and motion but that it views motion and change as phenomena based upon contradiction. Whereas traditional formal logic seeks to banish contradiction, dialectical thought embraces it. Contradiction is an essential feature of all being. It lies at the heart of matter itself. It is the source of all motion, change, life and development. The dialectical law which expresses this idea is the law of the unity and interpenetration of opposites...." [Ibid, pp.45-47; quoted from here. Quotation marks altered to conform with the conventions adopted at this site.]


Attentive readers will no doubt have noticed that the same brand of Mickey Mouse Science is prominent in the Hermetic tract and the Dialectical mantra intoned by comrades Woods and Grant.


Even so, DM-texts still make no attempt to explain with any clarity what it could possibly mean to suggest that 'dialectical opposites' could contradict one another. For example, who taught them to speak?


Unfair once more?


Not so.


Not, unless dialecticians mean something else by their use of "contradiction", which they have so far kept to themselves. If these 'opposites' do indeed 'contradict' one another, they must be able to talk.


[On this, see here, Interlude Eleven and Essay Eight Part Three. There is more on this in Essay Seven Part One. See also the discussion of Kant's concept of "real negation" in Appendix A.]




Returning to the main feature:


If we now read "A" as "wealth" and "B" as "poverty" once more, we would appear to have the following:


F63: Capitalism offers wealth, but delivers wealth and poverty, where wealth and poverty are opposites.


However, there are several problems with this paraphrase and, indeed, this option. One of these concerns the supposition that capitalism actually does offer wealth. Admittedly, for propaganda purposes its ideologues often claim it does -- but who believes them? Certainly, blatant lies like this can't serve as part of a socialist analysis.69


The following might therefore be regarded as a more viable option:


A1: Capitalism has the potential to offer wealth to all but delivers wealth and poverty, where wealth and poverty are opposites.


[F49a: Capitalism develops D, but actually delivers B and C, where B and C are opposites.]


In fact, this alternative has already been considered; it is just a variant on F49a. Once again, an unrealised potential can't contradict anything since it doesn't exist. So, even if it were true, A1 would be of no help in understanding what DM-theorists mean by their equation of forces with 'contradictions' in HM.


Someone could argue, for example, that the fact that there will be a sea battle tomorrow is contradicted by the fact that there won't (to use Aristotle's example). Neither of these scenarios is actual, but that doesn't stop them from contradicting one another.


Or so it could be maintained.


Certainly, those two sentences look contradictory (who has ever denied it?), but the question is, can both be true? That would have to be the case if this were an example of a 'dialectical contradiction' -- and, not insignificantly, they would have to imply one another (like the proletariat implies the capitalist class, so we have been led to believe), which they don't.


Once again: whatever else this, it isn't a 'dialectical contradiction'.


[The reader is also referred back to my earlier discussion of the distinction between "contradictory" and "contradiction".]


DM-enthusiasts regard their 'contradictions' as real material forces (they are a consequence, or they are the effects of such forces -- DM-fans are somewhat unclear about this, as we have seen), and the latter can only 'contradict' (in their sense of the word) whatever they can materially interact with, which plainly means that such factors have to co-exist -- as, indeed, Mao himself argued:


"The fact is that no contradictory aspect can exist in isolation. Without its opposite aspect, each loses the condition for its existence. Just think, can any one contradictory aspect of a thing or of a concept in the human mind exist independently? Without life, there would be no death; without death, there would be no life. Without 'above', there would be no 'below'.... Without landlords, there would be no tenant-peasants; without tenant-peasants, there would be no landlords. Without the bourgeoisie, there would be no proletariat; without the proletariat, there would be no bourgeoisie. Without imperialist oppression of nations, there would be no colonies or semi-colonies; without colonies or semicolonies, there would be no imperialist oppression of nations. It is so with all opposites; in given conditions, on the one hand they are opposed to each other, and on the other they are interconnected, interpenetrating, interpermeating and interdependent, and this character is described as identity. In given conditions, all contradictory aspects possess the character of non-identity and hence are described as being in contradiction. But they also possess the character of identity and hence are interconnected. This is what Lenin means when he says that dialectics studies 'how opposites can be and how they become identical'. How then can they be identical? Because each is the condition for the other's existence. This is the first meaning of identity." [Mao (1937), p.338. Bold emphasis added; quotation marks altered to conform with the conventions adopted at this site.]


Indeed, as Ira Gollobin also opined (quoting Engels):


"Opposites in a thing are not only mutually exclusive, polar, repelling, each other; they also attract and interpenetrate each other. They begin and cease to exist together.... These dual aspects of opposites -- conflict and unity -- are like scissor blades in cutting, jaws in mastication, and two legs in walking. Where there is only one, the process as such is impossible: 'all polar opposites are in general determined by the mutual action of two opposite poles on one another, the separation and opposition of these poles exists only within their unity and interconnection, and, conversely, their interconnection exists only in their separation and their unity only in their opposition.' in fact, 'where one no sooner tries to hold on to one side alone then it is transformed unnoticed into the other....'" [Gollobin (1986), p.115; quoting Engels (1891), p.414. Bold emphases added; quotation marks altered to conform with the conventions adopted at this site.]


The proletariat could hardly 'contradict' the capitalist class if one of them didn't exist! Same with the forces and relations of production --, and, indeed, with forces of attraction and repulsion.


Hence, while propositions about unrealised potentialities (or 'tendencies' -- or, indeed, sentences about future contingencies) might contradict one another (in the sense that they can't both become true, or both become false), in DM-terms an unrealised potential (or 'tendency') can't 'contradict' (in the sense that it actively opposes) something that isn't actual.


While it is possible to speak about 'contradictory tendencies' in an object or process, the point of referring to these as "contradictory" is that they can't both be actualised at once. So, for example, while it is possible for one end of a rather long iron bar to cool down while the other end is being heated (at the same time), it makes no sense to suppose that the same section of that bar (which could be specified in terms of precise volume intervals) can be in both states at once.


[If anyone thinks differently, they can e-mail me with their best shot. On the alleged 'contradictory tendencies' in capitalism, see here, here, here, here, and here.]


Perhaps then we should re-interpret F49 in the following manner?


F57: Capitalism develops productive forces capable of delivering wealth to all, but it actually delivers wealth to a minority, and poverty to most of the rest, where wealth and poverty are opposites.


[F49: Capitalism offers A, but delivers A and B, where A and B are opposites.]


However, in F57 we are confronted with a subtle change in the way that the "A" of F49 has been interpreted in the opening clause: it now stands for something like the "capacity to develop productive forces capable of delivering wealth". But, in the last clause it simply stands for "wealth", as before. Hence, F57 is actually equivalent to the following:


F49a: Capitalism develops D, but actually delivers B and C instead, where B and C are opposites.


Or perhaps:


F49b: Capitalism develops D (which has the potential to produce B or C), but in the end delivers B and C, where B and C are opposites.


Here, the 'contradiction' would seem to be between either:


(a) The capacity Capitalism has for delivering wealth and its actual delivery of poverty, or,


(b) The wealth it delivers to some and the poverty it imposes on the rest.


In the first case, clearly we don't have a contradiction. That is because, as we have just seen, a capacity is an unrealised potentiality, and as such it can't contradict something which does exist -- no more than, say, a woman's un-actualised capacity to play the flute contradicts her actualised expertise with the piano, or even her actualised state of not having a flute -- or, indeed, that of not being able to play the flute while she has to make do with a piano.


The second alternative above is no contradiction either, however much it offends our sensibilities. Option (b) is no more a contradiction than, say, £10,000 ($13,000) in one pocket contradicts £0.15 ($0.20) in another. Or no more than a £5 (or a $10) note in a millionaire's wallet (assuming this is all she has on her at the time) contradicts the £1000 ($1300) in a worker's pocket (who has just won a compensation claim, say) -- even if these two are sat next to each other at a UK Labour Party rally. To call these "contradictions" would be bizarre -- even on DM-terms. Are they 'struggling' with each other? Do they turn into one another? Does one imply the existence of the other?70


As we saw earlier, anyone who thought otherwise would be openly drawing attention to their own logico-linguistic naivety, if not perversity.


In any case, as we have also seen, there can be no literal contradiction between something that doesn't exist (i.e., the prospect of wealth under Capitalism, where this is 'meant to be' wealth for all) and something that does exist (i.e., the mixed fortunes of the people who have to endure conditions as they are).


Despite this, it might still be felt that the situation isn't as bad as the above makes out. The emphasis in F49 is on what Capitalism actually delivers, not on what it genuinely (or otherwise) offers. If "wealth" and "poverty" are real opposites, F49 could still serve in the way DM-theorists intend -- or, so it might seem.


F49: Capitalism offers A, but delivers A and B, where A and B are opposites.


Unfortunately, this rather desperate alternative reading diverts attention away from allegedly 'contradictory forces' onto their effects, once more. In that case, the nature of the direct relation between whatever the forces are that manage to produce these effects is still obscure, and not the least bit contradictory.


Nevertheless, even when consideration is given to such effects and the relation between them, a nagging question remains: just what is so contradictory about wealth and poverty existing side by side? Admittedly, to any socialist, this state of affairs is as intolerable as it is indefensible, but there still doesn't seem to be a literal contradiction involved here. True, this state of affairs may be paradoxical (but not to a Marxist); even so, the presence of one of these alleged opposites doesn't entail that an assertion that the other opposite also obtains is false, as would have to be the case if a literal contradiction were intended. They don't appear to imply one another, like the proletariat and the capitalist class supposedly do.71


If, on the other hand, we wish to re-define the word "contradiction" so that it becomes the equivalent of "paradox", "unjust", "something contrary to expectations", "deplorable" (and so on), all well and good. But that would merely concede the point being made in these Essays: that social reality is only 'contradictory' because of linguistic tinkering to that end, which naturally means that the claim that DM-'contradictions' haven't been imposed on the facts will have to be withdrawn. Seen in this way, DM-'contradictions' would, at best, be either figurative, or they would depend on the use of a word ("contradiction") that has been 'redefined' in order to produce the right result.72


Interlude Thirteen: Ordinary Language


Of course, someone might foolishly try to 're-define' their financial status by declaring that their bank balance of £5 ($7) was really one of £1,000,000 ($1,300,000). While this audacious ploy might make an ideal millionaire out of a fake one, it would have no material impact on their finances (except, perhaps, negatively, when they are found out).


Since the ordinary word "contradiction" already has a sense -- or, even a range of senses -- in everyday life, redefining it in ways that are unconnected with it/them, similarly has no physical effect on reality, no matter how ideal a temporary fix it might seem to be for one's ailing theory.


To be sure, and once again, it could be argued that dialecticians are at liberty to use words any which way they like, and that it isn't up to the 'thought-police' (such as the present author) to try to stop them.


As we saw here, DM-theorists can indeed use words as they please (not that they anyone's permission), but they can't then claim connotations for these words that wholly or partially apply to other words that already have an established use, which they then try to emulate, import, co-opt, or replace. So, they aren't at liberty to claim their use of "contradiction" is in any way connected with its ordinary use, or even with its role in FL, not without causing confusion -- but mercifully, so far, only to themselves.


In that case, this novel use of "contradiction" requires an explanation -- since the connections it once enjoyed with its supposed vernacular-, or FL-'twin' have long since been severed, leaving it adrift, and hence meaningless -- something that dialecticians have signally failed to provide (not that they have tried all that hard to produce one for well over a century).


And, that is why I have repeatedly been asking for such clarification in this Essay. [More on that in Essay Twelve Part One.]


However, as a matter of fact, DM-apologists aren't employing this word in any which way they please. DM-jargon has a chequered history and an equally chequered origin, which means it already possesses specific connotations, which they had no part in choosing or establishing. Just like those who use jargon associated with, say, the Christian Trinity (whose terminology, unsurprisingly, emerged from the same cess-pit of Neo-Platonic Thought that gave birth to Hegel's fantasies), dialecticians have appropriated this particular word (i.e., "contradiction") from Hermetic/Hegelian Philosophy alongside the confused ramblings of other mystics, which means that DM is in fact Mystical Christianity's direct descendant and now poor relation.


Dialecticians should feign no surprise, therefore, when they are accused of being covert mystics; because they can't explain what their words mean in comprehensible terms -- using the vernacular (as Marx enjoined) -- their terminology is as big a mystery to them as it is to anyone else!


Those who think that ordinary language is far too limited to be of any use in such contexts should read this and this, and then perhaps think again. They should also take issue with Marx himself:


"The philosophers have only to dissolve their language into the ordinary language, from which it is abstracted, in order to recognise it, as the distorted language of the actual world...." [Marx and Engels (1970), p.118. Bold emphases alone added.]




On the other hand, if the word "contradiction" possesses a special, DM-sense, which allows for its legitimate use in such circumstances, then DM-theorists have yet to say what that is.


In response, it could be argued that their use of the word "contradiction" implies opposition and/or tension. But, even though "wealth" and "poverty" are opposites in the ordinary sense, they don't seem to oppose each other in an active way, as one would expect they should if they genuinely illustrated the validity of the equation of 'contradictions' with forces. Admittedly, poverty acts as brake on development of the productive forces at certain points in history (warping the development of those who have to endure it, etc.), stoking up resentment, class hatred and (as a result) fomenting 'labour unrest'. But, over and above the influence these states of affairs have on human agents, these lifeless concepts appear to have no active connection with one another. Sure enough, the material conditions they express, or 'reflect', might indeed create tension in those who have to endure them, but none of the latter would describe what they feel by using the word "contradiction", unless, of course, a fast-talking DM-evangelist had sold them on the idea. In ordinary language the word can't be given such a meaning without altering the sense it already has.73


Furthermore, if this set of consequences is meant to be taken as a new gloss on F49 (by way of illustrating the alleged 'contradiction' between E1-, and E2-type events discussed earlier) then it, too, reduces to the claim that it is the effects of effects that are 'contradictory', and not the original effects themselves. Down this road there lies, I fear, yet another "bad infinity" --, which ends "who knows where?"


F49: Capitalism offers A, but delivers A and B, where A and B are opposites.


The second difficulty with this reading is that although wealth and poverty are genuine opposites (again, in the ordinary sense), they don't appear to be classic examples of dialectical-UOs (even if we knew what they were!). To be sure, under Capitalism the wealth of one class is connected with the poverty of others, but this is a familiar causal connection. They aren't internally-, or logically-related, despite claims to the contrary. That this is so can be seen from that fact that were this not the case, we would find we couldn't agree (with Engels) that under Capitalism poverty exists "where it need not be".


If there were a 'dialectical' (or "internal") "unity in difference" connecting poverty and wealth (like that which dialecticians allege between, say, the north and south poles of a magnet, or that between capitalist and worker (as classes)), then we couldn't argue that socialism will eliminate one at the same time as abolishing the other. But, the whole point of a socialist society is that all should become as wealthy as the productive forces will allow. If there were a logical link between these two states (poverty and wealth) then they would be inseparable in all modes of production and we would have to temper our slogans somewhat. We might then have to point out that in eradicating poverty, workers would be eradicating wealth, too. That we do not so argue -- we actually claim the opposite that socialism can produce wealth for all -- indicates that the relation between wealth and poverty isn't a logical (or internal) connection, but causal.


Of course, it could be argued that there is an internal/logical link between "wealth and poverty under capitalism". The above treats these terms abstractly. That objection will be dealt with below.74


A genuine example of an "internal relation" might help here: if the Prime Meridian at Greenwich were to be abolished, the whole system of longitudes would automatically go with it. Moreover, anyone employing this system correctly is able to derive conclusions about where they are on the planet in relation to the Prime Meridian. Where they are in terms of their latitude is therefore 'internally related' to that Meridian by a series of inferences based on a set of measurements and conventions established by international agreement. Of course, these days this is all done automatically, and has been greatly augmented by GPS guidance systems. But the point is still valid. This isn't at all like the elimination of poverty. Poverty will be eradicated not by destroying wealth, but by extending wealth production and establishing equitable forms of distribution -- and, of course, by abolishing class division (etc.).


It could be argued here that this misconstrues the nature of the link between poverty and wealth under Capitalism, turning it into something abstract that supposedly exists between two unchanging concepts. Contrary to this, dialecticians hold that wealth and poverty are dialectically linked --, and not just to each other. They are related to, and are constituted by, the Mode of Production in which they both exist. Hence, under Capitalism, wealth can't exist without the creation of poverty. To eradicate the latter, Capitalism must be abolished. In a fully socialist society, the present connection between wealth and poverty would vanish.


However, the link between wealth and poverty is still causal (wealth creates poverty under capitalism, and it does so for well-known historical, economic and social reasons); dressing these up in pseudo-logical/'dialectical' finery can't change that fact -- even if it does succeed in mystifying something that has clear social and material roots.


But, even if that weren't so, none of it makes sense in DM-terms, since wealth and poverty don't "struggle" with one another, nor do they change into each other, which they should do if the DM-classics are to be believed.


The basic problem here, of course, revolves around the anthropomorphism implicit in the idea that concepts can enter into struggle with one another. This mystification appears as part of the belief that because wealth and poverty are opposites they are actively oppositional and cause or initiate struggle, in and of themselves. On this account, it is the opposite/oppositional nature of concepts that creates or induces struggle -- whereas in reality it is clearly material conditions that cause it. Only by confusing a causal with a conceptual connection can DM even seem to gain some purchase -- that is, if this is what dialecticians mean here. But, as we have seen, this entire thesis is just one more consequence of the RRT and LIE (both defined in Essay Twelve -- this was also a conclusion reached in Part One of this Essay).75


It could be objected that DM-theorists don't disagree with this, even though they maintain that these material forces are "dialectically inter-linked". Hence, no dialectician of any sophistication thinks that concepts can, of themselves, cause, change, or initiate struggle, only that the material roots of struggle are mediated by the ideas people form of their circumstances and the contradictory interests these generate.


Worded differently, this wouldn't be inconsistent with anything written in these Essays, since it involves concepts drawn from HM.


Nevertheless, if the above is meant to illustrate the real meaning of F50, then we would once more have an example of the effects of the effects being used to illustrate the action of a force or set of forces. That impasse was criticised at length earlier.


F50: Capitalism offers A, but delivers C instead, where C is a paradoxical outcome.


However, dialecticians might object to the accusation that they believe that concepts enter into conflict with one another; they would surely point out this is vaguely how Hegel might have things (if it is worded more carefully). By way of contrast, they emphasise the fact that it is real people, and real forces in the material world that enter into conflict.


But, when the language dialecticians use is examined, the allegation that dialecticians anthropomorphise nature and society by projecting human qualities onto both of these forces itself upon us (no pun intended). [On this see Interlude Thirteen.]


[LIE = Linguistic Idealism; RRT = Reverse Reflection Theory.]


The animated contrast that is imagined to exist between dead concepts like these seems plausible only because they are viewed as the idealised equivalents of the real relations between human beings, reified in an inappropriate metaphysical or linguistic form. Human beings give life to the concepts they use, but under circumstances not always of their own choosing, and they do so as a result of their practical activity modified and shaped by ambient class and social relations. The reverse doesn't take place. 'Concepts' don't give life to human relations, although their use by human agents can affect the roles they play or assume in everyday life. They certainly modify the ideas that individuals from antagonistic classes form of their own material interests, etc. Unless we suppose concepts are agents in their own right (in a sort of inverted Hegelian form, whereby they perhaps walk the earth in place of human beings), they can't 'reflect' things that human beings haven't already sanctioned for them as a result of their own social relations (and by means of the above constraining factors). History is, after all, the result of the class war, not a consequence of the struggle between concepts.


[DM-supporters might be tempted to argue that the above is a travesty of  their theory; no Marxist dialectician believes that concepts enter into struggle with one another. I have already tackled that objection above.]


As should seem obvious, these comments are based on theoretical considerations drawn from HM, but this is precisely where that scientific theory can provide the interpretative sophistication which DM and 'Materialist Dialectics' obscure and then invert in an idealised or fetishised form.76


This shows, once again, that the inversion DM-theorists say they have inflicted on Hegel was, at best, merely formal, at worst, illusory.


In which case, it seems their theory can only 'work' in an Ideal or Mystical 'universe'.


Nevertheless, it could be objected once more that the above assertions are unfair because it was in fact dialecticians who first pointed out that FL uses lifeless and dead concepts, as a result of which it can't explain change.


[FL = Formal Logic; DL = Dialectical Logic; HM = Historical Materialism.]


However, the unwelcome truth is that it is DM-theorists who employ concepts that come to life only when they are anthropomorphised and are viewed as the abstract expression of conflict (i.e., in effect, these are the fetishised analogues of social forms, as we have seen -- for example, in Interlude Thirteen). This is revealed, for example, by their profligate use of words like "contradiction" and "negation" in connection with natural processes, and now in relation to social change (on this, see Interlude Ten).


In contrast, the rejection of this fetishistic approach re-humanises concepts -- but only in relation to social development and interaction -- by revealing them for what they are: the conditioned products of social relations among human beings. So, in HM, in place of the fetishised theories we find in DM, we have concepts enlivened by human practice, expressed in the material language of ordinary life (indeed, as Marx enjoined). In this way, it is possible for our description and analysis of the social world to become fully humanised -- a small but important step in the fight to make it fully human.


Once again, if this is regarded as unfair or inaccurate, the reader is referred back to:


(i) Essay Three Part One (for example, here and here), where the archaic linguistic moves underlying this pernicious form of Idealism were unmasked;


(ii) Essay Three Part Two, where the roots of this abstract approach to theory were traced back to traditional ruling-class and Idealist forms-of-thought;


(iii) Essay Two, where the dogmatic and Idealist nature of DM was exposed;


(iv) Essay Four, where the anthropomorphic nature of DL was laid bare;


(v) Essay Five, where the confused nature of the language Engels used (to depict motion) was debunked;


(vi) Essay Seven, where it was shown that the 'Three Laws of Dialectics' were based on a fetishised view of discourse, compounded by an unhealthy dose of Mickey Mouse Science;


(vii) Essay Eight Part One, where further aspects of this anthropomorphic doctrine were uncovered;


(viii) Earlier sections of this Essay, where the application to nature of Hegelian concepts was shown to be openly animistic; and,


(ix) Essays Twelve and Fourteen (summaries here and here), where these sordid details are traced back to ancient, ruling-class dogmas that no self-respecting socialist or materialist should want to touch with someone else's bargepole.


Indeed, it has been a unifying theme of all the Essays posted at this site that the application to nature of concepts drawn from Hermetic Philosophy has branded DM as an irredeemably Mystical and Idealist theory, and, further, that this has only succeeded in compromising the scientific status of HM. Anyone who still takes exception to the claim that dialecticians use animistic notions drawn from Hermetic Philosophy (where conflict is re-configured in linguistic terms, and then projected back onto nature and society) should feign no surprise when that is where this sorry tale has in fact been heading all along.


The solution is, therefore, for recalcitrant comrades to stop complaining, and point their fingers in the right direction: at the DM-classicists who imported these "ruling ideas" (upside down or 'the right way up') into Marxism.


Interlude Fourteen: Contradictions In Das Kapital?


[This used to form part of Note 70.]


However, Scott Meikle makes a valiant attempt to argue that some sort of sense can be made of the idea that there are indeed 'dialectical contradictions', for example, in capitalism. His case revolves around a short and relatively clear account of the alleged 'contradiction' between use-value and exchange-value -- or more pointedly, between the "relative form" and the "equivalent form" of value -- in Volume One, Chapter One, of Das Kapital.


Now, I don't want to enter into whether or not Meikle's interpretation of Marx is accurate; my concern here is whether he can explain how and why the relation between the relative and the equivalent form of value is indeed an example of a 'dialectical contradiction'. Moreover, since Meikle's comments are typical of the way that many Dialectical Marxists use language in this area -- and, indeed, how they conceptualise 'contradictions' supposedly at work in HM (this is especially true of theorists belonging to the HCD-tendency) --, an examination of his argument will help illustrate where many of them descend into a irredeemable confusion.


[Of course, in what follows I am well aware that many will take issue over Meikle's specific interpretation of Marx, or with some of the more detailed points he raises -- or even with his entire approach. I will, however, be looking at the work of others who have tried to make sense of a 'dialectical' interpretation of Das Kapital (with "dialectical" understood, not in its classical, but in its post-Hegelian sense) in a later re-write of this Essay. Until then, readers are redirected to the discussions here and here.]


This is how Meikle initially approaches the topic:


"All the contradictions of capitalist commodity-production have at their heart the contradiction between use-value and exchange-value. Marx reveals this contradiction to lie at the heart of the commodity-form as such, even in its simplest and most primitive form....


"The simple form of value itself contains the polar opposition between, and the union of, use-value and exchange-value.... [Marx writes that] 'the relative form of value and the equivalent form are two inseparable moments, which belong to and mutually condition each other...but at the same time they are mutually exclusive and opposed extremes.' Concerning the first he observes that the value of linen can't be expressed in linen; 20 yards of linen = 20 yards of linen is not an expression of value. 'The value of linen can therefore only be expressed relatively, that is in another commodity. The relative form of the value of the linen therefore presupposes that some other commodity confronts it in the equivalent form.' Concerning the second: 'on the other hand, this other commodity which figures as the equivalent, can't simultaneously be in the relative form of value.... The same commodity can't, therefore, simultaneously appear in both forms in the same expression of value. These forms rather exclude each other as polar opposites.'


"This polar opposition within the simple form is an 'internal opposition' which as yet remains hidden within the individual commodity in its simple form: 'The internal opposition between use-value and exchange-value, hidden within the commodity, is therefore represented on the surface by an external opposition,' that is the relation between two commodities such that one (the equivalent form) counts only as a use-value, while the other (the relative form) counts only as an exchange-value. 'Hence, the simple form of value of the commodity is the simple form of the opposition between use-value and value which is contained in the commodity.'" [Meikle (1979), pp.16-17. Italic emphases in the original.]76a


But, what evidence (or argument) is there to show that these are "polar opposites", let alone that they are 'dialectically-united'? Or, indeed, that there is a distinction here with a difference? And, why call this a "contradiction"? However, like so many others, Meikle neglected to say; he was nevertheless happy to help himself to the use of this word.


[There is, however, a relatively clear attempt to justify its use in Heilbroner (1980), pp.29-58, but more specifically, pp.41-42). I have examined Heilbroner's interpretation, below. Readers should note that I am not questioning Marx's use of non-dialectical terms, such as "relative form" and "equivalent form" [RF and EF, henceforth]. I have also discussed his use of the word "contradiction" here.]


Nevertheless, as we will see in Essay Eight Part Three, this way of talking is based solely on Hegel's egregious misconstrual of the 'negative form' of the LOI as equivalent to the LOC. In that case, what has Meikle got to offer the bemused reader that stands some chance, any chance, of filling the gaping hole Hegel left behind in his misbegotten 'theory'?


Apparently, only this: