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




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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 nearly thirty 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 to appreciate fully 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 25 years, I have heard all the objections there are! (Many of the more recent debates are listed here.)]


Finally, 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 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.]


Some 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 these 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 added links to subjects or issues that are part of common knowledge (such as recent Presidents of the USA, UK Prime Ministers, the names of rivers and mountains, 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 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, 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 these links when it becomes apparent that they have changed or have disappeared, I cannot 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.


As of February 2021, this Essay is just under 116,500 words long; a 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: 22/02/21.]


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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 They Properties Of Totalities?


(3) What Exactly Do Forces 'Contradict'?


(a) Different Types Of Force Couples


(b) AA-, And RR-Forces


(c) First Attempts At Clarification


(d) AR-Forces


(4) A Contradictory Theory?


(a) Literal Forces In Opposition


(b) The Revenge Of The Non-Existent


(c) Prevention And Its Discontents


(d) A Balanced Account Of Prevention?


(e) S&M?


(f) Hole To Let


(g) Too Many Forces Spoil The Broth


(5) Real Material 'Contradictions'?


(a) Sinking In Concrete


(b) Rees, Ollman And 'Concrete Forces'


(c) The Impertinent Explanation


(d) Conflict Resolution


(e) Where The Shoe Pinches


(f) Not What The System Ordered


(g) An Apparent Contradiction At Last!


(h) Opposite Tendencies I


(i) Opposite Tendencies II


(j) Last Chance Saloon


(6) True Contradictions?


(7) Last Rites


(a) Dialectics In ER


(b) Back To The Drawing-Board?


(c) Dialectics And The Revival Of Teleology


(d) Coup De Grace


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


(7) Contradictions In Das Kapital?


(8) Notes


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


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


(11) 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, I aim to sever the link that most dialecticians believe exists between 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.]


Be this as it may, Marxist dialecticians frequently 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 on who is telling the tale. But, dialecticians also inform us that this view of forces is only valid if it is backed-up in each case by a careful scientific and theoretical analysis -- with the results having been tested in some form of practice.1


Citations like those listed in Note 1 -- which make the above points -- can be multiplied almost indefinitely. To be sure, such passages are often accompanied with extensive qualifications -- again, depending 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 claims they make with adequate evidence3 -- or any at all --, but with whether the idea that forces can be used to model, illustrate or explain 'dialectical contradictions' makes any sense at all.


Gravity Is Reassuringly Undialectical


As we will see, the identification of forces with contradictions is thoroughly misconceived.4 There are a number of obvious initial 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, for this 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. So, if classical Physics is to be believed, it isn't easy to see how such forces could be viewed as 'contradictions'.5


Post-classical Physics offers even less comfort for DM-theorists. There, 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.6


And, this isn't just the case with 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.]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 these two say, it is reasonably clear that a mere "relation" between two bodies is incapable of making one or both of them move, unless there were some sort of a force operating between them -- or 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 in motion, is the result of 'contradictions', interpreted as opposing forces). Plainly, if there is only one force present (or perhaps even none at all!), there can't be any 'dialectical contradictions', to begin with.


Hence, it would seem that DM can't explain much -- if any -- of the bulk motion in nature.


Admittedly, Engels made a weak attempt to solve the orbital 'problem' by inventing a repulsive force, which he implausibly identified with "heat"; this fanciful notion has been critically examined in Note 7.7


John Molyneux has also weighed in with this 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.]


However, if Relativity is correct, there is no force of gravity. But 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 plausible, and "momentum" was a/the 'dialectical opposite' of the force of gravity, the following aspect of Molyneux's theory still would 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, those internal to 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 here 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 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 the should)?


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 even make sense 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" only as 'figurative contradictions' -- or, maybe, the other way round, interpreting 'dialectical contradictions' as 'figurative forces'. Either one or both of these could then form part of an analogical, or perhaps 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 theoretical retreat perhaps recommended to him by his admission that the concept of "force" was derived from ancient animistic/mystical theories of nature, hence its use in DM could 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 has two untoward consequences Engels appears not to have noticed:


(1) It makes his version of DM look even more positivistic that it already seems -- at least as it is presented in 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. The whole idea would then be little more than a "useful fiction", introduced in order to account for the phenomena instrumentally. This would make the identification of forces with contradictions even more problematic as a result (as will be demonstrated below). Plainly, and 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 contradictory relationship between bodies would become little more than a re-description of their relative motion. [Woods and Grant seem to be thinking along those lines, too, as we saw earlier.]


Unfortunately, in that case, there would be no interconnection between such bodies, which appears to be an essential factor required by other DM-principles -- for instance, where we are told that everything is "interconnected". This seems to mean 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 will have 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 detail in Part One.]


Not even the relative motion between bodies travelling in opposite directions could supply a credible dialectical connection here, should an interaction result from this. Clearly, 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, here), since the connection, or mediation, between moving bodies would clearly be missing. Hence, any subsequent interaction would 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.]


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 is no use at all. If DM is to work, forces must exist, and any reference made to them as 'contradictions', 'internally-related' to one another, must be concrete and literal.10


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 at all easy to see how figurative language is capable of filling the gaps in an explanation of objects and processes in the material world -- any 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, at least, no more than would describing a man as a "pig" imply he had 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 detailed below --, interpreting forces figuratively might prove to be the only viable way that contradictions could be 'interpreted' as 'forces', even if this 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' form of Instrumentalism and/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 figures of speech to begin with? Once more, describing a man as, say, a "pig" might perhaps account for his crude behaviour (but not on the basis that his anatomy or physiology is literal pig anatomy or physiology), but the utility 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.


'Contradictions' As Mathematical Models?


The first of these is connected with the way that forces are already represented in Mathematics and Physics, for example -- 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 were 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 sort of thing that could be physically moved away from one another -- 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 been any mathematics involved in such DM-descriptions. So, while a technician, 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? Can, for example, a moving object be more 'contradictory' than it used to be? Maybe 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?


(b) Forces in nature can be 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 can 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 true of 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.]


And, 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. Several 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 they could -- implies that in practice not even DM-fans think this analogy is at all apt, or, indeed, 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 on this.14a


Properties Of Totalities?


The second reason why this is an inappropriate way to depict 'contradictions' revolves around 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 as isolated from their surroundings) completely misconstrues their role in DM, 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' (i) Are internal to objects and processes causing them to change (as a result of an internal dynamic), (ii) Arise externally between objects as they form part of a mediated system, group of systems and processes, (iii) Merely arise from our description of objects and processes as 'contradictory', this perhaps resulting from our partial or relative knowledge of reality, etc., (iv) Derive from a combination of all three -- or, indeed, (v) Emerge because of some other factor about which we are ignorant.


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, which 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 included in 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 added; quotation marks altered to conform with the conventions adopted at this site.]


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 detail here and here.] Even so, 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 are 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" are in effect those which an object merely experiences in 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 'logical' anyway, but no less bogus for all that. Until then, see here.]


In addition, the proffered DM-response outlined a few paragraphs back fails to resolve the problems 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 it/they would be (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 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, this 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 is still unclear). 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, presumably, is the nature of their mediated 'unity in contradiction'. However, the "Totality" is related to nothing else that could condition it. So, if the "Totality" is a contradictory whole, then it would be so in a new and-as-yet-unspecified sense. The 'parts' of a 'dialectical contradiction' are supposed 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 -- although I have thrown this lazy inference into considerable doubt here). Not only does the whole here not imply any one of its parts, it could exist without many most its parts. Does the universe really imply Venus, or the Crab Nebula? The universe could surely have existed without Venus or the Crab Nebula, too. 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. 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) 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 (unless it 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 that 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, thus 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 if it is different.


[Anyone impatient with 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 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, 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' one another 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 it isn't, 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, AIDS). Conversely, if the identification of forces with contradictions is merely figurative, then DM would be indistinguishable from, say, metaphysical poetry.


[HEX = Hegelian Expansionism; AIDS = Absolute Idealism; CAR = Cartesian Reductionism.]


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


However, even if we assume this, the analogy 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'.


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


Many of the quotations given in Note 1 clearly imply that in DM only AR-forces are 'contradictory'. This type of force couple 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 considered. Hence, it is to them that I now turn.


AA- And RR-Forces


Unfortunately, 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


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 can be opposites. As we noted above, 'dialectical opposites' are not only supposed to imply each other, each can't exist without the other. Which A-force implies another A-force; which one 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 into, or out of, equilibrium. However, this 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 here in natural systems of forces (implicated in change, equilibria and in '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 is difficult 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 adapted to neutralise this 'difficulty', it would succeed in so doing only because of a linguistic dodge. In that case, any 'truths' that sprang into existence as a result would plainly be a by-product of yet another example of terminological juggling, and not because of the way the world happens to be -- which would in turn mean that dialectics had been read into nature.21


[However, there are dialecticians who claim that objects and processes possess many "opposites"; for example Gollobin (1986), p.122 (but even he says they are "paired").]


Of course, this whole metaphysic originated in the egregious and twisted 'logic' one finds in Hegel's work, 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 that anything-else-whatsoever. [On this, 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 demolish what is left of Hegel's already fractured system, which, as we have just seen, postulates that everything is paired with its own unique "other". Naturally, if true, this idea would mean that the Empire State Building, for example, could change into, say, a T Rex, and the Pacific Ocean could develop into George W Bush, and much else besides. Since things like this don't happen, so far as we know, we must conclude that, either:


(1) Hegel was right: objects and processes have only one unique "other", which 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' -- and the whole point of accepting this 'logical' exercise will now have vanished;




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


Nevertheless, it could be argued that in this context the word "opposite" really means "oppositional". This 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 manner --, 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 claimed.


However, this latest revision seems to be inconsistent with the claims made in several of the passages quoted in Note 1. These 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 seem to be so useful, -- no, strike that, so crucial -- 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. 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 move in 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 simply 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 but bodies, in the first place.24


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 (already) impressed motion of bodies 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 more) forces don't oppose each other; they oppose or augment whatever motion is already present in the system, however 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 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 (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 a force that affects it? Certainly they aren't unified opposites (i.e., opposites on the same type, so they are 'dialectically'/'logically' connected -- that is, the existence of one implying the existence of the other, in the Hegelian sense of this word, which, as we have seen, is a DM-requirement, too). Moreover, 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 -- although I have thrown that lazy inference into considerable doubt here). If it were 'dialectical', they would imply one another and each couldn't exist without the other.


At best, the forces involved might tend to produce an opposite motion (or change of motion, perhaps) to that which has already been impressed -- 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 made to seem to work by mis-describing the phenomena.25


Only those who feel confident that they can give a clear sense to the idea that forces and motion are ('dialectical') opposites are in any position to reject the above objection with anything more than a 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 this could be done (i.e., even if it were possible to provide 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 episodic 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 impressed motion (not other forces), and the idea that change was the result of systematically inter-related forces would have to be abandoned.


As should now seem obvious, each constituent in 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 other moving bodies, in the system).27 This would put a strain on the meaning of the word "opposite", once more, and this would remain in place until the meaning of that word had been altered accordingly, allowing several such items 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, in view of the fact that none of these forces would imply the others, and each could exist without the rest -- which should be the case with DM-'opposites'.]


Not only that, as we have also seen several times, given such ad hoc linguistic tinkering, dialectics would apply to nature and society only because of yet another subjectively applied linguistic convention.


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 as a grand theory capable of explaining change as a consequence of the 'contradictory' nature of reality -- or, as the result of the interplay between opposite forces -- now amount to little more than a few vague ideas about the relation between a force and the impressed motion 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 been 'adjusted' accordingly. If this is what DM-theorists mean when they come out with their impressive sounding 'dialectical' theories, then it seems that their theory can only be rescued from oblivion by making reality Ideal -- i.e., making the 'truth' of DM-theses sensitive to ad hoc linguistic 'tinkering'.


However, even if the above objections are misguided in some way, in DM-terms, none of it 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 more quotations like the above can be found here.]


Clearly, this force doesn't change into this movement, nor does this movement change into this force.


[Incidentally, this disposes of Weston's attempt to locate the second force in a gravitational field in '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 allegations. 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 an equal and opposite reaction, 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 one would follow upon the other: 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 F*, then F*, not N, would be the opposite of F, and F would turn into F*, not N!


[The same applies if we substitute "inertia" for "momentum", and/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.


To that end, let us imagine two bodies that are in collision: A and B. 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, 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 to 'struggle' with! 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!


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 both 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 these factors 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.


[The above is just a specific example of a more general, but fatal, defect that sits right at the heart of the DM-'theory' of change, exposed in extensive detail here. Nevertheless, this point can be generalised -- as it will be below -- to show that no two or more forces could 'contradict' one another in the way that dialecticians suppose.]


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 a clarification of what it could 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 thesis that UOs operate everywhere in nature from being 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, no contradiction can arise. In that case, F2 threatens to undermine this interpretation of DM, killing it for want of forces.29


It could be argued 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 objection will be examined later in this Essay.


This suggests we should reconsider an option left unexplored earlier; i.e., the one which argued that forces are the only legitimate candidates to be placed in such oppositional couples, not the motion they change or induce -- 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 contradicted one another before they combined to create the resultant, R.


On this view, forces are 'contradictory' only of other forces, and not of bodies or of already impressed 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 -- in so far as 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 -- and while this relative motion might subsequently affect their movement, it wouldn't internally-link such bodies. And yet, this is precisely the difficulty that exercised Traditional Philosophers as part of the classical metaphysical problem of the nature of forces; DM has simply reproduced it in an entirely 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 one another, for example -- although I have thrown that inference into considerable doubt here). But, unless DM-theorists have been keeping salient details to themselves, this isn't the case with relative motion. So, the relative motion of bodied can't be a 'dialectical' relation, whatever else it is. The same comment applies to forces, too. 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 in 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 been ascertained first. 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 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 progresses. 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, this 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 its turn, this implies that even if humanity never actually reaches this blessed state (i.e., of Absolute Knowledge), we can, in the here-and-now, make this inference: 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 there were no, 'contradictions' in the ultimate future state of knowledge of the "Totality", then either the DM-view of the limit of knowledge (where most if not all contradictions have been resolved) must be false, or the DM-belief that humanity is converging on that limit must itself be false, since there is no such limit. This is now implied by the DM-theory of knowledge: that reality is largely, or completely, a contradiction-free zone.33


Again, if this is what dialecticians mean by 'contradictory forces',34 then nothing may be so described until everything has been so described. [Again, I am taking for granted the conclusions I mentioned earlier. If readers find this latest assertion hard to accept, they should consult the full argument presented in those other Essays.] But, this reverses the dialectical picture, 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 a synoptic vantage point, 'contradictions' would disappear (or largely disappear -- the story gets a little vague at this point). Here, in contrast, the idea seems to be that we may only depict forces in nature as absolutely 'contradictory' after The Trumpet has finally been blown on 'dialectical' Judgement Day. The problem here is that this may only be done when all (or most) 'contradictions' have been resolved! Paradoxically, this in turn would 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!


One horn of this dilemma suggests that 'dialectical contradictions' don't really exist (since they are merely artefacts of 'relative knowledge') -- and if they don't, they can have nothing to do with change, either. The other option suggests that we can't now assert that they do exist (since we aren't in possession of Absolute Knowledge), so, because we aren't in possession of the full picture, we can't claim to know whether they cause change! Either way, a 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, this scenario is easier, and more natural, to interpret 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 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 more likely source of DM-'contradictions': AR-force couples.




In the previous section, it became clear that little sense can be made of the equation of 'dialectical contradictions' with  AA-, and/or RR-forces, and this turned out to have nothing to do with the difficulty of seeing whether or not such couples contained opposites -- which they manifestly don't. 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 that DM-theorists require 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, anyhow.36



Figure One: Grab This, Comrades --

It's A 'Dialectical Straw'...


An initial serious difficulty this idea faces is that 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.


However, even if they were opposites of the same type, these forces 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 in a vector calculus, but we have already seen that even this formal translation is of little assistance to DM -- which is 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, so that one can't exist without the other (unlike, say, the proletariat and the bourgeoisie, which are supposed to imply one another -- although I have thrown that lazy inference into considerable doubt here). 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. 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.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


Cases like these illustrate 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 regarding forces only as polar oppositional pairs could accommodate this particular property of natural forces.40 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


It could be objected here 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 reply does succeed 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 exactly 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 thus impossible to decide which of the 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 this number, and these alleged protons weren't really protons, and the element rarely if ever had a nucleus, and anyway it wasn't an element after all! 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 disappear by being reformed away; Imperialists could assist in the abolition of injustice; 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 boss-classes might even overthrow themselves!42


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 forcefully.


In fact, as we will see in Essay Nine Part Two, this is indeed how class collaborationists have argued: the allegedly 'contradictory' nature of the Guomindang, for example, 'allowed' the CCP to 'justify' forming alliances with them. It is also quite clear that DM provided 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 practically anything at all, and its opposite, in the same breath -- often by the same dialectician.


Of course, it could be pointed out that forces operate in history in more complex ways than those at work 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.43


Nevertheless, even if all of the above points turn out to be misguided in some way, there are other, 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 trivial. On the other hand, it could turn out that nothing could have been said in this regard, which would more obviously explain the long-term and deafening silence. Indeed, as will soon become clear, the latter 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 appears 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 social and natural conflict, locating them in the activities the 'gods' or other 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 nature itself.


Clearly, DM-theorists view material 'contradictions' as their primary concern; verbal wrangles are, obviously, only of peripheral interest. Even so, this idea is still no less analogical, for we were certainly aware of the latter sort of contradiction (i.e., those involving verbal wrangles) well before we were informed (by Hegel) of the former. In that case, even Hegel's argument must have proceeded from the social to the natural world, which is indeed what the history of the subject reveals: neither Hegelian nor 'Materialist Dialectics' existed in pre-historic times (nor even before the 18th century), but 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 --, DM-theorists have manifestly relied on an analogy drawn between the way human beings argue (or fight) and the way conflict seems to take place 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 could possibly be attributed to this way of picturing conflict. Even to this day, we still lack the material grounding that DM-theorists require.


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 'dialectically-united opposites', interpenetrating one another (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 will see, not even the opposite poles of a magnet, or positive and negative poles in atomic theory and electrodynamics. In which case, the application of DM to the non-social world is, at best, figurative and non-literal.


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 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 give a clear account of the precise nature of the connection between 'contradictions' and opposing forces. 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 seems 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.


[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. They 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 -- although I have thrown that hackneyed inference into considerable doubt here), and hence aren't 'interpenetrated'.


However, quite independently of these annoying '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 '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 in fact operative, then just one of E1 or E2 will be instantiated.


Clearly, in such circumstances there could be no 'contradiction' -- even 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


I will examine later the question whether E1 and E2, 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 -- although I have thrown that inference into considerable doubt here). So, whatever else this is, it can't be a 'dialectical contradiction'. This is the same fatal objection to this entire way of viewing 'dialectical contradictions' we have met several times in this Essay. However, 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, like the Monty Python ex-parrot, an ex-theory, it has gone to meet its maker:



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


So, despite this, we can concede for the purposes of argument that E1 and E2 are 'contradictories'. But, it now appears from the above, 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.


However, there 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).


[F11: Anything that prevents something else happening contradicts it.]


The problem here lies not so much with the non-standard use of language these sentences display, 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 the mind of NN 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.


One obvious fall-back position for dialecticians to occupy would be to argue that the actions mentioned above halted a series of events that would have led to the said drowning. In that case, those actions contradicted that series of events. This objection will be looked at more closely later -- 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 with which DM-theorists are concerned), then perhaps the following considerations might prove more acceptable. To that end, let us begin with this rather obvious assumption:


F16: Any process 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 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 above. 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, then those prevented events never happened (nor did the drowning), and hence didn't exist, and so can't have been 'contradicted'.


This objection also appears to be fatal to DM: if anything, forces actually prevent 'contradictions' from arising, and so can't be equated with what they thwart.


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 -- although I have thrown that clichéd inference into considerable doubt here. As we have seen time and again, this is a recurring problem which has sunk every attempt to breath life into the 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 return to consider a difficulty we met earlier, which was put to one side temporarily: the claim that forces -- not forces and effects, or simply effects, but 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 Note 55.]


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 appeal would have 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 Two -- 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 Note 24), 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, in my use of "pulling".]


In F22, the relevant force simply ceased to exist (or it was converted back into another force, 'potential' force, or some form of energy, etc.) when the switch had been 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).


Could 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 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 these, rather than with 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 clarify 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 does not 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 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.]


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 restricted 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 must 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, this 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' -- who are only too happy to wave the 'Revisionism' or the 'pedantry' card at anyone who has the temerity to innovate?


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 this is, indeed, what they claim, or what this theory implies.


Naturally, all this is independent of the far more fundamental question whether the thesis 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 say 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 -- although I have thrown that inference into considerable doubt here), 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 lift). 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. But, 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 these were 'opposites' they wouldn't interpenetrate each other.


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 Three: DM-Fan Ignores Sound Advice


Yet More S&M?


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


To that end, it might help if we re-examined a passage from Cornforth, 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.]


[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 this much with any clarity, he found had no use for any of the obscure words Hegel concocted). 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 least here. [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 been.55


[I have considered several promising looking objections to the above conclusions in Note 55, link above.]


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.


[That was established in Part One.]


Too Many Forces Spoil The Broth -- Or Is It Too Few?


It could be objected that the above results have been deliberately cherry-picked, tailored, and skewed to fit a desired end -- which is to malign DM come what may -- the choice of F24 (repeated below) being a prime example of this 'anti-dialectical approach'.


In that case, a much better way of representing the oppositional and contradictory nature forces might be the following -- in fact, with suitable changes in the 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 account given earlier clearly makes 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. [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 'dialectical interaction' -- let us say for now) we appear to have here an example of F37-type motion.


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' then several untoward consequences follow:


(1) This analogy would mean that 'contradictions' (just like forces) operate on a continuum. Hence, at any point along the path of the above particle the net force operating isn't equal to the net force at another point (in any one 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 that the latter option appears to have been one that Engels himself preferred 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 for 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 like these -- such as: forces represented by vectors.


Ignoring this '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. No contradiction seems possible if only one force -- the resultant -- is present; still less if no forces are at work (as 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 in the system, not one, or two.


This would, of course, create energy out of nowhere.58


To be sure, as part of our way of calculating resultants, we apply some mathematics to the relevant components, but that doesn't mean that nature does the same -- 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.


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 urgency!59


Moreover, on this view, forces are '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 should rightly be fed into the 'mystical-concept-crusher' as hopelessly anthropomorphic. Moreover, we have already seen that, whatever else they are, these forces aren't involved in a 'dialectical contradiction' here, 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 -- although I have thrown that inference into considerable doubt here.


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 inconsistency, 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 aired, 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".59a


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, which help account for the dynamic in class society.


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 Indeed, this word/concept seems to operate almost as a code word, 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, defining an 'in-group' while excluding those of the 'out-group', rather than genuinely applying in each and every case -- or in any case -- or, indeed, in a way that in the end means anything at all.


[Why they do this will be revealed in Essays Nine Part Two and Fourteen Part Two (when it is published).]


But, perhaps this, too, is unfair?


In order to substantiate the above allegations it might be wise to consider a few examples of the "real material contradictions" which supposedly underpin and then 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 century or so (even in the poorest regions of the planet), other factors have grown alongside this to counteract or undermine these developments:


"[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. Some paragraphs merged.]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 adjusted to agree with UK English.]


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 what to do to remedy them, they will all characterise them in the same was 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 that word simply because it is part of the 'Marxist tradition', adherence to which tradition 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 these 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 bother 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 even perhaps suffer expulsion, political isolation, or 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.]


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 -- "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, and for employing it seemingly 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 and decrepit world-view, along with this word, "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 found in 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 doctrine peppered with 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 "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 theses on the party faithful in order to 'justify', among other things, class collaboration, mass murder, splits and expulsions, all based 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.]


"Splitting" is therefore an "essential" part of this theory, and "struggle" is an "absolute". That must involve the relations between comrades, too. An emphasis on intra-party strife and splitting thus sits right at the heart of DM!


In which case, we needn't sit around waiting for the ruling-class to divide and fragment us, we are experts already!


[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 construct 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 serial disaster.


[Notice the use of "helped" here. DM is just one of the reasons for the long-term 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 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 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 at once seem capable of freeing humanity from want and oppression also appear to be inextricably linked with others that only succeed in intensifying and spreading both.


However, these by-now-familiar observations still leave the import of the alleged equation 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 of no use, therefore, in our search to find a viable way of equating forces and 'contradictions' in HM.


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


Nevertheless, this section is aimed at considering the last few remaining options left open to DM-theorists to make their ideas comprehensible, so F47 won't be abandoned just yet.


In fact, 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). Hence, 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" which 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.


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 employ 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.


[Most DM-fans will miss this point since their knowledge of logic is woefully defective. This, of course, hasn't stopped them pontificating on the subject as if they were all latter-day Aristotles.]


The only apparent way to situate this schematic noun phrase 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 bottle would be contradictory if it supplied drink 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 an 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 clear view 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 -- this 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 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 a 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 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 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.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.


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 indicated in Essay Five, if such a 'contradiction' were encountered, it would normally be viewed either as figurative or based on an undischarged ambiguity of some sort. There is no way around this convention this side of altering the meaning of the word "contradiction". And, even this would be of little help to DM-enthusiasts 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


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 have the following:


F63: Capitalism offers wealth, but delivers wealth and poverty, where wealth and poverty are opposites.68


However, there are several problems with this paraphrase and 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


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.


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 delivers to 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 skill 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 option above is no contradiction either, however much it offends our sensibilities. (b) is no more a contradiction than, say, £10,000 ($20,000) in one pocket contradicts £0.01 ($0.02) in another; or no more than a £5 ($10) note in a millionaire's wallet (assuming this is all she has on her at the time) contradicts the £1000 ($2000) 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 advertising 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.


Again, 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 we consider 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 it would have to do if a literal contradiction were intended. They don't appear to imply one another, like the proletariat and the capitalist class supposedly do -- although I have thrown that lazy inference into considerable doubt here.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 surgery to that end, and the claim that DM-'contradictions' hadn't been imposed on the facts would have to be abandoned. 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


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 these 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, and in Note 74.74


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 (defined in Essay Twelve -- and which was also a conclusion of Part One of this Essay).75


[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, doing so as a result of their practical activity, modified by ambient class and social relations. The reverse doesn't happen; '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, wherein perhaps they 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 constraints. 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 tackled that objection in Note 75.]


As should seem obvious, these comments are based on theoretical considerations drawn from HM, but that 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.


Their theory can only 'work' in an Ideal/mystical universe.


Last Chance Saloon


In that case, the only options left open are F50 and F51. They were:


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.


However, since these two are clearly variations upon F48 and F49, they don't appear to be viable alternatives. DM-apologists are welcome to make of them what they can.


True Contradictions?


Even so, dialecticians claim that there are indeed 'true contradictions' in reality. By far and away the most sophisticated of these endeavours is to be found in the work of Graham Priest. However, it is far from clear whether the 'contradictions' upon which he focuses are indeed 'dialectical' -- that is, should we ever be told with any clarity what a 'dialectical contradiction' actually is!


[Priest's work will be considered in more detail in an Additional Essay to be posted at this site at a future date. In the meantime, the reader should consult this and this.]


Veteran communist theoretician, the late Maurice Cornforth, also attempted to argue that there are 'true contradictions' in the natural and social world -- contrary to the view endorsed at this site, which is that a contradiction (in its simplest form, in logic) is merely the conjunction of a proposition with its negation, and which has nothing to do with 'what exists':


"The contradiction in things is a very familiar state of affairs. There is nothing in the least abstruse about it, and it is often referred to in everyday conversations. For example, we speak of a man as having a 'contradictory' character, or as being 'a mass of contradictions'…." [Cornforth (1976), pp.92-93.]


In which case, presumably, when we describe someone as a "bit of a puzzle" Cornforth thinks we mean that he or she can be purchased in a magic store or toy shop. Or that when we read this:


"All the world's a stage,

And all the men and women merely players;

They have their exits and their entrances" [William Shakespeare, As You Like It, 2/7.]


we should all try and remember our lines and stage cues, pay heed to the director, make sure the audience can hear us, and ignore the reviews.


Clearly, Cornforth has never heard of metaphor.


[Why this isn't a literal use of "contradiction" is considered in more detail below, where we will also see that "contradictory" isn't the same as "contradict", or even "contradiction".]


It is worth recalling that Hegel attempted to show that logical contradictions, and not so much ordinary contradictions, were far too one-sided, abstract and philosophically limited. His reconfiguration of this word was therefore intended to transcend the alleged 'Aristotelian' view of contradiction. (As far as I am aware, he was silent about the everyday use of "contradict", and its cognates.) Now, DM-theorists might want to use "contradiction" in a different way to Hegel -- whether or not his 'contradictions' have been turned "the right way up" or have been left upside down --, but, if that were so, their 'contradictions', the DM-variety, might not (obviously) actually transcend FL-contradictions. On the other hand, if that were so, it would make their criticisms of FL rather empty, since they wouldn't be addressing the same term. Nevertheless, they certainly intend their employment of this word should transcend the use of "contradiction" in FL, and that is why I have largely concentrated my attention to this area in this Essay.


However, it is also clear (from the examples they give) that DM-theorists -- like Cornforth and the rest considered below -- focus on what are plainly ordinary contradictions (as opposed to FL-contradictions, or even 'dialectical contradictions') when they try to show that there are 'true contradictions', or that 'contradictions' exist in nature and society. It is clear, too, why they do this: FL-contradictions are totally uninteresting (even when translated into the vernacular), and, what is worse, they are politically useless, too. Who, for example, is going to get excited about the following (these have been taken from a letter sent to Socialist Review a few years back by a supporter of this site):


A1: In capitalism, there is a drive to accumulate and there isn't (at the same time and in the same respect).


A2: Capitalism is governed by a blindly competitive market and it isn't (at the same time and in the same respect).


Even these two are only discursive equivalents of FL-contradictions.


As we saw in essay Four Part One, DM-theorists concentrate their attention on the simplest form of FL-contradictions: p & ¬p. Seldom (in fact never) do they consider more complex FL-contradictions. Here are just two of the latter sort:


V1: ¬[(p q) v (p r) (p (q v r))].


V2: ¬[¬(Ex)(Fx & ¬Gx) (x)(Fx Gx)].


[In the above, "(E...)" is the existential quantifier; "" is a biconditional sign (and stands for "if and only if"); "(x)" is the universal quantifier; "&" stands for "and"; "v" is the inclusive "or" (i.e, "and/or"); "¬" stands for the negation operator ("it is not that case that..."); "" is the conditional sign (i.e., "if...then"); "p", "q", and "r" are propositional variables; "F" and "G" are one-place, first-level predicate letters; and "x" is a second-level predicate-binding variable. (More details here, and here.)]


V1 reads: "It isn't the case that [(if p then q or if p then r) if and only if (if p then q or r)]."


V2 reads: "It isn't the case that [(there isn't something which is F and not G) if and only if (everything which, if it is F, is also G)]."


V2a: "It isn't the case that [(there isn't anything which is F and not G) if and only if (everything which, if it is F, is also G)]."


[V2a is perhaps a more colloquial semi-translation.]


Some might wonder when sentences like these would ever be used. However, in Mathematical Logic, the Foundations of Mathematics, Discrete Mathematics, and Number Theory -- to name but a few -- theorists use propositions like this all the time, and, indeed, many others that are far more complex still. (This links to a PDF.)


These are, of course, just two of the potentially infinite number of logical contradictions which can be generated in MFL. DM-theorists would be hard-pressed to find space -- even in their quirky universe -- for contradictions like these (i.e., once they have been interpreted).


[MFL = Modern Formal Logic; LEM = Law of Excluded Middle; PB = Principle of Bivalence.]


Moreover, dialecticians often conflate the LEM, the PB, propositional bi-polarity, and the LOC with one another -- and, indeed, all of them with opposites, inconsistencies, absurdities, contraries, paradoxes, puzzles, quandaries, oddities, irrationalities, oppositional processes, antagonism, forces, events that go contrary to expectations, alongside a whole host of other idiosyncrasies. In fact, they are so eager to see contradictions everywhere, that they find they have to tinker with the meaning of "contradiction" so that (for them) it becomes synonymous with "struggle", "conflict", and "opposition", as we will see.


In debate, DM-fans are often genuinely surprised to see examples of discursive FL-contradictions like those repeated below, or even the more formal examples posted a few paragraphs back. From this it is plain that they are totally oblivious of such contradictions, and when they see them they hastily reject them as relevant examples of what they intend when they use this word.


A1: In capitalism, there is a drive to accumulate and there isn't (at the same time and in the same respect).


A2: Capitalism is governed by a blindly competitive market and it isn't (at the same time and in the same respect).


[Here is a recent example of this (in the comments section at the bottom -- unfortunately, these comments are no longer available!). When confronted with an FL-contradiction, the comrade with whom I was debating -- Mike Rosen -- denied that this was what he meant. He wanted to show that there was a perfectly ordinary use of this word that picked out what Marx and other Marxists meant. And yet none of his examples were 'dialectical contradictions', either, which rendered the whole exercise rather futile -- as, indeed, I pointed out to him. There are many more examples like this in the debates recorded here. See also, Note 61a.]


On the one hand, whatever else DM-'contradictions' are supposed to be, they appear to be totally unrelated to FL-contradictions, and so can hardly surpass them. On the other hand, they have to be related to FL-contradictions, otherwise dialecticians will have to drop the pretence that DL is superior to FL.


In that case, in what follows, I will continue to refer to FL-contradictions in my criticism of DL-'contradictions'. If DM-fans mean something different by their use of this word, they should tell us -- and for the first time in over 150 years -- exactly what that is.


[There is much more on this topic here and here.]


However, Cornforth concedes the point that describing someone as "contradictory" involves a reference to their dispositions (or "tendencies"):


"This means that [they evince] opposed tendencies in [their] behaviour, such as gentleness and brutality, recklessness and cowardice, selfishness and self-sacrifice." [Cornforth (1976), p.93.]


Unfortunately, this prevents Cornforth's examples from being literal contradictions. He seems not to have noticed it.


Be this as it may, if the above is meant to commit Cornforth to a dispositional account of contradiction, then much of classic DM would become obsolete as a result. The fact that someone might have, say, a disposition to be brave in certain circumstances, but cowardly in others, in no way suggests he/she can be both of these at once. Indeed, what would that amount to? Standing one's ground while running away? Putting oneself in harms way to save or rescue someone else while shrinking from doing one or both? What is open to question, however, is whether the simultaneous actualisation of these dispositions (in certain states or performances) may be expressed by means of true propositions (and without ambiguity), that are both true at the same time.


Indeed, the fact that an iron bar, for example, can be red hot at one end and icy cold at the other at the same time isn't a contradiction (even though, plainly, an iron bar is at any time disposed to be either of these, and much else besides, at all times) -- but no one supposes (it is to be hoped!) that such a bar could actually be red hot and freezing cold all over, and in the same respect, at the same time.


[To be sure, the supposition that the entire bar could be both of these at the same time might be thought by some to be a contradictory supposition; and yet even this would merely be an inconsistency, not a contradiction, since both could be false if the said bar was in fact merely warm.]


Anyway, as noted above, the emotions Cornforth considers expressible by contrary suppositions are inconsistent, not contradictory. For example, if NN was said to be both angry and calm at the same time, that would only be a contradiction if it couldn't be false to assert NN was both. But, it would be false to assert both if NN were slightly agitated (in which state NN would be neither angry nor calm), for instance.


[Recall, two propositions are contraries, or are inconsistent, if they both can't be true, at once, but they can both be false, at once. Two propositions are contradictory only if they can't both be true and they can't both be false, at once.]


So, even if both of these states were actualisable at the same time (which is, of course, a rather difficult scenario to imagine, to put it mildly!), it still wouldn't be a contradiction!


On the other hand, if NN could be described (without ambiguity) in the following way:


N1: NN is both angry and not angry at the same time, and with respect to the same object of that anger,


we might have a genuine contradiction here. But, it is unlikely that Cornforth meant to be taken this way --, and it is even more doubtful whether he would have been able to say under what conditions he, or anyone else for that matter, would or could hold N1 true -- or under what conditions he/they could attribute to NN such odd actualisations.


Consider the following more precise example of this scenario:


N2: At time, t, NN is angry with MM for lying to her at t, and not angry with MM for lying to her at t.


Or, perhaps even more precisely:


N2a: At times, t1 and t2, NN is angry with MM at t2 for lying to her at t1, and not angry with MM at t2 for lying to her at t1. [t2 > t1]


Or, in more ordinary terms:


N2a1: NN is angry with MM today for lying to her yesterday and not angry with MM today for lying to her yesterday.


Naturally, there are several other possibilities allowed for in logic and ordinary language, such as the following:


N2b: At time, t1, NN is angry with MM at t1 for lying to her at t1, and not angry with MM at t1 for lying to her at t1.


Or, in ordinary (if somewhat stilted) terms, again:


N2b1: NN is currently angry with MM for lying to her just now and currently not angry with MM for lying to her just now.


Someone could object that it is possible to have mixed emotions at one and the same time. Perhaps, then, they might mean the following (confining our attention to N2, but not N2a or N2b, for simplicity's sake):


N3: At time, t, NN is both angry with MM for lying to her at t (because it was a violation of trust), and not angry with MM for lying to her at t (because she understands the pressures on MM when he lied).


In that case, N3 is really this:


N4: At time, t, NN is both φ-ing at t, and not ψ-ing at t.


Here, we have two different 'actions', or emotional states, involving different objects of a particular emotion (this is an example of the sort of  ambiguity mentioned above): anger at MM because it was a violation of trust (i.e., "φ-ing"), and lack of anger at MM because of extenuating circumstances (i.e., "ψ-ing"). Which is, of course, why caveat N1 was added earlier:


N1: NN is both angry and not angry at the same time, and with respect to the same object of that anger.


[Greek letters like "φ" and "ψ" are used in FL and Analytic Philosophy to help distinguish action-, or state-predicates (like "...walks", "...sits", or "...has refuted DM") from others (such as, " a man" or " a confused dialectician"). Naturally, several of these might overlap somewhat.]


As soon as we fill in the details concerning the nature of the emotion involved we can see that we have two different objects of the said anger, or two different states/actions, and hence no contradiction.


To be sure, someone might still object, but they will (like Cornforth) find it hard to say what the content of that objection amounted to without ignoring or editing out of the picture some object or other of the said anger/emotion, thus misrepresenting the intended situation.


[Which is, perhaps, why DM-fans dislike precision (i.e., they reject 'pedantry'); any attempt to state precisely what they mean undermines rather too many of the doctrines they unwisely imported from Hegel -- as we can now see happening with these 'contradictions'.]


In fact, by his use of the word "tendencies", Cornforth himself seems half ready to concede this point. But, not even he would want to describe the same action (performed by the same person) as, say, literally both gentle and brutal at the same time (without equivocation). While it is possible to ascribe contrary properties to the same object (e.g., one part of the aforementioned iron bar could be hot while another part is cold, as we have seen), a 'contradiction' may only be extracted from such familiar facts by someone who has never heard of ambiguity -- or, who is terminally confused. No one would think they had been contradicted by someone who asserted that the far end of an iron bar was red hot just after they themselves had asserted the near end was ice cold. Nor would they think they had been contradicted if someone had said they were angry today, but calm the day before -- or, indeed, that they were angry and calm about different things at the same time.


Anyway, as noted above, any description of the same action (that asserted it was literally both gentle and brutal at the same time, in the same respect and without equivocation) would merely be an inconsistency -- since both alternatives would be false if the said act was in fact neutral (i.e., if it was neither gentle nor brutal, but performed, or displayed, with equanimity, or indifference).


[However, the slow disintegration of the Communist Block finally caught up with Cornforth; in one of his last works [Cornforth (1980)], he systematically retracted most of the theses he had once declared were cornerstones of the "world view of the proletariat".]


Another benighted comrade has remained undeterred by such contradictory antics, and has vainly tried to defend the employment of this obscure notion (i.e., "dialectical contradiction"), appealing to (yes, you guessed it!) an everyday use of "contradiction" (re-posted below), in connection with contradictory behaviour, when it isn't at all clear that the examples he himself considered were even 'dialectical contradictions', to begin with!


But, what does this comrade mean by "contradictory behaviour"? Perhaps someone who stands and sits all at once? Or, maybe an individual who has a 'tendency' to do both? But, 'tendency' to do what? Stand and sit all at once? Or, who threatens to do one, or both? But what sort of threat would that be if it is impossible to carry out? Or, does this apply to someone who goes on strike and refuses to go on strike at the same time?


We aren't told. As usual, DM-fans offer their bemused readers what are less than half-formed thoughts and theories.


This benighted comrade tried to argue along these lines in a 'debate' with me over the UK Prison Workers' Strike, which took place a few years ago:


"I can contradict someone's statements. Can I also have contrary interests to yours? Could it reasonably be said that someone's behaviour was contradictory? Or that someone's interests were contradictory (in relationship perhaps to some goal they had)? Or that my interests contradicted yours? Certainly some data might appear contradictory in relationship to some enquiry we have about it.

"Does this not suggest that the notion of a contradiction is not exhausted by what might go on inside a proposition? In ordinary usage?"


Now, in relation to the aforementioned strike, it looks like this comrade meant his comments to apply to workers who support the state one minute, but act against it the next, or perhaps those who hold what appear to be inconsistent beliefs about one or both. But, put this way, this isn't even a contradiction (ordinary, or otherwise)! On the other hand, if these workers both supported and didn't support this strike at the same time (without ambiguity), that would have been a contradiction, but he plainly didn't mean that.


Of course, as we have seen, contraries aren't contradictions, and "contradictory" isn't the same as "contradiction". As indicated earlier, concerning two contrary propositions, both can't be true, but they both can be false (i.e., in this case, they would merely be inconsistent with one another), at once.


For example, the contraries "All swans are white" and "No swan is white" can't both be true (in a non-empty domain), but they can both be false -- for instance, if either or both of "Some swan is not white", or "Some swan is white" were true. But, two contradictory propositions can't both be true and can't both be false, at once. Again, dialecticians invariably ignore such "pedantic" details.


Moreover, if someone were asked to consider these two propositions: "All swans are white" and "Some swan is not white" they will have been presented with two contradictory propositions, but we would only have a contradiction if they were conjoined to give: "All swans are white and some swan is not white". "Contradictory" applies to propositions or clauses that could be conjoined to form a contradiction (or one of which could be used to contradict someone who asserted the other), whether or not they are so conjoined, or so used. "Contradictory" also applies to states and performances (among other things), which, if expressed in propositional or clausal form, could also be conjoined to yield a contradiction, whether or not they are so conjoined. In the same way, a vase can be described as breakable; that is, it can be broken whether or not it is actually broken. The term ("contradictory") can also apply to imperatives which would undo one another if acted upon -- such as "Open the door!" and "Close the door!".


[There are analogous distinctions and complications that also apply to "contradict" and "contradiction". See also here. We will see later how Kant succeeded in confusing himself and his readers by failing to notice such distinctions. Indeed, we have already seen how Hegel also managed to do this.]


There is a rather good example of this sort of 'dialectical confusion' in Simon Basketter's article in Socialist Worker about the aforementioned strike:


"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." [Paragraphs merged.]


Once more, what is the 'contradiction' meant to be, here? Maybe, it has something to do with the following considerations:


P1: Prison officers uphold the law.


P2: This either results from, or leads them into, holding right-wing ideas.


P3: But, this strike has forced some to defy or disrespect the law.


P4: However, later, when some prisoners protested, the same officers rushed back to work in order to control them.


Now, I have already commented on the loose, indeterminate and often indiscriminate way that dialecticians like to use "contradiction", but even given such conceptual profligacy, what precisely is the contradiction here?


Let us try again (using "NN" this time to stand for the name of a randomly selected prison guard who thinks and acts along the above lines, and "L1" to stand for a law he/she rejects, or opposes, even if only temporarily):


P5: NN upholds the law.


P6: NN has adopted a number of right-wing ideas.


P7: One day, as a result of the strike, NN says "Screw law, L1!" [No pun intended.]


P8: Later that day he acts in support of a totally different law.


Once more, where is the contradiction, here?


Now, if NN had said, "Screw all laws!" we might be able to cobble-together an inconsistency of some sort here (such as "Screw all laws!" -- i.e., "All laws ought to be screwed!" -- and "No laws ought to be screwed!"), but not even that is implied by the above story.


In fact, a contradiction in this case could be formed from something like the following: "All laws should be screwed" and "There is at least one law that shouldn't be screwed." Or, perhaps: "No laws should be screwed" and "There is at least one law that should be screwed."


To be sure, people say all sorts of odd things, and it is relatively easy to utter contradictory sentences. Who has ever denied that! [Look, I have just posted several contradictory sets of propositions in the previous few paragraphs.] The question is, can both be held true, or held false (or, in this case, advocated and repudiated, asserted and denied, as a moral or political code), at the same time and in same respect? Well, did anyone from Socialist Worker try to ascertain from the aforementioned prison guards if any of them would have both assented to and rejected the following at the same time: "All laws should be screwed" and "There is at least one law that shouldn't be screwed"; or, "No laws should be screwed" and "There is at least one law that should be screwed"? Apparently not.


Indeed, if NN had assented to "No laws should be screwed", we could safely infer from his later strike action that he no longer held it true. Plainly, as a result of the strike he must have come to accept the following alternative in its place: "I now think there is at least one law (namely, law, L1) that should be screwed".


And that would still be the case even if tomorrow NN went back to holding his former beliefs about every law. Dialecticians, least of all, shouldn't need reminding that people and things change!


Unless, that is, we think NN holds this odd belief: "I don't believe that there is at least one law that should be screwed and I also believe there is at least one law that should be screwed." Or, perhaps, "Screw L1 and do not screw L1!"


Even so, it is also reasonably clear that we could only attribute schizoid beliefs like this to NN if he were about to go insane, or had suffered a blow to the head. We certainly couldn't rely on such a confused character to help win a strike -- nor could we depend on him to report his genuine beliefs with any accuracy, either! He is just as likely to tell anyone who asks: "Yes I believe this and I do not...". Would Socialist Worker have even quoted such a confused individual? Hardly.


[No wonder 'dialectical reasoning' has been described as a form of "mental confusion".]


Elsewhere in my Essays, I allege that dialectics was itself based on little more than a series of egregious logical blunders committed by Hegel (even those on their feet, the 'right way' up --, or, upside down --, it matters not), but I alleged that DM-fans often base their assertions on half-formed thoughts, seriously garbled caricatures of logic (both formal and discursive) and laughably thin evidence (which is why I have branded DM, Mickey Mouse Science).


Simon Basketter's obscure claims amply confirm those allegations. For example, do these odd beliefs, held by prison officers, imply one another, like the proletariat implies the capitalist class, such that one can't exist without the other? No. [Although I have thrown that widely accepted inference about these two classes into considerable doubt here.] If not, they can't be 'dialectical contradictions' whatever else they are, can they? Did, Basketter even ask himself these questions? Apparently not. Then why on earth did he use this word?


So many questions, so few answers...


The impertinent explanation (from earlier) now looms its ugly head.


But, let us return to the benighted comrade from earlier and re-examine what he had to say, in order to see if anything useful can be extracted from it.


"I can contradict someone's statements. Can I also have contrary interests to yours? Could it reasonably be said that someone's behaviour was contradictory? Or that someone's interests were contradictory (in relationship perhaps to some goal they had)? Or that my interests contradicted yours? Certainly some data might appear contradictory in relationship to some enquiry we have about it.

"Does this not suggest that the notion of a contradiction is not exhausted by what might go on inside a proposition? In ordinary usage?"


Consider this first:


"Could it reasonably be said that...someone's interests were contradictory (in relationship perhaps to some goal they had)? Or that my interests contradicted yours? Certainly some data might appear contradictory in relationship to some enquiry we have about it."


Well, who can blame theorists for wanting to use old words in new ways? But, the above examples seem to be framed in ordinary language already. So why then the following claim?


"Does this not suggest that the notion of a contradiction is not exhausted by what might go on inside a proposition? In ordinary usage?"


Of course, these examples relate to what humans beings do, or can think, so they aren't much use in showing how there are, or can be, 'true contradictions' in nature.


Now this benighted comrade might not have noticed (but it was staring him in the face in the example I gave, and in the ones he listed) that contradictions can relate to the inner workings of one proposition just as they can apply to the connection between several propositions, at once, both in ordinary language and in logic. In which case, neither the complexities of logic nor the confused state of his thought-processes can be used to defend him from his self-inflicted errors -- for he himself provides his own counterexamples!


Consider this, for instance:


"Certainly some data might appear contradictory in relationship to some enquiry we have about it."


Unfortunately, this is far too vague to do much with. Perhaps this comrade meant something like the following (taking an example from Astronomy)?


D1: The measured distance to star, YY, is 4.8 million light years.


D2: The measured distance to star, YY, is 4.3 million light years.


But, these don't contradict one another, since the true distance to YY could be 4.5 million light years, making both D1 and D2 false.


And, it is irrelevant whether the true distance to YY is actually 4.8 or even 4.3 million light years. The fact is that it might not be, or might not have been, either of these.


It is worth recalling that if this were a genuine contradiction, D1 and D2 couldn't both be true and couldn't both be false at once (whether or not one of them was either of these). At best, therefore, D1 and D2 are inconsistent. So, even if D1 were true, it is still the case that both D1 and D2 couldn't both be true, but could both be false, at once. That wouldn't happen if they were contradictories -- unlike the following two, which are:


D3: The measured distance to star, YY, is 4.8 million light years.


D4: It isn't the case that the measured distance to star, YY, is 4.8 million light years.


Now, these two have to have opposite truth values (assuming, of course, that there is such a star); they both can't be true and they both can't be false. Given what we mean by "star", YY has to be some distance or other from the earth. One or other of D3 and D4 has to be true. Either YY is 4.8 million light years from earth or it isn't (or the meaning of the words used must have changed -- or the star itself has ceased to exist, etc., etc.).


Some might object that the above is misleading; the star will have moved while its distance is being measured so the above 'either-or' is misguided. FL can't cope with such changes, whereas DL can.


Or so it might be argued...


However, even though this star might have moved, all that this would mean is that D3 used to be true, and now it is false; and this in turn will imply that D4 was false but now it is true. My point still stands, therefore. They would still have opposite truth-values.


[Any who object to the use of the LEM in the above should read this, and then perhaps think again.]


[LEM = Law of Excluded Middle.]


To be sure, an inconsistency here might imply a contradiction, but it is far from clear that the benighted comrade meant this. But, even if he did, who has ever denied two propositions can contradict one another (if conjoined)? [Again, I have posted two of them above!] The point is, they can't both be true and they can't both be false at once.


DM-fans seem to want both to be true -- but, alas, that would automatically prevent them from being contradictory, or from forming a contradiction, to begin with!


Now, this comrade might have meant that raw data (not yet expressed in a propositional context or form) could contradict some theory or other. Perhaps then he meant these examples of raw data:


D5: 4.8 million light years.


D6: 4.3 million light years.


But, neither of these is capable of being true or false since they aren't even indicative sentences. And, if that is so, they can't contradict anything (since in order to do so they would both have to be capable of being true or false). Moreover, as soon as a (sentential) context is provided for them, they would merely be inconsistent, once more.


But, couldn't D3 and D4, or even D5 and D6, contradict the predictions of some theory/enquiry or other? Perhaps this is what is meant:


D7: Theory, TT, predicts that star, YY, is 5.7 million light years away.


D8: Observation tells us that YY is 4.8 million light years away.


And yet, the proposition "YY is 5.7 million light years away" is merely inconsistent with D8. This star could actually be 4.4 million light years away, making D7 and D8 both false.


In which case, we still don't have a contradiction!


So, until this comrade supplies us with clearer or more precise details about what he meant, little more can be done with his comments.


[I will, however, be looking in detail at how data can 'contradict' a scientific theory, alongside the confused things DM-fans have to say about this, in Essay Thirteen Part Two, when it is published.]


Be this as it may, is it possible, therefore, for an individual to have contradictory interests or goals in a relationship, as this comrade asserts? Perhaps by this he meant the following (for simplicity's sake, I will concentrate on potential or actual interests an individual might have; the argument can easily be extended to cover actual or potential goals -- those details will be left to the reader):


B1: NM has interest, A, in relationship, R.


B2: It is not the case that NM has interest, A, in relationship, R.


This appears to be a genuinely contradictory pair. If B1 and B2 were conjoined they would form a contradiction -- always assuming they both applied simultaneously and with no equivocation:


B2a: NM has interest, A, in relationship, R, and it is not case that NM has interest, A, in relationship, R.


But, did the benighted comrade mean this?


Apparently not. Well, what about the following?


B3: NM has interest, A, in relationship, R.


B4: NM has interest, B, in relationship, R.


B5: Interest, A, in relationship, R, contradicts interest, B, in relationship, R.


But, if we are talking about literal contradictions here (and not the loose and ill-defined dialectical-sort-of-contradictions we have come to know and loathe) then A and B in relationship R can only contradict one another if they are expressed in propositions (or in clauses), as indicated in B5a-B7:


B5a: Interest, A, contradicts interest, B.


B6: "A" stands for "I, NM, must love my partner".


B7: "B" stands for "It is not the case that I, NM, must love my partner".


It is hard to see how anything could be called an interest (as opposed to it being a vague sort of non-linguistic 'feeling') unless it were expressed in this way.


The question is can anyone assent to such conflicting interests all at once? Well, as we saw with NN above, people can assent to all manner of odd ideas and feelings, so there is nothing to prevent B6 and B7 from forming the content of someone's overall intentional or emotional make-up.


However, before we hastily slap a 'contradiction' label on this scenario, it is plain that this alleged contradiction can be disambiguated along lines that were suggested and attempted above (in relation to N3 and N4, reproduced again below) -- providing we supply plausible background details (ignoring, however, the complexities mentioned in N2a and N2b). That is because people don't just have interests simpliciter any more than they just have emotions simpliciter.


[For something to be an emotion it has to be object directed; so, we are angry with someone or something, fearful of something or someone, in love with someone or something, etc. Of course, an individual could just be in a fearful state, with no object of that fear, but that would be enough to diagnose him/her as (acutely or chronically) mentally disturbed or ill (in this case, they would be in the grip of an "irrational fear"). This wouldn't count as a genuine emotion, otherwise a mental disturbance wouldn't have been diagnosed. We can tell the difference between a genuine emotion and a mental disorder by the fact that the latter don't have clear objects (that aren't also delusional).]


As with most things connected with intentional behaviour, such things are goal-, or object-directed (which is why we use transitive verbs to characterise them). We wouldn't be able to make sense of someone who was just in love, but with no one or nothing in particular.


N3: At time, t, NN is both angry with MM for lying to her at t (because it was a violation of trust), and not angry with MM for lying to her at t (because she understands the pressures on MM when he lied).


N4: At time, t, NN is both φ-ing at t, and not ψ-ing at t.


[The reader is directed here for an explanation of these symbols.]


Hence, in this case, we would have something like the following (in an abbreviated, even if slightly stilted form, for clarity's sake):


N3c: NN feels she must love MM because of his caring for her, and NN feels she mustn't love MM for sleeping with her best friend.


[I have left N3c in a slightly stilted form so that it is clear what is being said.]


In that case, N3c is in fact this:


N5: NN feels she must love MM for φ-ing, and not love MM for ψ-ing.


As before, we have in effect two different objects of NN's love: his caring for her (i.e., "φ-ing") and his violation of her trust (i.e., "ψ-ing"). Which is, of course, why caveat N1 was added earlier (now re-written as N1a):


N1: NN is both angry and not angry at the same time, and with respect to the same object of that anger.


N1a: NN both loves and does not love MM at the same time, and with respect to the same object of that love.


Plainly, in N5, we have here two different objects of the said love, and thus no contradiction -- or, at least, no more than there would be here:


N6: NN saw MN in the distance with her binoculars.


N7: NN saw NM in the distance with her binoculars.


Here we have two different objects of NN's sight, MN and NM. If anyone thought these two propositions were contradictory, that would provide clear evidence they were in the grip of a serious linguistic confusion, not the author of a breakthrough in the science of optics.


[Indeed, N6 and N7 aren't even inconsistent with one another.]


It could be argued that the above examples in fact express the cause of those emotions, or whatever it was that occasioned them, not their objects. In fact, it isn't too clear that this is a distinction with a difference, any more than these are:


N8: MN in the distance caused NN to see him with her binoculars.


N9: NM in the distance caused NN to see him with her binoculars.


So, whatever the cause happens to be, the aforementioned emotions had different objects, and so aren't contradictory.


Of course, if this benighted comrade meant something other than this, he should perhaps learn to be a little clearer.


However, it might be objected that it is reasonably obvious that the contradiction here is this:


B7a: NN: "I must love my partner and it isn't the case that I must love my partner".


Once more, it is far from clear how this qualifies as a 'dialectical contradiction' -- that is, should we ever be told what one of these is. [Do they turn into one another, as the DM-classics tell us they should? And even if they did, how could anyone tell! Do they imply one another, as the proletariat and the bourgeoisie are supposed to? (Although, and once again, I have thrown that inference into considerable doubt here.)]


Ignoring this minor niggle for now, it is undeniable that human beings experience conflicting emotions like this all the time, but when faced with B7a, the normal reaction would be to respond with: "Er..., what on earth do you mean by that?", and we would be surprised if NN found it impossible to say why she felt this way. We would certainly expect some form of disambiguation or clarification of what she meant, perhaps along the following lines:


N3a: NN feels she must love MM because of his caring for her, and NN feels she mustn't love MM for sleeping with her best friend.


N3b: "I, NN, must love my partner MM because of his caring for me, and I, NN, feel I mustn't love MM for sleeping with my best friend".


If so, and once more, no contradiction would be implied.


But, even if B7a were an unambiguous contradiction, that would simply confirm the fact that contradictions in ordinary language and in logic are built around the content of propositions, and the logical links we hold between them -- undermining this benighted comrade's point:


"Does this not suggest that the notion of a contradiction is not exhausted by what might go on inside a proposition? In ordinary usage?"


The question now is, has anyone ever held the quoted propositions in B6 and B7 both true or both false at the same time? Or anything like them? Perhaps they have (who can say?), but how that shows that there are in fact 'true contradictions' in nature and society is still entirely unclear.


B6: "A" stands for "I must love my partner".


B7: "B" stands for "It is not the case that I must love my partner".


[B5: Interest, A, in relationship, R, contradicts interest, B, in relationship, R.]


As should seem obvious, the fact that someone believes (or holds) something to be true or believes something to be false doesn't automatically make it true or make it false!


[Once again, it is worth recalling here that two contradictory propositions can't both be true and can't both be false, at once. So, if someone does assent to two contradictory propositions, then they must believe both can be true or both can be false. That is they must (implicitly) deny the following: Two contradictory propositions can't both be true and can't both be false, at once. But, that would just mean they had misunderstood the word "contradiction" (or had perhaps been led astray by a persuasive re-definition of some sort). We certainly can't build a new science of human behaviour on the basis of confusions like this.]


However, it could be argued that because NN holds the quoted propositions in B6 and B7 both true -- when coupled with the fact that NN is an individual who exists in the real world --, that shows that it is at least possible to assert the existence of true contradictions. Once this possibility is allowed, the objections set out in this Essay can be seen for what they are: empty rhetoric.


B6: "A" stands for "I must love my partner".


B7: "B" stands for "It is not the case that I must love my partner".


Or, so it might be claimed.


Indeed, an argument somewhat like this was rehearsed by Roy Edgley a few years back:


"Since thought and theory are also part of reality and thus real objects that can be thought about, contradictions in thought, though not true of reality, certainly exist in reality; and it is only because they do exist in reality that they can be the object of criticism -- criticism for failing to be true of reality. Moreover, it is because two contradictory theories can't both be true that each bears a critical relation to the other: instantiated in actual thought this relation of logical opposition is in fact a critical relation of real opposition, Kant notwithstanding. It is no less logical opposition and no more simply natural 'conflict of forces' for taking the form of real historical and social struggle." [Edgley (1979), pp.24-25. Italic emphases in the original; bold added.]


The following would presumably be one such contradiction (although Edgley himself was apparently interested in more overtly scientific propositions), and one such existential claim:


B8: Let "p" be "I must love my partner and it is not the case that I must love my partner".


B9: In so far as p exists, contradictions exist in reality.


As Edgley admits, while a proposition like p wouldn't actually be true, it would still exist, and hence contradictions certainly exist (at this minimal level, at least). To be sure, it is an entirely different matter whether p is true or false; I will return to consider that option later. But, what about the claim that this argument shows that contradictions at least exist? Well, certainly those words exit, but that is no more illuminating than the following would be:


B10: Let "G" = "God". [I.e., "G" stands for the word, "God".]


B11: In so far as G exists, God exists in reality.


The question would still remain as to whether there is a 'God' or not.


[As those who know their logic will also know, Edgley has confused a propositional sign with a proposition (and perhaps also use with mention). B10 and B11 partially bring this muddle out.]


Someone might object: the above argument in fact confirms that the word "God" exists just as Edgley's argument shows that contradictions exist.


Well, all it shows is that a propositional sign or a simple sign exists (in some form or other, but the details become rather unclear when we look to Edgley to tell us where such signs actually exist), but who has ever denied that? Put another way, Edgley's argument is no more illuminating than would be an argument that had been aimed at showing 'God' exists, but which instead showed that the word "God" exists!


Once more, no one has ever questioned the existence of inscriptions of contradictions (indeed, these Essays contain scores of them), but that sheds no light at all on the claim that there are 'real contradictions', or 'true contradictions', in nature and society. If the mere thought of a contradiction, or an actual inscription on the page (or screen), were enough to show that DM-contradictions exist in the real world, then we should have to admit that there were 'real tautologies', too. But worse, we should have to accept LIE -- that is, the doctrine that solely from thought, or from words alone, substantive ontological conclusions (as opposed to trivial inscriptional conclusions) may be deduced. [More on that in Essay Twelve.]


[The word "inscription" above applies to physical marks on a page/screen/wall/blackboard/whitescreen/cavewall that aren't considered random, but are held to be the product of intentionality, part of a natural-, or even a formal-language -- or perhaps even a work of art, no matter how 'primitive'.]


[LIE = Linguistic Idealism; FL = Formal Logic.]


But, signs and inscriptions don't have such existential implications; plainly, if they did we should all have to believe in the actual existence of The Tooth Fairy and Bigfoot.


Edgley goes on to argue:


"Though a system of thought that is contradictory can't be true of its real object, this isomorphic relation between the structure of a society's thought and the structure of its material life thus gives sense to the idea that such thought is true to that material life: in being contradictory it 'reflects', and so discloses, though its content does not explicitly assert, the contradictory structure of the material life of that society." [Ibid., p.25. Italic emphasis in the original.]


Unfortunately, theorists are often careless over their use of the word "isomorphic"; how, it might be wondered, can a set of words be isomorphic to items in the world that they don't in any way resemble, some of which (words) are abstract common nouns, and many of which aren't even referential?


Putting this 'niggle' to one side for now, we may further wonder how Edgley knows this is indeed an "isomorphism" if none of his contradictions are true of capitalism, as he concedes. And his claim that this theory is "true to" capitalism is far from clear; how something can be "true to", but not "true of", a social system is something Edgley failed to explain.


Edgley also asserts that these linguistic contradictions (or at least the more theoretical examples to which he refers) are a "reflection" of "real oppositions" in society. That claim is partly defused below, and will be further laid to rest throughout this Essay. [See also here.]


Independently of this, Edgley makes a serious mistake (one that all DM-fans seem to commit, too): confusing contradictions in FL with what might or might not exist. As noted above, and in Essay Four Part One, FL makes no existential claims. To be sure, logicians as individuals might make such claims, but logic itself is neutral in this regard (since logic isn't an agent, and is capable of making no assertions, still less any about the world). While it is true that certain logical systems might need an ontology (or even a model) in order to work, even then, contradictions don't make existential claims; the background 'ontology' does that.


To repeat: in its simplest form, a contradiction in logic is merely the conjunction of a proposition with its negation, such that both can't both be true and both can't be false at once. So, the fact that inscriptions of contradictions exist has no bearing on this logical principle. Furthermore, FL doesn't rule out the existence of contradictions, since FL isn't a science, nor is it an agent. It neither rules in, nor rules out, the existence of anything. [In fact, in the construction of indirect proofs, logicians and mathematicians make use of contradictions all the time!] The study of logic, in this respect, revolves around the truth-functional implications that hold between a proposition and its negation. It isn't about existence in any shape or form.


In that case, contradictions can't "reflect" anything, for they represent just one form of the disintegration of the expressive power of language.


[There are many different definitions of "contradiction" in FL and Philosophical Logic; that topic is discussed in Essay Eight Part Three. More on this here, here and in Essay Twelve Part One.]


But, wait! The benighted comrade mentioned earlier has a powerful ally, none other than that outright charlatan, Freud:


"Perhaps someone is in the midst of an unhappy love affair and says 'I love him but I also hate him'. It's not just the statement but the feeling which is a contradiction surely? If Freud is held to describe the human individual not as a unified subject but a bundle of contradictory drives and desires, might one not imagine contradictory drives (if not desires) in a particular social system?

"Can I not have contradictory emotions about a subject, situation or person (I know I do about all sorts of things!)."


Thus, on the back of some egregious Freudian Pseudo-Science, this comrade is content to build his 'case'.


But, is there anything in these fraudulent Freudian fancies (even if we put to one side all the lies, deceit, client abuse, intellectual bullying, cocaine-induced fantasy, paranoia, and fabricated evidence that marked Freud's career)?


Well, once more, can people have, or be subject to, contradictory emotions? Perhaps these will suffice?


B12: NN hates Tony Blair.


B13: It is not the case that NN hates Tony Blair.


However, and once again, I rather think that the benighted comrade didn't mean a contradiction like this. Maybe he intended the following?


B14: NN both hates and loves Tony Blair.


This is entirely possible, if unusual (but it can surely be disambiguated along the lines suggested earlier).


However, it is worth noting that love and hate aren't automatically contradictory (when put in a propositional context), unless, say, hating someone implies not loving them; but, as the above quotation shows, it doesn't imply this! [That must be so unless by "contradiction" we mean something entirely different; if so, what?]


Moreover, we have already seen that B14 isn't even a contradiction, since it could be false -- that is, if NN were indifferent to Tony Blair.


Nevertheless, it is worth making the following points:


The reader will need to re-read the caveats posted here; she should note that in order to give content to this idea (if it is what was meant, or if these ideas mean anything at all), we had to use a propositional context to make the implications clear, once more.


This rather makes a mess then of the following rather rash comment courtesy of the benighted comrade:


"I'm just very puzzled about what it means to restrict the meaning of the term contradiction to a rule of formal logic. It's always been the least compelling of your arguments it seems to me. I don't understand the linguistic scandal that is supposed to be involved in talking about the human subject as a 'bundle of contradictory drives and desires' or talking about the capitalist system as encompassing contradictory tendencies (how TRPF [the tendency of the rate of profit to fall -- RL] is held to operate inside a concrete capitalist social formation for example)....


"I don't see how there can be anything ipso facto absurd or meaningless about such statements to anyone familiar with ordinary language." [Bold emphasis added.]


No "scandal" here at all; this comrade's badly garbled and ill-considered examples themselves imply the above conclusions -- that is, when we try to make sense of them. But, even he had to use propositions to inform us of these Freudian foibles.


[Supposedly contradictory drives and emotions were disambiguated above. The alleged 'contradictions' in capitalism have been dealt with here, and here. Finally, I have already pointed out, just as I pointed it out to this comrade, my concerns aren't solely with FL-contradictions.]


Now, it could be argued that certain brain states, underlying psychological or social forces are what lie behind the contradictory emotions and tendencies -- details which seem to have exercised this benighted comrade -- and it is here that the contradiction lies. [This also appears to be what motivated Professor Edgley's comments above.]


Unfortunately, the thesis that there are such things as 'contradictory forces' has been laid to rest in this Essay; but, the overall idea is susceptible to the next series of objections, anyway.


[The argument below also applies to the claim that there might be certain brain states, process, or psychological 'drives' -- or even social forces and tendencies -- at work, of which we are as yet unaware, that constitute such 'material contradictions', or which cause or 'mediate' them. They could even turn out to be those mythical Freudian fancies mentioned above. Who knows?]


Let us, therefore, call "Φ" the brain state or process, and/or psychological 'drive', and/or social force/tendency, that results in, 'mediates', or from which "emerges", the following:


B15: NN loves Tony Blair.


Or, in the first person:


B15a: I, NN, love Tony Blair.


Let us also label "Φ*" the brain state or process, and/or psychological 'drive', and/or social force/tendency, that results in, 'mediates', or from which "emerges", the following:


B16: NN hates Tony Blair.


Or, in the first person:


B16a: I, NN, hate Tony Blair.


So, "Φ" stands for the social or psychological force (etc., etc.) that 'mediates' (etc., etc.) "NN loves Tony Blair" (or its first person equivalent), and "Φ*" stands for the social force (etc., etc.) which 'mediates' (etc., etc.) "NN hates Tony Blair" (or its first person equivalent).


Let us further assume that Φ 'contradicts' Φ*, i.e., that they are 'dialectically-united opposites'.


Now, even given these assumptions, this theory still won't work!


According to the DM-classics -- where we are told that all things change into their opposites, and that they do so because of a "struggle" going on between them -- Φ must change into Φ*, and vice versa. But, Φ can't change into Φ* since Φ* already exists! If it didn't already exist, according to this theory, Φ couldn't change, for there would be no opposite with which it could 'struggle' in order to make it do just that!


And, it is no good propelling Φ* into the future so that it now becomes what Φ* will change into, since Φ* will do no such thing unless Φ is already there to make that happen!


Now, it could be objected that love can surely turn into hate, and vice versa. Indeed, it can, but the whole point of introducing Φ and Φ* was to show that if and when that happens, dialectics can't account for it -- and for the above reasons! This is quite apart from the fact that Φ and Φ* aren't love and hate, they are states and processes (etc., etc.) -- so, and once more, Φ can't turn into Φ* since Φ* already exists. 


[For those interested, this argument has been developed in extensive detail here, where 'social contradictions' are also analysed.]


Of course, if they aren't 'dialectically-united opposites' to begin with, then the above comrade's objection fails by default. Do these brain states (etc., etc.) imply one another? One can surely exist without the other. If so, they can't 'interpenetrate one another -- again, unlike, say, the capitalist class and the proletariat, which, so we are told, imply one another, such that one can't exist without the other (although, once more, I have thrown that hackneyed inference into considerable doubt here), and vice versa. So, once again, none of this makes sense, even in DM-terms!


Finally, the following represents an edited version of an exchange between myself and a far more reasonable comrade (whose name has been withheld at their request):


Comrade M (commenting on the dialectical use of the word "contradiction"): I mean what most people mean -- conflict, inner tension...


Rosa: Do they really? Give me one sentence drawn from ordinary language (the vehicle most people do in fact use, so what you say should appear there, somewhere) where such an interpretation could be put on the word "contradiction" -- i.e., one not infected with the sort of idealist guff you read in Hegel. An idealist will have no problem with asserting such things; if reality is Mind it can surely argue with itself. Not so a materialist who bases his/her science on the language of ordinary workers (ordinary language).


But, even then, why call such things "contradictions"? What link does this particular use have with the "gain-saying" of someone, which is what the word usually means? How is a conflict in society a contradiction?


Sure, you can re-define the word to mean whatever you like, but if we all did that we could re-define anything to mean anything, and we'd lose touch with meaning altogether.


Apart from that, you'd be forcing a view onto reality (contrary to what 'dialecticians' tell us they never do), not reading one from it. Linguistic Idealism -- as I asserted in those parts of my work I sent you -- would then automatically have raised its ideal head. Society would be 'contradictory', not because it really is so, but because we have re-defined it to be so. A linguistic dodge would have created a few empirical 'truths'; this is 'science' on the cheap...


Comrade M: Rosa said: "Give me one sentence..." Okay, what about "Don't you contradict me you little bastard!" Or "That's a contradiction in terms".


Suppose someone says "military intelligence" is a contradiction in terms. What they mean is that there is a conflict or a tension between the first and the second word, thus conjugated.


At any rate, you are berating a new convert. I can't be expected to know everything at once, much less know it as wisely as the central committee (you).


Rosa: First, the phrase "contradiction in terms" is either a misnomer or a rhetorical device. Why? Well, since contradiction has to do with truth and falsehood as much as it has to do with "gain-saying", and since one term on its own can't be true or false (only sentences and clauses can be), and since single words do not say anything, no term can contradict another.


In that case, "contradiction in terms" means something like "incompatible phrase(s)", as in "round square". Now, "A is round and it is square" would only be a contradiction if "A is round" were taken to mean "A is not square", but then you would not now have a contradiction in terms, just a sentential contradiction with no "conflict (or) inner tension" anywhere in sight.


And, if the above conclusion were rejected (for some reason), you still wouldn't have a "contradiction in terms" that expressed some sort of "conflict (or) inner tension", since, once more, words can't conflict (or be tense, or be in tension) because they aren't agents. Moreover, anyone who uttered a "contradiction in terms" would not necessarily be in "conflict (or) inner tension", just confused. And even if they weren't confused, the "contradiction in terms" they uttered wouldn't necessarily indicate "conflict (or) inner tension"; it could be a sign of all manner of things (ranging from lack of clarity, through puzzlement, to playfulness).


As to the idea that such a phrase could indicate the presence of "conflict (or) inner tension" I have no doubt, but if a "contradiction in terms" meant that a "conflict (or) inner tension" had to be present, it would mean this, and not merely could mean this, just as the truth of "not p" would mean the falsehood of "p" (as opposed merely to "not p" could mean the falsehood of "p"). So they can't be synonymous, as you allege.


[Apologies for the prolixity of that paragraph, but logic is a pain in the dictionary!]


But, even if this weren't so, "contradiction" here still wouldn't mean "conflict (or) inner tension", it would mean "gainsaying oneself or another", which could be true without an inner conflict being implied. It might be a joke, an attempt to puzzle, part of a game, a mistake, etc. The possibilities are endless. The attempt to squeeze this into an idealist boot can only succeed if the almost endless possibilities allowed for by ordinary language are ignored, or can be ruled out.


As for "Don't you contradict me you little bastard!", the verb "to contradict" in this command (it isn't in fact a proposition, so it can't itself be a contradiction, literally speaking -- not that you suggested it was) clearly means "gain-say". No quibble there. But, if it meant "conflict, inner tension", you would have:


"Don't you conflict/inner tension me you little bastard!", which is meaningless.


Even if we were to edit this down to:


"Don't you conflict with me you little bastard!",


it wouldn't mean the same as:


"Don't you contradict me you little bastard!"


One can conflict with someone without contradicting them, and vice versa (e.g., two friends could contradict each other (out of fun) without conflicting with each other, say). Hence these can't mean the same.


However "Don't you inner tension with me you little bastard!" can't be beaten into shape at all.


Of course, I should have also pointed out that if we already have words (such as "conflict") that capture what we mean, why is there any need to use "contradiction"?


Final Round-Up


Because dialecticians have so far neglected to explain with any clarity, or in any detail, what it means to equate forces in nature and society with 'contradictions', I have been forced to offer my own attempts at clarification (no pun intended). All have so far failed. In this last main section I will endeavour to present what I think is the only viable interpretation of the link between forces and 'contradictions'.


Dialectics In ER


We have seen that the concepts DM-theorists have imported from Hermetic Philosophy have badly failed them when any attempt is made to apply them to, or connect them with, the forces operating in nature and society. In that case, the impertinent answer to the question why hard-nosed revolutionaries insist on using such mystical terms in HM (offered earlier) is the only one left in the ring:


Dialecticians use obscure jargon like this simply because it is traditional to do so.


This means that this part of DM (already under intensive care in the Emergency Resuscitation Ward) is now ready to be measured for a pine overcoat and lowered six feet closer to the Earth's core.


A Last Desperate Attempt


However, before we call for a Hermetic High Priest to read DM the Last Mystical Rites, we should, I think, make one last attempt to resuscitate this moribund 'theory'.


In fact, we are now in a position to reconsider several earlier abandoned alternatives in an attempt to rescue this part of DM from its long overdue funeral.


Back To The Drawing Board


Below, I present another re-interpretation of the alleged connection between forces and 'contradictions', based on F6-F9, above:


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.


To these we can add the following:


F58: Force, P1, contradicts P2 in so far as some or all of E1 and E2 are contradictory (internally, or with one another).


Unfortunately, this latest re-interpretation can't work, either. That is because if one or both of E1 and E2 don't exist (as a result of the operation of P1 and P2) there can be no contradiction. As we have seen several times already, F58 would imply a 'contradiction' between sets of events not all of which co-exist.77


It looks, therefore, like this particular interpretative seam has been thoroughly worked-out; there is no gold in it, only slag. Unfortunately, what little 'gold' there was, mined long ago by Hegel & Co., turned out to be nothing but Iron Pyrites.


We need to find a new approach to save this rapidly fading 'theory' from being sent to the knackers yard.


DM And The Revival Of Teleology


The last remaining escape route left open to DM-theorists relies on reviving yet another interpretation which was postponed from earlier (no pun intended), wherein 'contradictions' were said to exist between the effects of forces (or between forces and the effects of other forces), rather than between forces themselves. One such alternative involved taking Engels's suggestion seriously: that forces should be edited out of the picture, leaving behind only the relative motion between bodies to give some content to the idea that 'contradictions' can cause change.


However, the first of these had to be abandoned because it meant that forces 'contradicted' prevented effects, implicating this part of the theory with the idea that forces could 'contradict' non-existent entities, once more. The second appeared to undermine the dialectical unity of nature.


Nevertheless, I now propose to examine a re-vamped version of the first of these alternatives, and one aimed at circumventing the difficulties noted above.


The good news is that this new option solves the problem created by the second alternative.


The bad news is that it introduces far worse difficulties of its own.


The aforementioned earlier attempt was based on the following:


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 P1 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".]


As we saw above, an existing force, P1, appears to 'contradict' a non-existent event (or series of events), which rendered this interpretation useless. The following re-vamped version is aimed at fixing that glitch:


F59: Event, E, consists of a set of inter-connected sub-events, E1-En.


F60: E1-En, form complexes of material interactions (of a sufficiently mediated and contradictory nature) within T, if ever they occur.


F61: Let P1 prevent some or all of E1-En from taking place.


F62: Therefore, some or all of E do not exist, will never exist, or do not take place.


F63: Hence, propositions that express the fact that one or more of E1-En have been prevented from taking place contradict propositions that express an expectation that they will occur.


Since, an expectation can exist alongside the realisation that it has been thwarted (in some cases), this appears to solve the problem.


However, F63 is clearly of little use since, not only would it be inapplicable throughout the Universe at all times, it doesn't even record a contradiction.


[That is because the propositions it contains are of the form "p and q" not "p and not p", as required -- where "p" is, say, "Ek has been prevented", and "q" is, say, "Ek was expected" --, when what was required was "Ek has been prevented" and "Ek has not been prevented", etc.]


F63 may be altered to circumvent this difficulty:77a


F64: Propositions that express the prevention of one or more of E1-En taking place contradict propositions that depict the dispositional properties of Pn, the set of forces that would have produced all of E1-En, but for the presence of P1.


One immediate problem with F64 is that it isn't at all clear what the "dispositional properties" of forces are. Objects certainly have dispositional properties as a result of their microstructure and their relationship with other bodies -- if, that is, the term "dispositional" is read in a traditional sense. [More on that in a later Essay.]


Even so, since forces aren't obviously body-like (although they can apparently be carried by bodies/particles -- if certain aspects of modern Physics are accepted --, but even there this phenomenon is explained in terms of transferred momentum, i.e., along neo-Engelsian lines),78 the ascription of dispositions to forces themselves perhaps amounts to a disguised reference to the affect forces could, or would, have on such bodies in certain circumstances. In that case, we would have here an explanation of "contradiction" that appealed to the effect of effects, once more.


[Anyway, F64 doesn't even record a contradiction since the propositions it expresses are of the form "p and q" not "p and not p", as noted earlier.]


Nevertheless, perhaps F64 can be re-jigged -- maybe along the following lines:


F65: Propositions that express the prevention of one or more of E1-En taking place contradict propositions that depict the normal operation of Pn, the set of forces that would have produced all of E1-En, but for the presence of P1.


Unfortunately, not only does F65 fail to record a contradiction (yet again: the propositions it expresses are of the form "p and q" not "p and not p"), so what it says returns us to a consideration of the inter-relationship between forces as a way of understanding 'contradictions', instead of the present model, which sought to interpret 'contradictions' as the relationship between forces and the effects of other forces.


Anyway, F65 is of little use: if the normal operation of Pn is prevented (so that it doesn't take place) there would be nothing for P1 to 'contradict'. This annoying, but recurring, 'problem' is precisely what prompted a turn to the current consideration of the actual effects of forces, since they do exist, as opposed to the prevented effects of forces -- or even forces which cease to operate --, which don't.


It now seems that unless we can specify how the effects of forces can 'contradict' other forces (or other effects), this part of DM will be as good as dead -- even if not yet buried or cremated. Maybe the following option will help revive it:


F66: Propositions that express the prevention of one or more of E1-En taking place contradict propositions that express the operation of Pn, such that the presence of E1 (i.e., an effect of P1) excludes some or all of E2-En.


However, this is no use, either, since it matters not how effectively some or all of E2-En are excluded; E1 may only 'dialectically contradict' that which exists, and, ex hypothesi, once excluded, E2-En would no longer be around to be 'contradicted' in this way.


The next suggestion constitutes, in my view, the only way to keep this dangerously ill part of DM alive:


F67: The prevention of one or more of E1-En taking place contradicts the aims of Pn, the set of forces that would have produced all of E1-En but for the presence of P1.


[However, F67 will need to be re-written in a 'propositional' form, but since that would make this example even more unwieldy than it already is, that task has been left to the reader.]


The good news is that since aims can exist where results and effects do not, we seem at last to have a genuine 'contradiction'.


The bad news is that this belated tonic soon turns into a dose of strychnine. That is because, of course, not only does F67 not record a contradiction (for reasons given several times already -- the propositions it expresses to are of the form "p and q" not "p and not p"), we can't attribute aims to forces unless we wish to introduce teleology and anthropomorphism into nature and society.


F67 can therefore only apply to forces under the control of human agents -- or to their animistically projected counterparts in reality -- that is, if we genuinely want to go down this route and picture nature in such a mystical light.


It is therefore no surprise that the only interpretation that appears to render this part of DM viable is one that reveals the anthropomorphism implicit in the concepts its theorists have imported from Hegel and Mystical Hermeticism.


Alternatively, it is equally unsurprising that this is the only option that underlines the reading that works in HM, one that puts forces under human control.79


Unfortunately, this now means that F67 can't help resuscitate this DM-cadaver.


Coup De Grace


It was noted earlier that there is a general problem that afflicts any attempt to identify forces with 'contradictions' -- i.e., if these are viewed as the result of dialectically-united 'opposites'. In connection with that we have also seen that DM-classicists argued that all such opposites turn into one another, into that with which they have struggled. But, is it even plausible to suppose forces are capable of doing this? Is it credible that a gravitational force, say, can turn into a magnetic force, or an electrical force? Do all R-type forces turn into A-type forces? Where in Physics is it postulated that gravity can become a repulsive force, its opposite?


Do any of them really 'struggle'? Undoubtedly, electricity and magnetism are inter-linked in modern Physics (and are in fact manifestations of one of the four fundamental forces, so we are told), but they don't 'struggle' with one another, and neither do the particles on which they depend. According to current theory, such forces are "carried" by exchange particles, but they aren't an expression of a 'struggle' going on between any particles.


To be sure, magnetic fields are reversible, as are electrical fields, but this isn't true of all fields (even though all four forces can change in many different ways), but it is far from clear that this is because of any 'struggle' going on between them, either. For example, the origin of the reversal of the Earth's magnetic field may lie deep inside the planet's core, or, perhaps, inside the crust --, or it may even have an external cause (with one set of theorists blaming meteor impact); scientists aren't sure. But, not one single Geophysicist, to my knowledge, is investigating the alleged 'contradiction', or even 'struggle', between North and South to find its 'real' cause.


[Of course, this magnetic phenomenon is a consequence of the direction of a field carried by certain particles, which simply reverses. But, it doesn't turn into its opposite. It could be argued that the direction of that field does indeed turn into its opposite; maybe so, but not as a result of one of those directions struggling with the other.]


If that is so, then even if it should out that every single one of the objections aired in this Essay are misguided in some way, the 'dialectical' equation of forces and contradictions doesn't work even in its own terms!


Do the Relations of Production really turn into the Forces of Production? Does a use value struggle with and then change into an exchange value? Do they imply one another like the proletariat implies the bourgeoisie? [Although I have thrown that inference into considerable doubt here.]


They should do if the DM-classics are to be believed.


For Dialectics, Truth Is 'The [W]hole' -- Alas, it's Six foot Deep


Since there appears to be no way that DM-'contradictions' can be given a literal, or even figurative, interpretation as forces (opposing or otherwise) that survives close scrutiny -- when applied in nature or society, in abstract or in concrete form --, this part of DM can at last be given a decent burial.


Indeed, we can even call its time of death: August 27th, 1770.80



Figure Four: Send No Flowers...




1. 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.]


"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.]


"[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.]


This is how Bukharin put things:


"[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.]


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.]


Here 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), quoted from here. Bold emphasis added.]


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.]


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.]


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 (38) is to Engels (1955), pp.95-96, 110. Quotation marks altered to conform with the conventions adopted at this site. Bold emphases added.]


It is interesting to note that Woods and Grant blithely record Engels's approving reference to Hegel's depiction of magnets as having 'souls' while failing to notice its mystical implications. How could this 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.


And here is 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 ad 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 (1995), p.156.]


One of the most recent dialecticians to connect forces with 'dialectical contradictions' is Thomas Weston [Weston (2012)]. I have now added some thoughts about Weston's article, here, here, here, here, here, and here.


We have already noted that one on-line dictionary 'defines' contradiction in somewhat similar terms, but since that is has already been commented upon (follow the above link for more details), no more will be said about it here.


2. Engels, for example, went to great lengths to qualify what he meant by "force" -- cf., Engels (1954), pp.69-86 -- where he doesn't even once consider the classic problems associated with interaction that had been highlighted by Leibniz, echoed, for example, by Schelling.


3. This was established in Essay Two.


Nevertheless, as we saw there, assertions like those listed in Note 1 function as a "form of representation", not as a summary of the available evidence. In many cases, broad DM-generalisations like these are made on the basis of little or no evidence at all. For example:


"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." [Engels (1954), p.211.]


"Processes which in their nature are antagonistic, contain internal contradiction; transformation of one extreme into its opposite…[is] the negation of the negation…. [This is a] law of development of nature, history and thought; a law which…holds good in the animal and 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." [Engels (1976), pp.179-80.]


Engels was quite happy to call such sketchy, half-formed, sub-hypotheses, "laws" even though they were based solely on a superficial survey of a limited range of examples -- each specially-selected and highly simplified -- drawn from the sciences of his day. And, even then, they were invariably badly-constructed or even entirely misconstrued. No wonder I have called this aspect of DM Mickey Mouse Science.


[Their role as a "form of representation" will be outlined in the section dealing with the RRT, in Essay Twelve Part Four.]


[RRT = Reverse Reflection Theory.]


[The phrase "form of representation" was taken from Wittgenstein's work; a brief outline of its meaning can be found in Glock (1996), pp.129-35. We will see Engels employing one such in Note 7, below. Also, follow the link to "norm of representation" given in Note 25.]


4. However, in one of these quotations, Engels clearly questions the identification of contradictions with forces:


"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.]


Even though Engels elaborated on this theme in the succeeding pages of DN, this passage alone completely undermines the subsequent DM-equation of forces with contradictions -- or, at least, forces with attraction and repulsion.


[Of course, this quotation was taken from unpublished notebooks, so it might not have represented Engels's more considered views. But he seems nowhere to have repudiated it.]


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


Nevertheless, this re-interpretation of the word "force" as a sort of shorthand for "simple forms of motion" is consistent with more recent approaches to the nature of forces, which sees them as an expression of the exchange of momentum between 'force-carrier particles' (which are themselves interpreted as 'perturbations in the field'). Even so, Engels's 'revised view' has serious consequences for DM that he appears not to have noticed. Several of these are examined in the main body of this Essay, and below, in Note 25.


5. Admittedly, this is a highly simplified picture, 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 one force only (in Classical Physics) -- and, plainly, with only one force, there can be no 'contradiction'. Now, since orbital motion encompasses most of the bulk movement in the universe, most of the motion in nature 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 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 change 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 a body around another is determined by the operation of the two forces of attraction that pass between them: body, A, attracts body, B, and vice versa.


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 forms of motion), despite the fact that with respect to the vast amount of the bulk motion in nature these 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 shows 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 here, 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, should we not say (and with more justification) that such forces aren't in fact contradictory, they are tautological? [On this, see Note 38, below. See also Note 6b.]


However, and once more, these attractive forces don't turn into one another, and they certainly don't imply each other (as, say, the proletariat is supposed to imply the capitalist class, and we are told that the one can't exist without the other -- although I have thrown that inference into considerable doubt here), so, whatever else they are, they can't be 'dialectical opposites. Either that, or the DM-classics were seriously mistaken.


And, even taking these two forces into account, it is their combination in a resultant force which causes, or which changes, the said motion.


Notwithstanding this, Thomas Weston makes a desperate 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. Italic emphasis in the original. Bold added.]


One moment Weston tells us that inertia isn't a force, the next he quotes Newton to the effect that it is (or, 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 this word with no attempt to justify it.


Indeed, as Weston admits, Hegel argued that the 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 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 (as 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 aren't, and can't be, causes.


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


[I have said more about this, here. I return to consider other aspects of Weston's ill-advised article, here, here, here, and here.]


[TOR = Theory of Relativity.]


6. Not that these two aren't complementary.


Again, this simplifies the picture considerably, but the point is still valid. Even if it could be shown that gravity is a property either of matter (as a result, perhaps, of the activities of the by now legendary "graviton"), of Spacetime, or, indeed, of something else, 'motion' through Spacetime would still fail to be a function of attractive and repulsive forces. [On this, see Jammer (1999), pp.iv-vi. It is also worth noting that this view has recently been challenged by, for example, Wilson (2007). More on this below.]


[In the previous paragraph, the word "motion" has been put in 'scare' quotes, since it is a moot point whether anything actually moves in four-dimensional Spacetime.]


6a. This isn't, of course, how nature is pictured in school or college Physics textbooks, where the word, "force", is still used for heuristic purposes. But, as Jammer notes, in higher Physics "force" has been edited out of the story, replaced by exchange particles.


This development is re-iterated by Nobel Laureate, Professor Wilczek:


"The paradox deepens when we consider force from the perspective of modern physics. In fact, the concept of force is conspicuously absent from our most advanced formulations of the basic laws. It doesn't appear in Schrödinger's equation, or in any reasonable formulation of quantum field theory, or in the foundations of general relativity. Astute observers commented on this trend to eliminate force even before the emergence of relativity and quantum mechanics.


"In his 1895 Dynamics, the prominent physicist Peter G. Tait, who was a close friend and collaborator of Lord Kelvin and James Clerk Maxwell, wrote


'In all methods and systems which involve the idea of force there is a leaven of artificiality...there is no necessity for the introduction of the word 'force' nor of the sense−suggested ideas on which it was originally based.'" [Quoted from here. By "sense-suggested", Tait is obviously referring to the origin of the concept of force in human interaction with the world and with other humans, a fact also acknowledged by Engels.]


[The above now appears in Wilczek (2006), pp.37-38. It should be pointed out that, compared with Jammer, Wilczek is in the end a little more equivocal on this topic.]


Again, this view has been criticised quite effectively in Wilson (2007).


[I will add a few comments on Wilson's article at a later date.]


However, there are alternative versions of Classical Physics (for example, Newton-Cartan Theory) in which the force of gravity can be "geometrised" away in this manner. On this, see Malament (2012), Manchak (2012), and Trautman (1965).


6b. Despite this, it could be argued that it is the relation between bodies that determines any subsequent change in motion, and hence this supports the idea that there is a contradiction here. But, in relativistic physics, it is the 'relation' between a body and the gravitational field in which it is embedded that changes its motion, and once that is admitted we have left far behind the idea that there are "contradictory forces" at work in any meaningful sense of the term.


Once more, it could be objected that there is still a relation between bodies in this case, since a more massive body will deform the gravitational field that surrounds it, thus changing the motion of the second body. Maybe so, but exactly how this is a 'contradiction' has yet to be explained. There seems to be no "struggle" going on here -- or are we to imagine that bodies 'struggle' with a tensor field or even with an abstract space (i.e., with mathematical structures), and then turn into one another (which they should do if the DM-classics are to be believed)? There is no 'unity' or 'identity in opposition' here; one body just happens to be situated in the deformed results of another body's field, and so moves along the geodesics there. Once again: if anything -- and if we absolutely have to employ a metaphor here --, because of the regular and smooth (non-developmental) nature of such movement, this looks much more like a 'dialectical tautology'!


7. For example, cf., Engels (1954), pp.73-80. I return this topic again, here and here.


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


Admittedly, Engels also 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 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." [Engels (1954), 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 say 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 this 'hypothesis' to Engels as a tentative 'explanation' of how the Solar System could have formed -- although even that is questionable since Engels explicitly based his ideas on the old Kant-Laplace model, itself nearly 100 years 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 -- a bit like Thomas Weston, in fact. This is a classic example of Engels using the ideas he inherited from Hegel as a dogmatic "form of representation", and, as we will see, a confused one, to boot.


Of course, such formal devices are used all the time in science; Engels however turned this particular example into a metaphysical thesis.


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


Indeed, Einstein himself wasn't above inventing forces to suit the requirements of his theory (the same was also true of Newton), 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" when they gained some traction. [On this, see Kuhn (1970, 1996), as well as Sharrock and Read (2002).]


Incidentally, an appeal to so-called 'centrifugal forces' (a bogus notion found in Classical Physics) won't save Engels's theory either, since these forces don't 'exist'. If anything they result from the application of a misleading shorthand for the way that rectilinear motion returns if the force responsible for centripetal acceleration ceases to operate, subjectively experienced in certain rotating systems.


8. In that case, for once, Engels's views would appear to be consistent with modern Physics (indeed, as indicated by Max Jammer)!


Engels also noted the anthropomorphic origin of this concept (something Woods and Grant, for example, failed to spot -- even though they quoted this passage!):


"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." [Engels (1954), p.82. Bold emphasis added.]


On the animistic and anthropomorphic origin of the concept of force, see Hesse (1961), Jammer (1999), and Agassi (1968), who references Francis Bacon's Novum Organum (Book One: Aphorisms; Aphorisms XXXVII-LXVIII) as a locus classicus of this idea.


DM-theorists aren't alone in finding their ideas embarrassed by an over-ambitious and incautious use of anthropomorphic concepts; the theses of metaphysically-motivated Philosophers and scientists have been similarly compromised in this way for many centuries.


[The ideological origin of phenomena like these is discussed in Essays Twelve and Fourteen (summaries here and here).]


9. Of course, not all objects that collide would be, or would have been, moving in opposite directions; many would be on trajectories inclined at some angle or other to those of the rest. Indeed, many move in the same direction, only at different speeds. It isn't easy to see how any of these can be seen as 'contradictory'.


[Classical problems associated with the 'ontology of interaction' will be posted here at a later date. However, there is an outline of these issues in Note 24. See also Note 6a. This was also discussed in Essay Eight Part One.]


10. It could be argued that forces are 'abstractions' constructed to assist in the scientific study of nature. But, when viewed this way the concept "force" becomes little more than a "useful fiction", only now located in a 'metaphorical universe' all of its own situated somewhere between genuine fantasies (such as ghosts and apparitions) and mathematical fictions (such as the centre of mass of the Galactic System to which our Galaxy belongs, the Virgo Supercluster). In that case, naturally, the 'objective' status of forces is fatally compromised. They would have no physical counterpart, which would mean that the real material correlates of DM-'contradictions' would be non-existent, too. I'm far from sure that many DM-fans will want to pursue this option too enthusiastically.


All this is quite apart from the fact that if forces were abstractions, no two individuals would agree about their nature. [That result was established in Essay Three Parts One and Two.]


11. Once more, this isn't a problem confined to DM-circles; scientific theories are shot-through with metaphor, and scientists use analogical reasoning all the time.


On the nature and use of metaphor and analogy in the sciences, cf., Baake (2003), Brown (2003), Benjamin, et al (1987), Guttenplan (2005), Hesse (1966), Ortony (1993), and White (1996, 2010). [Several of these base their ideas on Max Black's work in this area, which is extensively criticised in White (1996).]


However, there is as yet no satisfactory or definitive treatment of the content and significance of the use of figurative language in science. Unfortunately, given the ubiquity of such language, this means that the precise nature of scientific knowledge is, as yet, poorly understood. [I hope to say more on this in Essay Thirteen Part Two when it is published.]


12. This might be one particular use of the LEM that DM-fans would be wise not to question. If objects, states of affairs and processes were held to be both non-contradictory and contradictory at the same time, little sense could be made of the theory, even before it was examined.


[LEM = Law of Excluded Middle.]


Nevertheless, as with any application of the 'laws' of FL (but I prefer to called them rules), in any application to complex situations some sensitivity is required. In that case, it could be argued that DM is only committed to the view that parts of one system or process 'contradict' parts of another, while still others do not.


To be perfectly honest, it is impossible to give a clear answer to this volunteered response since DM is far too vague and sketchy for anyone (supporter or critic) to decide whether or not this is a legitimate reading. Perhaps it is both and neither at the same time?


Nevertheless, dialecticians do in fact speak about contradictions "growing", "intensifying", and "lessening" -- or, even of them being "resolved". But, this is clearly a subjective opinion since we are supplied with no units by which these supposed changes to 'contradictions' themselves may be measured, and no data to support such contentions; nor do DM-fans even so much as attempt to quantify them in any way (which, on its own, is a rather odd thing for an alleged science to omit).


However, if DM-apologists ever do decide to invent a unit here, we might make some progress.


Until then, may I suggest the 'Neg' as just such a unit?


So, one Neg could be defined as that strength, level, or intensity of a 'contradiction' necessary to make either (i) a stick (of arbitrary size) look bent in water, (ii) an object (again of arbitrary dimensions) look smaller as it recedes from the viewer, or maybe even required (iii) to make at least one capitalist or employer look fair to a randomly chosen worker (albeit, one that has been 'confused' or misled by "banal commonsense").


In that case, a Nano-neg would be enough to make an electron move, and a Pico-neg would enable it simultaneously to be a wave and a particle. Extending this, a Milli-neg would be strong enough to move a millipede. [The reader can decide for herself what a Centi-neg would be capable of setting in motion.] A Deci-neg would be sufficient to represent a formal contradiction in logic, while a Deca-neg (colloquially, "A Blair") would be enough to spin a pack of capitalist lies (about the affordability of, say, pensions), or even publish and endorse at least one 'dodgy' Iraq dossier.


Perhaps then, a Hecto(r)-neg would be sufficient to set off a factional dispute in yet another dialectically-distracted Trotskyist, Communist, or Maoist sect, while the class war itself would need a Kilo-neg to initiate a strike, a Mega-neg to motivate a massive anti-war movement, and a Giga-neg to prompt a proletarian insurrection. Moving up the scale, a Tera-neg would be enough to keep the Earth in orbit around the Sun, and, of course, a Yotta-neg sufficient to kick-start the 'Big Bang'.


We could even introduce a special unit to measure or record the contradictory stench created in the nostrils of most working-class people by the oppression, mass murder, counter-revolutionary antics, and sectarian in-fighting this misbegotten theory has helped motivate Dialectical Marxists to engage in throughout the twentieth century: the Rotta-neg.


All we would need then is an intrepid dialectician (perhaps one of those who claim to be able to derive fundamental scientific truths from thought alone -- by simply juggling with obscure Hegelian jargon, upside down or the 'right way up') to invent a "Neg-ometer" (and they could surely do this if they stopped wasting time writing yet another identical version of DM/'Materialist Dialectics', perhaps by just cutting and pasting large sections from the 'classics' -- as has usually been the case up to now) to measure these super-scientific 'dialectical contradictions'. That done, Mystical Marxism might at least begin to look precise and scientific for once. After all, if Scientologists have their E Meter, DM should at least have a Neg-ometer.


[To be honest, I would have suggested the "Con", here, instead of the "Neg" as a suitable unit with which to measure the strength of DM-'contradictions', but when I typed "Mega-con" into an earlier version of the above, that seemed to me to be a little too obvious -- and a mite too facetious. (Compare these comments with the suggestions made about dialectical "nodes"/"leaps", here.)]


13. This assumes, of course, that 'contradictions' have metaphorical 'geometric centres' and possess figurative 'separation radii'. [Well, maybe they can be photographed, weighed, have their toe- nails clipped and be given a new hair-do, too?]


Cheap debating points? Perhaps so; but if all parts of nature (animate and inanimate, macroscopic or microscopic) behave as if they can argue with each other -- which is how things are depicted in DM when its theorists picture objects and processes as 'contradicting' one another, bickering all the time (that is, if the word "contradict" is understood literally) --, in comparison the cheap shot above is hardly worth mentioning. DM takes the p*ss out of itself; it needs little help from me.


13a. Indeed, when asked to explain why this is a 'contradiction', Ian Birchall [aka 'Grim and Dim' -- his choice of pseudonym, not mine -- and I am not 'outing' a comrade here!] failed to respond. However, in a later thread he made another unsuccessful attempt to reply, as did a few other confused comrades. [Unfortunately, these links are now dead!] Readers are encouraged to read this lengthy exchange on this topic. [Unfortunately, this link is dead, too!] My thoughts on the 'arguments' of one of the egregious participants in this debate ('JohnG') can be found here and here, and now in a revised form here. [In general on this comrade, see here.]


The same always seems to happen whenever I ask dialecticians to explain why these are 'contradictions' -- even knowledgeable comrades soon begin to flounder!


As I noted in Essay One:


The vitriol, hostility, lies and smears I have had to face now for many years suggest I wouldn't last long in such circumstances!


[Please note, I am not complaining; I expect this level of vitriol. If I hadn't received it, I would conclude I had gone wrong somewhere!]


For example, in an e-mail exchange a few years ago, one prominent Marxist Professor of Economics -- Andrew Kliman no less -- expressed the fervent hope I should "Eat sh*t and die!" -- either that or quaff some Hemlock -- simply because I had the temerity to question the 'sacred dialectic'. I asked him to explain exactly what a 'dialectical contradiction' is, which he signally failed to do. His DM-vitriol was repeated here (in the comments section) in October 2013, but it was deleted by the moderators because of the violent and intemperate nature of the language the good Professor thought to use! Another SWP comrade (implicitly) accused me of being worse than the Nazis, and for the same reason! Incidentally, this particular comrade has now left the UK-SWP. Apparently, he still thinks 'truth is tested in practice'.


I have also critically evaluated what I consider the best (Marxist) response ever given to the question 'Exactly What is a Dialectical Contradiction', here.


February 2009 Update: Another attempt can be found here (this link is now dead!). In fact, the owner of this site (a Marxist economist) deleted my replies, since he found it far too problematic to defend his own use of "contradiction".


Autumn 2009 Update: Yet another attempt -- this time involving academic dialecticians, which began here (this link is now dead, too!) and continued here, here, here, here, here, and here -- was no less unsuccessful.


December 2011 Update: Here's another discussion (in the comments section), mainly between myself and Mike Rosen, on the nature of these obscure 'contradictions'. [Unfortunately, when Disqus -- the hosting service for the site to which the first of these links will take the reader -- was re-organised a few years ago, older comments sections were lost.]


[And here (this link is also now dead!) are another three attempts (to access the second of these, click on 'Comments').]


Several more examples of this DM-tendency to label anything and everything as "contradictory" can be found here, and in Note 14.


Indeed, a recent (March 2013) example illustrates this cavalier attitude shown toward the use of this word:


"In the Communist Manifesto Marx makes two contradictory assertions: 1. The ruling ideas in any epoch are the ideas of the ruling class. 2. The emancipation of the working class is the act of the working class itself." ['Mark', quoted from here, p.24. Italic emphasis in the original. In fact, Marx said this: "The ideas of the ruling class are in every epoch the ruling ideas...".]


But, why is this a contradiction? Or, rather, why are these statements by Marx even contradictory? As usual, we aren't told. Even so, it isn't hard to guess a possible answer -- as Tony Cliff points out:


"The fact that the working class needs a party or parties is in itself a proof of the cleavages in the working class. The more backward culturally, the weaker the organisation and self-administration of the workers generally, the greater will be the intellectual cleavage between the class and its Marxist party. From this unevenness in the working class flows the great danger of an autonomous development of the party and its machine till it becomes, instead of the servant of the class, its master. This unevenness is a main source of the danger of 'substitutionism'...." [Cliff (1960), p.126.]


In other words, the working class can't emancipate itself since it is dominated by ruling-class ideology -- and yet it must emancipate itself if socialism is to be won. This seems to be the 'contradiction' here. Indeed, as 'Mark' went on to point out:


"When workers fight back they find that some of the ideas once held, ruling class ideas, are challenged in the very process of struggle. Workers discover they can make speeches and organise solidarity. Racist or sexist ideas are challenged as people unite and fight back together. People change their ideas in struggle. Consciousness is contradictory.


"Those fighting back make up the vanguard of the class. The uneven nature of the class struggle across the class means we need a revolutionary party, one that orients on those engaged in struggle, the 'vanguard' of the class. Unevenness in the Party, as well as the need to totally reject ruling class ideology, means we need a central leadership in the Party." ['Mark' quoted from here, p.24.]


Hence, the "self-emancipation of the working class" can only materialise with the intervention of the party, which is somehow capable of freeing itself of bourgeois ideology -- or, rather its "central leadership" is capable of performing this miracle -- while the working class isn't! Of course, in struggle, as 'Mark' points out, workers often change their ideas, but nowhere does he suggest that they can free themselves completely from ruling-class ideology. If they could, there would be no need for a party! 


Well, this conundrum is ironic in view of the fact that Bolshevik-style parties -- and especially the "central leadership" -- and Marxists in general, have themselves been dominated by 23-carat gold, boss-class thought-forms (upside down or 'the right way up') for well over a century, as these Essays have amply demonstrated.


But, and once more, why the above example a contradiction, as opposed to an impossibility? Or just confused thought?


Again, we are left in the dark.


Here is another typical example of DM-profligacy in this respect, which surfaced in a letter sent to Socialist Worker at the end of August 2011:


"China's elite is contradictory


"I'm writing regarding Charlie Hore's article on economic growth during the reform period in China (Socialist Worker, 20 August). It doesn't mention the powerful contradictions that emerged within the ruling bureaucracy as a result of the reforms. Not all sectors of the bureaucracy have benefited from the reforms. There has been a shift from ideological campaigns towards a performance-based notion of state legitimacy. This has meant that many officials have experienced anxiety about their relevance in Chinese politics and have been dragged into protest movements. A socialist analysis has to make sense of these contradictions." [Bold emphasis added. Paragraphs merged.]


Again, no one explains why such things should be called "contradictions" when they are obviously far better described as "tensions" or "conflicts". For example, do these factors imply one another? No. Can one exist without the other? Yes. This is quite unlike the alleged 'contradiction' between the bourgeoisie and the proletariat, where one supposedly implies the other and where neither can exist without the other -- although I have thrown that widely accepted inference into considerable doubt here.


Some might conclude that this is just another example of Ms Lichtenstein's pedantry, but that isn't so. [On 'pedantry', see here.] There are important political reasons for rejecting the use of "contradiction" in the way it is used by Dialectical Marxists. [On that, see Essay Nine Part Two.]




(1) It 'allows' dialecticians to argue in favour of anything they like and its opposite (often this is done by the very same dialectician, on the same page or in the same speech!), no matter how anti-Marxist or counter-revolutionary this "anything" might prove to be. These are then often 'justified' on the basis that since everything is 'contradictory', and a 'unity of opposites', Marxist theory and practice should be contradictory, too!


(2) It is used to rationalise a whole raft of substitutionist tactics, strategies and moves on the basis that even though Marx insisted on the self-emancipation of the working class, we can substitute one or more of the following for the proletariat: (i) The Party, (ii) The Red Army, (iii) 'Third World' guerrillas, (iv) 'Progressive' nationalists, (v) Students, (vi) Sympathetic, left-leaning politicians, and/or (vii) An assortment of social forces, 'rainbow coalitions', and groups, no matter how contradictory this might otherwise seem. And concerning those who might object..., well they just don't 'understand' dialectics, or, indeed, the 'contradictory' nature of Marxism, the class war, the former USSR..., etc., etc.


(3) The use of this word 'allows' DM-fans to look at the protracted failure of Dialectical Marxism and fail to see it for what it is: a long-term and profound refutation of their core theory, 'Materialist Dialectics'. It also 'allows' them to interpret this abysmal record as the opposite of what it is -- on the grounds that appearances 'contradict' underlying 'essence'. So, if Dialectical Marxism looks hopelessly unsuccessful, a catastrophic failure, the opposite is in fact the case. This then encourages dialecticians to stick their heads in the sand while our movement slowly runs into those very same dunes.


(4) Because of (3), this word provides DM-acolytes with a source of consolation for the long-term ineffectiveness of their entire movement, its serial divisiveness and its ever present internecine warfare -- "Well, what else can you expect in a contradictory universe? Marxism should look the opposite of what it really is! Dialectics allows us to grasp this contradiction."


So, this isn't 'pedantry', nor is it merely 'academic' point-scoring; this word has had, and still possesses, disastrous political implications.


14. 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 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 sense (involving forces) something that does not (i.e., the proletariat's potential revolutionary role). As we have seen, dialecticians constantly use the word "contradiction" in inappropriate circumstances to depict things that seem quirky, odd, paradoxical, contrary to expectations, and so on -- almost as the mood takes them. [See, for instance, 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 (1996), p.87.]


What Lindsey German might have had in mind in the above passage is that there is what seems to be 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.


The questions here are: (i) do these 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, so we are told -- although I have thrown that inference into considerable doubt here)? The answer is in the negative in each case. That being so, whatever else it is, this 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.


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 this topic any further n 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, this puzzle also disappears.


Hence, German's worry about overcoming this 'contradiction' can now be shelved -- 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 be to stray into areas of HM, no more will be said about it here.


14a. It could be argued that in so far as forces in nature can be represented as vectors, then this is also the case with contradictions. That option will be considered presently.


15. E.g., Rees (1998), pp.5-8.


Any who object to my presumed use of the LEM here should check this out, and then perhaps think again.


16. It may be felt that this completely misconstrues the relation between parts and wholes in DM (wherein "the whole is more than the sum of the parts", etc.). However, that dubious dialectical doctrine has been examined in extensive detail in Essay Eleven Part Two, where it is shown to be as confused as other DM-theses.


17. Of course, it could be argued that this objectifies the Totality, thereby distorting it. But, if the Totality isn't a kind of object (even if it might be a changing 'object' of some sort), how can 'it' have any relation to 'its' parts, and how could 'contradictions' be properties of 'it'?


It could be objected that the Totality is in fact a process, and hence it would be an 'it' (or, a sort of 'it') in that sense. Naturally, the answer to these (and other) questions concerning this mysterious entity/process, the Totality, will have to be put to one side until DM-advocates tell us (if ever) what (if anything) they think 'it' is.


[They might find a few useful ideas (consistent with much else in DM) here.]


Despite this, it could be further objected that abstract reasoning like this demonstrates nothing since DM is concerned with verifiable, concrete material contradictions, which exist in the real world. That response has been examined here and here.


18. This assumes that these relations are symmetrical -- that is, that AR = RA, which seems reasonable enough. Another simplifying assumption is that these forces are 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.


In addition, most of the comments in this part of the Essay have 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.


A comprehensive scientific 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 of exchange particles -- here is a simplified visual display that explains how this idea is supposed to work; scroll down the page to the 'astronaut video'.]


However, it is possible that as science develops reference to forces (even in school Physics) will progressively disappear; cf., Jammer (1999), pp.iv-vi (quoted earlier). In that eventuality, if DM-theorists maintain their adherence to the doctrine that 'force' gives 'contradictions' a material grounding of some sort, their theory would become 'unscientific' by default. Either that, or they will have to abandon talk about 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.


Should this 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.). 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.


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 --, and definitely not yours truly.]


Nevertheless, with respect to the comments in the main body of this Essay, 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. Physicists get around this fatal flaw in their theory with a handful of ad hoc mathematical dodges. That alone suggests these theories are incomplete -- rather like the additional epicycles that were required to make Ptolemaic Astronomy 'consistent'.]


Clearly, this just complicates the point without altering it. In such a scenario we would have an ARA-system-of-forces, which would be even more difficult to interpret as 'contradictory'. As pointed out in the main body of this Essay, the meaning of the word "opposite" would have to be altered so that systems of forces could then have any number of 'opposites'. If so, these artificial 'contradictions' would be the product of an arbitrary choice of words, not 'objective' realities.


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 in fact 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 this later, too.]


20. This simple picture is, of course, ruined by the complexities found in nature. However, the more complications there are, the less applicable DM-concepts seem to be. In this case, we would have here an RARA-system-of-forces. Again, a choice would now have to be made whether we should widen the meaning of the word "opposite" to accommodate DM, or change DM in order to accommodate the facts. To date, DM-theorists have generally preferred the former to the latter.


Since AR-forces are discussed below, I will postpone comment until then.


21. This needn't be as serious a problem as is suggested in the main body of this Essay. As pointed out elsewhere, scientists do this sort of thing all the time. Unfortunately, this is bad news for DM since it confirms the view that science is a conventionalised social practice, and further substantiates the claim made here that metaphysical theses arise from a misconstrual of conventionalised linguistic forms as if they were fundamental features of reality. In short, the conventions we use to represent the world are confused with material truths about it.


This is about as crass an error as would, say, an assumption that reality itself must have an edge to it simply because every photograph or painting has one.


[This topic is examined in detail In Essays Twelve Part One and Thirteen Part Two, when the latter is published.]


21a. Or, perhaps even:


(3) This way of looking at the world is indeed as crazy as it looks!


[This topic is examined more extensively in Essay Eight Part Three.]


22. It might be felt that this Essay, indeed, this site, is so heavily biased against DM and any way of interpreting forces as 'contradictions', that scientific facts and theories have regularly been twisted and slanted so that they appear to be prejudicial to DM -- this latest allegation being the most recent example. Surely -- it could be argued -- accelerated motion in the real world is the result of several forces operating on a body; the ensuing motion simply follows as a result of their oppositional nature.


This volunteered response will be examined presently in the main body of this Essay.


23. Once more, it could be objected that there is no such thing as "empty space". But even if that were so, and the objects referred to in the main body of this Essay weren't situated in the said force field, any forces present would still fail to operate on each other, but only on any bodies in the system (if there are some). Hence, forces seem to affect bodies not each other. [See Note 24 on this, too.]


24. It could be argued that force fields do in fact interact, and they certainly alter one another. That objection, too, will be examined presently.


This is, of course, 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, on instruments (or, rather, a 'force' seems to be little more than the way scientists depict or measure certain relationships between bodies, as Engels, in an uncharacteristically sober mood, pointed out; on this, see Note 4) -- or on other 'fields'.


However, if forces are seen as particulate (that is, if certain particles are viewed as the 'bearers' of forces -- on that, see here), this 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.]


Hence, it would seem that this sort of interaction between forces could only take place if they were particulate in some way -- that is, if they registered some sort of resistance to one another (i.e., if they are impenetrable to some extent). If, on the other hand, they aren't particulate, it is hard to see how they could interact in any way, 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 of particulate interaction, after all).


[This has been questioned in Smith (2007). More on that presently.]


But, there are well-known classical problems associated with the idea that forces are particulate (these have been referenced 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.


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 are bodies; as noted earlier, many physicists 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.


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 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 this 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/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 this 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.]


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 are 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 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 added; quotation marks altered to conform with the conventions adopted at this site.]


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 scientific language), but they certainly indicate that at least some leading scientists are aware there is a problem.


[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 science or technology of any note has much to teach one that has, least of all about physics. Thus isn't to disparage Native American culture -- far form it -- it is  merely to point out that no such culture could be expected to compete with one that is technologically advanced.]


On this, also see Essay Eleven Part One.


25. 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. This 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 in reality 'interpenetrated' opposites' -- for example, in the way that we are told that capitalist relations of production imply the existence of the proletariat, and vice versa. [Although I have thrown that clichéd inference into considerable doubt here.] And, if these forces aren't 'internally related' then the dialectical theory of change simply falls apart.


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


[In fact, this topic is connected with "real negations", a concept introduced into Philosophy by Immanuel Kant. I will say more about this in Note 56 and Appendix A, below. Other related issues will be examined in Essay Thirteen Part Two, when it is published. Finally, this topic is connected with the fact that, where there is more than one force at work in the system, change in motion is caused by resultant forces, discussed in more detail here.]


To be sure, when forces are represented as vectors they can produce accelerations that appear to 'oppose' impressed motion already in the system. Ignoring for the present the fact that the use of such language is arguably anthropomorphic, 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. Even in physical reality, accelerations aren't 'disembodied beings' that inhabit the material 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 this seems odd, to say the least, since no accelerating body implies the existence of the velocity in another 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 this 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 sense can be given to 'equations' such as 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 (5), 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, in which forces appear as part of a "norm of representation" --, we can 'convert' forces into accelerations, compare magnitudes, and thus account for motion and change in motion.


Unfortunately, this is of little help to DM-theorists, since the translation of forces into relative accelerations means that forces are indeed "useful fictions", once more, which would 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-classicists).


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.


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


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 in this area, and (ii) The way we make sense of such equations. More specifically, this change in terminology 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 development of market economies in 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 these different categories. Since they had to be co-measured (to balance the books!), the mathematics involved was adjusted accordingly.


Hence, these new concepts were introduced by mathematicians, merchants, and bankers so that formerly incommensurable quantities could be compared analogically -- enabling, for example, the calculation of the exchange values 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 -- also allowed theorists to move beyond an earlier 'commonsense' approach to motion encapsulated in Aristotelian Physics, which enabled the foundations of modern mechanics to be laid 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' -- the latter of which was itself originally based on belief in an Ideal World that was anterior to, but more real than, the world we see around us. Since access to this Ideal World could be had by thought alone, it made sense to conclude that mathematics was also based on thought alone. In which case, mathematics itself must be founded solely on thought processes, on 'abstraction' (or later, on logic). This put the mathematician in touch with the 'Divine', and hence with pure concepts devised by 'God', a doctrine explicit in Plato. In fact, the universe itself was a reflection of 'Divine Thought', which made 'God' a Mathematician and the world a mathematical object of some sort -- a paradigm that still dominates much of Modern Physics, even the thought of physicists who are agnostics or atheists.


"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).]


"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.]


"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 to 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). I have added to Appendix B a lengthy passage from Plato (1997b), 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 a 'subjective experience' --, and that includes anything written in mathematics. Or does he have access to the world and to mathematical theorems that bypass the senses? If not, then even mathematics when it has been written down (or has been spoken) must also be a 'shadow', and hence can't represent 'reality'.


Anyone who thinks this misrepresents Tegmark need only read Chapter Nine of 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 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 propel epistemology back to where it was before the Critique of Pure Reason saw the light of day (this links to a PDF). [I have covered this topic extensively here. Readers are directed there for more details.]


Something like this, but maybe 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 '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.]


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


By way of contrast, the approach adopted here 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 has been based. Hadden's pioneering work is only prevented from being Marxist classic by the absence of a clear account of the nature and role of language, as well as 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, slightly spoilt by the author's attempt to use his admirably clear insights to try to make sense of talk about 'God'.]


Hadden's conclusions are themselves a development of ideas 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 study, Kaye (1998).


In that case, the admission that forces can be edited out of the picture (so that relative acceleration and motion may be regarded 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 confusing way of alluding to relative acceleration, or relative velocity. The connection between events could then only be explained in one of two ways, i.e., by:


(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 context; UO = Unity of Opposites.]


In either case, the connection between events and processes wouldn't be governed by any sort of physical mediation between them (or, indeed, the rest of the Totality) -- as DM requires -- since, on this view, moving bodies (with or without opposite velocities, or accelerations) would have no internal connection with any other bodies in motion.


At least an appeal to forces has the merit of appearing to supply a sort of mediating link between bodies in motion, or change, required by DM. Forces at least appear capable of connecting the latter in some sort of 'dialectical' relationship -- but, of course, that is only because a literal interpretation of forces like this depends on a prior acceptance of an animistic view of nature.


So, 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., CAR), which it sought to replace, or, at least, surpass.


As noted in the main body of this Essay, DM-theorists require forces to be part of the ontological fabric of the universe, which is why they become rather defensive, if not highly agitated and emotional, when the existence of forces is questioned. Except, even after they have been informed, they totally ignore the fact that Engels had already been there. So, in order for DM even to seem to work, its theorists require the existence of a world populated by anthropomorphic concepts (or what they supposedly 'reflect') -- e.g., forces --, which were themselves the 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 the alleged '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.] This seems to connect those sketchy ideas with more recent theories of motion, modelled by vector and scalar fields -- or even 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 --, all of which were constructed late in Engels's life or a generation or so after he died. But, once again, 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 heavily 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 be 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 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 lines.]


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


[In fact, 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'!


26. Those who still think that forces are capable of opposing motion, and can therefore contradict it, should consult the arguments presented in Note 25 above, and presently in the main body of this Essay, where this idea will be finally laid to rest.


However, it is worth pointing out that if it were correct that forces are capable of opposing motion, and can therefore contradict it, the thesis that forces 'contradict' one another will have already flown out of the non-dialectical window. Plainly, if forces oppose motion, they can hardly oppose each other. [Unless, of course, we agree with Engels that the concept of "force" should be ditched and replaced by "relative motion".]


27. In which case, it might be wondered whether only those bodies that approach each other along the same line of action (where the angle between their trajectories is 180°), or which operate in a force field (where the 'lines of action' of that field are similarly orientated at 180°) are to be counted as 'opposites'.


If not, will any angle (other than 90°) work?


However, since forces and velocities are vectors, or, rather, can be expressed as vectors, they can be resolved to circumvent this difficulty. Even so, any solution sought along these lines -- no pun intended -- would clearly be conventional, since the components of vectors don't exist in nature in any meaningful sense; they are merely an integral part of the calculating devices we use to help us make sense of any changes in motion (etc.). [On this, see Note 24 and Note 25 above, and Note 30, below.]


28. Anyone who thinks that the vector calculus is a description of reality would be suffering from the same sort of confusion as someone who thought that the weather, say, is the wavy lines, or the tangent fields, on a map -- which show, for example, wind direction and speed --, simply because a TV weather forecast, for instance, uses them. [On this see Note 25, above and Note 40, below.]


29. This section of the Essay might be dismissed as just the latest unsympathetic reading of yet another set of artificially modified DM-theses. Perhaps 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 aspect 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. Unfortunately, since 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 rabid DM-fan might find it difficult to visualise (let alone explain) a 'contradiction' between something that is real and something that isn't (in that it never existed, or was prevented from existing): i.e., the motion that would have occurred if the impeding force, P1, hadn't acted.


30. Admittedly, some vectors are invariant under certain transformations, but the physical interpretation of the operation of forces isn't a given; it is set by convention. On this, cf., Ellis (1963, 1965, 1976).


[Ellis (1976) was written in response to Hunt and Suchting (1969). See also Hanson (1965a, 1965b), and Jammer (1999).]


Mysteriously, however, Ellis has backtracked on his earlier views (for what appear to be instrumentalist reasons); cf., Bigelow, Ellis and Pargetter (1988), and the response to this in Jammer (1999), pp.iv-vi.


The difficulty with finding a physical analogue, or correlate, for vector spaces (or, worse, for any tensor extension to them) is examined in Cartwright (1983), pp.54-73; see also Hesse (1961). A recent challenge has been registered to this way of seeing forces in Jones (2007); on that, see Note 6a.


31. On this, see Note 24, Note25 and Note 30 above.


32. This topic was discussed in much more detail in Essay Seven Part One, where I have termed it the Dialecticians' Dilemma. See also, here.


33. On this, see, for example, here.


So, either: (i) there is no limit toward which knowledge is converging, or (ii) as knowledge advances, it must be the case that external reality is altered accordingly, or even (iii) it is now true to say that, in the limit, the world contains no contradictions at all.


Plainly, unless we are Idealists, (ii) can't be the case. We aren't to suppose (it is to be hoped!) that our knowledge of the world alters the 'objective contradictions' that allegedly power the whole of reality, so that as knowledge grows 'contradictions' slowly disappear. 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. 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 may be incorrect to assume 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 -- and if they are committed to the view that science can only advance if it overcomes or resolves contradictions in knowledge -- dialecticians must believe they can be resolved if we but knew more. 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 (perhaps because there are irresolvable contradictions in nature). But, if they also believe that there is no limit to scientific advance, then they must also believe that (vi) there is no limit to scientific advance and (vii) there is a limit. 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 correct).


Of course, this means that DM itself can only advance if this contradiction is resolved. Hence, either (viii) DM can't advance or (ix) dialecticians must hold that all contradictions are resolvable.


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


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


Again, the only apparent way of avoiding this fatal result is to deny that either (a) science can only advance by resolving all contradictions, or that (b) that Absolute Truth 'exists'.


However, the acceptance of option (i) 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 to that the idea 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. 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.


Naturally, these observations assume that the universe might be 'infinite' (a view that is held by many DM-theorists) and constantly changing. But, neither of these 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 are correct when they said:


"'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, and no such limit, then Engels's metaphor is defective, and Lenin was mistaken -- since, once again, there would be no such things as 'objective truth'.


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.]


To be sure, the above passage wasn't included in the 'official' version of AD, but it does tend to suggest that Engels believed either that (1) the 'objective' world is free from contradiction, or (2) it is free from contradiction with our thoughts about nature --, the first of which alternatives, it must be admitted, is impossible to distinguish from the second -- or even (3) in the limit there will be no contradictions at all in 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 be in contradiction with 'objective' reality (and thus with 'objective' theory itself, one presumes, even if this blessed state is never attained). So, if knowledge is to advance, even this 'contradiction' (i.e., the alleged 'contradiction' in motion) must be resolved, and thus removed. After all, it, too, might be a contradiction that we could resolve if only we knew more or we tried harder.


[But, 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 be able to decide even among themselves about this -- that is, without being branded 'Revisionists', sparking perhaps yet another dialectical dog fight, and then another debilitating split.


34. As noted above, it is entirely possible that this isn't what DM-fans really mean by "contradictory forces"; but then again it is also doubtful whether they have ever subjected their own theory to this level of scrutiny so that even they would be in any position to accept or reject this interpretation. Hence, as things now stand, there would be little point asking a DM-adept for an answer to this quandary (i.e., "Is this what you mean by 'contradictory force'?").


[And good luck to anyone who doubts my assessment of DM-fans' knowledge of their own theory! Personal experience stretching now across over thirty years has taught me that anyone foolish enough to ask a DM-fan to devote even so much as one minute to this topic will face no little personal abuse, misrepresentation, and 'scatological hostility', at best. (Here is just the latest example -- unfortunately that link is now dead! Here then is the next most recent.)


Compare this slipshod and superficial approach to theory with the care and attention to detail devoted by Marxist theorists when they analyse concepts employed in HM -- such as "the forces and relations of production", "ideology", "racism", "class", or "the tendency of the rate of profit to fall". Whole books have been written about ideology, class, and racism. Not one single book has been written about forces interpreted as 'contradictions'; not even one chapter!]


35. It is worth repeating here that these assertions are aimed neither at affirming nor denying DM-theorists' claims about the Totality, and that includes its supposedly 'contradictory' parts, since both those questions would be metaphysical, and hence non-sensical and incoherent. [That is because the denial of non-sense is also non-sense. The reasons for saying this take up most of Essays Twelve Part One and Eleven Parts One and Two.] As pointed out earlier, the intention here is simply to make patent the latent non-sense they contain.


Moreover, an appeal to 'relative truth' would be of little help here, either; surprising as it might seem, that notion was (inadvertently) torpedoed by Lenin himself!


36. As we saw earlier, these 'difficulties' revolve around the question whether it is (a) a force's effects, (b) the relative motion between objects, or (c) the interrelationship between bodies and/or processes, that are supposed to be 'contradictory'.


37. This is so on Hegelian and Aristotelian grounds.


So, even though, for example, male and female, hot and cold are 'opposites', a male dog isn't the opposite of a female flower, and a hot oven isn't the opposite of a cold can of beer. 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 hot oven the opposite of a cold oven, and so on. Logical  connections of this sort are essential if opposites are to count in DM as 'interpenetrated'.


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, if, say, a hot oven isn't the DM-'opposite' of a cold can of beer, then it is difficult to see how they can interact, with the one heating up the other on 'dialectical' grounds. But who doesn't know this can happen? 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 (which they would have to do if they were 'dialectical opposites')? And yet, if we were to believe Hegel and the DM-classics -- that only 'dialectical opposites' can interact -- then you couldn't warm your cold hands on anything other than a pair of warm hands!


38. Here we appear to have another ironic "dialectical inversion". In this case, the said forces wouldn't actually 'contradict', since they augment, one another -- even though they are still supposed to be 'opposites'. Perhaps then we should call such configurations "dialectical tautologies"?


On that basis, therefore, we might be able to construct an entirely new -- and, it must be admitted, wholly insincere -- theory of universal harmony. This is especially so if we recall that forces 'naturally combine' to form resultants, and opposites more often than not attract rather than repel each other (on that, see Note 40 and here), both of which phenomena are also connected with motion and change. As a result of such an 'inversion' -- putting DM 'back on its heels', as it were -- change would then be an expression of cooperation, not conflict. We could even re-introduce the idea of an 'Immanent Deity' (a suitable -- but no less obscure -- analogue of the DM-'Totality') to give this novel, insincere 'theory' the unity and cohesion it requires, claiming all the while that these ideas haven't been imposed on nature, merely read from it.


Since this 'theory' is based on a more realistic appraisal of the interplay between forces, who could reasonably object? We could even call this 'theory' "Anihalectics" (in that it eliminates dialectics). Any subsequent 'contradictions' implied by this 'theory' could, of course, be Nixoned away along classic DM-lines.


We could even declare -- with equal pomposity and 'justification' -- that anyone who disagrees with this new 'theory' just doesn't "understand" Anihalectics, ending all discussion. On the positive side, this 'theory' enjoys much more evidential support than the average DM-thesis -- given the fact that resultant forces govern every example of changes in motion in the entire universe, so far as we know.


On the negative side, however, this 'theory' would mean that class collaboration and harmony will 'inevitably' usher in the 'revolution'. [We saw that this was an implication of DM, anyway, here and here.]


Anyone critical of the above wholly insincere, fanciful and off-the-wall 'theory' should now point an equally censorious finger at DM, and for the same reason.


39. Even so, and once again, howsoever it is imagined that forces actually do manage to combine, change itself isn't initiated by contradictory forces, but by the above annoyingly 'harmonious' resultants.


40. Engels himself regarded the two poles of a magnet as a clear example of the unity of AR-opposites in nature (another idea he imported 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 got 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 -- or like 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 in fact 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 a 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 serious 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, for example, do electrons and protons 'struggle' if they attract one another? [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, these poles 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, only the relative motion induced by each force). Hence, once more, the two poles wouldn't be inter-related to each other directly as opposite AR-forces; they would just 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 each other as force upon force.


Again, this is probably one reason why Engels toyed with a positivistic re-interpretation of forces (i.e., 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 Five: Force Fields And Iron Filings


On the other hand, if by "force field" we mean the mathematical structures postulated by 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 Note 25, and will be again, below.]


Anyway, 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 'logically implies' the proletariat -- although I have thrown that inference into considerable doubt here). 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 already seen, it isn't easy to see how vectors can be regarded as 'contradictions' (or, indeed, 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 earlier).


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.)]


Naturally, this deflationary approach 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.). In response to this, 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 part 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. Nor do the concepts that mathematicians construct 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 can they be. They express rules for the manipulation of certain symbols that licence inferences we make about objects and processes in nature and society (or, indeed, in formal systems). At best, they set up complex analogies that assist in our understanding of objects, events and processes in the material world.


The development of Field Theory since Maxwell's day doesn't alter this picture in any way at all. 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, but plane segments or 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.


Furthermore, if abstractionism were true, no two mathematicians would or could agree with each other; indeed, 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.]


41. This could be regarded as a serious interpretive error -- given the fact that change is central to DM. But, the point being made in the main body of this Essay 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.


42. It is worth recalling here how Stalinists attempted to 'justify' the frequent, sometimes overnight, tactical and strategic 180°changes of direction they performed in the 1930s, on the basis that they were 'dialectical', when they had in fact been made for hard-headed political reasons. So, a pact with the Nazis appeared to make eminent good, 'dialectical' sense. Anyone who disagreed with this zig-zag approach to politics clearly didn't "understand" dialectics. Indeed, the above treaty was as good an example of a UO as one could wish to find. Who could complain? -- Except, perhaps, those motivated by "bourgeois" prejudice compounded by an antiquated reliance on FL? Or, those in the grip of an excessive "tenderness" toward treaties with fascists?


[This phenomenon has been illustrated with dozens of examples in Essay Nine Part Two. Except, of course, this wasn't a UO, since the existence of the Soviet State did not imply the existence of the Nazi State, or even the 'non-aggression pact'. DM-terms it made no sense.]


All manner of equally incongruous and counter-revolutionary UOs have be justified by this theory. [For instance, John Rees attempted to justify the "united front of a special kind" -- entered into by the UK-SWP a few years ago -- by appealing to yet another 'UO argument'. But, neither side of this 'UO' implied the other side, unlike the alleged connection between the proletariat and the bourgeoisie -- although I have thrown that lazy inference into considerable doubt here. Again, this didn't even make sense in DM-terms.] Because DM glories in contradiction it can be, and has been used to 'justify' any conclusion deemed expedient and its opposite -- this trick often performed by the same individual (or party hack) in the same speech, book or article. Hence, DM is an invaluable tool in the hands of opportunists and sectarians of every stripe.


[Again, more details can be found in Essays Nine Part Two and Ten Part One.]


43. Is this yet another 'dialectical tautology'?


43a. Of course, Hegel's ideas had roots in traditional, Mystical Thought, but the explicit use of 'contradictions', and the key role they assumed in his work, is unique and -- except for their presence in Zen Buddhism -- without precedence. This isn't to deny that philosophers and mystics have always appealed to oppositional forces (and UOs) in order to account for change and stability in nature and society, but they, too, had to employ words and concepts drawn from the vernacular -- as the late Professor Havelock pointed out (quoted earlier):


"As long as preserved communication remained oral, the environment could be described or explained only in the guise of stories which represent it as the work of agents: that is gods. Hesiod takes the step of trying to unify those stories into one great story, which becomes a cosmic theogony. A great series of matings and births of gods is narrated to symbolise the present experience of the sky, earth, seas, mountains, storms, rivers, and stars. His poem is the first attempt we have in a style in which the resources of documentation have begun to intrude upon the manner of an acoustic composition. But his account is still a narrative of events, of 'beginnings,' that is, 'births,' as his critics the Presocratics were to put it. From the standpoint of a sophisticated philosophical language, such as was available to Aristotle, what was lacking was a set of commonplace but abstract terms which by their interrelations could describe the physical world conceptually; terms such as space, void, matter, body, element, motion, immobility, change, permanence, substratum, quantity, quality, dimension, unit, and the like. Aside altogether from the coinage of abstract nouns, the conceptual task also required the elimination of verbs of doing and acting and happening, one may even say, of living and dying, in favour of a syntax which states permanent relationships between conceptual terms systematically. For this purpose the required linguistic mechanism was furnished by the timeless present of the verb to be --  the copula of analytic statement.


"The history of early philosophy is usually written under the assumption that this kind of vocabulary was already available to the first Greek thinkers. The evidence of their own language is that it was not. They had to initiate the process of inventing it....


"Nevertheless, the Presocratics could not invent such language by an act of novel creation. They had to begin with what was available, namely, the vocabulary and syntax of orally memorised speech, in particular the language of Homer and Hesiod. What they proceeded to do was to take the language of the mythos and manipulate it, forcing its terms into fresh syntactical relationships which had the constant effect of stretching and extending their application, giving them a cosmic rather than a particular reference." [Havelock (1983), pp.13-14, 21. Bold emphases added; quotation marks altered to conform with the conventions adopted at this site. Spelling modified to agree with UK English. Links added.]


On this, see Essays Twelve and Fourteen Part One (summaries here, here and here). Cf., also Barnes (2009), Kahn (1994, 2003), Lloyd (1971), and Seligman (1962).


44. This insurmountable obstacle lies in the path of all forms of Metaphysical Realism, so this isn't just a problem for DM-theorists. More on that in Essays Twelve Part One and Thirteen Part Two (when it is published).


45. Admittedly, this could be a complete distortion of DM, but, as we have seen many times, over the last hundred years or so dialecticians have been so preoccupied with reproducing almost word-for-word repetitions of DM-theses handed down to them by the Dialectical Classicists that they have neglected to think about them with due care, or with any clarity or depth. What is worse, there is precious little in the DM-Classics that is of much help to dialecticians themselves; so even they would be hard-pressed specifying exactly where and how this analysis itself represents a distortion.


Once again, there is an easy solution: DM-apologists are invited to produce their own clear account of the precise nature of the link between forces and 'contradictions' -- making this aspect of DM perspicuous for the very first time in its history.


Wisely, neutral bystanders won't be holding their breath...


45a. Since this Essay was originally written, a superficial attempt has in fact been made to specify the precise nature of the link between oppositional forces (or, to be more honest, oppositional "tendencies") and 'dialectical contradictions' -- in Weston (2012).


The following is a passage we have already had occasion to quote in part -- concerning an obscure comment in Das Kapital, where Marx added a throw-away line about 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); and (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. 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 be made to seem to work.


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


46. Of course, this initial attempt at clarification is unclear itself. We should normally want to distinguish the opposition between forces, P1 and P2, from that between events, E1 and E2, or indeed any pair-wise combination of all four. Complications like these will be examined in what follows (in fact, some of them were analysed earlier).


47. Admittedly, this qualification runs foul of the idea that everything in the Totality 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 the main body of the Essay (originally aimed at trying to make this aspect of dialectics clear) 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 is permanently engulfed.


48. I have omitted 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 at once 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 either on a mis-description, or on an un-discharged ambiguity --, and, of course, on the projection of logical categories onto nature. This was analysed in more detail in an earlier section, as well as in Essay Five -- and will be examined again in Note 67 and Essay Eight Part Three.


49. 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 argued 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 in the main body of this Essay, others later on -- for example, in Note 55.]


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 grip.


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, or to which it could refer, which means we would have a concrete example of change through 'internal contradiction'.


Or, so it could be maintained.


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 this point -- 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 and others will be considered 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 and they supposedly imply one another. So, whatever else it is, this can't be an example of 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", 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 that system, then, plainly, those objects can't be "self-moving". The volunteered response above simply reproduces this in a more abstract form.


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


Anyway, this volunteered DM-response will be tackled presently in the main body of this Essay -- and in more detail below, in Note 55.


50. It could be objected that forces actually make things happen, as opposed to preventing them. But, even then, this would be the case if only one force were to 'win out', as it were -- the resultant. Furthermore, making something happen is even less easy to interpret as a 'contradiction' than opposing or preventing something from taking place. In that case, once more, calling this a "tautology" would be far more appropriate.


Be this as it may, the analysis in the main body of this Essay was based on the idea that one of P1 or P2 brings about, or causes, its own event set as opposed to initiating the other set. So, even here, these forces do "make things happen".


Finally, it is rather odd arguing in one breath that forces don't prevent things, while in the next asserting that forces oppose one another! [On this, see the next sub-section.]


Maybe this DM-conundrum should simply be Nixoned...


50a. 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.


(***) "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)


(****) "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 appeals to a handful of rather obscure ideas connected with "negativity", here, 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, the two sides of the 'contradiction' in such cases must co-exist.


If so, it should prove 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.


Here, from what Weston says in paragraphs (***) and (****) above, "opposite" can be given a Weston-style spin so that it means something like "the opposite result of...", or "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 this 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 will 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, 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 in the main body of this Essay:


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.


We hit the same brick wall!


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


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 if that happens, the planet will enter into an orbital trajectory.


I take up this notion (i.e., "balancing"), and several other related issues, in the main body of this Essay (here, here, and here), but in more detail in Note 55, 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 ill-conceived since it was based on an egregious mis-interpretation of the LOI -- just as we have also seen that contradiction has nothing to do will cancellation.


[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 this, see below.]


[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 seen. 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!


51. The terminology used here isn't what I should prefer (for reasons set out in Essay One), but tinkering around with it won't make the conclusion any clearer. The following is, perhaps, a little more 'correct':


F16a: Anything that is prevented from occurring does not happen.


But, F16a is just a discursive tautology -- although I should prefer to call it a "grammatical remark", since it expresses a linguistic convention, or rule for the use of certain words.


52. It should be pointed out (once again!) that this 'new' account of the connection between forces and contradictions (advanced in the main body of this Essay) is only being offered tentatively since DM-theorists are hopelessly unclear in this area.


53. The phrasing of F24 might be considered prejudicial -- F24a perhaps being a slightly more acceptable version:


F24:  P1 contradicts P2 only if it counterbalances P2.


F24a: P1 contradicts P2 if it counterbalances P2.


This option will be considered presently in the main body of the Essay (as F27).


54. We saw in the passages quoted at the beginning of this Essay that several DM-authors regard disequilibria in nature and society as just important as corresponding equilibria, and in need of explanation. [Indeed, Weston seems to accept this reading, at least in so far as it pertains to the orbit of planets around stars (etc.).]


54a. To see this, compare F27 with the following:


S1: All things being equal, NN will arrive in London, UK, if she takes the M1.


[F27: P1 contradicts P2 if it counterbalances P2.]


But, S1 is a sufficient condition, not a necessary condition, so it doesn't rule out S2 or S3:


S2: All things being equal, NN will arrive in London, UK, if she takes the A1.


S3: All things being equal, NN will arrive in London, UK, if she takes the M40.


Since there are many different ways to travel to most cities -- even though none of them is necessary, they could each be sufficient -- none is unique in this regard, which they would be if they were necessary.


So, S1-S3 are sufficient, not necessary, conditions. Of course, if there were one and only one way to get to London, that would be both a necessary and sufficient condition.


[Often the former is expressed by the use of "only if". The Wikipedia article on this topic isn't a model of clarity; the Stanford Internet Encyclopedia of Philosophy article is much better, but far more complicated. This is perhaps the best article on-line for those new to logic.]


The verb phrase "All things being equal" (also called a ceteris paribus clause) is required, here, since it is assumed that other adventitious events don't prevent NN reaching her destination, such as a crash, a breakdown, a phone call cancelling the trip, an illness, etc., etc. If this caveat is allowed, then S1-S3 are sufficient conditions, otherwise, plainly, they aren't -- simply travelling along a road doesn't guarantee you'll arrive at your destination!


There are in fact several suppressed ceteris paribus clauses in most of the futile attempts I have made to render this part of DM clear. I have left them out in order to reduce complexity.


55. 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:


T1: 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.


[Here, "event" can be interpreted as widely, or as narrowly, as is required so that it is compatible with a 'dialectical' view of causes, or of "mediations", and their effects.]


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, even this 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:


T2: 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.


T3: 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.


T4: 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 even prevent Ei, it can't have 'contradicted' it, either. 


We hit the same brick wall.


Consider now this variant on T3:


T5: 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:


T6: 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:


T7: 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.


T8: In the 'normal course of events', let each event, Ei, cause the next event, Ei+1.


T9: However, Ei+1 failed to occur because P prevented Ei causing it.


T10: Hence, P contradicted Ei.


There are several problems with the above:


(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, 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? And yet, it ought to do one or both 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.


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 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.]