Essay Four Part One: Formal Logic And Change


[This Essay should be read in conjunction with Essays Five and Six.]




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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.]


It is also worth pointing out that a good 50% of my case against DM has been relegated to the End Notes. This has been done to allow the main body of the Essay to flow a little more smoothly. Indeed, in this particular Essay, most of the supporting evidence is to be found there. 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 raised 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 done this in Essay One.]


If readers skip this material, then my answers to any objections they might have will be missed, as will the extra evidence and argument. [Since I have been debating this theory with comrades for over 25 years, I have heard all the objections there are! Many of the more recent on-line debates are listed here.]


I have endeavoured to keep this Essay as simple as possible, minimising technicalities, since -- sad to say, -- most dialecticians appear to know little or no logic, and seem to care even less about it. This can be seen from the crass things they say about it -- even academic Marxists slip up in this regard --; on that, see here. In that case, the indulgence of those who know their logic is required; this Essay has not been written for them. Anyone who wants to read more substantial accounts of the approach to logic and language I have adopted in this Essay should consult the many works I have referenced in the End Notes and in other Essays posted at this site.


It is also worth noting that phrases like "ruling-class theory", "ruling-class view of reality", "ruling-class ideology" (etc.) used at this site (in connection with Philosophy and DM) aren't meant to imply 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, this 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 further details.




As of April 2015, this Essay is just under 73,000 words long; a much shorter summary of some of its main ideas can be accessed here.




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



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(1) Formal Logic [FL] Versus Dialectical Logic [DL]


(a) A 'Troubled' Relationship


(b) Dialectical Fabulation Strikes Again


(2) FL And Change


(a) Unfounded Allegations


(b) Validity And Truth


(3) FL Allegedly Uses 'Fixed' Definitions And Categories


(a) Variables And Change


(b) Static Terms Or Slippery Arguments?


(c) Change Of Denotation


(d) An Annoying Counter-Example


(e) Other Systems Of Logic Unknown To Dialecticians


(4) Conceptual Change


(a) Dialectical Change: Conceptual Or Material?


(b) Conceptual Change -- Or Conceptual Distortion?


(c) Logic and Change


(d) Real Material Change


(5) Merely Academic?


(6) Is DL A 'Higher From' Of Logic?


(7) Was There Any Logic After Aristotle?


(8) Explaining Change


(9) 'Thesis, Antithesis, Synthesis' -- Debunked


(10) The Crass Things Dialecticians Say About FL


(11) And About Ordinary Language


(a) Mistaken Assumptions


(b) Descent Into Hegelian Confusion


(c) Ordinary Language Is Not A Theory


(d) Ordinary Language Does Not 'Assume' Things Are Static


(e) Ordinary Language Different From 'Commonsense'


(f) Ordinary Language Not Ideological


(12) Notes


(13) References


Summary Of My Main Objections To Dialectical Materialism


Abbreviations Used At This Site


Return To The Main Index Page


Contact Me

Formal Logic Vs Dialectical Logic


A 'Troubled' Relationship


The relationship between DL and FL has not been a happy one. Nevertheless, dialecticians in general take great pains to make it clear that while they do not reject FL, they regard its scope as somewhat limited. For example, in TAR, John Rees commented as follows:


"[T]he dialectic is not an alternative to 'normal' scientific methods or formal logic. These methods are perfectly valid within certain limits…. [But] formal logic…has proved inadequate to deal with the 'more complicated and drawn out processes'." [Rees (1998), p.271. Quotation marks altered to conform to the conventions adopted at this site.]


This attitude is now as widespread as it is endemic among DM-theorists:


"The old logic has fallen into Verachtung [disrepute]. It requires transformation.... The old, formal logic is exactly like a child's game, making pictures out of jig-saw pieces....


"In the old logic there is no transition, development (of concept and thought), there is not 'eines inneren, notwen-digen Zusammenhangs' [an inner, necessary connection] of all the parts and 'Übergang' [transition] of some parts into others." [Lenin (1961), pp.96-97. Quotation marks altered to conform to the conventions adopted at this site.]


"The Aristotelian logic of the simple syllogism starts from the proposition that 'A' is equal to 'A'…. In reality 'A' is not equal to 'A'. This is easy to prove if we observe these two letters under a lens -– they are quite different to each other. But one can object, the question is not the size or the form of the letters, since they are only symbols for equal quantities, for instance, a pound of sugar. The objection is beside the point; in reality a pound of sugar is never equal to a pound of sugar -– a more delicate scale always discloses a difference. Again one can object: but a pound of sugar is equal to itself. Neither is true (sic) -– all bodies change uninterruptedly in size, weight, colour etc. They are never equal to themselves." [Trotsky (1971), pp.63-64.]


"Dialectics is the logic of change....


"To understand the significance of this compare it with what is know as 'formal logic' (originally developed by Aristotle and usually thought of as the rules of sound thinking). The basic idea of formal logic is that something either is the case or is not the case, but that it can't be both at the same time. For example, the cat is on the mat or it is not on the mat.


"For many purposes formal logic is useful and necessary. But as soon as you take movement and change into account, it ceases to be adequate. A cat moving goes through a moment when it is in the process of passing onto the mat or in the process of passing off it -- when it is both on and off the mat. Dialectics is in advance of formal logic because it enables us to grasp this contradiction." [Molyneux (1987), pp.49-50.]


"It is necessary to acquire a concrete understanding of the object as an integral system, not as isolated fragments; with all its necessary interconnections, not torn out of context, like a butterfly pinned to a collector's board; in its life and movement, not as something lifeless and static. Such an approach is in open conflict with the so-called 'laws' of formal logic, the most absolute expression of dogmatic thought ever conceived, representing a kind of mental rigor mortis. But nature lives and breathes, and stubbornly resists the embraces of formalistic thinking. 'A' is not equal to 'A.' Subatomic particles are and are not. Linear processes end in chaos. The whole is greater than the sum of its parts. Quantity changes into quality. Evolution itself is not a gradual process, but interrupted by sudden leaps and catastrophes....


"The problem is that the categories of formal logic, drawn from quite a limited range of experience and observation, are really valid only within these limits. They do, in fact, cover a great deal of everyday phenomena, but are quite inadequate to deal with more complex processes, involving movement, turbulence, contradiction, and the change from quality to quality." [Woods and Grant (2007), pp.86-88. Quotation marks altered to conform to the conventions adopted at this site.]


"Formal Logic starts from the proposition that A is always equal to A. We know that this law of identity contains some measure of truth…. Now…when we go to reality and look for evidence of the truth of the proposition: A equals A…we find that the opposite of this axiom is far closer to the truth." [Novack (1971), pp.32-33.]


[We will encounter dozens of passages like these as this Essay, and the next five, unfold.]


The problem seems to be that even though it is acknowledged that FL works well enough in certain areas, it can't seem to cope with change, with "long drawn out processes" and the complex, 'contradictory' nature of reality. That is because it operates with a "static" view of the world --, or, at least, it employs "fixed and immutable" concepts.


[DL = Dialectical Logic; FL = Formal Logic; AFL = Aristotelian Formal Logic; TAR = The Algebra of Revolution; i.e., Rees (1998).]



Dialectical Fabulation Strikes Again


Nevertheless, as we will soon see, when these allegations are examined a little more closely than DM-theorists themselves have so far managed to do, they bear little resemblance to the truth.



FL And Change


Unfounded Allegations


In fact, as is well known, Rees's comments echo Hegel's criticisms of the FL of his day, which was itself a garbled and bowdlerized version of AFL.1


The reasoning behind this attitude is outlined for us in TAR:


"Formal categories, putting things in labelled boxes, will always be an inadequate way of looking at change and development…because a static definition can't cope with the way in which a new content emerges from old conditions." [Ibid., p.59.]


The claim that concepts aren't 'static', but develop and change was central to Hegelian Idealism. Even so, dialecticians are careful to emphasise that even though their ideas have been derived from one of the most notorious sources of AIDS ever committed to paper, their theory is an inversion of that system, which has put the dialectic "back on its feet", and which has extracted its "rational core". This enables DM-theorists to provide a materialist account of change through contradiction, when tested in practice.


Or so we have been told.


[AIDS = Absolute Idealism.]


Whatever merit these claims turn out to have (which is zero, as we will see as the rest of this Essay and Essay Eight Parts One, Two and Three unfold), I propose only to examine here the idea that FL can't cope with change because it relies on a "fixed" and "static" view of the world, and is somehow the enemy of change. Again, to quote Rees:


"The reason why formal logic is often forced to abandon its own procedures in the face of the facts is that it attempts to analyze a living, evolving reality with static concepts. Formally things are defined statically, according to certain fixed properties -- colour, weight, size, and so on…. [This] is satisfactory only under conditions where the scale of change is not vital to our understanding…. But for more complex tasks in politics, history, and science generally, this will not do. Common sense and formal logic are agreed on static definitions…. But 'dialectical thinking analyzes all phenomena in their continuous change….'" [Ibid., pp.272-73. Quotation marks altered to conform to the conventions adopted at this site.]


However, and consistent with other dialecticians (who, as e have seen, make similar assertions), Rees failed to substantiate these allegations with quotations from, or references to a single ancient or modern logic text. In fact, in relation to FL, DM-authors in general rely on little other than unsupported allegations like these. Moreover, as we will also see, while doing this they fail to explain precisely how AFL is handicapped in the way they say -- save they merely repeat the same baseless assertions year after year.


And they all appear to make almost identical claims. [Irony intended.]


Little evidence of the Heraclitean Flux here, it seems!


[MFL = Modern Formal Logic.]


Indeed, as is easy to show, the revolution over 120 years ago that transformed MFL -- which development was largely the result of the work of Frege -- has gone almost completely un-noticed by the majority of dialecticians.2 The old Aristotelian syllogistic, which DM-theorists almost invariably confuse with the whole of FL, is now merely of interest to antiquarians, historians and arch traditionalists -- and, of course, dialecticians who are sublimely unaware of these profound changes.


[Irony intended again.]


Admittedly, throughout its history Logic had been confused by many with an assortment of unrelated disciplines -- such as, Metaphysics, Epistemology, Ontology, Theology, Psychology (and the so-called "Laws Of Thought"), Mathematics, and Science. In such circumstances, it is understandable that the only legitimate role that FL can assume -- the study of inference -- was all too easily lost or forgotten. This is, alas, just one more tradition DM-fans have been only too happy to appropriate, maintain and elaborate upon.3



Validity And Truth


One explanation for this sorry state of affairs is that DM-theorists have been led astray by an elementary mistake -- an error that novices often make --, that is, of confusing validity with truth. Hence, as will soon become apparent, the limitations DM-theorists attribute to FL merely arise from their own misidentification of rules of inference with logical and/or empirical truths, but not from the supposed inability of FL to accommodate change.4


Unfortunately, this accusation is far easier to make than it is to substantiate. That isn't because it is incorrect, but because dialecticians rarely bother to say exactly why they regard FL as defective -- that is, over and above merely asserting it is, copying this idea off one another generation upon generation without making any attempt to justify or substantiate it.


Neither is it to claim that DM-theorists fail to make the point that FL is defective because it deals with "static" forms, etc. Far from it, they all join in the chorus, as we have seen. It is simply to underline the fact that they are quite happy to rely on the mere repetition of this baseless claim without ever bothering to check whether or not it is correct -- or, for that matter, without explaining what it could possibly mean.5


To be sure, the confusion between rules of inference and logical/metaphysical 'truths' dates back to Aristotle himself. And it isn't hard to see why this should be so. If a theorist (or, indeed, and entire culture) believes that everything was create by some 'god' or other, then truths about nature will reflect how that deity must 'think' and thus how 'he/she/it' actually went about creating everything. That would 'naturally' link how 'correct' thinking about nature with divinely instituted and fundamental features of 'reality'. Skip forward many centuries and this error re-appeared in Hegel's work as part of a mystical/ontological doctrine connected with the alleged self-development of concepts -- which was itself the result of an egregious error over the nature of predication (examined in Essay Three Part One), and an even worse error over the LOI.


[LOI = Law of identity.]


However, just as soon as  this misbegotten 'ontological' interpretation of FL is abandoned, the temptation to identify it with science (or with the "Laws of Thought") loses whatever superficial plausibility it might once seemed to have had. If FL is solely concerned with inference then there is no good reason to saddle it with metaphysical baggage of this sort, and every reason not to do so. On the other hand, if there is a link between FL and metaphysical/scientific truths -- as legend would have us believe --, then that fact (if it is one) needs substantiation. It isn't enough just to assume such a link exists, as is generally the case in DM-circles.


In addition, the idea that truths about fundamental aspects of reality can be uncovered by an examination of how human beings reason is highly suspect in itself; but, like most things, so much depends on what is supposed to follow from that assumption. As we will see, the line taken on this issue sharply distinguishes materialist thought from Idealist myth-making. Unfortunately, to date, DM-theorists have been more content with tail-ending Traditional Philosophy in supposing that logic can function as a sort of earth-bound cosmic code-cracker, capable of unmasking profound truths about hidden aspects of reality -- aka "underlying essences" -- than they have been with bothering to justify this entire line-of-thought. Nor have they been concerned to examine the motives that gave birth to this class-motivated approach to Super-Knowledge (invented in the 'west' in Ancient Greece).6


[On the ancient idea that language 'reflects' the world and that truths about nature can be derived from words/thought alone, see Dyke (2007). The reader mustn't assume, however, that I agree with Dyke's metaphysical conclusions (or with any metaphysical conclusions whatsoever); indeed, as Essay Twelve Part One shows, the opposite of this is in fact the case -- I regard them as non-sensical and incoherent.]


Of course, modern logicians are much clearer about the distinction between rules of inference and logical truths than their counterparts were in the Ancient World (or even in the Nineteenth Century!), but that fact just makes the criticisms DM-theorists level against FL even more anachronistic and hard to justify.


Anyway, in the end, if materialists are to reject the above mythical approach to nature adopted in Ancient Greece -- and Hegelian Ontology --, as surely they must, then the idea that FL is a part of science becomes even more difficult to sustain.


Indeed, how is it possible for language to 'reflect' the logic of the world if the world has no logic to it?


Which it can't have unless Nature were Mind.


If the development of Nature isn't in fact the disguised development of Mind, (as Hegel supposed), how can concepts drawn from the development of Mind apply to Nature, unless it is Mind?


Of course, dialecticians have responded to this with an appeal to the RTK (i.e., the sophisticated version of that theory); but, as we shall see (in Essays Three and Twelve), that, too, was an unwise move.


[RTK = Reflection Theory of Knowledge.]


This means that if FL is solely concerned with the inferential links between propositions -- and isn't directly concerned with their truth-values -- then the criticism that FL can't account for change becomes even more bizarre.


It is instructive to recall that since the Renaissance 'western' humanity has (largely) learnt to separate religion from science so that the sorts of things that used to be said about science (for example, that it was the "systematic study of God's work", etc.) look rather odd and anachronistic today (that is, to all but the religious). In like manner, previous generations of logicians used to confuse logic with science and the "Laws of Thought", and they, too, did this for theological/ideological reasons. In that case, one would have thought that avowed materialists (i.e., dialecticians) would be the very last to perpetuate this ancient confusion.


Clearly not.


Indeed, as will be argued at length later, only if it can be shown (and not simply assumed) that nature has a rational structure would it be plausible to suppose that there is a connection between the way human beings think and reason and the underlying constitution of nature. Short of that, the idea that there is a link between the way we draw conclusions and fundamental aspects of 'reality' loses all credibility. Why should the way we knit premises and conclusions together mirror the structure of the universe? Why should our use of words have such profound 'ontological' implications, valid for all of space and time?6a


Indeed, how is it that certain metaphysical truths are only capable of being derived from/expressed in Indo-European grammar? Was this group of humans blessed by the 'gods'? Are there really "subjects", "copulas" and "predicates" out there in nature -- minor grammatical features found almost exclusively in this one family of languages?


On the other hand, if it could be shown that the universe does have an underlying, 'rational' structure, then the conclusion that nature is Mind (or, that it has been constituted by Mind) would be difficult to resist. If all that is real is indeed 'rational', then the identification of rules of inference with the "rules of thought" -- and with fundamental metaphysical truths about "Being" -- becomes irresistible.


As noted above: the histories of Philosophy, Theology and Mysticism reveal that from such esoteric assumptions it is but a short step to the derivation of truths from thought alone. A priori thesis-mongering and Idealism thus go hand-in-hand; if nature is Ideal, then truths can legitimately follow from thought/language alone. In several other Essays posted at this site (for example, here and here) we will see that this is a step DM-theorists (and metaphysicians of every stripe) have been only too happy to take -- and many times over, too.


Nevertheless, there is precious little evidence to suggest that DM-theorists have ever given much thought to this particular implication of the idea that DL reflects the underlying structure of reality -- i.e., that their brand of logic implies reality is Ideal. If logic does indeed reflect the structure of 'Being', then 'Being' must be Mind.


[On this, see Essay Twelve Part Four, to be published early in 2014 -- summary here.]


This conclusion only strengthens further the suspicion that the much-vaunted materialist "inversion" -- supposedly carried out on Hegel's system/method by early dialecticians -- was merely formal, which in turn can only mean that DM is simply an inverted form of Idealism. If this is so, then questions about the nature of Logic can't but be related to the serious doubts raised at this site about the scientific status of DM. In that case, if Logic is capable of revealing scientific truths about nature -- as opposed to its being a systematic study of inference, and only that --, then it becomes harder to resist the conclusion that DM is indeed just another form of Idealism that has yet to come out of the closet.


Anyway, since the aim of this section is to examine the specific allegations DM-theorists level against FL, that particular topic will be addressed in other Essays posted at this site (in this case, Essay Three Part One, and  Essay Twelve Parts One and Four).



FL And "Static" Definitions


As it turns out, there is good reason to question the usual claim advanced by dialecticians that FL deals only with "static" definitions (etc.).



Variables And Change


Far from it being the case that FL is wedded to changeless forms, even traditional AFL employed variables to stand for propositions and predicates (general terms) long before they appeared in mathematics. This fact alone shows that traditional AFL was no more incapable of handling change than is modern Mathematics.7


As Engels himself pointed out, the introduction of variables into Algebra allowed mathematicians to cope with change. If that is so, it isn't easy to understand why DM-theorists believe that traditional FL can't cope with change, too. If mathematicians are currently able to depict change by their use of variables, why deny this of traditional formal logicians who used the very same device at least 2400 years ago?


Of course, it could always be argued that variables that relate to quantities (as they feature in mathematics) aren't at all the same as the variables that relate to concepts, properties or qualities (as they are employed in FL). This is undeniable, but not relevant. The point is that either sort of variable allows for change, even if this is so in different ways.



Static Terms Or Slippery Arguments?


Despite this, does the charge that FL can't cope with change itself hold water? In order to answer this question, consider a valid argument form taken from AFL:


L1: Premiss 1: No As are B.


L2: Premiss 2: All Cs are B.


L3: Ergo: No As are C.8


In this rather uninspiring valid argument schema the conclusion follows from the premisses no matter what legitimate substitution instances replace the variable letters. [Examples are given in Note 8.]


So, L3 follows no matter what. But, the argument pattern this schema expresses is transparent to change: that is, while it can cope with change, it takes no stance on it. Some might regard this as a serious drawback, but this is no more of a failing here than it would be, say, for Electronics to take no stance on the evolution of Angiosperms (even though electronic devices can be used to help in their study). Otherwise, one might just as well complain that FL can't predict the weather or eradicate MRSA.


Moreover, the truth-values (true or false) of each of the above premisses do depend on the interpretation assigned to the schematic letters. The premisses of L1 aren't actually about anything until they have been interpreted; before this has been done they are neither true nor false. Not only that, but the indefinite number of ways there are of interpreting schematic letters like those in L1 means that it is possible for changeless and changeable items to feature in any of its concrete instances.


[That was the point behind the observation made earlier that dialecticians and logical novices often confuse validity with truth; the above schema is valid, but its schematic propositions can't be true or false, for obvious reasons.]


Of course, when the method of truth-tables is used, truth-values are assigned to such schemas, but, in this case, what is being considered are the truth-values of interpreted propositions, should any be assigned.


To illustrate the absurdity of the idea that just because FL uses certain words or letters it can't handle change (or that it uses nothing but 'rigid' terms), consider this parallel argument:


(1) If x = 2 and f(x) = 2x + 1, then if y = f(x), y = 5.


(2) Therefore x and y can never change or become any other number.


No one would be foolish enough to argue this way in mathematics since that would be to confuse variables with constants. But, if this is the case in mathematics, then DM-inspired allegations about the alleged limitations of FL are all the more bizarre -- to say the least.


Of course, it would be naïve to suppose that the above considerations address issues of concern to DM-theorists. As TAR itself points out:


"Formal categories, putting things in labelled boxes, will always be an inadequate way of looking at change and development…because a static definition can't cope with the way in which a new content emerges from old conditions." [Rees (1998), p.59.]


But, as a criticism of FL, this is entirely misguided. FL doesn't put anything in "boxes", and its practitioners don't deny change as a result.


[Sure, some logicians might have, or have had metaphysical reasons for denying change, but that can't be blamed on logic.]


Indeed, without an ability to reason discursively (along lines that have been formalised in FL, but which have been explored more extensively in Informal Logic), dialecticians would themselves find it impossible to argue rationally.


For example, the argument above (from TAR) appears to draw certain conclusions from apparently 'fixed definitions' (or 'fixed'/'relatively fixed' uses) of words, like "change" and "static", in order to make certain points about change itself. If, however, Rees's argument is now deliberately and uncharitably mis-interpreted (that is, if we copy the tactics used by dialecticians when they deliberately misconstrue FL) it would soon turn into a self-refutation. Hence, in order to point out the supposed limitations of FL, Rees found he had to use the sorts of things he accused FL of employing: i.e., "static" terms.


Of course, if this unsympathetic way of reading Rees's book were correct -- or fair -- then it would mean that if he and other DM-theorists want to argue validly about the limitations of FL using "static" categories such as these, their arguments would rapidly self-destruct.


If, on the other hand, dialecticians were to employ 'non-static categories' consistent with their own precepts, then that would undermine any conclusions they hoped to 'derive' just as quickly. That is because such categories (having no fixed meanings) would sanction no inferences, for it isn't possible to decide what follows from what if the meaning of the terms employed is indeterminate (or is liable to change). So, while it is unwise of DM-theorists to criticize FL for employing supposedly changeless categories, it would be even more inept of them to do this while using terms whose meanings are apt to change unpredictably. Hence, in practice, DM-theorists must either ignore their own principles and argue from 'fixed categories' about the limitations of FL, or they must construct a case against FL using 'slippery' terms, which would establish nothing whatsoever.


Like it or not, rational criticism of FL can't succeed, or proceed, if either tactic were adopted.9



Change Of Denotation


The schematic letters employed above do not in fact possess "definitions" (only interpretations), hence questions as to their 'fixity' or otherwise are entirely misplaced. The flexibility of interpretation permitted/encouraged here -- even with respect to traditional schematic argument patterns like the one given above -- enables change to be accommodated by the simple expedient of varying the substitution instances of each and every schema. Such moves will have the effect of re-distributing truth-values among the constituent sentences without affecting the associated inferences.


Unfortunately, even this might still fail to address the worry exercising DM-theorists, which seems to revolve around the alleged superiority of DL over FL -- especially in its alleged ability to depict complex change through 'internal contradiction'.


Admittedly, whatever one thinks of the ability or inability of classical FL to handle change, few question its intolerance of 'true contradictions'. However, since this section of the Essay is concerned largely with a narrow range of logical issues, I will postpone the examination of DM-theorists' appeal to dialectical change through 'contradiction' until later Essays.10



An Annoying Counterexample


Nevertheless, a more effective way of rebutting the claim that FL can't handle change would be to provide a counterexample to it. The one given below is based on a very simple pattern drawn from MFL, which employs a valid argument form despite the changes it records when interpreted. This is in fact an example of the schema known as Modus Ponendo Ponens (MPP):


1     (1) P®Q.  A.

2     (2) P.        A.

1,2  (3) Q.        1, 2, MPP11


The following is an apt interpretation of MPP:


1     (1) If atoms of 64Cu undergo beta decay then 64Ni

            atoms, positrons and neutrinos are formed. A

2     (2) Atoms of 64Cu undergo beta decay. A

1,2  (3) Therefore,  64Ni  atoms,  positrons and neutrinos

            are formed.  1, 2, MPP


This simple interpretation of MPP (and one involving reasonably rapid change) is perhaps as good a counterexample as one could wish to find that refutes the claim that FL can't handle transformations in nature (and society). Moreover, there are countless other inferences that MPP itself can instantiate, and many inferential forms other than MPP, all capable of depicting change equally well, when suitably interpreted.11a


This indicates that DM-theorists' accusations aimed at MFL are even less accurate than those they direct at AFL. Of course, the example above will hardly satisfy dialecticians, since no "new content" has been added in the conclusion. Fortunately, this is relatively easy to fix. Consider this one premiss argument:


Premiss 1: All dialecticians are human beings.


Ergo: The refutation of a dialectician is the refutation of a human being.


Here, the conclusion 'contains' more than the premiss, so new content has 'emerged', with no dialectics anywhere in sight. [And, as an additional bonus, it depicts change to our dialectical friends into the bargain.] This argument form is used in Mathematics and in Science all the time to derive results not available to those who are still super-glued to the old logic -- and, of course, those who are unaware of this fact.


However, dialecticians will still wonder if the changes depicted above are at all relevant to their concerns. DL is said by them to be superior in that it can account for social change, that is, it handles changes of far greater complexity than the above examples illustrate.


Nevertheless, these examples were aimed at countering the specific claim that FL can't handle change. In later Essays we will see that DL itself can't account for changes of any sort -- whether these are simple or complex, and whether they occur in nature or society. In that case, no matter how poorly FL copes with change (if that is the case), DL fares incomparably worse.



Other Systems Of FL


Of even greater significance is the fact that over the last hundred years or so theorists have developed several post-classical systems of logic, which include modal, temporal, deontic, imperative, epistemic and multiple-conclusion logics (among others). Several of these systems sanction even more sophisticated depictions of change than are allowed for in AFL, or even MFL (i.e., so-called 'Classical Logic').12



Conceptual Change


Notwithstanding all of this, the feeling may perhaps persist that the above examples still employ "fixed concepts" and "static definitions". Unfortunately, because DM-theorists seldom (if ever) provide examples of what they mean by a "fixed concept" -- or what they imagine formal logicians take these to be, should the latter even accept/recognise this prejudicial description of what they do, or intend -- it isn't easy to make much sense of their complaints.12a


However, there are several confusions that might lie behind, or which might be motivating this odd belief in 'changeable'/'changeless' concepts.



Change In DM -- Conceptual Or Material?


The first confusion involves DM-theorists' own analysis of material change; they frequently depict it in terms that are highly reminiscent of the Hegelian doctrine which holds that change is fundamentally conceptual. How else are we to interpret the following words from TAR that any account of change must explain how: "…new content emerges from old conditions"? [p.59.] How else are we to interpret the following words of Lenin's?


"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. Emphasis in the original.]


"[Among the elements of dialectics are the following:]…internally contradictory tendencies…in this [totality]…and unity of opposites…. [E]ach thing…is connected with every other…[this involves] not only the unity of opposites, but the transitions of every determination, quality, feature, side, property into every other…." [Ibid., pp.221-22.]


Or, Trotsky's:


"Cognizing thought begins with differentiation, with the instantaneous photograph, with the establishment of terms -- conceptions in which the separate moments of a process are placed from which the process as a whole escapes. These terms-conceptions, created by cognizing thought, are then transformed into its fetters. Dialectics removes these fetters, revealing the relativity of motionless concepts, their transition into each other. (S. Logik, I. 26-27)" [Trotsky (1986), p.97-98.]


[Or, the many others comments that have been listed here?]


Admittedly, Rees appealed to the materialist inversion that has allegedly been imposed on Hegel's system (to turn it into "materialist dialectics", and put it "back on its feet"), as, indeed, did Lenin and Trotsky; but all three pointedly failed to explain how conceptual change is related to material change, upside down or 'the right way up'. Precisely how is it possible for a concept or a category to change if neither of them is material? And it won't do to suggest that concepts, for example, change because the objects they 'reflect' change, since that would be to confuse concepts with objects, once more. Does the concept of colour, for example, change every time a leaf turns from green to brown? Or, a traffic light from red to green, and then back again? [In fact, in Essay Three Part One we saw that this approach to concepts represents a dead end. We will have occasion to examine it again in more detail soon.] Nor will it do to argue that concepts change because we reflect on them (that is, if we employ the 'sophisticated' version of the RTK, here), since that would be to treat concepts as objects, once more.


It might be thought that concepts somehow 'appear in the head' as objects of "cognition". In that case, the question becomes: does the concept of colour change when any of us thinks about a traffic light altering from red to green, and then back again? Indeed, does the concept of colour -- as it might be apprehended by an individual apprehender -- change in such circumstances? But, how could we (or she) possibly tell? If we have lost touch with the old 'concept' of colour (since it will have changed), with what could we compare the new 'concept' of colour to be able to declare it had in fact changed?


The problem now facing DM-theorists is how to explain 'mental objects' like this (these 'images'/'reflections'/'concepts' supposedly in our heads) while successfully avoiding reductionism -- or, indeed, bourgeois individualism.12b


[RTK = Reflection Theory of Knowledge. The 'sophisticated version involves the active input of human "cognition" and practice, as opposed to the 'naive' version which (apparently) doesn't, but which merely stresses the passive 'subject' of perception/knowledge. Both theories will be criticised in Essay Three Part Six.]


[It is worth pointing out here that I am not denying conceptual change, merely questioning what dialecticians could possibly mean by "fixed concepts".]


Furthermore, how is it possible for change to material objects to be recorded by our use of concepts? In DM-writings, as already noted, the impression is given that these two sorts of change are simply the same, or that one is a reflection of the other. Or, to be more honest, the impression is that little thought has actually gone into either sort of change (that is, over and above the regurgitation of the 'sanitised' (mystical) ideas dialecticians have inherited from Hegel, which they have supposedly put back 'on their feet').


[The word "sanitised" has been used here because of the way that DM-theorists appropriate the Christian/Hermetic concepts Hegel inflicted on his readers, which they supposedly put 'the right way up' in order to render them 'consistent' with materialism. This ploy is reminiscent of the way that Christian theologians, for example, re-interpret the mystical passages of the Book of Genesis (as 'allegorical' or 'figurative'), 'sanitising' them in order to render them 'consistent' with post-Enlightenment sensibility and/or modern science.]


It could be objected that the above comments ignore the dialectic that operates between the "knower and the known", just as it fails to take note of the fact that our concepts change in accord with the development of material and social reality -- as well as in response to practice. Admittedly, DM-theorists have made some attempt to explain the relationship between these two sorts of change (material and conceptual) along such lines, but, as noted earlier, they have done this by means of a detour into the RTK, buttressed by an appeal to practical activity, linked to a materialist analysis of the dialectical relationship between the abstract and the concrete. Since these topics are addressed in other Essays posted at this site, no more will be said about them here.



Conceptual Change -- Or Conceptual Distortion?


A second (perhaps hidden) source of confusion could be the fact that conceptual change isn't at all easy to depict. Indeed, if it should emerge that conceptual change can't be pictured using traditional (or even DM-) terminology, then the accusation that DL is superior to FL would become even more difficult to sustain. In order to motivate this approach, a brief discussion of some of the problems involved in expressing conceptual change might be in order. Consider, therefore, the following sentence:


C1: Green has changed.


The word "green" in such circumstances would normally be understood as the name of an individual (as opposed to a term signifying a concept). However, if it were to be made clear that C1 related to the colour green, and not to someone called "Green", it would probably be re-interpreted in the following way:


C2: This patch of green has changed.


That is because little sense can be made of the idea that the concept green (expressed in C3 below) could have changed (for reasons that will be explored presently). In which case, C1 (interpreted now as C2) would perhaps be understood as alluding to a change in the colour of a material object, or part of an object -- but not to the concept green itself. That can be seen if the following sentence is substituted for C1:


C3: The concept green has changed.


Despite what C3 seems to say, the phrase "the concept green" is longer an expression for a concept, it is a singular term designating an object! This would transform the supposed concept into an object of some sort.


As noted earlier, if the concept itself had changed, or it were being asserted that it had changed -- and we take this concept to be a 'mental entity' of some sort. apprehended in some way by each individual -- then it would be impossible to decide it had changed. With what could we (as individuals) compare our supposedly subjective apprehension of the concept green if or when it had changed? All we would have would be a fading memory of the 'old concept green', which, ex hypothesi, would also have changed! Otherwise the concept green, as we individually apprehend it, won't actually have changed -- any attempt to access the 'old concept green' will have to appeal to our current apprehension of the concept green to be able to refer to it.


Hence, in order to access a memory of the 'old concept green', something like the following would have to be 'cognised':


G1: My memory of the concept green is such and such, which tells me my current apprehension of the concept green has changed.


Or, more generally:


G2: My memory of the concept greenn is such and such, which tells me my current apprehension of the concept greenn+1 has changed. 


But, if this is so, then it is plain that if this is to be of any use to the individual concerned, the concept greenn itself cannot have changed, for if it had then it wouldn't be possible to decide if it had in fact changed, unless, of course, we had access to an 'even older concept of green' (or 'an even older memory of the concept green') that hadn't changed, pushing this 'analysis' one stage further back -- otherwise the following would be the case:


G3: My memory of the concept greenn-1 is such and such, which tells me my past apprehension of the concept greenn has changed. 


And so on.


Of course, if this were so, there would be no such thing as "the concept green" to change, just a potentially infinite set of fading memories of something that now no longer resembles the current concept green as apprehended by the individual concerned. [The 'relative stability' argument is batted out of the park here and here.]


Finally, if the memory of the concept green hasn't changed, then there would be 'fixed and changeless concepts', after all -- namely this one.


[There are other, perhaps more fundamental reasons, explored in Essay Three Parts One and Two, that fatally weaken the theory that concepts are items we cognise individually. They will be covered briefly in what follows, and in the End Notes associated those comments.]  


Be this as it may, it now becomes difficult to say precisely what "the concept green" designates -- at least not without completely misconstruing what C3 is apparently trying to say about 'the concept green' itself. As noted above, "the concept green" can't in fact pick out the concept it appears to designate since that would transform its supposed target (what the "the concept green" seems to signify -- i.e., 'the concept green') into an object -- now denoted by the definite description "the concept green". Naturally, that would fatally compromise the distinction between concepts and objects, all the while failing to pick out the originally intended concept.13


C3: The concept green has changed.


The paradoxical nature of sentences like C3 can be illustrated by a consideration of the following sentence:


C4: The concept green is a concept.


If it is first of all assumed that C4 is well-formed, then it looks like it is analytically true. In fact, and on the contrary, C4 is analytically false! That is because (once more) "the concept green" is a singular term, and as such it signifies an object, not a concept!14


Alas, absurd sentences like C4 are to metaphysicians what carrots are to donkeys; based on linguistic monstrosities like this, some theorists hastily conclude that language -- or 'thought' (or 'reality', or 'everything') -- must be defective, or it must be contradictory, or it must be paradoxical, or it must be this or that. [That is because Traditional Philosophers thought they could dictate to 'reality' what it must be like based on their own misuse of language.] With reasoning like this one might just as well argue that if a metre rule, say, has been manufactured incorrectly, the same must be true of everything it has been, or will be used to measure! To be sure any recorded lengths will be incorrect, but the objects themselves will remain unaffected.


From linguistic sins such as these -- committed by our philosophical ancestors -- much of subsequent Metaphysics has descended without modification by unnatural selection. Unfortunately, DM isn't the only defective progeny of mutant syntax such as this.15


In that case, it isn't possible to specify how concepts change by means of sentences like C3; in such contexts the logical role occupied by terms that supposedly signify concepts transforms them in such a way that they no longer work either as concept expressions, or as expressions signifying concepts.16


C3: The concept green has changed.


[It is important to note that I am not denying that concept expressions can be nominalised, only that nothing metaphysically deep or 'ontological' follows from this superficial linguistic manoeuvre. Nor am I denying conceptual change!]


Of course, it could be objected that the mere fact that we can't express conceptual change in the manner specified above doesn't mean that it doesn't happen; after all, reality isn't constrained by the supposed limitations of language. Maybe not, but if an option of this sort can't be put into words without the sort of distortion outlined above (or, if when it is, what it appears to say undermines what some might attempt to use it to say) then no option has been presented for anyone to consider.


Not only that, the above response clearly trades on the supposition that there are indeed concepts in reality that can change; but that itself would be true only if reality were mind-like. No one supposes -- it is to be hoped(!) -- that concepts pre-dated the evolution of sentient life, or that they reside in a sort of 'limbo world' waiting to be thought about, and only then do they begin to change (which seems to be Hegel's position).


On the other hand, if reality isn't mind-like, there are concepts in nature for our minds to reflect.


Alternatively, again, if it is claimed that the mind does indeed reflect reality, and it employs concepts in order to do this, it must distort reality in so doing (that is, it must do this in so far as there are no concepts 'out there' for it to 'reflect').


Now, we saw in Essay Three Part One that the defective logic dialecticians inherited from Hegel (where the misconstrual of the "is" of predication as an "is" of identity was based on an even earlier (ancient) confusion over the nature of predicate expressions, re-interpreted as the names of abstract particulars) had already predisposed them toward making this mistake -- i.e., the confusing objectual with conceptual change.


Only if concepts are viewed as abstract objects of some sort (in the 'mind' or in 'reality') does it become 'natural' to conflate these two sorts of change.


So, no wonder then that dialecticians who take logical advice from Hegel end up talking about concepts developing, and berate the rest of us with tall tales about the 'limitations' of FL, because of it supposedly uses 'fixed concepts'!


We can now see where the real problem lies; it isn't with the 'fixed concepts of FL', but with the slippery jargon found in DL, which terminology is in turn based on a crass syntactical error committed by a set of ruling-class hacks in Ancient Greece! And they did this because it was conducive to their world-view to re-configure reality conceptually. [Until Essay Twelve is published in full, there are brief explanations why I have alleged this here, here, and here. (It is also worth pointing out that the above remarks won't be fully understood by anyone who hasn't read Essay Three Part One.)]


In that case, it is still unclear what exactly is being proposed by those who speak about 'changing' or 'developing' concepts. Once more, this is not to suggest that we can't make sense of conceptual change. Far from it; it is a constant feature of our social life. But, we can't do so by means of a philosophical theory that relies on an egregious distortion of language, and on doctrines heavily infected with AIDS.


[AIDS = Absolute Idealism.]



Logic And Change


Despite the above, it is possible to express conceptual change in FL by means of an ascent into Second Order Logic.


Now, this latest twist doesn't contradict the observation made in the previous sub-section (i.e., that what seem to be empirical truths about concepts can't be expressed in language -- it was in fact maintained that they can't be directly expressed by means of distorted sentences), since higher order logic is, among other things, a calculus that expresses rules of inference, not logical (or any other) truths.


In Second Order Logic, expressions for concepts become variables ranged over by Third Order Quantifiers, and so on.17


Even so, such systems only indirectly relate to our ordinary use of words for change. Indeed, despite what certain Philosophers (and DM-theorists) claim, the vernacular is perfectly capable of expressing change; that is partly because the word "change" is an ordinary language term itself, and partly because the vernacular was invented by those who interface with material reality in collective labour (etc.) on a daily basis -- i.e., workers. In fact, as will be demonstrated below, and in Essay Six, ordinary language is capable of expressing change far, far better than the obscure language found in Hegel, or in DM. The vernacular contains literally thousands of words that are capable of depicting change and development in almost limitless detail.17a



Real Material Change


Again, it could be objected that the above considerations all revolve around the linguistic expression of change; whether or not the latter is possible isn't relevant to the concerns expressed by DM-theorists. Their interest lies in studying real material change in nature and society, tested in practice, and by intervention and experiment -- in order to help change the world and bring an end to class society. If this is so, then most of the above comments appear to be either academic at best, or misguided at worst.


Or, so it could be maintained.


Nevertheless, it is worth noting once more that the points raised earlier were specifically aimed at the DM-thesis that FL can't handle change, not at whether material change is or isn't different from any of our attempts to depict it. Hence, the above complaint is itself misplaced. Since FL expresses only certain aspects of some of the inferences we make, or are able to make, in ordinary life -- formalising but a fraction of the discursive principles implicit is our capacity to reason, communicate and picture the world, truly or falsely -- a defence of FL can't suddenly pretend that our powers of depiction and the media by means by which we accomplish this, aren't relevant. [Nor indeed can any attempt to show the opposite.]


[Of course, Informal Logic captures even more of the above.]


Anyway, the DM-account of material change is analysed in detail in several of the Essays posted at this site (for example, in Essays Five, Seven and Eight Parts One, Two and Three), where it will be shown that dialecticians themselves are incapable of doing the very thing they find fault with in FL -- that is, accounting for, or even depicting, change!



A Purely Academic Issue?


At first sight, it would seem obvious that a logical system based on a static view of the world -- as it is alleged of FL -- would have few if any practical consequences/applications. On the other hand, it would appear equally clear that a different logical system based on the opposite view of reality -- as is also claimed of DL -- should have countless practical applications in science and technology.


Oddly enough, the exact opposite is the case: DL has no discernible practical or scientific applications, and has featured in none of the advances in the natural or physical sciences (and arguably none even in the social sciences) -- ever. Worse, DL has made no contribution to technological innovation.18


[Arguments to the contrary are rebutted in Note 18 (link above), and Note 20.]


In stark contrast to this, FL has played an invaluable role on the development of science and mathematics, and has featured in countless applications in technology and the applied sciences.


Indeed, one excellent example among the many of the impact FL on technology is the development of computers. Their origin goes back many centuries, but advances in mathematical logic (post 1850) proved to be decisive. The invention of Boolean and Fregean Logic, the mathematical logic of Russell, Whitehead, Hilbert, Peano, von Neumann and Church (etc.) -- along with the logico-mathematical work of Alan Turing -- all helped make possible the development of these machines. FL has not only contributed to the evolution of software and of computer languages, the principles of Propositional Calculus govern the operation of all standard processors (etc.).19


In addition, there are numerous other examples of the practical applications of FL, ranging from Cybernetics to Code Theory, and from Linguistics to Game Theory and Discrete Mathematics. The question is: Can DM-theorists point to a single successful application of DL in technology, or in the natural and physical sciences? The answer is reasonably plain; they can't. But, this glaring failure becomes all the more revealing when it is remembered that dialecticians repeatedly claim that their 'logic' is superior to FL when it is applied to the material world.


This is perhaps one paradoxical mismatch between DM and recalcitrant reality that can't be solved by the simple expedient of "grasping" it.20



DL -- A 'Higher Form' Of Logic?


What then of the general boast that DL is a superior form of logic? Is there any way of confirming this? Perhaps there is; TAR's author claims that DL does not reject FL, and neither is it:


"[A]n alternative to 'normal' scientific methods or formal logic…. Formal Logic, like Newtonian physics, has proved inadequate to deal with 'more complicated and drawn out processes.' So the dialectic stands in the same relation to formal logic as Newtonian physics stands to relativity theory or, as Trotsky puts it, as 'that between higher and lower mathematics'." [Rees (1998), p.271.]


If it can be shown that DL does all that Rees claims for it, then perhaps the academic quibbles noted above can be set aside. The rest of the Essays posted at this site are aimed at examining these claims, and more. However, a few awkward initial problems need to be addressed before the main picture can begin.


First of all, while it is clear that Relativity has largely superseded Newtonian Physics it isn't at all obvious that this is related to the latter's inability to deal with "drawn out processes". Still less clear is what exactly FL and DL have in common that makes Trotsky's analogy with higher and lower mathematics at all apt. If anything, the opposite appears to be the case: DM-theorists are only too happy to begin their discussions of FL by pointing out that many of what they (but no one else) take to be its central tenets are in fact fundamentally defective. This includes the LOI, the LOC and the LEM (among others). [This allegation is documented below, and in Note 23.]


Although lower mathematics is clearly limited in scope, none of its precepts are defective and professional mathematicians do not criticise it in any way --, quite unlike the attitude adopted toward FL by DM-theorists, who continually excoriate it.


[LOI = Law of Identity; LOC = Law of Non-Contradiction; LEM = Law of Excluded Middle.]


Secondly, and as will be demonstrated in Essays Five and Six, Trotsky's attempt to criticise the LOI and Engels's 'analysis' of motion collapse into incoherence with remarkable ease. In stark contrast, higher mathematics does not disintegrate when we pass beyond its 'lower' forms. In fact, far from being able to handle "more complicated and drawn out processes", DL has great difficulty in coping with an ordinary bag of sugar and the movement of the average cat!


Furthermore, higher and lower mathematics aren't inconsistent with each other. Hence, we do not find mathematicians correcting ordinary addition or multiplication, nor do we find them expanding on the limitations of, say, the equal sign, the cube root function or quadratic equations. Admittedly, higher mathematics contains concepts and rules not found in lower mathematics, but there is no suggestion that the latter's procedures and symbols are defective, or that they are the very opposite of what they are normally taken to be. Compare this with the sort of comments made by DL-enthusiasts about FL:


"Trotsky saw that it was the inadequacies and contradictions of formal logic that drove theorists toward dialectical formulations. Even those who pride themselves on a 'deductive method', which proceeds 'through a number of premises to the necessary conclusion,' frequently 'break the chain of syllogisms and, under the influence of purely empirical considerations, arrive at conclusions which have no connection with the previous logical chain.' Such ad hoc empirical adjustments to the conclusions of formal logic betray a 'primitive form of dialectical thinking.'" [Ibid., p.272.]


Again, it is worth pointing out that fundamental criticisms of FL (like these) advanced by DL-fans are seldom if ever substantiated with examples drawn from the work of a single logician.21 Add to this Lenin's remarks:


"The inaneness of these forms of formal logic makes them deserving of 'contempt' and 'derision'…. Hegel shrewdly adds [concerning the Syllogism]: 'Boredom immediately descends when such a syllogism is heard approaching.'" [Lenin (1961), pp.93, 177. Quotation marks altered to conform to the conventions adopted at this site.]


It would be difficult to find a single mathematician who is as dismissive of lower mathematics as Lenin is of FL, or any modern scientist, for that matter, who would be prepared to call Aristotle or Newton's work "inane" and fit only for "contempt" and "derision".22



Was There Logic After Aristotle?


As already noted, DM-theorists (but particularly those who are active revolutionaries) almost invariably identify FL with AFL -- and, worse, with that bowdlerized version caricatured in Hegel's two badly misnamed books on logic. DM-theorists of earlier generations (such as Engels, and possibly Dietzgen) may perhaps be excused in this regard, since they largely wrote before the revolution that took place in logic in the decades after the 1870s; later Marxists are not so easy to excused.


[AFL = Aristotelian Formal Logic; MFL = Modern Formal Logic.]


For example, we find Trotsky (who was otherwise reasonably up-to-date in his knowledge of the sciences) writing the following in his "Open Letter to Burnham" -- approximately 60 years after MFL was initiated by Frege, and approximately 30 years after Russell and Whitehead's Principia Mathematica was first published:


"I know of two systems of logic worthy of attention: the logic of Aristotle (formal logic) and the logic of Hegel (the dialectic). Aristotelian logic takes as its starting point immutable objects and phenomena…. [P]lease take the trouble to inform us just who following Aristotle analysed and systematized the subsequent progress of logic." [Trotsky (1971), pp.91-92.]22a


To which Burnham not unreasonably replied:


"[A]part from Aristotle, the only 'logic worthy of attention' is that of -- Hegel…. Comrade Trotsky, as we Americans ask: where have you been all these years? During the 125 years since Hegel wrote…[,] after 2300 years of stability, logic has undergone a revolutionary transformation…in which Hegel and his ideas have had an influence of exactly zero….


"In a most sarcastic vein, you keep asking me to 'take the trouble to inform us just who following Aristotle analysed and systematized the subsequent progress of logic'…as if this demand were so obviously impossible of fulfilment that I must collapse like a pricked balloon before it…. Do you wish me to prepare a reading list, Comrade Trotsky? It would be long, ranging from the work of the brilliant mathematicians and logicians of the middle of the last century to…the monumental 'Principia Mathematica' of Russell and Whitehead…." [Burnham (1971), pp.236-37.]


Unfortunately, wilful ignorance like this among dialecticians has not noticeably changed much since Trotsky's day (with the notable exception of the work of logicians like Graham Priest, of course). Hence, we still find socialists of otherwise impeccable dialectical credentials repeating Trotsky's ill-informed opinions time and again, still confusing FL with AFL, still clinging to the dogma that Aristotle is and always will be the last (and only) word on the subject.


Worse still, Dialectical Marxists compound this inexcusable ignorance with an open failure to grasp what few degenerate ideas they mistakenly attribute to Aristotle.23



Explaining Change


Turning to specifics: according to its supporters, the superiority of DL over FL arises partly from its ability to explain change and partly from the understanding it gives of the contradictory behaviour of nature and society, thus assisting in the revolutionary transformation of the latter. This, it is claimed, FL can't adequately do.


However, not even mathematics can provide a scientific account of change -- even if it does play a major role in science. Mathematical objects have no causal impact on reality; they nowhere appear in nature.24 And yet, this does not mean that mathematics is inferior to a 'higher' brand of 'Dialectical Mathematics'. Why DM-theorists use an analogous argument to depreciate FL is therefore puzzling.


Of course, some DM-theorists have attempted to offer their own account of the superiority of 'higher' over 'lower' mathematics, based, for example, on Engels's interpretation of Descartes's introduction of variables into Algebra, and on some rather obscure notes left by Marx concerning the nature of Differential Calculus.25


Nevertheless, DM-apologists claim that when linked to a detailed analysis of material causes, their theory can provide a scientific account of change. This idea is discussed in detail in Essays Five, Seven Part One, Eight Parts One, Two and Three, and then systematically dismantled.





1. Key (relevant) aspects of Hegel's 'logic' are taken apart here -- more will be added when the rest of Essay Twelve is published (summaries here and here).


Nevertheless, dialecticians tend not only to confuse FL with the garbled version of AFL studied in Hegel's day (but see here), they disregard, ignore or underplay the significant advances in FL that have taken place over the last 125 years. It is no exaggeration, but more than 95% of FL is less than 150 years old. However, you'd never be able to guess that by reading any randomly selected DM-text. Quite the opposite in fact; naïve readers would be tempted to conclude from what they find there that FL has stood still for over 2400 years. This from the self-styled 'Apostles of Change'!


[These negative comments do not, of course, apply to the work of Graham Priest. His work will be the subject of a special Essay to be published at this site at a later date. In the meantime, readers are invited to consult Goldstein (1992, 2004), Slater (2002, 2007b, 2007c), and this review, by Hartry Field.


Field has now published a book on the paradoxes, where he is able to show that the Dialetheic and Paraconsistent Logic Priest favours can't even handle the paradoxes of truth, which had in fact been one of the main motivators for this branch of non-standard logic -- i.e., Field (2008), pp.36-92.]


On the subject of Hegel's dismissal of, say, the LOC, see Hanna (1986) and Pippin (1978). The views of these two authors will also be critically examined in a later Essay. However, the best Hegelian account of this aspect of Hegel's work that I have read in the last 25 years [i.e., Hahn (2007)] will be examined in Essay Eight Part Three -- where the best Marxist account [i.e., Lawler (1982)] has already been analysed in detail.


On the LOC in general, see Horn (2006) -- although, I have e-mailed Professor Horn about his claim that the LOI can be found in Aristotle's work; he tells he will now try to locate where Aristotle's acknowledges this 'law'.


Update October 2009: Professor Horn tells me that this comment will be changed in the next update later this year. More on that, here and here.


Update August 2011: The latest version of Professor Horn's article (i.e., Horn (2010)) now contains no reference to Aristotle accepting the LOI.


I have just read Deborah Modrak's book on Aristotle (i.e., Modrak (2001)); she devotes an entire section to Aristotle's views of identity -- pp.194-98. However, Modrak concentrates on Aristotle's views on sameness; identity itself is conspicuous by its absence. Certainly, there is no mention of the LOI.


The Kneales, however, quote two passages (from Topics and from De Sophistici Elenchi (On Sophistical Refutations)), which might seem, to some, to contradict the above; here is the one from Topics:


"Whether two things are 'the same' or 'different', in the most literal of the meanings ascribed to 'sameness' (and we said that 'the same' applies in the most literal sense to what is numerically one), may be examined in the light of their inflexions and coordinates and opposites. For if justice be the same as courage, then too the just man is the same as the brave man, and 'justly' is the same as 'bravely'. Likewise, too, in the case of their opposites: for if two things be the same, their opposites also will be the same, in any of the recognized forms of opposition. For it is the same thing to take the opposite of the one or that of the other, seeing that they are the same. Again it may be examined in the light of those things which tend to produce or to destroy the things in question of their formation and destruction, and in general of any thing that is related in like manner to each. For where things are absolutely the same, their formations and destructions also are the same, and so are the things that tend to produce or to destroy them. Look and see also, in a case where one of two things is said to be something or other in a superlative degree, if the other of these alleged identical things can also be described by a superlative in the same respect. Thus Xenocrates argues that the happy life and the good life are the same, seeing that of all forms of life the good life is the most desirable and so also is the happy life: for 'the most desirable' and the greatest' apply but to one thing.' Likewise also in other cases of the kind. Each, however, of the two things termed 'greatest' or most desirable' must be numerically one: otherwise no proof will have been given that they are the same; for it does not follow because Peloponnesians and Spartans are the bravest of the Greeks, that Peloponnesians are the same as Spartans, seeing that 'Peloponnesian' is not any one person nor yet 'Spartan'; it only follows that the one must be included under the other as 'Spartans' are under 'Peloponnesians': for otherwise, if the one class be not included under the other, each will be better than the other. For then the Peloponnesians are bound to be better than the Spartans, seeing that the one class is not included under the other; for they are better than anybody else. Likewise also the Spartans must perforce be better than the Peloponnesians; for they too are better than anybody else; each then is better than the other! Clearly therefore what is styled 'best' and 'greatest' must be a single thing, if it is to be proved to be 'the same' as another. This also is why Xenocrates fails to prove his case: for the happy life is not numerically single, nor yet the good life, so that it does not follow that, because they are both the most desirable, they are therefore the same, but only that the one falls under the other.

"Again, look and see if, supposing the one to be the same as something, the other also is the same as it: for if they be not both the same as the same thing, clearly neither are they the same as one another.

"Moreover, examine them in the light of their accidents or of the things of which they are accidents: for any accident belonging to the one must belong also to the other, and if the one belong to anything as an accident, so must the other also. If in any of these respects there is a discrepancy, clearly they are not the same." [Aristotle (1984g), p.255. I have used the on-line version here, which renders this passage differently to the Kneales -- i.e., Kneale and Kneale (1978), p.42.]


The passage from De Sophistici Elenchi reads as follows:


"For only to things that are indistinguishable and one in substance does it seem that all the same attributes belong...." [Aristotle (1984h), p.305.]


The on-line version is more-or-less the same (no pun intended):


"For only to things that are indistinguishable and one in essence is it generally agreed that all the same attributes belong...." [Quoted from here; Part 24.]


There are only three sentences in the above that could plausibly be equated with the LOI (no pun intended, again); I have highlighted them in bold. The first speaks about things being "absolutely the same", but, the more recent, published translation, has this as " the case where one of two things is said to be something or other in a superlative degree, if the other of these identical things can also be described by a superlative in the same respect" [Aristotle (1984g), p.255, section 152.5], which, although it uses the word "identity", neither employs, nor implies, the LOI. Aristotle, a quintessentially 'common sense' philosopher, is plainly using different ordinary terms for sameness as much he can -- no pun intended, once more; indeed, as I have done in Essay Six.


The second and third highlighted passages certainly anticipate the 'Indiscernibility of Identicals', and the 'Identity of Indiscernibles' -- even though Aristotle doesn't use the word "identical". However, this is plainly the closest Aristotle came to enunciating the LOI, but it still isn't the LOI. Nowhere do we see "A is identical to A", or even "A = A", of DM-lore.


Indeed, Aristotle derides anything that even smacks of this 'law'. What is more, the LOI features nowhere in his logic (again, contrary to the allegations advanced by DM-fans).


[LOC = Law on Non-contradiction; FL = Formal Logic; AFL = Aristotelian Formal Logic; LOI = Law of Identity; DL = Dialectical Logic.]


Update October 2014: I have just been made aware of this comment found in Hamilton's Logic:


"The law of Identity, I stated, was not explicated as a coordinate principle till a comparatively recent period. The earliest author in whom I have found this done, is Antonius Andreas, a scholar of Scotus, who flourished at the end of the thirteenth and beginning of the fourteenth century. The schoolman, in the fourth book of his Commentary of Aristotle's Metaphysics, -- a commentary which is full of the most ingenious and original views, -- not only asserts to the law of Identity a coördinate dignity with the law of Contradiction, but, against Aristotle, he maintains that the principle of Identity, and not the principle of Contradiction, is the one absolutely first. The formula in which Andreas expressed it was Ens est ens. [Being is being -- RL.] Subsequently to this author, the question concerning the relative priority of the two laws of Identity and of Contradiction became one much agitated in the schools; though there were also found some who asserted to the law of Excluded Middle this supreme rank." [Quoted from here (accessed 04/10/2014). I haven't yet been able to check this source. Links added.]


2. These allegations will be substantiated presently.


3. Again, these allegations will be substantiated in Note 4.


Of course, limiting FL solely to the study of inference is controversial. DM-theorists clearly see logic (properly so handled -- in its 'higher form',  DL) as part of science, and as a tool for investigating the world and how to change it. As such, DL forms an extension to Metaphysics -- although DM-theorists interpret the word "metaphysics" in an idiosyncratic manner, and would question the previous assertion. Be this as it may, dialecticians certainly see DL as a source of knowledge and of criticism, capable of revealing fundamental aspects of reality if used correctly and if tested in practice. That idea will be tackled head-on in Essay Twelve Part One, and later in the main body of this Essay.


In the meantime, when I speak of FL, I mean it in the sense outlined in the main body: as the study of inference -- which is the view adopted by most modern logicians. On this, see Note 4 and Note 5.


4. Validity is a formal property of argument schemas (formal patterns), whereas truth is a 'property' of propositions. [The word "property" is in 'scare' quotes since this term is being used technically, if not figuratively, here.] If the only legitimate role FL occupies is the study of inference, then, as such, it is only indirectly related to the 'search for truth'. Logic is therefore a science only in the wider (German) sense of the term -- that is, it is a systematic study of an area of enquiry (which is, in this case, of course, inference).


[The definition here is incorrect, as I have pointed out in the discussion pages.]


[The confusion of FL with science proper is discussed below, in Note 5.]


For a clear definition of validity, see, for example, Tomassi (1999), pp.2-19, or Priest (2000), pp.1-6.


5. In line with many others (mostly those who know very little, if any, logic), DM-theorists in general labour under the widespread illusion that FL is the study of the "Laws of Thought", or it is the "Science of Cognition" -- that is, that it is one of the sciences proper. For example, consider Lenin's description:


"Logic is the science of cognition. It is the theory of knowledge…. The laws of logic are the reflections of the objective in the subjective consciousness of man.... [These] embrace conditionally, approximately, the universal, law-governed character of eternally moving and developing nature." [Lenin (1961), p.182. Italics in the original.]


Here is Engels:


"In every epoch, and therefore also in ours, theoretical thought is a historical product, which at different times assumes very different forms and, therewith, very different contents. The science of thought is therefore, like every other, a historical science, the science of the historical development of human thought. And this is of importance also for the practical application of thought in empirical fields. Because in the first place the theory of the laws of thought is by no means an 'eternal truth' established once and for all, as philistine reasoning imagines to be the case with the word 'logic'." [Engels (1954), p.43. Quotation marks altered to conform to the conventions adopted at this site.]


"As soon as each special science is bound to make clear its position in the great totality of things and of our knowledge of things, a special science dealing with this totality is superfluous. That which still survives, independently, of all earlier philosophy is the science of thought and its laws -- formal logic and dialectics. Everything else is subsumed in the positive science of nature and history." [Engels (1976), p.31.]


And, here is Trotsky:


"Hegel himself viewed dialectics precisely as logic, as the science of the forms of human cognition....


"What does logic express? The law of the external world or the law of consciousness? The question is posed dualistically [and] therefore not correctly [for] the laws of logic express the laws (rules, methods) of consciousness in its active relationship to the external world....


"Thought operates by its own laws, which we can call the laws of logic...." [Trotsky (1986), pp.75, 87, 106. Trotsky is apparently referring to Hegel's Introduction to The Science of Logic (i.e., Hegel (1999), pp.43-64.]


We also find Novack, for instance, defining logic as:


"…the science of the thought process. Logicians investigate the activities of the thought process which goes on in human heads and formulate the laws, forms and interrelations of those mental processes." [Novack (1971), p.17.]


Lenin, Trotsky and Novack have clearly confused logic with psychology. If logic were the science of what went on in people's heads, then logicians would busy themselves with brain scans, surveys, psychometric tests, and the like. They certainly would not waste their with all those useless definitions, theorems and proofs.


And do dialecticians seriously think that people actually cogitate in syllogisms? [As we will see, Trotsky certainly did!] Or, that they use the formal calculi found in Principia Mathematica when they reason? They must if they believe that logicians study how people actually think.


Well, not only does Trotsky reckon human beings think in syllogisms, he believes chickens do, too!


"The chicken knows that grain is in general useful, necessary and tasty. It recognises a given piece of grain as that grain -- of the wheat -- with which it is acquainted and hence draws a logical conclusion by means of its beak. The syllogism of Aristotle is only an articulated expression of those elementary mental conclusions which we observe at every step among animals." [Trotsky quoted in Woods and Grant (1995), p.89. A copy is available here (near the bottom of the page). In fact this appears in Trotsky (1973), p.400.]


Unfortunately, Trotsky failed to say how he knew so much about the logical skills of these Aristotles of the bird world -- or why, if animals have known about these things for so long, it took a genius like Aristotle to 're-discover' them about 1 million years after we left the 'animal kingdom', and countless million since 'we' branched off from our common ancestor with the birds!


Moreover, if chickens are such 'natural logicians', then perhaps among them there is a Feathered Frege, a Rooster Russell or even a Peano of the Poultry World?



Figure One: Aristotle, Frege, And Russell?


How far down the pecking order do we descend? If a chicken chooses seed on the basis of a syllogism, do toads select flies on the same basis? Do ticks opt for deer this way, too? Perhaps locusts are logical as well, and reason that if all fields are good to ravish, and this is a field, it too is good to ravish? [Except, of course, the syllogism is categorical, and isn't the least bit hypothetical. Maybe then locusts have mastered Stoic Logic, which is hypothetical in form?] And what about the humble Hydra? Does it munch away at single-celled organisms having discovered Aristotle's syllogism hundreds of millions of years before he happened upon it? What about e-coli? Does it select which mammalian gut to invade on this basis, too? And what about the flu virus? Does it reason that all human noses are good, and then proceed to infect another one as a result? But if all of these take place in nature, then these organisms must all be natural logicians. If not, then chickens aren't either.


Anyway, in what sense can a chicken be said to know about " general"? Are they also expert abstractors? But, newly hatched chickens will peck away at grain, too, having had no schooling in the time-honoured ways of Poultry Philosophers. Perhaps they receive lessons inside the egg? When they have passed their eggxams, they are allowed to break out of their shells -- having learnt another syllogism about egg shells in general, and, presumably one about syllogisms in general, too.


Unfortunately, however, the syllogism is a severely limited logical form. [On that, see here, and especially here.] In which case, one would have thought that chickens would have gone on at least to master Stoic Logic -- and then perhaps even aspects of Boolean Algebra.


On the basis of passages like these it isn't easy to defend the above dialecticians from the accusation that they don't know what they are talking about. Even so, what they say is in fact quite representative of opinion in dialectical circles. In their defence, though, it is worth pointing out that they inherited this idea from an ancient tradition in logic (one also influential on Kant and Hegel) that logic is a sub-branch of Philosophical Psychology.


However, FL is no more the science of thought than Geometry is the study of where to stand -- or the rules of Cricket/Baseball represent the science of ball hitting. Science is descriptive, explanatory and predictive. The theorems of FL are constitutive and normative.


This topic is extensively discussed in Shanker (1998), pp.63-120. Cf., Coffa (1991), pp.113-67, Baker (1988), and the general comments in Button, et al. (1995). Cf., also Brockhaus (1991), pp.65-106. [See also my comments over at Wikipedia on this.]


6. In Essays Twelve and Fourteen the connection between this way of thinking and ancient religious and mystical views of reality will be examined. The ideological impact on revolutionaries of the latter will also be detailed in Essay Twelve (summary here) and in Essay Nine Parts One and Two.


6a. It could be replied that if language is part of the world, it must have coded into it all sorts of things that are part of reality, too. This response will be defused in Essay Twelve, where it will be shown to depend on subtle forms of LIE. [A shorter version of that Essay can be found here.]


[LIE = Linguistic Idealism.]


It could also be argued that our minds work the way they do because it was evolutionarily advantageous for our ancestors. Individuals whose thoughts did not mirror the world would find it difficult to survive and reproduce. This is in fact a rather poor argument, which I will dispense with in Essay Thirteen Part Three. However, for present purposes all we need note is that even if this were the case, our thoughts need only 'mirror' the material world, and not these 'underlying essences', for our ancestors to survive. How, for example, could their thoughts mirror this hidden world of 'essences' (revealed by Traditional Philosophers only a few thousand years ago) when they are inaccessible to the senses? How could such imponderables assist in their survival in any away at all?


It could be objected that their capacity to form abstract thoughts would enable them to form general ideas about nature, which would free them from the immediacy of the present and allow them to take some, albeit limited, control of their surroundings. This would definitely assist in their survival.


However, as argued at length in Essay Three Parts One and Two, abstraction in fact destroys generality, hence, if our ancestors had access to these 'hidden essences' by means of abstraction, that would in fact have seriously reduced their chances of survival.


This is, of course, quite apart from the fact that it is bizarre in the extreme to claim that our ancestors, hundreds of thousands of years ago, were aware of these invisible 'essences' -- and thus coded them into language -- which 'essences' were in fact conjured into existence only a few thousand years ago by some rather crass grammatical and logical verbal tricks concocted by Greek Philosophers.


[The verbal tricks that Ancient Greek Philosophers performed in order to concoct such fanciful theories are detailed in Barnes (2009), Havelock (1983), Kahn (1994, 2003), Lloyd (1971), and Seligman (1962) -- although these authors do not characterise these terminological gyrations in the pejorative way that I have. I will be dealing with this topic in more detail in Essay Twelve Part Two.]


This isn't to argue that our ancestors didn't use general nouns, but general nouns are not the same as the 'abstract general ideas' of Traditional Philosophy. Readers are directed to the above two Essays for more details.


7. One has only to leaf through, say, Aristotle's Prior Analytics to see that this is no invention.


This is what the late Professor Nidditch had to say:


"One has to give Aristotle great credit for being fully conscious of this [i.e., of the need for a general account of inference -- RL] and for seeing that the way to general laws is by the use of variables, that is letters which are signs for every and any thing whatever in a certain range of things: a range of qualities, substances, relations, numbers or of any other sort or form of existence....


"If one keeps in mind that the Greeks were very uncertain about and very far from letting variables take the place of numbers or number words in algebra, which is why they made little headway in that branch of mathematics...then there will be less danger of Aristotle's invention of variables for use in Syllogistic being overlooked or undervalued. Because of this idea of his, logic was sent off from the very start on the right lines." [Nidditch (1998), pp.8-9. Italic emphasis in the original.]


A comprehensive history of Logic can be found in Kneale and Kneale (1978); the rapid degeneration that Logic underwent after Aristotle's death is outlined in Peter Geach's article: 'History of the Corruptions of Logic' (i.e., Geach (1972b)). [For Aristotle's use of variables, see Barnes (2009), pp.264-359.]


8. With respect to this argument schema, the only condition validity requires is the following: if, for a given interpretation, the premisses are true then the conclusion is true. That claim is not affected by the fact that schematic premisses themselves can't be true or false, since such schema express rules, and are hypothetical. [A clear explanation can be found here.] To be sure, Aristotle did not see things this way, but I do. [Even so, I have assumed here that these schemas are categorical, that is, that they aren't hypothetical.]


One interpretation of L1 (given in the text) that might illustrate this is the following:


Premiss 1: No moving object is stationary.


Premiss 2: All objects with zero velocity are stationary.


Ergo: No moving object is one with zero velocity.


[Certain stylistic changes were required here to prevent this ordinary language interpretation becoming somewhat stilted.]


The above syllogism is valid, and would remain valid even if all motion ceased. But, it also 'copes' with movement, and hence with change, as is clear from what it says.


And we do not have to employ what seem to be 'necessarily true' premisses (or, indeed, this particular argument form) to make the point:


Premiss 1: All human beings are aging.


Premiss 2: All Londoners are human beings.


Ergo: All Londoners are aging.


Admittedly, the term "aging" is not of the type Aristotle would have countenanced in a syllogism, so far as I can determine. However, if we free Aristotle's logic from his metaphysics, the inference is clearly valid, and based on a syllogistic form. Anyway, the term "aging" can easily be replaced by a bona fide universal term (such as "the class of aging animals"), to create this stilted but genuine syllogism:


Premiss 1: All human beings are members of the class of aging animals.


Premiss 2: All Londoners are human beings.


Ergo: All Londoners are members of the class of aging animals.


[Except, of course, Aristotle would have employed "All men" in place of "All human beings".]


To be sure, the above changes are not of the sort that interest dialecticians, but, as I note in the main body of this Essay, examples like this have only been quoted to refute the claim that FL can't cope with change. Combine that idea with the additional thought that dialectics can't cope with change itself (on that, see here), and the alleged 'superiority of DL over FL turns into its own opposite. Which is yet another fitting dialectical inversion.


There is an excellent account of Aristotelian Logic in Smith (2011).


And there is an equally useful account of MFL (i.e., now confusingly called "Classical Logic") in Shapiro (2013).


Readers should also consult Hirsch (2004), which, while deeply flawed represents a major step in the right direction. [However, the editors of the on-line journal in which Hirsch (2004) appears did not see fit to publish my reply.]


9. Naturally, this raises issues that lie at the heart of this dispute: whether or not concepts change over time as a result of inherent logical/rational processes. This aspect of DL (uncongenial as it is to the sort of Historical Materialism that refuses to make concessions to any form of mysticism) will be examined in Essay Fourteen Part Two.


This also raises questions about the relative stability of meaning in language. That topic is dealt with in more detail in Essay Six -- here and here. See also here.


[LOI = Law of Identity.]


10. The reader should consult Essays Five, Six, Seven and Eight Parts One Two and Three on this.


11. In fact, MPP was known to the Stoics, circa 200 BCE. This item of breaking news has yet to penetrate the adamantine skulls of majority of 'dialectical logicians'. It looks like 2200 years is not quite long enough.


On Stoic Logic, see Kneale and Kneale (1978), pp.158-76, and Mates (1953).


In the argument in the main body of the Essay, "A" stands for "Assumption". The un-bracketed numbers relate to the premises used on each line to derive the conclusion, and the bracketed numerals refer to the line numbers. [In this, I have partially followed Lemmon's method of presentation. Cf., Lemmon (1993).]


An introduction to Natural Deduction (a system devised by Gerhard Gentzen) can be found in Lemmon (1993); an axiomatic approach to logic is set out in Hunter (1996); more advanced logic can be found in Bostock (1997) and Mendelson (1979). A recent and comprehensive survey of modern mathematical logic can be found in Hinman (2005).


Unfortunately(!!), Gentzen was either a Nazi or he entertained Nazi sympathies. On this, see here; but this should no more affect our opinion of his work in logic than Hegel's political and social views affect how dialecticians regard his 'logic'.


11a. Care must be taken not to confuse interpretation in logic with interpretation in other disciplines or, indeed, in ordinary discourse. "Interpretation" in logic relates to the substitution instances that result when variables are replaced with the relevant terms drawn from ordinary or technical languages, etc., according to the syntax and semantics of the formal system in question.


It might be objected that the antecedent and consequent here aren't propositions -- that is, "Atoms of 64Cu undergo beta decay" and "64Ni atoms, positrons and neutrinos are formed" aren't capable of being true or false. That is correct, but the argument isn't beyond repair. However that repair would render the clauses involved highly stilted, if not unwieldy. The repaired version of the opening assumption would then read something like this:


A1: If an atom of 64Cu undergoes beta decay at T(1), then an atom of 64Ni, k positrons and m neutrinos are formed at T(2).


Where the temporal and numerical variables are also well defined. However, I rather think that A1 is scientifically uninteresting and possibly unverifiable, but that is no fault of logic.


12. The details of these other systems of Logic can be found in Goble (2001), Hughes and Cresswell (1996), Haack (1978, 1996), Hintikka (1962), Jacquette (2006), Prior (1957, 1967, 1968) and Von Wright (1957, 1963). A general survey of some of the background issues raised by Classical and Non-Classical Logic can be found in Read (1994). In fact, Graham Priest (who is both a defender of certain aspects of dialectics, and an expert logician) has written his own admirable introductions; cf., Priest (2000, 2008). Also worth consulting are the following:


Despite this embarrassment of riches, freely available on the internet, DM-fans steadfastly cling to their studied ignorance, maintaining this self-inflicted nescience all the while pontificating about FL as if each one were a latter-day Aristotle. [Anyone who doubts this need only examine, say, Trotsky's lamentably poor 'answer' to James Burnham, in Trotsky (1971), pp.91-119; 196-97, 232-56. See also, here and here.]


12a. This isn't strictly true; several examples of the rather weak attempts made by DM-theorists to argue that logic uses 'fixed concepts' will be examined below.


12b. Of course, as we will see, the former (i.e., reductionism) is avoided by DM-fans by the simple expedient of a flat denial, with no attempt at explanation other than a reference to the Part/Whole dialectic (criticised in Essay Eleven Part Two). The second consequence (i.e., bourgeois individualism) is simply ignored. In fact, in my 30-year hike across this Dialectical Desert, I have only ever encountered one author (Bertell Ollman) who even so much as recognises this implication of the 'dialectical theory of knowledge', and even then he merely kicks it into the long grass for future consideration. [On that, see here.] 


13. When I am alluding to a concept, I will put any expression by means of which I attempt to do this in 'scare' quotes --, e.g., 'the concept green'. When I employ an expression by means of which I attempt to do this (i.e., when I merely mention it), I will quote it -- e.g., "the concept green".


[As the reader will no doubt appreciate, this is an absolute minefield, so this section of the Essay will need to be re-written several times in order to make sure that I do not fall into the very trap I a attempting to highlight.]


The distinction between concepts and objects (or rather, the distinction between concept expressions and singular terms) is needed, otherwise propositions would turn into lists, and thus fail to say anything.


[This topic was discussed in detail in Essay Three Part One (and again briefly below, in Note 14). Many of the issues raised here are outlined with admirable clarity in Gibson (2004), and in extensive detail In Gaskin (2008). However, Gaskin's 'solution' is no solution at all; I will say more about why that is so in a later Essay. See also, Davidson (2005), pp.76-163.]


Anyway, dialecticians themselves appear to require this distinction, otherwise their theory would be little different from "crude materialism"; they need concepts to remain concepts (and not turn into objects, or even the names thereof) or risk losing the capacity to express generality. [This was also explained in detail in Essay Three Part One (link above).]


Indeed, if concepts and objects were one and the same, there would seem to be no advantage in seeking a conceptual account of change in, or to, material objects, for that would turn it into an abstract account of change experienced by objects, not concepts, only now it would be entirely unclear what the former 'objects' were (i.e., these 'objects-cum-concepts'), and how they could account for anything.


Of course, part of the problem here is that, following on from Kant and Hegel, concepts are viewed by DM-theorists as quasi-mental structures (images!), processes, or 'representations' of some sort -- the latter, in some cases, indistinguishable from a capacity to represent to ourselves the so-called "Universals". This clearly blurs the distinction between concepts and objects (or, indeed, the names thereof); DM-concepts appear to be a peculiar sort of abstract object.


[Again, the insurmountable problems this creates for Traditional Philosophy, and DM, were detailed in Essay Three Part One; the distinct advantage of the neo-Fregean approach to concepts, adopted at this site, are outlined here, here, and here.]


A brief account of the history of the introduction of this word (Begriff) into Philosophy (in the 17th century by Leibniz), can be found in Caygill (1995), pp.118-21. For Hegel's use of this word (and its cognates), see Inwood (1992), pp.58-61.




However, as far as the alleged change to concepts is concerned there seem to be only two possibilities: C2 and C3. Neither looks at all promising:


C2: This patch of green has changed.


C3: The concept green has changed.


(1) In C3, "The concept green" could be designating all green objects. On reflection, this seems unlikely since C3 is specific in its reference to "the concept green", not to the objects that happen to instantiate it. Even though all or most of the said objects could change, it would still leave the 'concept' itself unaffected. Indeed, all green things seem to change at some point, but if the 'concept' also changed, we wouldn't be able to express this fact in any obvious way.


So much was at least clear to Plato, but he (or at least later Platonists) 'solved' this problem by turning general words either into the names of abstract particulars (i.e., the "Forms"), or other singular terms that designate them, thereby destroying generality. [On this, see Essay Six, here.] Hence, this alternative would also leave the phrase "the concept green" no longer behaving as a general, but as a singular term, which would, plainly, no longer be operating as a concept expression. Concept expressions are general; singular terms manifestly aren't.


[Having said that, the complex ways that Greek Philosophers and Logicians attempted to grapple with knotty problems like this are covered in Barnes (2009), pp.93-167.]


(2) "The concept green" could refer to an 'abstraction' residing perhaps in some 'mind' or brain -- or, which somehow 'inhered' in all objects that shared the designated 'property'). But, again, on reflection, this expression can't designate a 'collective idea of green', for there is no such thing. [Why that is so -- if Abstractionism were a true theory, or family of theories --, is explained at length in Essay Three Parts One and Two.] And, even if there were such an idea, calling 'it' a concept would be inept since, ex hypothesi, 'it' would then be an 'object', or collection of 'objects', not a concept. Moreover, if all green objects shared this common property, designating it this way would deny it that very role, since 'The concept green' itself would be an object, not a general property!


Of course, either option would simply confirm the view that it isn't concepts that change, but objects that instantiate them which do.


The problem here is that we can't express in indicative sentences the logical role that concept expressions play without distorting that very role; any attempt to do so simply destroys their capacity to function in the way we might imagine. [This is connected with the main theme of Essay Twelve Part One -- that is, that any attempt to formulate theories about how language 'latches onto the world', how it allegedly reflects nature, will always collapse into non-sensicality and/or incoherence.] While Frege was aware of this 'difficulty', he couldn't account for it; Wittgenstein, I think, 'solved' this 'problem' by dissolving it. On this see the references given below.


The illusion that we can refer to conceptual change (perhaps in the crude manner envisaged in TAR and other DM-texts) is created by the transformation that concept expressions undergo when they are situated in new, but non-standard sentential contexts -- for example, if direct reference to them is attempted, or they are designated by singular expressions, and those terms are then situated in indicative sentences (for example, in C3).


As C1 and C3 show, the claim that concepts can change rests on the nominalisation or particularisation of concept expressions -- by means of a Proper Noun (e.g., "Greenness"), or a definite description (e.g., "The concept green"), which, once more, turns what should be a general expression into a singular term. This then motivates the idea that because singular terms denote objects -- which can and do change -- these newly nominalised/particularised 'entities' must similarly be subject to change, and in like manner.


[Particularisation is the process by means of which general words are turned into singular expressions (Proper Names, Definite Descriptions, etc.), which then supposedly designate Abstract Particulars. (However, it is important not to confuse particularisation with Hegel's use of "particular".) This is not to suggest that the 'subject' term of such sentences can only be singular terms.]


C1: Green has changed.


C3: The concept green has changed.


Change in or to objects thus becomes a model for conceptual change, but only because when an endeavour is made to refer to, or denote, concepts we are forced to nominalise/particularise concept expressions. Naturally, this linguistic move is the first false step in the running together of these two distinct sorts of change.


In Essay Three Part One we saw how this simple error spawned a philosophical pseudo-problem, lasting the best part of 2500 years, over the nature of 'Abstractions', 'Universals', 'Categories', 'Ideas', 'Forms' and 'Concepts'.


However, it is worth adding that these 'abstract objects' were only conjured into 'existence' because the distinction between concepts and objects had been obliterated -- again by means of yet another grotesque distortion of language, as Marx suggested:


"The philosophers have only to dissolve their language into the ordinary language, from which it is abstracted, in order to recognise it, as the distorted language of the actual world, and to realise that neither thoughts nor language in themselves form a realm of their own, that they are only manifestations of actual life." [Marx and Engels (1970), p.118. Bold emphases added.]


[Although, I'm not suggesting that Marx saw things this way, there are hints in his early work that he was moving in this direction in the 1840s. On that, see here, and here.]


Metaphysicians have repeatedly made mistakes like this, constantly falling prey to what might be called the "Nominalisation/Particularisation Fallacy". Those who have been misled along such lines seem to think that if a clause (or phrase) can be nominalised/particularised then there must be something (visible or invisible, in the 'mind' or in 'Platonic Heaven') that answers to it. [This misconception is related to the 'Fido-Fido' fallacy highlighted by Gilbert Ryle.]


So, on that basis, it is concluded that 'the concept green' must exist (somewhere!) because the expression signifying it has just been particularised and/or nominalised. Again, such inferences have only ever been justified by nominalisations/particularisations of this sort -- which conjure into existence 'abstract objects' at the drop of a noun.


This error also motivates the idea that since the ordinary use of words prevents such linguistic tomfoolery, technical devices must be invented that permit it -- and words like "Form", "Concept", "Being", "Property", "Category", "Nothing" and "Becoming" are invented and then pressed into service. The supposed meaning of such empty phrases now appears to allow profound 'philosophical' truths, valid for all of space and time, to be derived from thought alone. In this way, the 'thoughts' (of lone thinkers, divorced from the constraints social life puts on the use of language) seem able to penetrate to the heart of reality, uncovering 'hidden truths' in the comfort of their own heads. But, the only rationale for such moves is a terminological trick motivated by an inept transformation of concept expressions into the names of abstract particulars.


In DM, this (already distorted) approach to the vernacular resurfaces as part of the claim that the logic of ordinary discourse must be "surpassed" by the use of highly obscure jargon -- mined, for example, from Hegel's Logic --, which not only permits such 'word magic', it insists on it.


However, since singular terms aren't concept expressions (nor vice versa), moves like this must always fail. That is because, in order to pick out the alleged reference of a general term, a singular term supposedly denoting it has been introduced. But, this term now designates an abstract object -- it has to be abstract, for if it weren't, there would be no need for this charade. So, these newly introduced expressions no longer operate as general terms, but as singular expressions. Hence, because of this ancient segue, concepts now appear to be strange sorts of objects -- or, alternatively, objects now look like a peculiar sort of concept -- that can stand in relation to other objects. [This observation will be expanded upon in Essay Twelve (in order to reveal where, for example, Hegel's account of truth goes badly astray). These moves also underlie all the (Idealist) talk about "internal relations" that one finds in DM. More on that in Part Two of this Essay.]


Now, instead of finding fault with the linguistic distortion that originally created such abstractions (but which moves can't work anyway since they destroy the unity of the proposition -- this was explained in Essay Three Part One), dialecticians assume that reality itself must be 'contradictory'. That in turn is because it is now 'clear' to them that a singular expression can't be identical with a Universal, so the Universal must be transmogrified into an Abstract Particular.


[Essay Three Part One showed how Hegel adopted the Medieval Identity Theory of Predication. So, in sentences like the following:


S1: Blair is a man,


what we are really supposed to have is:


S2: Blair is identical with Man/Manhood.


But, since Blair can't be identical with the Universal, Manhood, we must conclude:


S3: Blair is not identical with Manhood.


Or, even:


S3a: Blair is a non-man.


But, this, too, misrepresents Blair, so we are forced (by the 'development' of these 'concepts) to conclude:


S4: Blair is not a non-man.


From such tortured 'logic' the NON emerged.


I won't attempt to justify such moves (and not just because I don't think they can be defended!), since I am only concerned here to abbreviate a complex argument, the background to which can be found here, here and here -- where I cover the traditional confusion of general words (concept expressions) with the names of Abstract Particulars.]


These bogus moves suggest that further adjustments now have to be made to the original 'concepts', indicating -- to those taken in by this linguistic conjuring trick -- that there is "movement" in 'concepts', by means of which they are now said to possess "identity-in-difference", which doctrine forms the basis for, or even the motor of, universal development. That is because these artificial 'concepts'/'objects' now seem capable of change, since they have been modified in a way that makes them resemble material objects.


We can see this, too, in Hegel's confusion of the LOI with the LOC, in the course of which he ran together concepts, objects, propositions, and judgements -- along with a whole host of other things. This is something that dialecticians in general also do (and that includes HCDs), since their thinking has been heavily skewed by their uncritical acceptance of that Hermetic bungler's logical howlers. (Anyone who objects is, of course, accused of 'pedantry'.)


In this way, a bogus (local) change, imposed on a handful of ordinary words, is taken to reflect an 'essential' feature of the development of everything in nature, for all of time --, which is then promptly imposed on reality.


[In Essay Twelve, an epistemological version of this dodge will be called the RRT. The implication of the latter theory is that, despite what its supporters tell us, language is no longer said to reflect the world, the world is made to reflect the distorted language imposed on it. This represents an essential move in the setting up of the pernicious strain of LIE underpinning Hegel's work. (We saw here and here how the entire dialectic is based on a series of logical blunders of this sort.)]


[LOI = Law of Identity; LOC = Law of Non-Contradiction; LEM = Law of Excluded Middle; RRT = Reverse Reflection Theory; LIE = Linguistic Idealism; HCD = High Church Dialectician (explained here).]


We can see this, too, in Hegel's ambitious 'derivation' of 'Nothing' from 'Being', which is a verbal trick that only works if 'concepts' are treated as objects of some sort ('named' by the words "Being" and "Nothing", for example).


[This 'argument' (unwisely praised by Lenin and Trotsky!) is destructively analysed in Essay Twelve Part Five (summary here). This tangled rat's nest -- otherwise known as Hegel's Logic -- is in fact a sub-Aristotelian Grimoire replete with syntactic screw-ups like this, which have been unwisely accepted by Hegel-groupies ever since.]


We can see this happening, too, in these words of Engels's:


"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, 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 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 (1975), p.457, and Marx and Engels (2004), pp.463-64. Bold emphasis added.]


"The fact that identity contains difference within itself is expressed in every sentence, where the predicate is necessarily different from the subject; the lily is a plant, the rose is red, where, either in the subject or in the predicate there is something that is not covered by the predicate or the subject…. That from the outset identity with itself requires difference from everything else as its complement, is self-evident." [Ibid., pp.214-15. Bold emphasis alone added.]


Engels clearly saw concepts as object-like. [More on this, here.]


Plainly, such artefacts of the imagination can't undergo change in the material world (at least not in the way that objects do), and that is why these tendentious manoeuvres have to take place in the 'hidden' world of the 'mind', even though all we have been presented with is a set of distorted words by way of 'proof' that any of this has actually happened.


Indeed, this 'linguistic miracle' is so profound that it can, on its own, create a whole world of changing 'concepts', hidden from human gaze, which 'exist' in, and which constitute a world that is more real than the material world from which they have allegedly been 'abstracted'. In fact, this 'occult world' encapsulates the essence of the material world, its a priori structure and dynamic.


As noted earlier, Hegel performed this conjuring trick on 'Being' to produce 'Nothing', and hence 'Becoming':


"Being is the indeterminate immediate; it is free from determinateness in relation to essence and also from any which it can possess within itself. This reflectionless being is being as it is immediately in its own self alone.


"Because it is indeterminate being, it lacks all quality; but in itself, the character of indeterminateness attaches to it only in contrast to what is determinate or qualitative. But determinate being stands in contrast to being in general, so that the very indeterminateness of the latter constitutes its quality. It will therefore be shown that the first being is in itself determinate, and therefore, secondly, that it passes over into determinate being -- is determinate being -- but that this latter as finite being sublates itself and passes over into the infinite relation of being to its own self, that is, thirdly, into being-for-self.


"Being, pure being, without any further determination. In its indeterminate immediacy it is equal only to itself. It is also not unequal relatively to an other; it has no diversity within itself nor any with a reference outwards. It would not be held fast in its purity if it contained any determination or content which could be distinguished in it or by which it could be distinguished from an other. It is pure indeterminateness and emptiness. There is nothing to be intuited in it, if one can speak here of intuiting; or, it is only this pure intuiting itself. Just as little is anything to be thought in it, or it is equally only this empty thinking. Being, the indeterminate immediate, is in fact nothing, and neither more nor less than nothing.


"Nothing, pure nothing: it is simply equality with itself, complete emptiness, absence of all determination and content -- undifferentiatedness in itself. In so far as intuiting or thinking can be mentioned here, it counts as a distinction whether something or nothing is intuited or thought. To intuit or think nothing has, therefore, a meaning; both are distinguished and thus nothing is (exists) in our intuiting or thinking; or rather it is empty intuition and thought itself, and the same empty intuition or thought as pure being. Nothing is, therefore, the same determination, or rather absence of determination, and thus altogether the same as, pure being.


"Pure Being and pure nothing are, therefore, the same. What is the truth is neither being nor nothing, but that being -- does not pass over but has passed over -- into nothing, and nothing into being. But it is equally true that they are not undistinguished from each other, that, on the contrary, they are not the same, that they are absolutely distinct, and yet that they are unseparated and inseparable and that each immediately vanishes in its opposite. Their truth is therefore, this movement of the immediate vanishing of the one into the other: becoming, a movement in which both are distinguished, but by a difference which has equally immediately resolved itself." [Hegel (1999), pp.82-83, §130-34. Italic emphases in the original.]


Attentive readers will no doubt have noticed that Hegel refers to each these 'concepts' with an "it", and asserts that 'they' can or can't have properties/'determinations' (just like any other object), failing to spot that by doing this he destroyed their generality, nullifying the whole exercise. [This argument will be returned to the mystical swamp from which it slithered in Essay Twelve Parts Five and Six.]


It could be argued that Hegel is talking about conceptual subordination here not object-concept subsumption. The former involves concept-to-concept predication, whereas the latter involves concept-to-object predication. [On this, see Redding (2007), pp.85-114.] The problem with this response is that Hegel strangled it even before birth when he nominalised the 'concepts' he employed (such as "Being", "Nothing" and "Becoming").


These days, the bedraggled occupants of Hegel's Hermetic House of Horrors -- DL-fans -- also claim to have a method that supposedly gives 'life' to 'concepts' (by nominalising them as abstract particulars), when in fact it kills them by destroying their capacity to express generality -- vitiating the whole exercise.


Hence, and once more, a move in language is held to mirror, or to reveal, movement in thought/reality --, but, as noted above, the former is held (by Idealists and naive DM-fans alike) to reflect changes which are far more profound than plain and simple material development. Indeed, 'conceptual change' of this sort is said to drive material development. In this way it turns out that nature is 'dialectical' only because of a series of logical/syntactical blunders, which 'allowed' Dialectical Magicians to conjure the underlying logic of 'Being' and 'Becoming' into existence -- literally from 'Nothing' --, as these merge into, and re-emerge from, 'Nothing'.


The Big Bang from the Big Distortion.


It is worth re-emphasising here that the only 'evidence' for these 'impressive' moves is this inept analysis of a relatively minor, indicative sentential form found almost exclusively in Indo-European languages!


However, what finally emerges at the end of this ancient Linguistic Conjuring Trick is not in fact an account of how concepts change, but how a bogus linguistic ceremony can be substituted for a genuine account of change in the material world!


This inept syntactical 'research programme' (now over 2400 years old) deliberately runs together the logical roles played by singular and general terms, names and concept expressions. [Why this was deliberate is explained in Essay Twelve (summary here).]


Be this as it may, for present purposes it is also worth asking the following question: If these logical 'categories' (the singular and the general -- concepts and objects) are 'identical', how is it possible to depict the functioning of either or both of them? Surely, a name only functions as a name alongside other expressions that aren't names. Similarly with predicates/concept expressions. If every word named something (concrete or abstract), how could we say anything about anything, and hence name anything?


As was argued in Essay Three Part One, if sentences were composed solely of names (or singular terms), they would be no different from lists. Lists fail to say anything -- unless they are articulated by the use of concept expressions/predicates, and only then if the latter aren't viewed as designating abstract particulars.


Propositions, on the other hand, can be used to assert or deny things. That being so, propositions can't contain only names and/or singular terms. Otherwise we would not be able to assert or deny anything by means of them.


Of course, this is part the reason why DM-'propositions' collapse into non-sense and incoherence; the inept syntactical theory dialecticians have inherited from Hegel and Traditional Thought denies them any sense by turning the sentences used to express them into mere lists, preventing them from saying anything at all. On top of that, the radical misuse of language upon which this supervenes, means that DM is incoherent, to boot.


14. Of course, this depends on what we mean by "concept". Few deny they have to be expressed by general terms (or that they feature in language as general terms), but definite descriptions (like "The concept green") aren't general, but singular. This just underlines the problem; any attempt to talk about concepts in this way destroys their generality (as we saw in Essay Three Part One).


Compare the following with C3:


[C3: The concept green has changed.]


C5: This leaf is green; next month it will be brown.


C5a: These leaves are green; next month they will be brown.


C5 succeeds in depicting change -– but, plainly, that is because it expresses the changes experienced to an object (or, in C5a, to a set of objects), not a concept.


In the first half of C5, the concept green is expressed by the use of the one-place predicable "ξ is green", which, when applied as a rule to the singular term, "This leaf", maps onto the first clause of C5: "This leaf is green".


[It could be objected that if the comments reported in this Essay are correct, the above sentence -- i.e., "The concept green is expressed by the use of the one-place predicable "ξ is green" -- is itself ill-formed. Well, it certainly lacks a sense -- it can't be true or false -- but this isn't a problem for the account being presented here; that is because the 'offending' sentence (i.e., C3) is itself a rather badly-worded rule -- in which case, it doesn't need to be true or false to be understood. More on this in Essay Twelve Part One. (And it is badly-worded only because of the constraints under which I am working here -- defending ordinary language in the face of those who seem happy to distort it: DM-fans and Traditional Theorists!).


The use of these rather odd looking stencils (i.e., "ξ is green") is explained here. It is further justified, here, and below.]


[Incidentally, a predicable is an expression that is capable of being predicated; it is a predicate when it is so predicated.]


By way of contrast, in C3, the phrase "The concept green" operates as a singular term, which can't express a rule, whereas "ξ is green" can. [Why that is so is also explained in Essay Three Part One.]


Nevertheless, "The concept green", acting now as a singular term (when coupled with the one-place predicable "ξ has changed"), maps onto sentences like C3 -- plainly, when the phrase "The concept green" is used to complete it.


But, because of this, C3 is no longer an ordinary sentence. Despite what it seems to say, it can't now be about 'the concept green'. That is because -- although "The concept green" purports to pick out a concept -- as a singular term it can only designate an object. This means that C3 is now radically misleading. While C5 itself succeeds quite uncontroversially in expressing material change, C3 fails to depict anything at all because of its distorted linguistic form.


C3: The concept green has changed.


C5: This leaf is green; next month it will be brown.


Even if (per impossible) the phrase "The concept green" could designate anything (non-misleadingly), it couldn't serve as an archetype for the role that legitimate concept expressions play in sentences like C5. Once more, that is because a singular term (i.e., "The concept green") can't express a rule, which is what the ordinary use of "ξ is green" manages to do.


Anyone who understands the convention expressed by "ξ is green" -- i.e., that sentences can be formed by replacing "ξ" with singular expressions (or other legitimate subject terms) -- will have mastered a rule for the sue or "green" (in such contexts). [Again, why that is so is also explained in Essay Three Part One.]


So, "ξ is green", as it features in the formation of sentences like C5, is the linguistic expression of a rule. Of course, ordinary speakers plainly aren't aware of stencils like "ξ is green", nor need they be. These stencils merely assist us in understanding the patterns that are illustrated in our formation and use of such simple sentences. Nor does it mean that this is the only way that C5 can be analysed, or that we have to view things like this; but this way of depicting our use of language brings out the rule-governed way we all form sentences like C5. One distinct advantage of picturing things in this manner is that it helps show that a singular term like "The concept green" can't express a rule, whereas "ξ is green" can.


This is, of course, just a formal way of making the point that description is different from naming, or designating -- which distinction remains valid no matter how we try to depict or formalise it.


However, the actual marks on the page/screen (i.e., "ξ is green") are nowhere to be found in C5. This incomplete expression is in fact the common pattern that underlies all the legitimate sentences that can be formed from it by the substitution of singular terms for the gap marker "ξ" -- as in, "This apple is green", "That lawn is green", "Your shirt is green", etc. The rule-governed use of the template "ξ is green" allows for the formation of an indefinite number of propositions in the same way -- again, even though it nowhere appears in any of its instances.


[As already noted, there are other ways of looking at such sentences, but none, I think, brings out the nature of the patterns underlying the rule-governed way we produce and understand indicative sentences -- or, at least, none that do so without falling onto the nominalisation/particularisation trap mentioned earlier.]


Moreover, the singular term used in C3 (viz.: "The concept green") can't actually do what was intended for it -- that is, it can't depict a grammatical 'truth' about the role the stencil "ξ is green" occupies in C5 (or, indeed, the role that "is green" plays in C5).


C3: The concept green has changed.


C5: This leaf is green; next month it will be brown.


[This underlies a theme that runs through Wittgenstein's work: that we can't express by means of indicative propositions how key logical/grammatical aspects of language work -- this is the point underlying the so-called "saying/showing" distinction that Wittgenstein drew in the Tractatus.]


However, this will certainly not be the aim of anyone who wants to use a sentence like C3. In fact, the use of C3-type sentences (or even the more obscure versions found in DL -- their use in modern philosophical logic is another matter entirely) was originally aimed at unmasking nature's hidden 'essences', which supposedly underpin all of reality. So, if dialecticians want to say something like the following, they will simply end up saying nothing comprehensible (as we saw here):


"Thus, for instance, if I affirm: 'John is a Man' I affirm that 'John' is a particular specimen of the general (or 'universal') category 'Man'. I understand what 'John' is by subsuming him under (or 'identifying him with') the wider category 'Man'.


"Metaphysical reasoning proceeds on the tacit or explicit assumption that the general category 'Man' and the particular category 'John' exist independently of each other: that over and above all the Particular 'Johns' in creation…over and above all particular men, there exists somewhere -– and would exist if all particular men ceased to be, or had never been -– the general category 'Man.'


"…The dialectical method traverses this rigid metaphysic completely. The category 'Man' includes, certainly, all possible 'men.' But 'Man' and 'men', though distinct, separate, and separable logical categories, are only so as logical discriminations, as ways of looking at one and the same set of facts. 'Man' -- is -- all men, conceived from the standpoint of their generality -- that in which all men are alike. 'Men' is a conception of the same fact -- 'all men' -- but in respect of their multiplicity, the fact that no two of them are exactly alike. For dialectics, the particular and the general, the unique and the universal -- for all their logical opposition -- exist, in fact, in and by means of each other. The 'Johniness' of John does not exist, can't possibly be conceived as existing, apart from his 'manniness'. We know 'Man' only as the common characteristic of all particular men; and each particular man is identifiable, as a particular, by means of his variation from all other men -- from that generality 'Man' by means of which we classify 'all men' in one group.


"It is the recognition of this 'identity of all (logical pairs of) opposites,' and in the further recognition that all categories form, logically, a series from the Absolutely Universal to the Absolutely Unique -- (in each of which opposites its other is implicit) -– that the virtue of Hegel's logic consists….


"Let us now translate this into concrete terms. John is -- a man. Man is a category in which all men (John, and all the not-Johns) are conjoined. I begin to distinguish John from the not-Johns by observing those things in which he is not -- what the other men are. At the same time the fact that I have to begin upon the process of distinguishing implies…that, apart from his special distinguishing characteristics, John is identical with all the not-Johns who comprise the rest of the human race. Thus logically expressed, John is understood when he is most fully conceived as the 'identity' of John-in-special and not-John (i.e. all man) in general.


"…When I affirm that 'John is a man' I postulate the oppositional contrast between John and not-John and their coexistence (the negation of their mutual negation) all at once. Certainly as the logical process is worked in my mind I distinguish first one pole, then the other of the separation and then their conjunction. But all three relations -- or better still, the whole three-fold relation -- exists from the beginning and its existence is presupposed in the logical act…." [Jackson (1936), pp.103-06. Quotation marks altered to conform to the conventions adopted at this site.]


That is because they will have seriously distorted language in an attempt to say what they imagined they wanted to say. In the above, "The category 'Man'" can't tell us anything about the logical role of " a man" (or if you like "ξ is a man") in "John is a man". But, the bogus form of words used by comrade Jackson is typical of the way that DL-fans express themselves, and typical of the way that Traditional Theorists have expressed themselves for the last 2400 years.


Hence, C3-type sentences attempt to say something about what it is that predicates (or concepts) allegedly refer to (or "reflect") -- and this, too, involves further confusions between talk about talk and talk about things, to put it more crudely. In this particular case, C3 is trying to say that whatever it is that " green" supposedly denotes, or refers to, has itself changed.


However, as we have seen, " green" does not operate referentially!


In that case, there is no "underlying reality" here for it to point to or 'reflect'.


This isn't because I am here asserting that there is no such things as 'underlying reality'/'essence', it is that language can't be forced into saying there is without lapsing into incoherence -- indeed, as Marx suggested.


To put this another way: if there were "essences" of this sort 'out there', somewhere in reality (howsoever this is conceived), then they can't be the referents of predicate expressions, since the latter are not singular terms. They do not operate referentially; they are descriptive or attributive.


[Naturally, these observations completely undermine the DM-theory of knowledge. More details on this here, and in the rest of Essay Three, when it is published.]


But -- just to continue this ancient metaphysical fantasy a little longer --, if "essences" constituted the general features of reality, then none of our general terms could be used to denote them. Any attempt to do so would transform the general terms used in such any such endeavour into singular expressions, and that would imply that the 'general features of reality' were in fact abstract particulars (as we saw in Essay Three) --, at the same time as robbing language of its capacity to express generality (once more, by turning predicates into singular terms).


So, instead of reporting a change to a concept (as had been intended), C3-type sentences indirectly record a bogus logico-grammatical transformation that has been imposed on a concept expression -- such as "ξ is green" --, changing it into a singular term which allegedly names/designates an 'abstract particular', such as 'The Concept Green'.


C3: The concept green has changed.


C5: This leaf is green; next month it will be brown.


Change in the material world (properly expressed in sentences like C5) would in this way have been conflated with a series of spurious changes that have been imposed on concept expressions (in 'propositions' like C3). As we have seen, movement in material reality can't be depicted this way, and that is what prevents dialecticians from expressing the very thing they had claimed they had all along wanted to do.


So, by tinkering around with the capacity ordinary language already has for expressing change, dialecticians have merely produced empty strings of words.


'Philosophical' sentences like C3 try to express the logical role of concept expressions by constructing what seem to be empirical propositions about language itself, or about concepts themselves; but in order to do that they have to change concept expressions into singular terms, which now allegedly refer to, or which designate something suitably "abstract", and non-material. But, if predicate/concept expressions don't refer, and can only be made to do so by altering them in the above manner, then it is little wonder that sentences like C3 create confusion or generate 'paradox', and thus provide endless/useless employment for generations of Traditional Theorists. This philosophical farce is then compounded by those who then to try to solve the pseudo-problem that this logical wrong turn generated. It is no surprise, therefore, that this 'problem' has resisted all attempts to solve it for over two thousand years.


Unfortunately, there is no way out of this logical hole. As soon as concept expressions are transformed into singular terms they cease to express concepts; they now denote objects, or supposed objects (albeit, 'abstract objects'). Worse still, in so doing they misrepresent the role that ordinary, materially-grounded concept expressions (like "ξ is green") play in sentences like C5.


Naturally, this means that no philosophical theory of conceptual change is possible -- and that includes the theory found in the runt of the litter, DM.


[Of course, this doesn't mean that we can't make sense of conceptual change by other means. How this is to be achieved will be entered into in a later Essay. (Spoiler: we can track conceptual development by attending to the way that our use of certain words changes.)]


For example, consider these attempts to state putative truths about a specific concept:


C6: The concept green is a concept.


C7: The concept green is a concept expression.


C8: "The concept green" is a concept expression.


C9: F is a concept expression.


C10: F is a concept.


C11: "F" is a concept expression.


C12: "F" is a concept.


[To be sure, several of the above blur the use/mention distinction, but this does not, I think, materially affect the point I wish to make.]


The apparently analytic 'truth' in C6 is, if anything, analytically false, since "The concept green" is plainly not a concept but an object (or rather it designates one)! Hence, and paradoxically, C6 is 'true' just in case it is 'false'! [However, if pressed, I would merely point out that C6 is ill-formed, so it can't be either true or false.]


C7 is even worse, for it suggests that a denoted object is in fact a linguistic expression. C8 is worse still: "The concept green" can't be a concept expression since it is a singular term. C9 and C10 are fake concept expressions; the letter "F" (as opposed to what it stands for) can't be a concept expression -- its just a letter! If, instead, "F" is used, as in C11 and C12, it becomes a singular term again, denoting whatever the key to this particular schema says it denotes.


[Some might wonder how we can ever set-up an adequate logical syntax; but whatever we set-up, when we do this, we aren't listing  a set of truths, merely expressing rules for the use of certain symbols (and these are formal rules we don't need in ordinary language, since the overwhelming majority of us use sentences like C5 every day of our lives, and without any fuss.]


The locus classicus for modern discussion of this topic is Frege (1892), upon which much of my own thinking has been based. [However, anyone not familiar with Frege's work will find the latter article very difficult; they might be advised to begin with Geach (1961), Beaney (1996), and Noonan (2001).]


Further background to this topic can be found in Davidson (2005), pp.76-163, Dummett (1955, 1981a, 1981b), Fisk (1968), Gaskin (2008), Geach (1976), Gibson (2004), Jolley (2007), Potter and Ricketts (2010), Slater (2000) -- now reprinted in Slater (2002, 2007a) -- and Textor (2010). For an alternative view, see Kenny (1995), criticised in Slater (2000). There is an excellent survey of where the debate is now situated (concerning the 'reference' of predicates, or even predicate expressions) -- or, at least where it was a few years ago -- in MacBride (2006). Having said that, MacBride doesn't consider the effect the traditional view -- that predicates do refer -- has on the unity of the proposition (discussed at length in Essay Three Part One).


15. Distorted language like this motivates metaphysical systems in general; indeed, much of Traditional Philosophy is based on muddles such as these. [On that, see Essay Twelve Part One.]


[Examples of confusions like this are given throughout this site; this particular one was analysed in detail in Essay Three Part One. See also Note 13 and Note 14, above.]


This partly explains why ontological and epistemological fairy-tales have had to be concocted in order to invent the 'objects' to which the terms introduced can refer/relate (such as Forms, Universals, Ideas, Concepts, Categories, and the like). Naturally, this means that 'Ontology' (as an entire discipline) is completely bogus.


16. On this, see Note 13 and Note 14, above.


17. Higher-order Logic is outlined in Boolos and Jeffrey (1980), pp.197-207, and Enderton (1972), pp.268-89. See also, here.


17a. Nevertheless, one bemused commentator has attempted to respond to this point (but without checking the detailed argument presented in Essay Twelve (partially reproduced below), in the following manner:


"Now this is very odd. Ordinary people are just as metaphysical and superstitious as the educated, though there is evidence to indicate that special types of superstitious thinking may be endemic to certain classes. But clearly ordinary language, its richness notwithstanding, is inadequate as is, due to imprecision as well as its ideological content, including inappropriate metaphorical content. At the very least, why else would we need the apparatus of formal logic, mathematics, notational systems, technical terminology, ideology critique?" [More on this here and here. Bold added.]


The reader will no doubt have noticed this commentator's use of metaphor (highlighted in bold) in his bid to criticise ordinary language for doing likewise. This can only mean that this criticism itself (unwisely written in ordinary language, too, it seems) suffers from the same unspecified 'limitations' this critic claims to have found in the vernacular. Hence, no safe conclusions may be drawn from what he says -- indeed, and as we will see (in the next section), this hackneyed attack on the vernacular disintegrates alarmingly quickly.


Moreover, the above comments reproduce the usual confusion of 'commonsense', or everyday beliefs (disguised as "ideological content" and "superstitious beliefs"), with ordinary language. In that case, they are worthless, anyway. As will be argued in detail below, the fact that in ordinary language we can negate every indicative sentence expressing a 'commonsense'/'superstitious'/ideological belief shows that ordinary language can't be identical with 'commonsense'/'superstition'/ideology.


And since this critic unfortunately gave no examples of the "ideological" contamination of ordinary language with allegedly suspect 'beliefs', not much can be made of that unsupported allegation, either.



Ordinary Language


Dialecticians' Mistaken Assumptions


[This section is a continuation of Note 17a.]


This is how the contrary argument will be put in Essay Twelve (some of it has already been posted in Essay Six, but it is re-presented here in a highly edited form):


John Rees put things this way:


"Ordinary language assumes that things and ideas are stable, that they are either 'this' or 'that'. And, within strict limits, these are perfectly reasonable assumptions. Yet the fundamental discovery of Hegel's dialectic was that things and ideas do change…. And they change because they embody conflicts which make them unstable…. It is to this end that Hegel deliberately chooses words that can embody dynamic processes." [Rees (1998), p.45.]


The problem with this passage is that it gets things completely the wrong way round. It is in fact our use of ordinary language that enables us to refer to change. Technical and philosophical jargon (and especially that which was invented by Hegel) is practically useless in this regard since it is wooden, static and of indeterminate meaning, despite what Rees asserts. [Any who think differently are invited to reveal us which Hegelian terms can do what the words in the list below (or their equivalent in German) already do for us, and better.]


As is well-known (among Marxists), human society developed because of its constant interaction with nature and as a result of the struggle between classes. In which case, ordinary language could not fail to have developed the logical multiplicity (and vocabulary) to record changes of limitless complexity.


This is no mere dogma; it is easily confirmed. Here is a greatly shortened list of ordinary words (restricted to modern English, but omitting simple and complex tensed participles and auxiliary verbs) that allow speakers to refer to changes of unbounded complexity and duration:


Vary, alter, adjust, amend, make, produce, revise, rework, improve, enhance, deteriorate, depreciate, edit, bend, straighten, weave, merge, dig, plough, cultivate, sow, twist, curl, turn, tighten, fasten, loosen, relax, ease, tense up, slacken, bind, wrap, pluck, carve, rip, tear, mend, perforate, repair, renovate, restore, damage, impair, scratch, bite, diagnose, mutate, metamorphose, transmute, sharpen, hone, modify, modulate, develop, upgrade, appear, disappear, expand, contract, constrict, constrain, shrivel, widen, lock, unlock, swell, flow, ring, differentiate, integrate, multiply, divide, add, subtract, simplify, complicate, partition, unite, amalgamate, fuse, mingle, connect, link, brake, accelerate, fast, slow, swift, rapid, hasty, protracted, lingering, brief, heat up, melt, freeze, harden, cool down, flash, shine, glow, drip, bounce, cascade, drop, pick up, fade, darken, wind, unwind, meander, peel, scrape, graze, file, scour, dislodge, is, was, will be, will have been, had, will have had, went, go, going, gone, return, lost, age, flood, swamp, overflow, precipitate, percolate, seep, tumble, plunge, dive, float, plummet, mix, separate, cut, chop, crush, grind, shred, slice, dice, saw, sew, knit, spread, coalesce, congeal, fall, climb, rise, ascend, descend, slide, slip, roll, spin, revolve, bounce, oscillate, undulate, rotate, wave, splash, conjure, quick, quickly, slowly, instantaneously, suddenly, gradually, rapidly, briskly, hurriedly, lively, hastily, inadvertently, accidentally,  carelessly, really, energetically, lethargically, snap, drink, quaff, eat, bite, consume, swallow, gulp, chew, gnaw, digest, ingest, excrete, join, resign, part, sell, buy, acquire, lose, find, search, pursue, hunt, track, explore, follow, cover, uncover, reveal, stretch, distend, depress, compress, lift, put down, fetch, take, bring, carry, win, ripen, germinate, conceive, gestate, abort, die, rot, perish, grow, decay, fold, empty, evacuate, drain, pour, fill, abandon, leave, many, more, less, fewer, steady, steadily, jerkily, smoothly, awkwardly, expertly, very, extremely, exceedingly, intermittent, discontinuous, continuous, continual, emit, push, pull, drag, slide, jump, sit, stand, run, sprint, chase, amble, walk, hop, skip, slither, crawl, swim, fly, hover, drown, submerge, immerse, break, collapse, shatter, split, interrupt, charge, retreat, assault, squash, adulterate, purify, filter, raze, crumble, erode, corrode, rust, flake, demolish, dismantle, pulverise, disintegrate, dismember, destroy, annihilate, extirpate, flatten, crimple, inflate, deflate, terminate, initiate, instigate, replace, undo, reverse, repeal, abolish, enact, quash, throw, catch, hour, minute, second, instant, moment, momentary, invent, devise, teach, learn, innovate, forget, rescind, boil, freeze, thaw, cook, liquefy, solidify, congeal, neutralise, evaporate, condense, dissolve, process, mollify, pacify, calm down, excite, enrage, inflame, protest, challenge, expel, eject, remove, overthrow, expropriate, scatter, distribute, surround, gather, hijack, assemble, attack, counter-attack, charge, repulse, defeat, strike, occupy, picket, barricade, revolt, riot, rally, march, demonstrate, mutiny, rebel, defy, resist, lead, campaign, educate, agitate, organise...


Naturally, it wouldn't be difficult to extend this list until it contained literally thousands of words (on that, see here), all capable of depicting countless changes in limitless detail (especially if it is augmented with the language of mathematics, science and HM). It is only a myth put about by Hegel and DM-theorists (unwisely echoed by Rees) that ordinary language can't adequately depict change. On the contrary, it performs this task far better than the incomprehensible and impenetrably obscure jargon Hegel invented in order to fix something that wasn't broken.


Dialecticians like Rees would have us believe that because of the alleged shortcomings of the vernacular only the most recondite and abstruse terminology (invented by Hegel, the meaning of much of which is unclear even to Hegel scholars!) is capable of telling us what we already know -- and have known for tens of thousands of years -- that things change!


Of course, as Rees himself implicitly concedes, Hegel's leaden language has to be translated into 'ordinary-ish' sorts of words for the rest of us to be able to gain even a dim appreciation of the obscure message it supposedly contains (that was the whole point of his précis of a key Hegelian 'deduction' (discussed in detail Essay Twelve Part Five -- summary here); cf., pp.49-50 of TAR) --, which apparently was that we can't understand change without such assistance!


But, if we already have ordinary terms (like those listed above) that enable us to talk about and comprehend change, what need have we of Hegel's obscure terminology?


Conversely, if, according to Rees, ordinary language is inadequate when faced with the task of translating Hegel's observations into something we can understand, then how would anyone be able to grasp what Hegel meant -- or even determine whether he meant anything at all?


On the other hand, if we are capable of comprehending Hegel's obscure ideas only when they are written in ordinary-ish sorts of terms, why do we need his convoluted jargon to reveal to us what our language is capable of expressing anyway -- when (on this supposition) it must have been adequate enough for just such a successful re-casting of Hegel's ideas (by commentators like Rees) for the rest of us to grasp?


If ordinary language is able to capture what Hegel meant, in what way is it defective? If it can't, then how might we ever understand Hegel?


Not surprisingly, if Hegel were correct, no one (including Hegel himself!) would be able to understand Hegel --, for, ex hypothesi, his words would then be un-translatable in terms that anyone could comprehend.


Conversely, once more, if Hegel's words are translatable, this can only mean that we already have the linguistic resources available to us to understand change (etc.) perfectly well. In turn, this implies that on the one hand if Hegel were correct, no one would be able to understand him, while on the other, if he were incorrect -- and we could understand him enough to be able to say even that much -- no one need bother.


[QM = Quantum Mechanics.]


It could be objected that it isn't necessary to translate Hegel into ordinary language to understand him (any more than it is necessary to understand, say, QM in like manner); hence the above comments are completely misguided.



Descent Into Confusion


In response it is worth making the following points:


1) If that were the case, how would we ever be able to tell if anyone had ever understood Hegel? It would be no use pointing to the many hundreds of books and articles devoted to his work (which books and articles themselves defy comprehension, as I hope to show in Essay Twelve), any more than it would be to point to the many books and articles there are on the Christian Doctrine of the Trinity (a dogma that originated in the same Neoplatonic morass that spawned many of Hegel's ideas) as proof that this obscure notion is comprehensible. In fact, Hegel scholars are little more than expert reproducers of jargon; that doesn't mean that any of it makes any sense.


2) The word "understand" is in ordinary language already.


3) The analogy with QM is unfortunate in view of the fact that leading physicists themselves admit that QM is incomprehensible.


"Those who are not shocked when they first come across quantum theory can't possibly have understood it." Niels Bohr


"If you are not completely confused by quantum mechanics, you do not understand it." John Wheeler


"There was a time when the newspapers said that only twelve men understood the theory of relativity. I do not believe there ever was such a time. There might have been a time when only one man did, because he was the only guy who caught on, before he wrote his paper. But after people read the paper a lot of people understood the theory of relativity in some way or other, certainly more than twelve. On the other hand, I think I can safely say that nobody understands quantum mechanics…. I am going to tell you what nature behaves like. If you will simply admit that maybe she does behave like this, you will find her a delightful, entrancing thing. Do not keep saying to yourself, if you can possibly avoid it, 'but how can it be like that?' because you will get 'down the drain,' into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that." [Feynman (1992), p.129. Bold emphases added.]


"Quantum mechanics makes absolutely no sense." Roger Penrose


Indeed, there is no theory in science that isn't shot through with metaphor and analogy. [See also this quotation from physicist, David Peat.]


Other points will be dealt with below.


The idea that ordinary language can't cope with rapid, slow or protracted change may perhaps be summarised by the following sentence (which seems to capture something of what Rees had in mind -- those who think otherwise are encouraged to shelve their doubts for a few more paragraphs):


H1a: Ordinary language can't account for or depict change.


But, is H1a itself written in ordinary language? It certainly looks like it. If it is, it is pertinent to ask what the word "change" in H1a actually means.


If we, as ordinary speakers, do not understand this word, what precisely is it that Hegel and Rees are presuming to correct? We may only be educated if we know of what it is that we are ignorant -- that is, if we already know what change is so that we can at least say that the word "change" does not match some ideal we might have of it by so much or so little. But, ex hypothesi, we are not supposed to know this since our language is allegedly inadequate in this area. [Several obvious objections to this line of argument are considered below.]


This shows that the argument here is not solely about language, but about what it conveys to us -- in this case, what our words convey about change. Indeed, if we want to study change, we can only get a handle on it by the use of words (albeit connected with material practice, etc.), like those listed above. For example, who on earth ever learnt to use words like those listed above by reading Hegel?


Contrast H1 with the following:


H1b: Ordinary language can't account for or depict quantum phenomena.


The situation with regard to change is not at all like the comprehension of QM, where knowledge and technical expertise is essential.


"Change", as it appears in H1a (that is, if H1a is in the vernacular), can't be an example of the technical use of language, unlike the complexities hinted at in H1b. Of course, if H1a isn't in the vernacular, then the technical word "change" it contains will need to be explained in terms of the ordinary word "change", so that we might grasp what this confusing, but typographically identical technical word "change" actually means. And if that is so, the ordinary word "change" would have to feature in that new explanation, which, of course, would just take us back to where we were a few paragraphs back. If we don't understand the ordinary word "change", then we certainly can't use it to help explain its technical cousin. Without such an elucidation, if we don't know what the technical term "change" means, H1a would be incomprehensible. That is because H1a would now contain at least one word (i.e., "change") that on this view no one -- not one single human being -- yet understands. Unfortunately, this would mean that our re-education can't be initiated by means of H1a, or, indeed, by any other sentence that uses this as-yet-to-be-explained word (i.e., "change").


Of course, that would also imply that the 'dialectical' development of this word/'concept' can't begin, for as yet, all that aspiring dialecticians would have available to them would be this empty word (i.e., "change"). For all the use it is, it might as well be "slithy tove".


It could be objected here that while our use of ordinary terms helps us partially grasp the nature of change, Hegel's language/method provides the wherewithal to comprehend the concept (or the real processes it depicts when his ideas are put the 'right way up') more fully -- 'dialectically' and 'scientifically', as it were. So, it isn't true that dialecticians don't understand the technical sense of "change" (or its dialectical equivalent, or equivalents) applied to natural and/or social phenomena. 


Perhaps then Rees meant the following?


H2a: Ordinary language can't fully grasp change.


H2b: A specially created terminology/method is required to enable its comprehension.


But, once again, what does the word "change" in H2a mean? Is it being used in the same way that we use the ordinary word "change"? Or does it possess its own 'special', technical sense, which has yet to be explained? If it does mean the same as the ordinary term, then where does our common understanding of that word (and what it relates to) fall short? Why do we need a theory to explain something we already understand?


On the other hand, if our common understanding of this word (and what it relates to) is defective -- if users of this word do not understand it -- then H2a is incomprehensible as it stands, since it contains a word (i.e., "change", once again) that no one (as yet) comprehends. Until we know the extent of our ignorance (or, indeed, where this word falls short) -- or even what the subject of this query actually is --, all the technical/dialectical terminology in the world is of no use, even to dialecticians!


Alternatively, if the word "change" in H2a has its own 'special meaning', what is it? And if it does, what sort of criticism of ordinary language do H2a and H2b represent if they do not actually use the vernacular term "change", but a technical alternative? Indeed, if in H2a the word "change" has a technical sense, how can that word with its special sense be used to criticise the ordinary word "change" (or point out its limitations) if the ordinary word "change" is not itself being used?


Furthermore, if the word "change" and/or its associated terms have a special dialectical meaning, how could that meaning possibly help anyone correct the ordinary word if we still do not understand the ordinary word? And how might dialecticians explain to themselves, or even to one another, what this special 'dialectical' meaning is if all they have to begin with is the defective, ordinary word "change", a word that no one yet comprehends? This side of a clear answer to these questions, H2a is as devoid of sense as H1a ever was.


Again, in response it could be argued that H2a is not about our understanding of the meaning of a word; it merely reminds us that ordinary language can't be expected to operate outside its legitimate sphere of application (i.e., "beyond certain limits"). No one expects ordinary language to cope with complex issues found, say, in the sciences, or in philosophy, or in relation protracted and complex social change. This impugns neither common understanding nor the vernacular; it simply reminds us of their limitations.


Doubtless this is correct, but unless we are told in what way the ordinary word "change" -- as we now understand it -- falls short of whatever it is it is supposed to fall short of, a dialectical extension to our knowledge can't even begin. So, the complicated somersaults that dialecticians subsequently perform (with their words/'concepts') are irrelevant; given this view, we still do not know what the initial word/'concept' "change" means -- or if we do, we still do no know in what way it falls short of this assumed 'dialectical ideal'.


In fact, if the meaning of the word "change" is indeterminate as it now stands, dialecticians can't even begin their warm up exercises, let alone impress us with their complex gyrations. They can hardly correct our supposedly faltering grasp of the ordinary word "change" (and what it relates to) without also having to use it. And just as soon as they do that, their own sentences would be subject to the same unspecified shortcomings.


This shows that H2a is directly about our understanding of this word (and what it relates to), for if the word "change" (as it is used in H2a) does not mean what the ordinary word "change" means, then the meaning of H2a itself must be indeterminate, since the criticism it presents of the vernacular is now devoid of content. And that is because it contains at least one word whose meaning is not yet understood -- "change".


Again, it could be objected that no one is claiming that the ordinary word "change" is understood by no one at all (as the above responses would have it), only that it can't handle complex processes that occur in nature and society.


But, if our understanding of the word "change" is even slightly defective (in these areas), we certainly can't use it while pretending to correct it. We can't feign comprehension of a word for the sole purpose of revising its current (supposedly defective/limited) meaning. That is not because this would be a difficult trick to pull off, it is because it is no more of an option than, say, pretending (to oneself) to forget the meaning of a word while actually using it!


Conversely, if the word "change" has no meaning (or if it is unclear what it means, or, indeed, if we do not fully understand it or what it relates to), then, plainly, neither that word nor its meaning may be corrected by means of any sentence that also contains this 'suspect' word (as we saw in H2a). Once more, any attempt to do so must involve the use of this defective word, thus compromising any sentence in which it appears.


H2a: Ordinary language can't fully grasp change.


So, if it is true that our grasp of this word is defective (in any way at all), then those very same imperfections/limitations will be inherited by any sentence used by those who seek to correct it -- such as H2a (or its preferred 'dialectical' equivalent). Clearly, in that case, prospective revisers of the vernacular would not be able to comprehend what they themselves were trying to reform, since they would be in the same boat as the rest of us, using a word with unspecified shortcomings.


On the other hand, if such linguistic/conceptual 'reformers' understand the word "change" differently from the rest of us, then any proposed modification to ordinary language would only apply to their own special use of this novel term -- i.e., to a word that is typographically similar to the ordinary word "change" (but which is still itself of undisclosed meaning) --, and not to "change" as it is used in ordinary language.


The claim here, therefore, is that with respect to the word "change", it isn't possible for anyone even to begin to say in what way it fails to mean what it is ordinarily taken to mean (or by how much or how little it falls short of this), or even to entertain the possibility that it might or might not mean whatever it now means, without using that word in any attempt to do so, or in a way that was free from the very same unspecified uncertainties.


It could be argued that this would make the translation of foreign words into, say, English impossible. In addition, it would render dictionaries totally useless.


Neither of these objections is at all relevant. We translate foreign words into English using words we already understand, and which translated words were understood by those who use that (foreign) language before they were translated. In contrast, the above ruminations concern the use of a word in relation to which it is not possible for anyone to point out its limitations without also using this word in that very act. And, plainly, any sentence in which this word is used can't fail to inherit those unspecified limitations, making any such sentence equally defective.


On the other hand, if sentences which use "change" have a clear sense, then that word must be alright as it is, vitiating the whole exercise.


More-or-less the same comment applies to the use of a dictionary, the successful employment of which depends on its authors defining unknown terms to us in words we already understand. If, however, no one knows what "change" really means (or if it has unspecified shortcomings), then no one would know precisely what was being corrected/defined, or how to go about doing it. And that observation also applies to those who edit and compile dictionaries.


Consider an example taken from Essay Six: if someone wanted to know what "meskonator" meant, but could find no one who knew (and there was no one who knew), then, plainly, it would not appear in a dictionary. If, on the other hand, someone claimed to know what this word meant, but they also let slip that there were unspecified 'difficulties' with their comprehension of this word, but could say no more, then that word would still not appear in a dictionary. Dictionaries typically contain words that human beings use, or have used, with comprehension. [That is not to suggest that everyone comprehends every single word in a dictionary -- but if no one did, such words wouldn't be listed.]


Again, it could be objected that we correct each other regularly over the misuse of certain words. That would not be possible if the above comments were true.


Once more, this is not relevant. If and when we correct one another, at least one party to that social interaction would have to understand the corrected words aright, before they were corrected. In the above (with respect to "change", and because of this theory), this is not the case.


Some might feel that my comments rely on the word "change" having one and only one correct meaning, but this too is incorrect. Howsoever many meanings this word has in ordinary language, no one would be able to use it in any sentence seeking to correct that use if every one of its meanings was defective in some as-yet-unspecified sense. Or, less radically, if this were the case merely with respect to a restricted sub-set of its relevant ordinary connotations (i.e., those of concern to dialecticians).


Moreover, any attempt to specify what these 'shortcomings' are can't work either. Consider the following 'attempt' to revise/correct the word in question:


H3: "Change" does not mean what ordinary language would lead us to believe; it means: "development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality."


If so, then H3 should be re-written as follows:


H4: "Development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality" does not mean what ordinary language would lead us to believe; it means: "development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality."


[Any who think this argument is ridiculous are encouraged to shelve those worries for a few paragraphs. Its point will soon become clear.]


The replacement of the word "change" in H4 with what it allegedly means just creates an incomprehensible sentence (and the same would happen with respect to any of its cognates -- indeed, Hegelians/DM-theorists can replace the proposed 'dialectical meaning' of "change" offered above with whatever formula they deem fit, the result will not change (irony intended)).


[Incidentally, this argument (and those above) can be generalised to cover any and all attempts to 'correct' the vernacular.]


If it is now objected that the above example is unfair/ridiculous, then it behoves that objector to indicate in what way our ordinary material words for change (or what they relate to) fall short of whatever they are supposed to fall short of -- without actually using the word "change" (or any of its synonyms) anywhere in that attempt.


Short of doing that, that objector's own use of this word (or one of its cognates) to express his/her objection (howsoever mild or nuanced, or 'dialectically-motivated' it is) will be subject to the very same unspecified shortcomings, and the objection itself would fail for lack of determinate content.


In that case, however, such an objector would find him/herself in a worse predicament than the rest of us (allegedly are). That is because he/she will now be unclear, not just about our ordinary words for change, but about the application of his/her own non-standard, jargonised replacement for them, because he/she will necessarily be unclear about what they were supposed to be replacing/correcting!


That was the point of the ridiculous example recorded in H4.


Now, it could be objected that this particular manoeuvre confuses use with mention; in H3 the word "change" is not being used, merely mentioned, so its replacement with "Development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality" (which is what that word is used to mean) is illegitimate.


Fair enough; in that case consider then the following:


H3a: Change does not mean what ordinary language would lead us to believe; it means: development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality.


If so, then H3a should be re-written as follows:


H4a: Development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality does not mean what ordinary language would lead us to believe; it means: development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality.


Once more, if the word "change" (now used, not mentioned) in H3a actually means something else (or, the processes in reality it supposedly depicts are not as we ordinarily take them to be), implying that we are all currently mistaken about its real meaning, then H3a must be meaningless, too -- or, at best, it must be of indeterminate sense.


In that case, the only way that H3a could be made comprehensible would be to replace the meaningless term it contains (i.e., "change") with words that H3a tells us constitute its 'real meaning' -- as illustrated in H4a.


The result is, if anything, worse.


It could be argued that the above would mean we would not be able to correct inadequacies in the use of any word whatsoever. For example, someone might choose to say that the war in Iraq was "unfortunate". If the above were correct, no one would be able to point out that this word is wholly unsuited in such a context.


Again, this is an irrelevant objection. The word "unfortunate" in the above counter-example is not being criticised because it is inadequate in all its applications, only that it is the wrong word to use here. In this case, no one would be seeking to correct or revise the meaning of "unfortunate", nor suggest that it was universally inadequate. Indeed, it is easy to see this word is inappropriate here because of what it already means.


This is not how things are with "change". Indeed, if DM-theorists are right, that word has unspecified universal inadequacies, which 'shortcomings' must of necessity also feature in the very act of pointing this alleged fact out -- nullifying that criticism.


It could be objected that this is not in fact the case with the use of "unfortunate"; someone could complain about the use of this word along the following lines:


H5: "Unfortunate" is totally inadequate to capture the magnitude of the unmitigated disaster in Iraq.


Once more, the use of H5 would only work in this context if the above objector was appealing to the current meaning of this word, not seeking to alter or revise it, as was the case with H3 and "change".


Again, it could be argued that the type of 'analysis' paraded in H3 and H4 could be applied to any word with equally ridiculous results. Consider, for example, the following:


H6: "Recidivist" means "a second offender; a habitual criminal; often subject to extended terms of imprisonment under habitual offender statutes."


H7: "A second offender; a habitual criminal; often subject to extended terms of imprisonment under habitual offender statutes" means "a second offender; a habitual criminal; often subject to extended terms of imprisonment under habitual offender statutes."


Transforming H6 into H7 shows how misguided the above comments are; the definition of any word can be reduced to absurdity if that definition is substituted for the word in question, as was attempted in H4.


Or so this objection might go.


However, the difference here is that H6 does not seek to re-define the given word, or point out its 'real' meaning (the latter of which is supposed to be different from its accepted sense), as was the case with H3.


On the other hand, had H6 been the following the above objection might have had a point:


H8: "Recidivist" does not mean what we ordinarily take it to mean (i.e., "a second offender; a habitual criminal; often subject to extended terms of imprisonment under habitual offender statutes...."), it means "A, B and C".


Where "A, B and C" stands for the preferred replacement, or 'real meaning' of the defined term. In that case, we could legitimately conclude:


H9: "A, B and C" does not mean what we ordinarily take it to mean, it means "A, B and C".


In this case, the only way that H8 could be made comprehensible would be to replace the meaningless term it contains (i.e., "recidivist") with words that H8 tells us constitute its 'real meaning' -- as illustrated in H9. In so far as H8 seeks to re-educate us about a word we do not yet understand, it collapses into absurdity in H9.


Recall, given this analogy, it isn't the case that only one individual failed to comprehend "recidivist" (just as it wasn't the case earlier that only one individual failed to comprehend "change"). If this analogy is to work, no one on the planet would have to understand this word.


[Naturally, H9 is absurd. But that is because no one in their left or right mind would try to tell us that the rest of us do not understand a certain word, and that only they do.]


It could now be objected that this would undermine the use of stipulative definitions, or re-definitions of certain words -- that is, definitions which establish by fiat new meanings to words already in use, or newly introduced words.


Again, this worry is misplaced. Stipulative definitions do not seek to re-define the meaning of ordinary words in their entirety, merely introduce a new meaning, or extend the old. That was not the case in H3.


Once more, it could be objected that this would mean that language couldn't change, or that we wouldn't be able to understand earlier uses of typographically similar words, perhaps those from hundreds of years ago.


However, the latter half of the above worry is just a variation of the 'translation' objection fielded earlier. The reader is therefore referred back to it.


The first half of this objection is, though, slightly more complex. Unfortunately, in that it uses the word "change" to make its point, it can hardly be advanced by someone querying the universal applicability of that very word! Hence, until it is rephrased in a way that does not use this word (or any other related ordinary word for change), not much can be done with it.


Nevertheless, this account of the ordinary use of "change" (in this Essay) does not rule out the evolution of language. To see this, consider the following:


H10: The word "XXX" used to mean "YYY", but now it means "ZZZ".


But, H10 is not:


H11: The word "XXX" does not mean, and has never meant, "YYY", but now it means "ZZZ".


The account in this Essay does not deny words meant different things in the past, or will do so in the future, only that whatever they legitimately mean/meant will alter, or will have altered.


The 'dialectical theory' under review here is in fact saying something far more radical. It is telling us that a specific word, "change" (and its related terms), never in the entire history of humanity captured what dialecticians would now like to tell us is the 'real meaning' of "change". The 'dialectical' view is in fact a more extreme version of H11.


In response, it could be objected that despite this, the approach adopted in this Essay still can't account for linguistic change. "Indeed," an objector might continue, "why can't we inflict some of Ms Lichtenstein's own medicine upon the above sentences?" Perhaps in the following manner?


H12: The word "XXX" used to mean "YYY", but now it means "ZZZ".


H12b: The word "XXX" used to mean YYY, but now it means ZZZ.


Perhaps along these lines:


H12c: The word "ZZZ" used to mean "YYY", but now it means "ZZZ".


H12d: The word "ZZZ" used to mean YYY, but now it means ZZZ.


Which neatly mirrors H3 and H4:


H3: "Change" does not mean what ordinary language would lead us to believe; it means: "development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality."


H4: "Development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality" does not mean what ordinary language would lead us to believe; it means: "development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality."


Initially, in response to this latest criticism, it is worth pointing out that the more radical versions of H3 and H4 (i.e., H3a and H4a) were in the end the preferred alternatives, and they were chosen in order to neutralise the use/mention objection:


H3a: Change does not mean what ordinary language would lead us to believe; it means: development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality.


H4a: Development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality does not mean what ordinary language would lead us to believe; it means: development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality.


This would mean that H12a is now irrelevant.


If, however, we modify H10 accordingly, my response might become clearer:


H13: "XXX" used to mean YYY, but now it means ZZZ.


Perhaps an actual example will help:


H14: "Lunatic" used to mean someone affected by the moon [Skeat (2005), p.351)], now it means they are insane.


Hence, on the view advanced here, the old word still means what it used to mean; all we have now is a modern, typographically identical token of it with a new meaning. But, no one is questioning that earlier meaning. No one is suggesting that several centuries ago people did not mean by "lunatic" someone affected by the moon.


Now, if would-be critics want to revise a word in common use, all well and good; but this can't affect the ordinary meaning that that word currently has. Such a revision would merely relate to this new and typographically identical word, with its new and/or extended meaning. However, and on the contrary, no attempt could be made to undermine or question the use that a word already has without that revision itself descending into incoherence, as we have just seen.


It could be objected once more that all this misses the point; a philosophical understanding of change (as it features in the natural and social sciences, on the lines advocated by dialecticians) does not seek to replace ordinary language, which is quite adequate in its own sphere of application. It is aimed at augmenting our comprehension of natural and social development for political (or other) purposes. The vernacular is inadequate only when we try to use it to account for complex processes in the natural or social world; this is where Hegel's ideas can be of genuine assistance (i.e., when the "rational core" of his system has been separated from its "mystical shell", of course).


Or so this latest response might go.


However, as we will see in other Essays posted at this site, not only is the above incorrect in general (in that it is the conceptual wealth expressed in ordinary language which enables the depiction and comprehension of both simple and complex changes in nature and society), it is misguided in particular. That is because we are still in the dark as to what it is that dialecticians are proposing, or what they are presuming to add to our understanding of a word neither they nor anyone one else yet fully comprehends --, that is, if their 'theory' is correct. Once more, if our (collective) understanding of this word (or any other) is defective, then any use of that word in an attempt to correct such unspecified defects (or even vaguely hint at them) must self-destruct, too.


Of course, it could be argued that there is no such thing as a "collective understanding" of this or any other word. That complaint will be tackled head-on in Essay Thirteen Part Three. Suffice it to say here that if this were the case, then dialecticians themselves would be even more in the dark as to what they were effecting to revise/criticise, since they could not now appeal to a standardised set of meanings, commonly held, that they are seeking to 'correct'/extend.


After all, Hegel himself had to appeal to the limitations of "the understanding" to motivate his own (defective) 'logic'. If there is no such thing as "the understanding", then his theory can't loop the first Hermetic loop. As should seem obvious: in order to criticise 'commonsense' and/or common understanding, it isn't a good idea to tell us there is no such thing!


Quite apart from that, we would surely be unwise to listen to dialecticians trying to extend our knowledge of 'change', nor yet to those regaling us with the 'superiority' of their 'theory', if  they have yet to succeed in explaining clearly to the rest of us a single one of their theses (which, as I have shown in these Essays, they have failed to do) -- or, indeed, until they have repaired the gaping holes I have punched in Hegel's 'logic' elsewhere at this site (for example, here).


Howsoever limited ordinary language is -- or isn't --, when it is used properly in HM it makes eminent good sense. DM (with its obscure Hegelian jargon and radically defective 'logic') has yet to come with a couple of parsecs of this minimal pre-condition (and that comment applies to 'systematic' and 'academic' dialectics, too --, perhaps even more so).



In addition, but far worse, dialecticians can't account for change themselves (on this, see Essays Five, Six, Seven, and Eight Parts One, Two and Three).


Hence, their assistance is not needed.


Quite the reverse in fact; if accepted, their 'theory' would set back the scientific study of nature and society by at least half a millennium, given its reliance on a mystical and enchanted view of natural and social development. We might as well ask Astronomers, for example, to take account of Astrology in their endeavour to explain the universe.


[Small wonder then that Dialectical Marxism is to success what George W Bush is to intellectual achievement.]


In that case, as far as competing (scientific or philosophical) theories aimed at helping us understand the world and how to change it are concerned, DM/'Materialist Dialectics' does not even make the bottom of the reserve list of viable candidates.


HM, minus the Hegelian gobbledygook, on the other hand, is more than adequate.


And that is why we can be confident that not even Hegel understood this part of his own 'theory'. That isn't because it is a difficult theory, nor yet because it employs specialised terminology (which is completely incomprehensible to the untrained reader). Nor is it even because Hegel did not use H3 (or anything like it). It is because of the fact that as soon as any attempt is made (by anyone -- even a person of "genius") to correct ordinary language -- or, just as soon as the vernacular is dismissed as defective or even slightly flawed, and its terms are held to be deficient when applied beyond "certain limits", requiring that they be "surpassed", by-passed or revised -- all meaning evaporates. [A similar, but more detailed argument about what Hegel did or did not understand about his own theory can be found here.]


To repeat, it isn't possible to pretend to understand an ordinary word like "change" and then claim that it is defective (whether or not "speculative reason" initiates/demands this). Either the objector's understanding of this word is defective -- and the ordinary term is alright as it is --, or the ordinary word is defective and no one (including that objector) actually understands it.


In the latter case, there would be nothing comprehensible left to modify; in the former, no one need bother.



Ordinary Language Is Not A Theory


It could still be objected to this that since ordinary language is inadequate in most scientific and technical contexts (let alone in Metaphysics), it needs reforming, supplementing or augmenting in some way.


And yet, science has managed to make significant progress over the last four hundred years without having to reform the vernacular, even if scientists have had to develop specialised and technical languages of their own. The problem (if such it may be called) only occurs when attempts are made to translate scientific concepts into ordinary language. Since there is no scientific need to do this (although there may be several powerful ideological and economic reasons why some might want to do it, as will be argued in Essay Thirteen Part Two), the alleged clash with ordinary language is completely fictional.


Of course, no one is suggesting that ordinary language can be used in highly complex theoretical areas of study (although, even the most technical scientific and mathematical papers have to use some ordinary words at some point), but that is no more a limitation on the vernacular than it is a defect of Das Kapital that it can't predict winning lottery numbers.


Metaphysics originally arose out of the belied that there are philosophical 'problems' concerning aspects of reality and human existence, which, it seems, only expert theorists are capable of solving (or even of understanding).


Keith Thomas highlighted a similar tactic among 16th century magicians:


"It would be tempting to explain the long survival of magical practices by pointing out that they helped provide many professional wizards with a respectable livelihood. The example of the legal profession is a reminder that it is always possible for a substantial social group to support itself by proffering solutions to problems which they themselves have helped to manufacture. The cunning men and wise women had an undoubted interest in upholding the prestige of magical diagnosis and may by their mere existence have helped to prolong a mode of thinking which was already obsolescent." [Thomas (1972), p.295.]


Even though Thomas finally rejects this as an adequate explanation of this phenomenon, he notes that the 'special' skill these magicians arrogated for themselves (that is, being able to solve 'problems' they had in fact invented) provided them with a level of prestige and social standing they would not otherwise have enjoyed.


Of course, with respect to superstition and magic, Marxists must take into account the alienated lives and beliefs of susceptible audiences -- which would have included, of course, many ordinary people.


Clearly, this is not true of Metaphysics, which was (and still is) practiced almost exclusively by rather more 'select' and exclusive social groups. Hence, Thomas's reason for rejecting his own tentative explanation of the persistence of magical beliefs (i.e., that magicians provided a service which ordinary people actively sought) does not apply to Metaphysics. Moreover, his account explains neither the overwhelming influence Metaphysics has had on almost every aspect of Western thought for 2500 years (it is indeed a "ruling idea"), nor the longevity of Traditional Philosophy (with precious little to show for it after all that time and effort --, so this pointless activity can't be justified on economic grounds). Of course, Thomas's comments were not designed to do this.


However, one reason usually given for the prevalence/ubiquity of metaphysical beliefs is that everyone (including ordinary folk) at some time in their lives has philosophical thoughts of some sort, or asks metaphysical questions. This is supposed to show that philosophical problems enjoy universal appeal and legitimacy. Hence, the argument could go: if everyone thinks metaphysically (at least at some level), its existence can't be the result of its invention by an elite group of thinkers.


Nevertheless, it is worth noting the following four points in response to this:


(1) It is important to distinguish the confused musings -- on such things as the nature of space, time, 'God', 'good' and 'evil' and the purpose of human existence -- that most individuals indulge in from time to time in their lives from the systematic study of metaphysical questions by those who have the necessary leisure time and training to do so (i.e., professional philosophers, theorists, and rich or sponsored 'amateurs').


(2) It isn't being suggested here that metaphysical beliefs were invented by the ruling-class (or their hangers-on), only that the systematic study of Metaphysics is the sole preserve of those who have (knowingly or not) consistently promoted a theoretical view of reality which has almost invariably been conducive to the interests of the rich and powerful. [On this, see Essay Twelve; a summary of which can be found here.]


(3) The fact that ordinary people indulge in amateurish metaphysical musings from time to time no more makes Metaphysics a legitimate pursuit than it would do the same for religious or theological discourse. Ordinary people are not somehow turned into theologians if they wonder whether there is a 'god'. However, if and when they do so ponder, that still fails to legitimate Theology. The same applies to Metaphysics.


(4) The confusion endemic in both groups (that is, in professional, leisured metaphysicians and in ordinary/lay amateurs) derives from one source: the misconstrual of socially-sanctioned forms of communication as if they stood for the real relations between things, or, indeed, those things themselves. [This analysis is substantiated in Essay Twelve Part One.]


However, and independently of this, only 'professional metaphysicians' have an ideological motive for projecting these social norms back onto the world as fetishised reflections of social reality in a systematic fashion. This they do because: (1) Their theses mirror the world as they see it (i.e., as governed by hidden forces, concepts and/or "essences"), and (2) It assists in the legitimation of class division, inequality, oppression and exploitation -- historically, it is quite easy to show that this has indeed been the case with the majority of metaphysical systems --, and (3) These days, it is good for the CV. [All these are expanded on greatly in Essay Twelve.]


Lay metaphysicians, on the other hand, have no class-based motivation to fetishise their own language in such a manner -- not the least because to do so would clash with the way they already employ the vernacular in their everyday interface with material reality and with one another. [This is not to suggest that other forms of fetishisation can't distort their ideas; far from it!]


In fact, if ordinary folk were to talk like metaphysicians in their everyday life, they would probably find themselves re-classified as psychotic, or delusional.


Which reminds one of the old joke:


A: "The great questions of philosophy interest me: Who am I? What am I? Where am I?"


B: "Sounds more like amnesia to me!"




C: "Is this the Philosophy Department?"


D: "If we knew the answer to that, we wouldn't be here."


To be sure, it is the insular existence of professional metaphysicians that protects them from themselves (as it were). It is only when they have to engage in everyday practical activities alongside the rest of us that their metaphysical theories look decidedly weird, if not completely ridiculous --, even to them (as David Hume acknowledged):


"I dine, I play a game of backgammon, I converse, and am merry with my friends; and when after three or four hours' amusement, I would return to these speculations, they appear so cold, and strained, and ridiculous, that I cannot find in my heart to enter into them any farther.


"Here then I find myself absolutely and necessarily determin'd to live, and talk, and act like other people in the common affairs of life. But notwithstanding that my natural propensity, and the course of my animal spirits and passions reduce me to this indolent belief in the general maxims of the world, I still feel such remains of my former disposition, that I am ready to throw all my books and papers into the fire, and resolve never more to renounce the pleasures of life for the sake of reasoning and philosophy." [Hume Treatise Book I Section VII.]


Clearly, that is because it is in daily life where the alleged clash between philosophical musings and 'commonsense' actually occurs and really matters. When metaphysicians have to behave like 'ordinary folk' in the real world, their metaphysical fancies lose all credibility.


Naturally, this means that in ordinary surroundings this 'Emperor' looks naked even to 'true believers'.


[On this, see Cowley (1991).]


Since ordinary language has developed in an unplanned way over tens of thousands of years it can be imprecise and ambiguous, and it is manifestly 'non-scientific' (i.e., non-technical). Not only that, its vocabulary is suffused with vagueness and its surface grammar encourages users to form, or to think about, potentially misleading sentences (but these are such only to the unwary, the unwise or the obtuse), forgetting, albeit temporarily, that we/they do not use words this way in ordinary life.


However, this does not mean that ordinary language is defective in any way. Far from it, ordinary language was founded on conventions and material practices our species has developed over tens of thousands of years, during which time it functioned perfectly well as a means of communication. The vagaries of ordinary language enable its users to communicate effectively over a much wider area than would otherwise be the case if it were overly precise.


When required, however, precision is relatively easy to achieve; indeed, at the risk of extreme pedantry, almost any degree of accuracy is attainable. [It is worth recalling here that much of mathematical vocabulary is in fact part of ordinary language.] In addition, the potentially misleading grammatical forms which the vernacular contains only succeed in misleading users when they attempt to reflect on language itself (which we/they are ill-equipped to do -- why this is so will be explored in Essay Twelve, and Essay Thirteen Part Three). This doesn't happen when users apply it in everyday life; in the normal course of events such potentially misleading grammatical forms do not interfere with communication, nor do they puzzle speakers, since such puzzles do not arise in such circumstances.


These considerations not only account for the vibrancy of ordinary language, they shed light on the source of many of the 'paradoxes' and 'philosophical problems' created by its misuse. While ordinary language couldn't function without these features -- vagueness, ambiguity, metaphor, synonymy, antonymy, etc. --, they can foster misunderstanding if they are not handled with due sensitivity, or, dare I say it, with no little common sense. Nevertheless, these aspects also lend to language sufficient space to enable a seemingly limitless expansion of its expressive and communicative powers -- in the Arts, for example.


However, the downside of this is that it is all too easy to misconstrue ordinary language when users try to reflect on it theoretically -- i.e., when language "goes on holiday" (to paraphrase Wittgenstein). This occurs whenever the vernacular is employed in areas that are either far removed, or are insulated from everyday material practice/life, or when its representational forms are confused with its communicational forms, and vice versa. As will be argued at length in Essay Twelve Part One, 'philosophical problems' arise whenever grammatical rules are misconstrued as empirical propositions, which are then taken to represent substantive features of the world (DM-theorists, for example, do this in connection with the LOI, the LOC -- when they confuse these rules with super-empirical theses --, and with the use of the word "not", confusing it with a destructive/preservative process in nature and society). When language is viewed primarily as representational medium, its grammar fetishised, LIE is the inevitable outcome.


[LIE = Linguistic Idealism; LOI = Law of identity'; LOC = Law of Non-contradiction.]


[The development and substantiation of these allegations forms one of the main themes of Essay Twelve (summary here). Other comments connected with this will be published in other Essays at a later date. (For example, whether language is a means of representation is discussed in Essay Thirteen Part Three.) There it will be shown that representational theories of language (among other things) were invented by traditional theorists keen to argue that discourse (and particularly written language) is really a secret code -- which they alone were capable of understanding -- that maps-out or mirrors hidden, underlying and "essential" aspects of reality (conveniently inaccessible to the senses). This then allowed them to claim that this code (expressed in impenetrable jargon -- kept this way to exclude the 'unwashed') enabled them to re-present to themselves 'God's' thoughts, thereby providing for their sponsors in the various ruling elites that history has inflicted on humanity an epistemological and ontological rationalisation of the status quo (which 'justification' varied as each Mode of Production and form of the State required).


In order to do this, traditional theorists had to undermine and belittle the communitarian and communicational aspects of language (the latter two of which had been the original form, created by those involved in collective labour), and thus the vernacular. That explains why practically every single traditional Philosopher (and now every DM-theorist almost without exception) denigrates, to a greater or lesser extent, the ordinary language of the working class.]


Now, as far as the conflict between the vernacular and philosophical or metaphysical language is concerned, there can be no incongruity -- that is, no more than there is a genuine clash between, say, the nonsense rhymes of Edward Lear and ordinary discourse. This is, of course, because metaphysical language is non-sensical.


Admittedly, ordinary language has changed in countless ways over the course of history. We are now capable of forming sentences and expressing thoughts that our ancestors couldn't. Doubtless this process will continue. But, ordinary language remains the highest and final court of appeal for human beings in their efforts to understand anything.15 That is because the historically-conditioned conventions within which we learn to apply the vernacular express and delimit our capacity to comprehend anything whatsoever.


This claim might appear somewhat dogmatic, but it isn't. It is based on the simple observation that words like "understand", "comprehend", "know" and "grasp" are themselves ordinary language terms, and they gain whatever meaning they have from the conventions and practices governing their use at present. They do not receive it from an imaginary or ideal usage, nor do they derive it from abstractions that are accessible only to philosophers and scientists -- or even Marxist intellectuals. Words like those mentioned above can't themselves be challenged without that attempt itself collapsing into incoherence -- as was illustrated earlier in connection with "change", and will be illustrated again elsewhere at this site with other similar terms.


The bottom line is that while scientists may quite legitimately invent new terminology to suite their needs, scientific language itself can't confront (or reform) ordinary language without undermining itself.


Moreover, ordinary language isn't a theory; it neither encapsulates a "folk ontology" nor a "folk metaphysics". It isn't identical with common sense, but it isn't unconnected with it.


These seemingly dogmatic assertions will now be defended.


Ordinary Language Does Not 'Assume' Things are Static


The vernacular is not a theory since every empirical proposition in ordinary language is pairable with its negation, and so can be contradicted. No theory can have this happen to all its propositions -- or have them so semantically accommodating. [This particular argument will be defended and then illustrated with examples in Essay Thirteen Part Two, when it is published.]


This means that Rees was wrong when he asserted that:


"Ordinary language assumes that things and ideas are stable, that they are either 'this' or 'that'…." [TAR, p.45.]


Ordinary language can't assume anything -- plainly, it is human beings who "assume" things. Clearly, they do this by means of language. Unless language had the capacity to allow for the possible truth or falsehood of such assumptions, and/or their negations, then no "assuming" could begin. That is, of course, because assumptions can be wrong as well as right.


Moreover, the rich vocabulary of ordinary language allows the "assumption" to be made that objects can and do change -- and in complex ways, too. Indeed, ordinary language enables its users to speak of countless different types of change in seemingly limitless detail. A long (but greatly shortened) list of some of the words in the vernacular that enable this was given earlier. Hence, and despite what Rees says, the sophisticated nature of ordinary language permits the formation of the following sentences that readily depict change:


H78: This protest is increasing in size as we watch.


H79: That case is becoming too heavy for the children to carry.


H80: This venue is now too small for our meetings.


H81: This spider's web is beginning to disintegrate.


H82: This train is being re-painted.


H83: That light over there is defective; it keeps flickering.


H84: This is how to lose members rapidly: spout dialectics at them.


H85: This dispute is no longer about working conditions.


H86: This entire continent is moving closer to Asia.


H87: That is how to break an egg.


H88: This is how to change workers' minds.


H89: This π-bond breaks in less than 5 nanoseconds if the molecule is rapidly heated.


H90: In an instant the pickets had re-grouped ready for the next police charge.


Many of the above sentences are somewhat stilted because they have been deliberately tailored to use the words "this" and "that" (i.e., the form of words that Rees employed to caricature the vernacular) in order to show that "things and ideas" are not "assumed" to be stable -- contrary to Rees's assertion. However, this list at least demonstrates that even using Rees's unlikely and highly restrictive phraseology, ordinary language is capable of expressing material changes (especially if it augmented with scientific and/or mathematical vocabulary) that Hegel's tortuous prose can't emulate -- that is, not without re-employing terms taken from ordinary language to assist it do just that.19


Even given this highly constrained form of language, the above list of sentences can be extended indefinitely. Of course, if the full range of devices available to ordinary speakers is called upon (H90 being just one example), then it would be possible to form an indefinitely large set of sentences of far greater sophistication (than anything dreamt of in Hegel's work) depicting changes of every imaginable type.


This shows that ordinary language is capable of depicting (and thus permitting the explanation of) change in the real world far better than any philosophical language yet devised.


Now, this is not something that a sophisticated user of English (like John Rees) should have to have pointed out to him -- even though my having to do this is a sad comment on the intellectual decay that dialectical thought induces in those held in its thrall.20



Ordinary Language And 'Commonsense'


'Commonsense' is often confused with ordinary language. Unfortunately, the term "commonsense" is rather vague.22 Bertrand Russell once claimed it encapsulated the "metaphysics of cavemen", but even he would have been hard-pressed to say what it was, let alone how he knew so much about it.23


If the word has any clear meaning, it appears to denote an inchoate (but changing) set of beliefs and opinions that most (all?) human beings are supposed to possess (whether they are aware of it or not). But, if this were so, it would imply that these beliefs must have been communicated telepathically from individual to individual, one generation, or one community, to the next, across the planet and down through the ages. How else are we to account for the alleged universality of 'commonsense'? And yet, at no point in life has a single human being ever been tutored in 'commonsense'; no one runs through its canonical ideas at school, at their parents' knees or even behind the bike sheds at break with their friends. Nobody studies 'commonsense' at college, nor do they take tests in it or receive a diploma confirming their competence.


Of course, if this is so, we should perhaps stop calling it "common".


One thing is clear therefore about 'commonsense': it can't be all that common or we should all be experts at identifying its core ideas and saying where they have come from; but nobody seems able to do this.23a


Moreover, if 'commonsense' is encapsulated in ordinary language, it is remarkably well hidden, for, as noted above, no one seems able to list its main precepts. In that case, no society in history could possibly have agreed over what should be included in 'commonsense', and what should be left out. Hence, the idea that 'commonsense' today is the same as it was ten thousand years ago (or even last week), and identical across culture (or the opposite), if correct, must be one of the best kept secrets in history. If no one ever talks about it and no one knows what it includes, it is no surprise it is a complete mystery how it is propagated within  or between populations, or how one generation passes 'commonsense' on to the next.


Is it in the water? Is it genetically encoded?


But, if that were the case, we would all possess the same set of 'commonsense' beliefs; and yet we do not -- apparently.


Or, rather, it seems that no one is able to say whether or not we share the same set, since no one is capable of listing the 'commonsense' beliefs held by everyone -- or indeed anyone. Still less is it clear how 'commonsense' may be distinguished from merely widely held beliefs.


For example, is it a 'commonsense' belief that dogs have four legs, or a widely held belief? What about the belief that grass is green or that the sky is often above our heads? And how could anyone confirm the existence of these beliefs/attitudes without biasing the result?24


Typically, the sorts of beliefs some associate with 'commonsense' include ideological, metaphysical, religious, 'folk', mystical and superstitious notions, and the like. But, this list of likely candidates varies according to who is telling the tale.


In that case, one is tempted to say that the idea that there is such a thing as 'commonsense' must be a "scientistic folk belief" itself, since it isn't based on any clear evidence --, at least none that hasn't already been 'tainted' by the sorts of ideas many would include in 'commonsense', itself.24b


However, since nobody appears to know which beliefs are on the favoured list, and which aren't, the word itself is something of a misnomer. If 'commonsense' had ever lived up to its billing, we would all be much clearer about its content; it would, after all, be eminently common.


Even so, almost invariably the relationship between 'commonsense' (whatever it turns out to be) and ordinary language is assumed to be reasonably straightforward; indeed, the latter is supposed to contain or express the former. So clear is this link imagined to be, and so universally is this belief itself held, that no one (literally no one (!) -- as far as I have been able to ascertain) questions it. Even Wittgenstein made this mistake!


But, while no competent language-user is in much doubt about his or her own language, nobody seems to be able to say what 'commonsense' is. Even though not all of us have a mastery of speech equal to that of its most accomplished practitioners, no one (novice or adept alike) seems to know what 'commonsense' is. This is quite remarkable if the two are as intimately connected as we have been led to believe.


The case for identifying the two is no less questionable. As noted above, ordinary language is supposed to contain or to express 'commonsense' ideas. However, when pressed to supply details those wishing to lump the two together are often reduced to making a few vague references to things like sunrise, solid objects, colour vision, the possession of two hands, an imprecise collection of psychological or 'mental' dispositions and/or 'processes', an assortment of perceptual conundrums, a handful of proverbs and 'wise' sayings, a few vague moral, political and ideological inanities, as well as the odd superstition or two. [On this see, here.]


In fact, the haste to identify the two is not just unwise, it is ideologically-motivated (as will be demonstrated in Essay Twelve, summary here).


On the other hand, had more than a moment's thought been devoted to this pseudo-identity, its absurdity would have been immediately obvious: if ordinary language were identical with 'commonsense', it would be impossible to gainsay any of its alleged deliverances in the vernacular.


The plain fact is we can.


And easily.


Not only are we able to deny that tables are solid, that the sky is blue, that the earth is flat, round or cucumber-shaped, that NN believes (for most p) that p, that sticks do not bend in water, that Queen Elizabeth II is sovereign in Parliament, that water falls off a duck's back, that Rome was built in a day, that an apple a day will tend to minimise visits from the doctor, that φ-ing is wrong (for any conventional φ), that Capitalism is fair, that human beings are 'naturally' selfish, we can do all of these in every known language that possesses the relevant vocabulary. That, of course, is the whole point of the negative particle.25 If ordinary language were identical with 'commonsense', none of this would be possible.


To be sure, many of the beliefs entertained by our ancestors we no longer accept, but as far as the connection between 'commonsense' and the vernacular is concerned, sentences drawn from it gain their sense because of the conventions set by social practice. Although we can express our beliefs in ordinary language, the sense of a sentence does not arise from any of the beliefs we possess, nor from any we have inherited from the past. That is because beliefs themselves are dependent on language and thus on our capacity to articulate them accordingly. And we can be sure of that fact if language is social, otherwise beliefs could not be communicated, let alone formed.26


Just as social practices themselves can't be altered individualistically (any more than the value of money can), the conventions underpinning language can't be revised at will by any one individual or group (except perhaps at the margins).27 The conventions implicit in our practices at any point in time of course change and grow in accord with social development. They are, at basis, an expression of our "species being" and are intimately connected with our relationship with the world, with one another and with previous generations.28


Hence, just as it would it be impossible for an individual to bury, hide or incorporate a set of beliefs in ordinary language in order to form the backbone of 'commonsense', it would be equally impossible for a group to do so.


In that case, it really isn't up to a revolutionary, or party of revolutionaries (or anyone else, for that matter), to disparage such a vitally important expression of our collective (but changing) nature as human beings. Whether they do so or not is plainly up to them; the 'penalty' (if such it may be called) for even attempting to do so is not always immediately apparent. However, anyone who does try to undermine the vernacular will soon find their ideas descending into incoherence (as was demonstrated above with the respect to the word "change", and will be again in other Essays posted at this site in relation to other words). In that sense, attacking the vernacular is not a viable option, since such a strategy would automatically self-destruct.


This means this is not an ethical issue -- but, it is a logical and political one. The latter half of that assertion will now be substantiated....


[The rest of this can be found in Essay Twelve when it is published.]



Additional Notes


15. Since the application of ordinary language underpins our understanding of anything whatsoever, it is, as noted above, the court of last appeal, which, although not democratic in one sense (we do not determine what something means by counting heads), it is in another: language is materially-grounded in the practice of the vast majority -- i.e., those who, through their labour, interface with material reality and with one another every day. This means that certain features of ordinary language can't be 'reformed' without ipso facto undermining our ability to comprehend anything at all. And that helps explain why traditional/metaphysical attempts to do so rapidly fall apart, and why they are fundamentally undemocratic (in the second sense, in that they have been invented by a tiny minority, and are not developed out of collective labour and communal life), as well as how, in Marxism, this endeavour is in fact connected with substitutionist thinking. [Cf., Wittgenstein (1974). More on this in Essay Nine Parts One and Two.]


Moreover, many key scientific concepts have themselves been derived from ordinary language by analogical and metaphorical extension (etc.), as noted above. Indeed, even though it is possible to comprehend a scientific theory without having to translate it into the vernacular, the former can't succeed in undermining the latter without fatally compromising that very attempt. [This slide into incoherence was illustrated above, and in more detail in Essay Three Part Two.]



19. Anyone who doubts this is welcome to try to express in 'Hegel-speak' what sentences H78-H90 manage to say quite easily without such 'assistance'.


20. Max Eastman's comment springs to mind here:


"Hegelism (sic) is like a mental disease -- you cannot know what it is until you get it, and then you can't know because you've got it." [Eastman (1926), p.22.]


These words were, of course, written when Eastman still regarded himself as a Leninist.


[I first encountered Eastman's work after about four-and-a-half years into this project. Some of the ideas expressed in the Essays posted at this site had clearly been anticipated in his writings, but only some.]



22. It needs underlining here that these comments aren't aimed at the ordinary use of the term "common sense", just its philosophical/'dialectical' deployment, highlighted in the text, and at this site, as "commonsense".


The original meaning of the term "common sense" (i.e., as it occurs in Aristotle's work) isn't relevant to the discussion here since the philosophical use of this term parted company with Aristotle's meaning long ago.


Be this as it may, the majority of commentators seem to think this word relates to a body of commonly held (often reactionary) beliefs, values or opinions, However, and by way of contrast, in ordinary use it appears in sentences like the following:


C1: Use your common sense! Don't put your hand in the lion's cage!


C2: Have you no common sense? What on earth made you try to debate with a Nazi?


C3: It's just common sense. No one in their right mind would rummage around in a waste disposal unit while it is switched on.


C4: As the hurricane approaches, the public is advised to listen to the advice given by the emergency services and to use their common sense. Don't go for a walk along the promenade, for example!


Admittedly, the above depend to some extent on certain beliefs held about ourselves and the world around us, but the difficulty computer programmers have in reproducing human behaviour shows that this is not just a matter of holding certain beliefs. Indeed, human beings can be well aware of certain facts, and still act in a way that will prompt the above comments. I am sure we have all met such individuals.


To be sure, politicians will use the word "commonsense", or the phrase "common sense", to defend all manner of right-wing, reactionary and populist ideas, but then they will say anything. [The ideological use of this phrase will be examined below.]


23. As Michael Dummett points out [in Dummett (1979), pp.390-93] there is no such thing as "the commonsense" view of the world.


23aIf 'commonsense' beliefs were culturally 'relative', each generation would possess a different, or slightly different, set of 'commonsense' beliefs -- even if there was some overlap in places. In that case, of course, there would be no such thing as 'commonsense'. It would still be a mystery, however, how such beliefs could be passed on from one generation to the next, or between individuals, if no one knows what these beliefs are.


It could be argued that this might occur at a non-conscious level, as attitudes and 'values' are passed down the generations, or as they are randomly acquired during a lifetime (perhaps as a result of the mass media or the education system, etc.).


Now, even if that were so (but the idea will be questioned in Essay Three Part Four), it would still be unclear exactly what was being 'passed on'. Indeed, no one -- researchers and subjects alike -- seems capable of saying what this is (over and above mentioning certain aspects of the vague list mentioned earlier). This then would be the first area of scientific research where no one knew what they were talking about!


And it is no use doing a survey; either the survey questions will bias the result, or the questions will be too vague to be of any use. [But see Note 24b, below.]


That is quite apart from the fact that if these beliefs were acquired in the random manner suggested, they wouldn't be all that common (except, perhaps, as the result of a giant fluke).


24. Again, since I do not accept the philosophical use of this term I will not try to solve this intractable problem for those who do.


24b. By that I mean that anyone attempting to show that 'commonsense' beliefs are accepted by all/most human beings would have to use evidence that was itself 'contaminated' with these allegedly 'commonsense' beliefs; for instance, that there are medium-sized objects in the world called "human beings", that there are such things as colours (so that, for example, claims that human beings believe there are colours is not itself an empty claim), just as there are edges, corners, surfaces and holes, so that the words by means of which such ideas might be expressed have a meaning, and so on. In short, if this evidence is to make sense to the rest of us (and, indeed, to anyone hoping to sell us this tale), those using it will have to take for granted many 'commonsense' ideas themselves.


25. The sophisticated use to which us humans are capable of putting the negative particle, at least in English, is explored at length in Horn (1989).


26. That controversial claim will be defended in Essay Thirteen Part Three.


27. Unless, of course, this is done to extend language. That aside, the abrogation of linguistic rules results in the production of incoherent non-sense; naturally, both of these aims could form part of the intent of an aspiring abrogater (for creative purposes, or for effect, or whatever). However, the creative extension of language undertaken by writers and poets (etc.) still has to make some sort of sense. Think of the work of James Joyce; Joyce did not just write total gibberish, or randomly bash away at his typewriter.


Again, this does not undermine the comments made in the main body of this Essay. While language does indeed develop, those responsible for helping it on its way do not do so by undermining the use of words we already have; if anything, they do so by extending language, creating novel uses for it, augmenting its vocabulary, and so on.


However, on certain aspects of the imaginative extension of language, see White (1996, 2010), and Guttenplan (2005). More on this in Essay Thirteen Part Three.


28. Spelled-out more fully, this would provide some grip for the word "material" as it is used in many of these Essays. That task will be attempted when this project is finished.


The above ideas about ordinary language and common sense are developed and defended in the following: Button, et al (1995), Cowley (1991), Cook (1979, 1980), Ebersole (1967, 1979a, 1979b), Hacker (1982a, 1982b, 1987), Hanfling (1984, 1989, 2000), Ryle (1960), Macdonald (1938) and Stebbing (1958). [It has to be said that, as far as can be ascertained, all of these authors confuse ordinary language with common sense. Or, at least, they do not distinguish between them as clearly as I have done.] See also Uschanov (2002), and his longer article posted here. Coates (1996) also seems to muddle these two up, too.


The ruling-class and their hacks have always denigrated the vernacular and the common experience of ordinary folk. It is even less edifying to see Marxists (like this commentator, if he is a Marxist!) doing the same thing.


More details on this topic will be given in Essay Twelve (summary here), but an excellent recent account can be found in the opening sections of Conner (2005).


As far as the propensity of the 'lower orders' to form 'superstitious' beliefs is concerned (a phrase this commentator does not use, but his intentions are reasonably clear), why we should pay any more attention to that phenomenon than we do to religious belief in general (when it grips ordinary folk) is unclear. But, even if it were clear, its philosophical (as opposed to its sociological, psychological or political) implications would still be in doubt. As noted above, since we can, in the vernacular, negate every single ideological, racist, and superstitious belief, these can't be identical.



Ordinary Language And Ideology


Again, this is how I put things in Essay Twelve (see also, here and here):


Admittedly, ordinary language may be used to express the most patent of falsehoods and the most regressive of ideas, but it can't itself be affected by "false consciousness" (and this is not the least because the notion of "false consciousness" is foreign to Marx; on that see here), nor can it be "ideological".


Without doubt, everyday sentences can express all manner of backward, racist, sexist and ideologically-compromised notions, but this is not the fault of the medium in which these are expressed, any more than it is the fault of, say, a computer if it is used to post racist bile on a web page. Ideologically-tainted ideas expressed in ordinary language result either from its misuse or from the employment of specialised terminology borrowed from religious dogma, sexist beliefs, reactionary ideology, racist theories and superstitious ideas. This is not to suggest that ordinary humans do not, or can't, speak in such backward ways; but these are dependent on the latter being expressed in ordinary language, but are not dependent on that language itself.


It is worth pointing out at this stage that this defence of ordinary language is not being advanced dogmatically. Every user of the vernacular knows it to be true since they know that for each and every sexist, racist and ideologically-compromised sentence expressible in ordinary language there exists its negation.


This is why socialists can say such things as: "Blacks aren't inferior"; "Human beings aren't selfish"; "Wages aren't fair", "Women aren't sex objects", "Belief in the after-life is baseless" -- and still be understood, even by those held in thrall to such ideas but who might maintain the opposite view. If ordinary language were identical with 'commonsense' -- and if it were ideological (per se), in the way that some imagine -- you just couldn't say such things. We all know this to be true -- certainly, socialists should know this --, because in our practical discourse we manage to deny such things every day.


In this regard, it is as ironic as it is inexcusable that there are revolutionaries who, while they are only too ready to regale us with the alleged limitations of ordinary language -- on the grounds that it reflects "commodity fetishism", "false consciousness" or "static thinking" --, are quite happy to accept (in whole or in part) impenetrably obscure ideas lifted from the work of a card-carrying, ruling-class-warrior like Hegel. Not only are his theories based on alienated thought (i.e., mystical Christianity), his AIDS was a direct result of a systematic fetishisation of language.


[AIDS = Absolute Idealism.]


This commentator also had the following to say:


"This project is inherently frustrating on so many levels, as Homer Simpson would say. On the one hand Rosa shows up the shameful ignorance of a century of Marxism-Leninism, marshalling in the process a prodigious array of sources on logic and mathematics, and also on the sciences, information that is urgently needed by her audience in view of the ignorance she contests. On the other, that so much energy should be invested to prove so little is tragic....


"Rosa occasionally acknowledges partial exceptions, but she has been so traumatized by the mountains of Trotskyist drivel she was force-fed, as well as its Stalinist counterpart, she rarely gets beyond that to see what else might be done or has been done with the dialectical tradition....


"Had Rosa not so precipitously dismissed 'academic Marxism', while copiously citing from other academics with expertise in mathematics, logic, and analytical philosophy, she would be better positioned to exploit their contributions as well as pinpoint their weaknesses. The whole history of critical theory is an excellent case in point, perhaps the best case. The Frankfurt School, their precursors, associates, and successors, all fell down on logic and mathematics. Nonetheless, they provided the tools to decipher the ideological phenomena of their time...."


The reason why so much has been 'wasted' on "so little" is that the political traditions to which the above commentator refers (which are dominated by Dialectical Marxism) have actually damaged to our movement over the last 130 years.


In contrast, academic Marxism and/or 'systematic dialectics' has largely been ignored in these Essays since it is politically irrelevant. Indeed, this current can damage nothing except the brains of those who still think it has anything worthwhile to offer humanity (which fact those so afflicted are not likely to appreciate for the reasons Max Eastman underlined). And, they are welcome to their political cul-de-sac.


Far from being force-fed on an exclusive diet of Trotskyist and Stalinist 'drivel', I have been studying academic Marxist writings now for more than twenty-five years (indeed, at the time of writing this, the Bibliography to my thesis stretches to over 90 pages, containing references to over 3000 books and articles by academic Marxists, among others). To be sure, this brand of dialectical gobbledygook is not the 'low grade drivel' one encounters in certain Trotskyist/Stalinist works, but it is high grade drivel nonetheless --, and politically inept drivel at that (since it is written by human beings who, for all their expensive education, by and large, can't write a clear sentence to save their lives). [For example, I expose some of the high grade 'drivel' one finds in Marcuse (1968), here. Chomsky's comments are also well worth reading.]


As I note elsewhere about these currents in Dialectical Marxism:


(1) Low Church Dialecticians [LCDs]:


Comrades of this persuasion cleave to the original, unvarnished truth laid down in the sacred DM-texts (written by Engels, Plekhanov, Lenin, Stalin, Trotsky, or Mao). These simple souls are highly proficient at quoting endless passages from the holy books in answer to everything and anything, just like the faithful who bow to the East or who fill the gospel halls around the world. Their unquestioning faith is as impressive as it is un-Marxist.


They may be naive, but they are at least consistently naive.


In general, LCDs are blithely ignorant of FL. Now, on its own this is no hanging matter. However, such self-inflicted and woeful ignorance doesn't stop them pontificating about FL, or from regaling us with its alleged limitations at every turn -- allegations based on ideas they have unwisely copied from Hegel, surely the George W Bush of Logic.



Figure Two: Advanced Logic Class At Camp Hegel


LCDs are, by-and-large, active revolutionaries, committed to 'building the party'. Alas, they have unwisely conspired to do the exact opposite, helping keep their parties small because of the countless splits and expulsions they engineer. This is a rather fitting pragmatic contradiction that the 'Dialectical Deity' has visited upon these the least of its servants.


Of course, LCDs can't see the irony in all this (even when it is pointed out to them -- I know, I have lost count of the number of times I have tried!), since they too haven't taken the lens caps off.


So, despite the fact that every last one of these short-sighted individuals continually strives to "build the party", after 140 years, few revolutionary groups can boast membership roles that rise much above the risible. In fact, all we have witnessed since WW2 is yet more fragmentation, but still no mass movement.


[Anyone who doubts this should look here, here, here, and here -- or, now, here.]


Has a single one of these individuals made this connection?


Are you kidding!?


The long-term failure of Dialectical Marxism and its core theory (i.e., 'Materialist Dialectics') are, it seems, the only two things in the entire universe that are not 'interconnected'.


(2) High Church Dialecticians [HCDs]:


These Marxists are in general openly contemptuous of the 'sophomoric ideas' found in most of the DM-classics (even though many of them seem to have a fondness for Engels's first 'Law').


More often than not, HCDs reject the idea that the dialectic operates in nature, sometimes inconsistently using Engels's first 'Law' to justify this 'leap' (which tactic allows them to claim that human history and development are unique), just as they are equally dismissive of simple LCD souls (see above) for their adherence to every last word in the classics.


[Anyone who is familiar with High Church Anglicanism will know exactly of what I speak.]


HCDs are mercifully above such crudities; they prefer the mother lode -- direct from Hegel, Lenin's Philosophical Notebooks and/or the writings of assorted latter day Hermeticists -- such as: György Lukács, Raya Dunayevskaya, C. L. R. James, Tony Smith, Tom Sekine, Robert Albritton, Chris Arthur, Bertell Ollman, Judith Butler, and Slavoj Zizek.


This heady brew is often fortified with a several kilos of hardcore jargon drawn straight from that intellectual cocaine-den, otherwise known as French Philosophy -- including the work of such luminaries as Maurice Merleau-Ponty, Jean Paul Sartre, Roland Barthes, Louis Althusser, Michael Foucault, Alain Badiou, Jacques Derrida, Gilles Deleuze, Pierre Bourdieu, and, perhaps worst of all, Jacques Lacan. Or, maybe even from that conveyor belt of systematic confusion: the Frankfurt School -- which includes the work of Max Horkheimer, Theodor W Adorno, Herbert Marcuse, Walter Benjamin, and later, Jürgen Habermas, among many others.


[I have discussed Marcuse's attitude to Wittgenstein and 'Ordinary Language Philosophy', here.]


Or, even worse still, that haven of intellectual heroin: the work of Edmund Husserl, Martin Heidegger and Hans-Georg Gadamer.


HCDs are generally, but not exclusively academics. In common with many of those listed above, tortured prose is their forte, and pointless existence is their punishment.


[Any randomly-selected issue of, say, Radical Philosophy or Historical Materialism, will provide ample evidence of the baleful influence of many of the above on erstwhile left-wing intellectuals. (See also here.)]


At least LCDs like to think their ideas are somehow relevant to the class struggle.


In contrast, High Church Dialectics is only good for the CV.


[Plainly, the sanitised dialectics HCDs churn out isn't an "abomination" to that section of the bourgeoisie that administers Colleges and Universities, or who publish their journals.]


Nevertheless, both factions are well-stocked with conservative-minded comrades happy to appropriate the a priori and dogmatic thought-forms of two-and-a-half millennia of boss-class theory, seldom pausing to give any thought to the implications of such easily won knowledge. If knowledge of the world is a priori, and based solely on armchair speculation, reality must indeed be Ideal.


[Some might object that the above is a caricature of dialectical thought; it is based on evidence and on the practice and experience of the party. That naive belief was laid to rest in Essay Two and in Part One of Essay Nine. It is worth adding that there are notable exceptions to these sweeping generalisations -- some academic Marxists do actively engage with the class struggle; the point is that their 'High Theory' is irrelevant in this regard. Indeed, I can't think of a single example of the work of an academic Marxist which has had an impact on the class war -- except perhaps negatively. (Any who disagree are invited to e-mail me with the details.) One or two comrades have tried to think of practical applications of 'the dialectic'. I have shown that these attempts fail, here and here.]


This has meant that the baleful influence of Hegelian Hermeticism becomes important at key historical junctures (i.e., those involving defeat and/or major set-back), since it acts as a materialist-sounding alternative to mainstream traditional thought -- indeed, as we saw was the case after 1905 in Russia.


Dialectics (especially those parts that have been infected with the lethal HCD-strain) thus taps into thought-forms that have dominated intellectual life for over two thousand years -- i.e., those that define the 'legitimate' boundaries of 'genuine' philosophy, and thus those which amount to little more than a systematic exercise in dogmatic thesis-mongering, aggravated by the invention of increasingly baroque, dogmatic theories.


Hence, because of its thoroughly traditional nature, DM is able to appeal to the closet "god-builders" and dialectical mystics that revolutionary politics seems to attract -- and who, in general, appear to congregate at the top of this ever-growing pile of dialectical disasters.


Indeed, I will continue to ignore the vast bulk of the material churned out by HCDs just so long as it remains irrelevant to the course of the class war. I suspect the Sun will cool first.


If that is regarded by this commentator as "tragic", so be it.


And I use modern Analytic Philosophy and Modern Logic since both are incomparably superior to the Hegelian gobbledygook upon which most academic Marxists dote. In addition, the methods Analytic Philosophy and Modern Logic (or, at least those that I use) deliver clear results.


Other things this commentator says have either been dealt with already at this site, or are too vague to do very much with.


Further remarks on this commentator's response to other Essays posted at this site can be found here and here.


18. Naturally, DM-apologists will want to deny this (indeed, they do deny it!), but apart from claiming that scientists are all "unconscious dialecticians", their evidence peters out alarmingly quickly. [This is examined in more detail in Note 20, below.]


Of course, if the claim that all scientists are "unconscious dialecticians" is still to be maintained, then what is to stop Buddhists, for example, claiming that all scientists are "unconscious followers of The Eightfold Path"?


This is no joke; some already have! On that, see McFarlane (2003) -- and, of course, the works of Fritjof Capra, except, in his case, scientists are perhaps "conscious" Daoists! Cf., also Wilber (1984). A useful and timely corrective can be found in Stenger (1995).


But, why don't we go the whole hog? Why not claim that scientists are "unconscious head-hunters"; there is about as much evidence to support that wild idea, too.


The historical connections between FL and science are detailed throughout, for example, Losee (2001); similar links with mathematics can be found in Kneale and Kneale (1978), pp.379-742, with a brief survey in Nidditch (1998). There is a clear summary of the connection between Fregean FL and advances in mathematics in Beaney (1996), pp.1-117, 269-77. However, the best introductions are Weiner (1990, 1999, 2004) and Noonan (2001); and for the general background, Giaquinto (2004). There is an excellent short introduction to Frege's life and work in Potter (2010), although anyone unfamiliar with modern logic might find that book tough going.


The relation between science and DM will examined in more detail in Essay Thirteen Part Two.


For a more illuminating discussion of the way that contradictions can be managed -- at least in Mathematics -- cf., Floyd (1995, 2000). For the same in science, see Harrison (1987).


19. Cf., Davis (2000), Hodges (1983), and Dyson (1997). The importance of Alonzo Church's work on the λ-Calculus can be judged by the fact that it underpins most programming languages.


Woods and Grant try to minimise all this with the following dismissive comment:


"There are two main branches of formal logic today -- propositional calculus and predicate calculus. They all proceed from axioms, which are assumed to be true 'in all possible worlds,' under all circumstances. The fundamental test remains freedom from contradiction. Anything contradictory is deemed to be 'not valid.' This has a certain application, for example, in computers, which are geared to a simple yes or no procedure. In reality, however, all such axioms are tautologies. These empty forms can be filled with almost any content. They are applied in a mechanical and external fashion to any subject. When it comes to simple linear processes, they do their work tolerably well. This is important, because a great many of the processes in nature and society do, in fact, work in this way. But when we come to more complex, contradictory, non-linear phenomena, the laws of formal logic break down. It immediately becomes evident that, far from being universal truths valid 'in all possible worlds,' they are, as Engels explained, quite limited in their application, and quickly find themselves out of their depth in a whole range of circumstances. Moreover, these are precisely the kind of circumstances which have occupied the attention of science, especially the most innovative parts of it, for most of the 20th century." [Woods and Grant (1995), p.99.]


We will have occasion to look at these wildly inaccurate claims later on, but apart from brushing modern logic under the carpet with a simple put-down, these two authors offer their readers not one single example of a technological application of DL, even though they try vainly to 'expose' the alleged limitations of FL.


And while we are at it, it is also worth pointing out that these two have manifestly confused logical falsehood with invalidity, when they say "Anything contradictory is deemed to be 'not valid.'" Validity has nothing to do with contradiction (in fact, one rule (RAA) actually depends on it!).


Moreover, anyone who thinks that, say, QM threatens the LEM would do well to read Harrison (1983, 1985), and then think again. In that case, "quantum logic" poses no threat to the LEM since it has merely forced us to reconsider what we count as a scientific proposition. [For a different view, see Slater (2002), pp.177-79.]


[QM = Quantum Mechanics; LEM = Law of Excluded Middle.]


Of course, computers have had an incalculable affect on the world, all thanks to the Propositional Calculus.


However, DL does have a less well appreciated practical outcome: it succeeded in confusing comrades like Woods and Grant.


[Woods and Grant's other baseless claims will be picked apart in Part Two of Essay Seven.]


20. Admittedly, this is a controversial claim -- but only in so far as some have thought to controvert it.


As pointed out in Note 18, so divorced from reality have dialecticians become that some even claim that scientists are "unconscious dialecticians", and because of this they then imagine that the successes of science can be attributed to DL! For example, George Novack refers his readers to a series arguments put forward by the famous French Physicist, Jean-Pierre Vigier -- who was also a Dialectical Marxist -- in a public debate with Jean-Paul Sartre, which took place in December 1961. In the course of that debate, Vigier responded to the criticism that DM has no practical scientific applications with the following (I am relying here on Novack's summary):


"The existentialist [Sartre -- RL] resents and rejects the rationalism and objectivity of science. It supposedly leads us away from real being, which is to be perpetually sought, though never reached, through the ever-renewed, ever-baffled effort of the individual consciousness to go beyond our human condition. The terrible destiny of the human race is like 'the desire of the moth for the star/the night for the morrow/the devotion to something afar/from the sphere of our sorrow'.


"So the exasperated existentialist Sartre flings as his trump card against the dialectics of nature the current crisis in science. 'There has never been, I believe, as grave a crisis as the present one in science', he cries to Vigier. 'So when you come to talk to us about your completed, formed, solid science and want to dissolve us in it, you'll understand our reserve.'


"Vigier calmly replies: 'Science progresses by means of crises in the same manner as history; that's what we call progress. Crises are the very foundation of progress.' And he concludes: 'The very practice of science, its progress, the very manner in which it is today passing from a static to a dynamic analysis of the world, that is precisely what is progressively elaborating the dialectic of nature under our very eyes.... The dialectic of nature is very simply the effort of the philosophy of our time...of the most encyclopaedic philosophy, that is, Marxism to apprehend the world and change it.'


"This ringing affirmation will appear bizarre to Anglo-American scientists who may respect Vigier for his work as a physicist. They summarily disqualify dialectical logic on the ground that, whatever its philosophical or political interest, it has no value in promoting any endeavour in natural science. If the method is valid, the anti-dialecticians say, then purposeful application by its proponents should prove capable of producing important new theories and practical results in other fields than the social. Marxists are challenged to cite instances where the dialectical method has actually led to new discoveries and not simply demonstrated after the fact that specific scientific findings conform to the generalisations of dialectical logic.


"The most splendid contribution of this kind in recent decades has been Oparin's theories on the origin of life, which are widely accepted and have stimulated fruitful work on the problems of biogenesis and genetics. The Soviet scientist's theory is based on the hypothesis that the random formation and interaction of increasingly complex molecules gave rise to the simplest forms of living matter, which then began to reproduce at the expense of the surrounding organic material.


"Oparin consciously employed such principles of materialist dialectics as the transformation of quantity into quality, the interruption of continuity (evolution by leaps), and the conversion of chance fluctuations into regular processes and definite properties of matter, to initiate an effective new line of approach to one of the central problems of science: How did inanimate nature generate life on earth? Such cases would undoubtedly multiply if more practicing scientists were better informed about the Marxist method of thought." [Novack (1978b), pp.245-46. I have used the on-line version here. Quotation marks altered to conform to the conventions adopted at this site; spelling modified in line with UK English. Typos corrected.]


However, we have seen in Essay Seven Part One that these 'dialectical laws' are so vague and imprecise (that is, where any sense can be made of them), they can be made to conform to practically any theory or scientific fact one chooses.


Even so, what basis is there in the claim that Oparin "consciously employed" such principles, whether or not they are valid?


[In fact, upon reading the above comments, I promptly obtained a copy of Oparin's book -- Origin of Life -- but could find no dialectics in it at all, conscious or unconscious. Surprisingly, Oparin mentions Engels only five times in the entire book [Oparin (1953), pp.31-33, 131, 136], dialectics and its 'laws' not once. And even where he mentions Engels, it is only in connection with (1) his idea that proteins are important for life and (2) his criticisms of spontaneous generation.]


Of course, the first point worth making is that while Novack is at pains elsewhere to distance his own brand of Trotskyist 'superior', dynamic dialectics from the 'wooden, scholastic and lifeless' form that was allegedly on display in Stalin's Russia (cf., p.232), he is quite happy to quote the work of a Stalinist scientist (and state apparatchik, too!) in support. Perhaps then Stalinist Dialectics isn't quite so "ossified and scholastic" as Novack would have us believe. On the other hand, if it is "ossified and scholastic", it can't have been used by Oparin to make any useful discoveries! Novack seems to want to have it both ways -- but then that is what one has come to expect of DL-fans.


The second point is that scientists in Stalin's Russia learnt rather quickly that if they didn't appeal to the 'laws' of dialectics in their work (and those 'laws' as they were interpreted by the party hacks at that time) they soon disappeared (cf., the career of Nikolai Vavilov). So, Oparin's "conscious employment" of DM was more of a conscious desire to preserve his own hide than it was an application of "conscious" dialectics. That suspicion is confirmed by the Wikipedia article on him:


"The influence of the Marxist theoretical concept of dialectic materialism, the official party-line of the Communist Party, fit Oparin's definition of life as 'a flow, an exchange, a dialectical unity'. This notion was enforced by Oparin's association with Lysenko." [Quoted from here. Bold added. This passage has now been slightly changed.]


However, Birstein disagrees that Oparin did this to save his neck; he claims Oparin did it in order to advance his career:


"I strongly disagree with [those] who justified Oparin's behaviour [in supporting Lysenko -- RL] as the condition necessary for his survival....


"In fact, nothing threatened Oparin's survival. He was an academic and director of the Institute of Biochemistry, which then was not directly involved in the study of genetics or evolutionary theory. He was not attacked by Lysenko or Prezent [a Lysenko supporter, DM-fanatic and self-styled 'philosopher' -- RL] in the press. He simply was an opportunist who saw his chance to advance his career in exchange for his support of Lysenko. Academician Schmalhausen, Professors Formozov and Sabinin, and 3000 other biologists, victims of the August 1948 Session, lost their professional jobs because of their integrity and moral principles and because they would not make compromises with their consciences." [Birstein (2001), p.289. Details of the above events can be found on pp.255-62.]


And we all know what wonderful results were obtained by Lysenko when he tried to apply dialectics to agriculture, don't we? [On Lysenko, see below.]


The third, and perhaps more important point is that Novack nowhere tells us what these "quantities" and "qualities" are that Oparin is supposed to have taken into account. We have already seen that DM-fans are quite happy to make stuff up as they go along (especially with respect to this particular 'law'), using 'flexible' and 'malleable' 'definitions' (or, what is more often the case, no  definition at all!) of "quality" as the need arises; so Novack's lack of detail here is no surprise.


Anyway, here is how Wikipedia summarises Oparin's work in this area:


"As early as 1922, he asserted the following tenets:


1. There is no fundamental difference between a living organism and lifeless matter. The complex combination of manifestations and properties so characteristic of life must have arisen in the process of the evolution of matter.


"2. Taking into account the recent discovery of methane in the atmospheres of Jupiter and the other giant planets, Oparin suggested that the infant Earth had possessed a strongly reducing atmosphere, containing methane, ammonia, hydrogen, and water vapour. In his opinion, these were the raw materials for the evolution of life.


"3. In Oparin's formulation, there were first only simple solutions of organic matter, the behaviour of which was governed by the properties of their component atoms and the arrangement of these atoms into a molecular structure. Gradually though, he said, the resulting growth and increased complexity of molecules brought new properties into being and a new colloidal-chemical order developed as a successor to more simple relationships between and among organic chemicals. These newer properties were determined by the interactions of these more complex molecules.


"4. Oparin posited that this process brought biological orderliness into prominence. According to Oparin, competition, speed of cell growth, survival of the fittest, struggle for existence and, finally, natural selection determined the form of material organization characteristic of modern-day living things.


"Oparin outlined a way he thought that basic organic chemicals might have formed into microscopic localized systems, from which primitive living things could have developed. He cited work done by de Jong on coacervates and research by others, including himself, into organic chemicals which, in solution, might spontaneously form droplets and layers. Oparin suggested that different types of coacervates could have formed in the Earth's primordial ocean and been subject to a selection process that led, eventually, to life." [Quoted from here; accessed 09/10/11; changes to the on-line text incorporated 24/03/15. Spelling altered to conform to UK English. Links in the original.]


However, Point 1 above isn't unique to DM, so that can't be attributed to this theory. Neither are Points 2 and 4. We might seem on firmer ground with Point 3, however; but, as noted above, this can't be seen as an application of the 'Law of the Transformation of Quantity into Quality', either -- not until we are told what these new 'qualities' are. If these 'qualities'/'properties' are the result of novel arrangements of the constituent atoms of each molecule involved (as the above suggests), then this too can't be an example of Engels's 'Law' in action.  Here is what I have argued in Essay Seven Part One on this:


Engels...said the following:


"For our purpose, we could express this by saying that in nature, in a manner exactly fixed for each individual case, qualitative changes can only occur by the quantitative addition or subtraction of matter or motion (so-called energy)…. Hence it is impossible to alter the quality of a body without addition or subtraction of matter or motion, i.e. without quantitative alteration of the body concerned." [Engels (1954), p.63. Bold emphases added.]


In response, once more, it is worth pointing out that this makes a mockery of Engels's claim that such "qualitative changes" [i.e., new arrangements of the atoms] can only come about through the addition of matter and/or motion, and that it is "impossible" to alter a body "qualitatively" in any other way. [Possible objections to this line-of-argument are neutralised here.]


So, if anything, Oparin was "consciously" failing to apply Engels's 'Law', since these new molecular arrangements manifestly do not involve the addition of matter or energy. [Again, several obvious objections to this response were neutralised in Essay Seven Part One (link above).]


But, what about the claim that increased complexity results in the 'emergence' of new 'qualities"? I will deal with "emergent properties" in Essay Three Part Three. Independently of that, what about the following claim advanced by Vigier? 


"Oparin consciously employed such principles of materialist dialectics as the transformation of quantity into quality, the interruption of continuity (evolution by leaps), and the conversion of chance fluctuations into regular processes and definite properties of matter, to initiate an effective new line of approach to one of the central problems of science: How did inanimate nature generate life on earth?" [Novack (1978b), p.246.]


But, where is the "interruption of continuity" here? Does Vigier imagine that, for example, nature incorporates elementary particles into organic molecules until that amounts to the addition of a new atom, and thus a "leap"? Presumably not. On the other hand, maybe he thinks that atoms are added one at a time; if so, there's no continuity here, just discontinuity.


Here is what I have written on this (also from Essay Seven Part One), after quoting several DM-theorists:


"With this assurance Herr Dühring saves himself the trouble of saying anything further about the origin of life, although it might reasonably have been expected that a thinker who had traced the evolution of the world back to its self-equal state, and is so much at home on other celestial bodies, would have known exactly what's what also on this point. For the rest, however, the assurance he gives us is only half right unless it is completed by the Hegelian nodal line of measure relations which has already been mentioned. In spite of all gradualness, the transition from one form of motion to another always remains a leap, a decisive change. This is true of the transition from the mechanics of celestial bodies to that of smaller masses on a particular celestial body; it is equally true of the transition from the mechanics of masses to the mechanics of molecules -- including the forms of motion investigated in physics proper: heat, light, electricity, magnetism. In the same way, the transition from the physics of molecules to the physics of atoms -- chemistry -- in turn involves a decided leap; and this is even more clearly the case in the transition from ordinary chemical action to the chemism of albumen which we call life. Then within the sphere of life the leaps become ever more infrequent and imperceptible. -- Once again, therefore, it is Hegel who has to correct Herr Dühring." [Engels (1976), pp.82-83. Bold emphasis added.]


"It is said, natura non facit saltum [there are no leaps in nature]; and ordinary thinking when it has to grasp a coming-to-be or a ceasing-to-be, fancies it has done so by representing it as a gradual emergence or disappearance. But we have seen that the alterations of being in general are not only the transition of one magnitude into another, but a transition from quality into quantity and vice versa, a becoming-other which is an interruption of gradualness and the production of something qualitatively different from the reality which preceded it. Water, in cooling, does not gradually harden as if it thickened like porridge, gradually solidifying until it reached the consistency of ice; it suddenly solidifies, all at once. It can remain quite fluid even at freezing point if it is standing undisturbed, and then a slight shock will bring it into the solid state." [Hegel (1999), p.370, §776. Bold emphasis alone added.]


"[I]t will be understood without difficulty by anyone who is in the least capable of dialectical thinking...[that] quantitative changes, accumulating gradually, lead in the end to changes of quality, and that these changes of quality represent leaps, interruptions in gradualness…. That is how all Nature acts…." [Plekhanov (1956), pp.74-77, 88, 163. Bold emphasis alone added.]


"The 'nodal line of measure relations'... -- transitions of quantity into quality... Gradualness and leaps. And again...that gradualness explains nothing without leaps." [Lenin (1961), p.123.  Bold emphasis alone added. Lenin added in the margin here: "Leaps! Leaps! Leaps!"]


"What distinguishes the dialectical transition from the undialectical transition? The leap. The contradiction. The interruption of gradualness. The unity (identity) of Being and not-Being." [Ibid., p.282. Bold emphasis added.]


"Dialecticians call this process the transformation of quantity into quality. Slow, gradual changes that do not add up to a transformation in the nature of a thing suddenly reach a tipping point when the whole nature of the thing is transformed into something new." [Rees (2008), p.24. Quotation marks altered to conform to the conventions adopted at this site.]


The argument here is plainly this: (1) Quantitative increase in matter or energy results in gradual change, and hence that (2) At a certain point, further increase breaks this "gradualness" inducing a "leap", a sudden "qualitative" change.


But, this doesn't happen in the Periodic Table! Between each element there is no gradual increase in protons and electrons leading to a sudden change -- there are only sudden changes as these 'particles' are added! For example, as one proton and one electron are added to Hydrogen, it suddenly changes into Helium. Hydrogen doesn't slowly alter and then suddenly "leap" and become Helium. The same is true of every other element in the Table. In that case, one of the 'best' examples dialecticians use to 'illustrate' this 'Law' in fact refutes it! There is no "interruption" in gradualness.


Now, this is a more honest reading from the extant data, is it not? And not a single foisting anywhere in sight!


These comments also apply to the other examples drawn from Organic Chemistry [quoted by Engels (and Woods and Grant (1995), examined in Note 4 of Essay Seven Part One); cf., Engels (1954), pp.161-63 and (1976), pp.65-68].


Furthermore, between each of the organic molecules (to which DM-theorists refer) and the next there is no gradual increase in atoms leading to a sudden change -- once again, there are only sudden changes as atoms are added! For example, as one atom of carbon and two atoms of hydrogen are added to Butyric Acid, it  suddenly changes into Valeric Acid. Butyric Acid doesn't slowly alter and then suddenly "leap" and become Valeric Acid. The same is true of every other molecule in similar series. In that case, another one of the 'best' examples dialecticians use to 'illustrate' their 'Law' in fact refutes it! There is no "interruption" in gradualness, here, either.


Once again, if Oparin did use this idea, then, whatever else he was, he wasn't a "conscious dialectician".


It is worth noting that Fundamentalist Christians claim the same sorts of things for their belief in the literal truth of the Book of Genesis (as do Muslim literalists, too); indeed, even mainstream believers put the advancement of science down to divine guidance. [On that, see here.] This is one straw, it seems, that both wings of modern mysticism (religious and 'dialectical') appear eager to clutch, for all the good it does them.


Dialecticians have been forced into this corner since, of course, few human beings have ever heard of dialectics. Outside of the old Communist Block and its satellite states it is reasonably certain that there aren't enough dialectical scientists to fill a medium-sized cinema.


But, if as we are constantly being told, scientists are stuck with the rusty old concepts that FL has bequeathed to them (this fable is retailed countless times in RIRE; here are just a few of the places where it does this: pp.42, 67, 69, 82, 83, 85, 86, 87, 88, 89, 91, 94, 95, 96, 97, 98, 99, 106, 107, 119, 132, 148, 152, 156, 234, 255, 354, 365, 387, 406; even John Rees has joined in -- cf., TAR, pp.3-4), how would it have been possible for human knowledge and technique to advance quite so dramatically over the last 350 years? If, in practice, scientists actually use these 'decrepit, outmoded, formal categories', and science has advanced as a result, doesn't that amount to a practical refutation of the idea that FL is inferior to DL?


Well, you would think this was a safe inference to draw, but DL addles the brain to such an extent that it would be unwise to expect its victims to make such a simple deduction.


[RIRE = Reason in Revolt, i.e., Woods and Grant (1995); TAR = The Algebra of Revolution, i.e., Rees (1998).]


On the other hand, is there a scrap of evidence to show that there is (or there has been) a single scientist who is (or who was) an "unconscious" dabbler in the Dialectical Black Arts? If there is, dialecticians would be well advised to keep it to themselves no longer.


[The example of Mendeleyev is dealt with here. Novack claims (Novack (1978), pp.254-55) Ernst Mayr used DL in his work simply on the basis of Mayr's ruminations about evolutionary novelty), but that would have been news to Mayr! Of course, whenever Mayr referred to an animal's head, that was sufficient to prove he was an 'unconscious head-hunter', too.]


And what of the few supposedly genuine examples on offer where dialectics has been used in science? If the work of Lysenko is anything to go by, we must surely conclude that DL hasn't been a ringing success: Lysenko's theory held Soviet agriculture back for over 30 years.


[On Lysenko, see Birstein (2001), Graham (1973, 1987, 1993), Joravsky (1970), Lecourt (1977) [this links to a PDF], Medvedev (1969), and Soyfer (1994). For a different view, see Lewontin and Levins (1976). See also here.]


Of course, if and when things go wrong in non-Soviet or non-DM science, dialecticians don't attribute that to "unconscious dialectics"; rather they put it down to "bourgeois logic", "formal thinking" or an unwise adherence to "commonsense", etc. Which is rather odd, given the fact that all the evidence suggests that logic (both Formal and discursive) has actually helped scientists refine and test their theories for centuries -- while there is none whatsoever that DL has featured anywhere at all.


Small wonder then that dialecticians also believe that appearances 'contradict underlying reality'; given the above, they would, wouldn't they? Even so, this is, of course, an odd sort of thing for materialists to have to argue: if the material world contradicts a certain idea, ignore reality and cling to that idea!


For sure, dialecticians consciously do that! And here is one: this is Herbert Marcuse, commenting on Hegel:


"The doctrine of Essence seeks to liberate knowledge from the worship of 'observable facts' and from the scientific common sense that imposes this worship.... The real field of knowledge is not the given fact about things as they are, but the critical evaluation of them as a prelude to passing beyond their given form. Knowledge deals with appearances in order to get beyond them. 'Everything, it is said, has an essence, that is, things really are not what they immediately show themselves. There is therefore something more to be done than merely rove from one quality to another and merely to advance from one qualitative to quantitative, and vice versa: there is a permanence in things, and that permanent is in the first instance their Essence.' The knowledge that and appearance and essence do not jibe is the beginning of truth. The mark of dialectical thinking is the ability to distinguish the essential from the apparent process of reality and to grasp their relation." [Marcuse (1973), pp.145-46. Marcuse is here quoting Hegel (1975), p.163, §112. Quotation marks altered to conform to the conventions employed at this site. Minor typo corrected.]


Marcuse nowhere criticises Hegel for this Idealist approach to knowledge; quite the reverse, in fact, he endorses it.


In fact, and on the contrary, all the signs are that dialecticians are pretty visible practitioners of self-delusion. So: on the one hand we are told that dialectics is and always has been central to revolutionary practice -- and that revolutionary cadres have to be, always were and still are over-flowing with conscious dialecticians --, on the other, we have witnessed little other than the constant failure of Dialectical Marxism to seize the masses, or even so much as lightly hug them.


Hence, if we are to believe this tale, conscious dialectics seems to be super-glued to long-term failure; 'unconscious' dialectics appears to be welded to success!


What conclusion should we draw from the above? Perhaps this: Every revolutionary should copy other scientists and become consciously ignorant of DL. Maybe then our movement will experience some success.


[Or would this recommendation reveal yet another failure to "understand" dialectics on my part?]


Admittedly, certain 'dialectical' biologists have claimed that DL has had an important part to play in the study of living systems -- for instance, the authors of DB, along with several notable members of the Communist Party from a few generations back (e.g., Haldane, Levy and Bernal). [Also see Lewontin and Levins (2007), and here. In fact, the authors of DB tell us they consciously use DL in their work. However, in a debate with Levins a few years back, it became apparent that he, like so many other DL-fans, has a very insecure grasp of logic.]


[DB = The Dialectical Biologist; i.e., Levins and Lewontin (1985).]


Unquestionably, an appeal to organic wholes and interconnectedness makes some sort of sense in the Life Sciences and in the study of social development. However, this admission doesn't mean we have to accept the entire DM-enchilada, and opt for universal Holism. [On this, see Essay Eleven Part One and Part Two.] Anyway, as will be demonstrated throughout the rest of this site, the concepts found in DL and DM are far too vague and incoherent for them to play a useful role in any of the sciences. [So, it is little wonder conscious dialecticians helped ruin Soviet Agriculture and Genetics, or that subsequent dialecticians found they had to appeal to all those 'unconscious dialecticians' in non-Soviet science in order to try to undo the damage.]


But, do any DM-fans regale us with the following salutary tale involving the 'dialectical ruminations' of Olga Lepeshinskaya (a personal friend of Lenin's)?


"In the 1920s Lepeshinskaya discredited the work of her supervisor, Alexander Gurvitch, who investigated biophotons and mitogenic rays. She claimed that low doses of ultraviolet light were released by dying cells that had been treated with high doses of UV light. Later she claimed that cells could propagate by disintegration into granules which could generate new forms of cells, different from the parental cells. Also, crystals of inorganic matter could be converted into cells by adding nucleic acids. Further, she espoused spontaneous generation and the presence of a 'vital substance'. These claims were propagated as official dogma in the Soviet Union. A claim that soda baths fostered rejuvenation led to a temporary shortage of baking soda. She based her career on claims to observe de novo emergence of living cells from non-cellular materials, supporting such claims by fabricated proofs which were 'confirmed' by others eager to advance in the politicized scientific system. Actually, she filmed the death and subsequent decomposition of cells, then projected these films reversed.


"In May 22–24, 1950 at the special symposium 'Live Matter and Cell Development' for the USSR Academy of Sciences and the USSR Academy of Medical Sciences that was supported by Stalin and chaired by Alexander Oparin, Lepeshinskaya gave the keynote speech, and her discoveries were celebrated as revolutionary by the invited audience. She was the recipient of the Stalin Prize for that year, and her ideas became mandatory instruction in biology. In 1952 a second conference took place to demonstrate 'using experimental methods' that the bourgeois Virchowian concept of cell development (only a living cell can produce another cell) was replaced by a 'new dialectical-materialistic theory on the origin of all living cells from non-living matter.' While her impact and dogmatic dominance have parallels to those of Lysenko, her claims were never officially renounced but just faded away.


"She involved her daughter Olga and her son-in-law Vladimir Kryukov in her work; in contrast, her husband, Panteleimon Lepechinsky, thought little of it. 'Don't you listen to her. She's totally ignorant about science and everything she's been saying is a lot of rubbish' he told a visitor...." [Wikipedia, accessed 09/10/11. Quotation marks altered to conform to the conventions adopted at this site.]


Birstein adds a few extra details:


"Academician Aleksandr Oparin (1894-1980) was another who gained significantly from the August 1948 Session. In 1949 he became secretary academician of the Biology Division instead of Academician Orbeli. In contrast to Prezent, he was a serious scientist and the author of a theory on the origin of life. The first version of his book Origin of Life was published in Russian in 1924, and the English edition that appeared in 1938 was widely read by Western scientists. He became corresponding member of the academy in 1939, academician in 1946, and director of the Bach Institute of Biochemistry in 1946. But from the 1940s-1960s, Oparin was more a Soviet official than a scientist. Besides his positions at the academy, in 1950 he was appointed a member of the International Council for Peace, and in 1952 and 1962, he was elected vice president of the International Federation of Scientists.


"During his years of power, Academician Oparin was an open pro-Lysenkoist. I have already mentioned his role in the tragic fate of Sabinin [pp.255-56 -- RL]. He became even more famous as a supporter of Olga Lepeshinskaya and her pseudotheory on 'the origin of cells from noncellular matter.'


"Lepeshinskaya (1871-1963), and old Bolshevik, a personal friend of Lenin, and an active Party functionary, started her biological studies in the 1920s, when she was over fifty years old. In the 1930s, she published a few papers on 'the origin of cells from non-cellular matter,' which were seriously criticised by many scientists, including Professor Koltsov [an outspoken critic of Lysenko -- RL]. It was evident that all Lepeshinskaya's 'discoveries' were simply based on artefacts (i.e., artificial substances or structures formed during the preparation of microscopic slides) obtained because of poorly and nonprofessionally made histology preparations (she worked at home with her daughter, granddaughter, and daughter's husband, who assisted her)....


"Finally, with the help of another old Bolshevik, F. Petrov, in 1945 Lepeshinskaya managed to publish a monograph under the same title as here theory. It had a forward written by Lysenko and one of his closest co-workers, the VASKhNIL [Lenin All-Union Academy of Agricultural Sciences -- RL] academician Ivan Glushchenko. The book described Lepeshinskaya's experiments in which, for instance, red blood cells 'were developed' from yolk.


"After Lysenko's victory in 1946 and using her Party connections in the Central Committee, Lepeshinskaya initiated a joint meeting of the Academy Biology Division, the Medical Academy, and representatives of the Agricultural Academy. This meeting took place on May 22-24 1950. Academician Oparin presided over the commission that organized it. He formulated the goal of the meeting:


'The attempts to create living systems are possible...only in the Soviet Union. Such attempts are not possible anywhere in capitalist countries because of the ideological position.... I think that the goal of the meeting should be the criticism and destruction of...the last basics of Mendelism in our country, the Virchowian description of the cell theory [i.e., that a cell can be originated only from another cell].'


"Twenty-seven speakers praised Lepeshinskaya's alleged discovery.... Some of them were forced to speak by personal order from the Central Committee.


"The same year (1950), Lepeshinskaya received the highest Soviet award, the Stalin Prize. Two years later, in 1952, with the involvement of Oparin, a second joint conference of the Medial Academy and the Academy Biology Division on the problem of cell origin was organized. As Lepeshinskaya declared '[U]sing experimental methods...a new dialectical-materialist theory of the origin of all cells from non-living matter has been developed.'


"All this nonsense was stopped only after Stalin's death. However, Oparin continued to be an admirer of Lysenko. In 1954 he wrote:


'The August 1948 Session of the VASKhNIL and the joint session of the USSR Academy of Sciences...had a profound influence on the development of Soviet biological science. They were turning points after which all branches of biology in our country started to be developed on the basis of materialistic principles of the Michurinist biology and Pavlov's physiology.... Our duty is to continue to guard biological science from the influence of foreign reactionary concepts of Morganism and vitalism.'" [Birstein (2001), pp.260-62. Quotation marks altered to conform to the conventions adopted at this site]


[See also Wetter (1958), pp.451-55, and Grant (2007), pp.277-80.]


Was all this pseudoscience a result of a "conscious application" of DL, too?


It could be objected that any theory (including FL) can be misused. Indeed, but how can one possibly tell if DM has been used correctly, or not? After all, it sanctions the derivation of anything a theorist chooses, and its opposite (often by the very same theorist, sometimes on the very same page, or the in very same paragraph, or the in very same speech!). [Dozens of examples of this phenomenon can be found in Essay Nine Part Two. (Link omitted.)]


Nevertheless, the authors of DB advance certain claims (which TAR quotes approvingly; e.g., p.4) that require brief comment:


[1] Levins and Lewontin maintain that something called the "Cartesian mode" [i.e., Cartesian Reductionism, CAR] has dominated post-renaissance science; unfortunately, they failed to substantiate this claim and simply left it as a bald assertion:


"The dominant mode of analysis of the physical and biological world and by extension the social world...has been Cartesian reductionism. This Cartesian mode is characterised by four ontological commitments...:


"1. There is a natural set of units or parts of which any whole system is made.


"2. These units are homogeneous within themselves, at least in so far as they affect the whole of which they are the parts.


"3. The parts are ontologically prior to the whole; that is, the parts exist in isolation and come together to make wholes. The parts have intrinsic properties, which they possess in isolation and which they lend to the whole. In the simplest case the whole is nothing but the sum of the parts; more complex cases allow for interactions of the parts to produce added properties of the whole.


"4. Causes are separate from effects, causes being the properties of subjects. and effects the properties of objects. While causes may respond to information coming from the effects.... there is no ambiguity about which is causing subject and which is caused object...." [Levins and Lewontin (1985), p.269.]


However, these allegations are themselves couched in rather broad, general and somewhat vague terms. While it is undeniable that some philosophers and scientists adopted parts of the world-view that these two attribute to CAR, many rejected it. Indeed, since most of the theorists who allegedly adopted this mode-of-thought (if it is one) were devout Christians, they could hardly posit 'parts separate from wholes' given what they found in the book of Genesis. Naturally, that depends on what one means by "separate". [On this, see below.] It is worth noting that the authors of DB cite no sources (primary or secondary) in support of their views -- and no wonder, since that would have undermined the neat picture they hoped to present.


Admittedly, different forms of atomism dominated early modern science, but Atomic Theory and the belief in the existence of molecules wasn't universally accepted among scientists until after the publication of Einstein's work on Brownian motion and the work of Jean Baptiste Perrin, approximately 100 years ago. [Cf., the remarks on this topic in Miller (1987), pp.470-82; a detailed history can be found in Nye (1972).] Also, worthy of note is the fact that classical Atomic Theory (propounded by Dalton) had to be rejected before these newer innovations became generally accepted. [Cf., Laudan (1981).]


[There is an illuminating discussion of these developments in Toulmin and Goodfield (1962), pp.193-305. See also Mason (1962), Brock (1992), Pullman (1998), and Pyle (1997).]


DB's authors also ignore the fact that many scientists and philosophers (these two roles were not really distinguished before the middle of the 19th century) up until about 150 years ago almost invariably depicted the unity of the world in theological/mystical terms. Many of the pioneers of modern science (and Philosophy) openly accepted Hermetic, Rosicrucian, Alchemical, Occultist, Kabbalist, Neo-Pythagorean, NeoPlatonic and Teleological theories of the origin and nature of the world. On this see: Bono (1995), Copenhaver (1990, 1998), Coudert (1995, 1999), Debus (1956, 1977, 1978, 1987, 1991), De León-Jones (1997), Dobbs (2002), Easlea (1980), Faivre (1994, 1995, 2000), Harkness (1999), Henry (1986), Hughes (1992), Katz (2005), Linden (2003), Lenoir (1982), McGuire (1967, 1968), McGuire and Rattansi (1966), Newman and Grafton (2001), Newman and Principe (2005), Pagel (1986), Principe (1998), Ross (1983a, 1998), Shumaker (1972), Vickers (1984), Webster (1976, 1982), White (1999), and Yates (1991, 2001, 2004). See also here.


As George Ross notes:


"During the middle of the seventeenth century, there was a growing consciousness of a divide between two rival and apparently incompatible world-views. On the one hand, there was the materialist, mechanist picture, according to which the world was to be understood exclusively in terms of particles of matter interacting with each other in accordance with the laws of motion. On the other hand, there was the spiritualist, occultist picture, according to which some or all natural phenomena were to be understood in terms of the sympathies and antipathies of spiritual beings acting purposefully. An important dimension of Leibniz's philosophy was his project of synthesising these two approaches through a new set of concepts which would do justice to the insights of each." [Ross (1983b).]


And, the impact of Christianity on the development of Western science is undeniable; a particularly illuminating account can be found in Hooykaas (1973). The book on this is, of course, Webster (1976).


In fact, it is arguable that DM itself represents a return to an earlier and pre-enlightenment, enchanted view of nature. Given the fact that this doctrine [DM] originated in the theories of prominent Natürphilosophers (i.e., Schelling and Hegel), who themselves derived their ideas from previous generations of Hermetic Mystics (for example, Plotinus, Proclus, Porphyry, Iamblichus, Pseudo-Dionysius, (and the shadowy figure, Hermes Trismegistus), John Scotus Eriugena, Meister Eckhart, Raymond Lull, Nicholas of Cusa, Giovanni Pico Della Mirandola, Marsilio Ficino, Giordano Bruno, Paracelsus, Valentin Weigel, Jacob Böhme, Emanuel Swedenborg, and Friedrich Christoph Oetinger), this isn't the least bit surprising. [Details can be found in Essay Fourteen Part One (summary here). A few sources are cited below.]


Finally, and connected with he above, DB omits any mention of the strong Organicist and Holistic tradition in modern science (represented most notably in the works of people like Herder, Goethe, Schelling and Oken). Emerging out of the aforementioned Hermetic and Neo-Platonist philosophies of the Renaissance, this strand of thought underpinned Natürphilosophie, just as it inspired Vitalist and Romantic views of nature. As is clear, this take on the world dominated the thought of those in the Romantic Movement, and from whom Hegel derived much inspiration. This alone casts doubt on DB's simplistic picture of the development of science since Descartes time. Post-Renaissance scientific thought therefore was both Atomist and Organicist. [On this, see Holmes (2008).]


However, of much more interest are the common metaphysical threads running through most of theoretical science and all of Traditional Philosophy, which cast DM in a rather more compromising light -- certainly more than the authors of DB imagine, or might be prepared to admit.. [A political context will be given to this phenomenon in later Essays (notably Nine Part One, and Essays Twelve and Fourteen Parts One and Two; summaries here and here).]


On the Hermetic influences on Hegel, see J White (1996), pp.36-43, and Magee (2008); the Introduction to the latter has been posted here. On Goethe, see Bortoft (1996), Naydler (1996) and Tantillo (2002). Cf., also Collingwood (1960) and Lovejoy (1964). On the Natürphilosophie of thinkers like Böhme, Schelling, Oken, Kielmeyer and Goethe, see Benz (1983), Mason (1962), pp.349-62, O'Regan (1994), Richards (2002) and Tuveson (1982). On Oersted's influence on Engels, cf., Graham (1973), and Williams (1980). See also, Brown (1977), Harrington (1996), Horn (1997), and Weeks (1991, 1993). There is an excellent summary of some of the above, and their influence on Hegel, in Beiser (2005), pp.80-109; see also Heidelberger (1998).


To be fair, Rees does go on to argue that a holistic view of nature on its own is insufficient to distinguish DM from other superficially similar systems of thought. [However, on this, see here.] Nevertheless, the examples he gives of other holistic belief systems were pointedly taken from religious/mystical views of the world: for example, we are referred to Roman Catholic and Taoist beliefs. [Rees (1998), p.6.] Moreover, Rees failed to mention the important Organicist tradition in post-Renaissance science, nor did he alert his readers to the latter's influence on Schelling and Hegel (and hence on Engels). Admittedly, not all those who advocated these systems believed that change was caused by contradictions, but many thought that things were ruled by dialectically-connected and inter-related opposites, distinguishable from Hegel's 'contradictions' in name alone; on this, see Essay Fourteen Part One (summary here), and Appendix One of Essay Two.


Even so, it is also clear that DB's authors have themselves adopted a mildly revisionist view of Engels's work in this regard; in fact, they go so far as to say that "much of what he wrote about [the physical world] seems quaint" [DB, p.279]. True, DB's authors also interpret contradictions as opposing forces [DB, p.280], but in Essay Eight Part Two it will become clear how unwise a move that is. Nevertheless, in their characterization of CAR, DB's authors pointedly failed to argue that the absence of an appeal to "contradictions" (to account for change) was one of its weaknesses. Perhaps this was an oversight, but it does ruin the neat picture Rees tried to paint.


(2) DB counterposes DL to CAR, as a superior method, at least in the Life Sciences -- and by implication throughout the whole of Science. However, as we will see in other Essays posted at this site, DL introduces into epistemology its own far more pernicious virus: HEX.


[HEX = Hegelian Expansionism; this is explained in Essay Ten Part One.]


Small wonder then that the vast majority of scientists (outside of the old Stalinist block, and/or their 'fellow travellers') have completely ignored DL, if they have ever heard of it. [On Soviet Science, see Birstein (2001), Graham (1973, 1987, 1990, 1993, 1998), Joravsky (1961), Kojevnikov (2004), Krementsov (1997), Pollock (2006), Soyfer (1994), and Vucinich (1980, 2001).]


Trotsky himself commented on a related fact:


"In order to deal me a blow in the most vital spot Burnham informs me that in the university textbooks on logic that he deals with, the dialectic is not mentioned at all. He should have added that in the university courses on political economy Marx's labour theory of value is not mentioned either, or it is mentioned only under the sign of condemnation. And the main thing that should have been mentioned is that in the university textbook there is no mention, or only a condemnation, of historical materialism. In the courses in civil law there is no exposition, or only a condemnation, of the socialist attitude toward property forms, etc., etc.... From the fact that the dialectic is not mentioned in the university textbooks [it is essential] to draw some conclusions about the class nature of official scholarship -- its fear of revolution, the inability of bourgeois thought to go beyond the limits of empirical tasks, etc. For Burnham and his ilk the banning of Marxism from official scholarship suffices to disprove the scientific nature of Marxism." [Trotsky (1973), p.403.]


To be sure, there is plenty of prejudice against Marxism in academic circles (and elsewhere), but the reason DL isn't mentioned in logic textbooks can't be put down to bourgeois hostility since Hegel was a quintessential bourgeois philosopher himself -- whose work and ideas are, alas, experiencing a significant revival even among Analytic Philosophers (for reasons that will be explained in Essay Twelve). [On that, see for example, Redding (2007).] And yet, DL still fails to make it into logic textbooks. The reason for that is plain (and it is analogous to the reason Astrology doesn't make it into academic textbooks on Astronomy, or why Crystal Healing fails to make it into Medical textbooks): it isn't even logic.


Nevertheless, Rees refers his readers to several other theorists who have tried to find some sort of a scientific role for DL. [TAR, p.120; note 60.] Such attempts to squeeze science into an ill-fitting dialectical boot will be considered in detail in Essay Thirteen Part Two. [On David Bohm, however, see Essay Seven Part One.]


21. In fact, Trotsky might have had in mind here the way that certain systems of classical modern logic (for example, that which is presented in Principia Mathematica) employ non-logical principles in an attempt to provide a logical foundation for Mathematics. In the case of Principia, for instance, the so-called "Axiom of Infinity" and the "Axiom of Reducibility" might match Trotsky's description. On the other hand, in view of the additional fact that Trotsky seems to have been totally ignorant of MFL this is highly unlikely. More likely he was merely repeating hear-say. [However, it is just possible he might have got this idea from Jean Van Heijenoort.]


Nevertheless, this criticism (if it is what Trotsky meant) only applies to foundational work in one branch of MFL connected with the so-called "Logicist" program. Whatever the limitations and failings of Principia (in particular), or of Logicism (in general) amount to they do not necessarily affect other systems of MFL. On this, cf., Bostock (1997), Hunter (1996) and Kneale and Kneale (1978), pp.435-742. On the failings of Logicism (at least, Frege's version of it), see Noonan (2001).


In fact, it may soon prove possible to solve the paradox that stopped Frege's program in its tracks (i.e., Russell's Paradox). Should this come to pass, it wouldn't mean that Logicism had become a viable option once more -- even if it isn't susceptible to the limitations many think are suggested by Gödel's Theorem --, but it would mean that at least one reason why certain DM-theorists reject it will have disappeared.


Recently, much work has gone into this area following upon Crispin Wright's attempt to reconstruct Frege's system (in Wright (1983)). On this, see the excellent review article in MacBride (2003); see also the discussion articles by Ian Rumfitt, William Demopoulos and Gideon Rosen in Philosophical Books 44, July 2003, and the reply to these by Crispin Wright and Bob Hale in the same issue: Rumfitt (2003), Demopoulos (2003), Rosen (2003), Hale and Wright (2003). See also, Boolos (1998), Burgess and Rosen (1997), Demopoulos (1997), Dummett (1981a, 1981b, 1991, 1993, 1998a, 1998b), Hale (1987), Hale and Wright (2001), Heck (2011), Schirn (1998), Slater (2000, 2002), Teichmann (1992), Wright (1992, 1998a, 1998b).  Cf., also the special edition of Dialectica 59, 2, 2005, which is entirely devoted to this aspect of Frege's work. A note of caution, though, is registered in Burgess (2005).


However, the most profound criticisms of Principia (and of Logicism in general) were advanced by Wittgenstein. The best discussion of this topic can be found in Marion (1998). See also, Shanker (1987), Rodych (1997, 1999a, 1999b, 2000, 2002, 2011), and, in general, Hintikka (1996). In addition, cf., Floyd (forthcoming, 1 and 2). See also here.2


22. Modern-day dialecticians also find it almost impossible to resist the temptation to make similarly derogatory remarks about FL. Here is what comrades Woods and Grant had to say:


"It is necessary to acquire a concrete understanding of the object as an integral system, not as isolated fragments; with all its necessary interconnections, not torn out of context, like a butterfly pinned to a collector's board; in its life and movement, not as something lifeless and static. Such an approach is in open conflict with the so-called 'laws' of formal logic, the most absolute expression of dogmatic thought ever conceived, representing a kind of mental rigor mortis. But nature lives and breathes, and stubbornly resists the embraces of formalistic thinking. 'A' is not equal to 'A.' Subatomic particles are and are not. Linear processes end in chaos. The whole is greater than the sum of its parts. Quantity changes into quality. Evolution itself is not a gradual process, but interrupted by sudden leaps and catastrophes. What can we do about it? Facts are stubborn things." [Woods and Grant (1995), pp.82-83.]


"The subject and the predicate of the conclusion each occur in one of the premises, together with a third term (the middle) that is found in both premises, but not in the conclusion. The predicate of the conclusion is the major term; the premise in which it is contained is the major premise; the subject of the conclusion is the minor term; and the premise in which it is contained is the minor premise. For example,


a) All men are mortal. (Major premise)

b) Caesar is a man. (Minor premise)

c) Therefore, Caesar is mortal. (Conclusion).


"This is called an affirmative categorical statement. It gives the impression of being a logical chain of argument, in which each stage is derived inexorably from the previous one. But actually, this is not the case, because 'Caesar' is already included in 'all men.' Kant, like Hegel, regarded the syllogism (that 'tedious doctrine,' as he called it) with contempt. For him, it was 'nothing more than an artifice' in which the conclusions were already surreptitiously introduced into the premises to give a false appearance of reasoning." [Ibid., p.86. Quotation marks altered to conform to the conventions adopted at this site.]


However, the example these two give of a syllogism is not one that Aristotle would have recognised. [This is in fact a very common error; you will find it repeated in many a bad logic text, and in the writings of those who have not studied Aristotle too carefully.]


Aristotle would have denied it was a legitimate syllogism in view of the fact that it has a particular middle premiss which is not governed by a what we would now call a quantifier expression (e.g., "Some", "All", "Every", and "No"), but relates to a named individual.


And as far as Kant's comment is concerned (and this is an almost universal error, too), there are many valid arguments where the conclusion is not "contained" in the premisses. One such was given here. Several more can be found here.


Woods and Grant's book is full of errors like this (many of which have remained in the Second Edition, despite Alan Woods having been informed about them), just as it is replete with snide remarks about FL -- a subject about which these two seem to know as much as they do about the whereabouts of Lord Lucan and Shergar. [On this, see Note 23.]


22a. And he was repeating these obsolete ideas in unpublished notebooks:


"Human thought has assimilated the cosmogony of Kant and LaPlace, the geology of Lyell, the biology of Darwin, the sociology of Marx, which analyse every existing thing in the process of its uninterrupted change, evolution, development, catastrophes, etc. But for formal logic the syllogism remains immutable; it does not appear as an instrument, a historical lever of our consciousness in the process of its adaptation to external nature with the aim of learning about nature in a word, not a concrete historical formation conditioned by the circumstances of time and place, including the structure of our consciousness, the scope of its experience, etc. On the contrary, the syllogism appears as a once-and-for-all-given form of comprehending external events. The syllogism stands above these events, above humanity itself and its consciousness, above matter, and is the eternal beginning, immutable and all-powerful, for it controls all our activity; in other words the syllogism is invested with all the attributes of God." [Trotsky (1973), pp.401-02.]


But, these comments were already out of date sixty or seventy years before they were written.


23. Thesis, Antithesis, Synthesis Debunked


[This forms part of Note 23.]


Practically every book and/or article I have consulted on DM has included an egregious attempt to 'define' the so-called 'three laws' of FL. Why dialecticians imagine there are only three such laws is something of a mystery, anyway -- but it may have something to do with the mystical nature of the number three itself, which resurfaces in what some ill-informed dialecticians think is Hegel's method: "Thesis, Antithesis, Synthesis".


Indeed, here is what Hegel expert Terry Pinkard had to say about 'the triad' (in an interview):


"Britannica: One of the things most associated with Hegel's thought is the thesis/antithesis/synthesis scheme, the process by which reality unfolds and history progresses. But you claim this never appears in Hegel's work.


"Pinkard: This myth was started by Heinrich Moritz Chalybäus. It appears in a history he wrote of recent German philosophy (published in the 1840s), in which he said, roughly, that Fichte's philosophy followed the model of thesis/antithesis/synthesis, but Hegel went further and cosmologized that notion, extending it to the entire universe. The book was widely read (apparently the young Marx was one of its readers), and the idea stuck. It's still touted in a lot of short encyclopedia entries about Hegel. Like many little encapsulations of thought, it has the virtue of being easy to understand and easy to summarize. It's just not very helpful in understanding Hegel's thought. It has also contributed to the lack of appreciation of Hegel in Anglophone philosophy. It's not too hard to point out all the places where it doesn't apply, dismiss it as a kind of dialectical trick, and then just go on to conclude that Hegel isn't worth reading at all." [Interview here.]


Add to that these detailed comments:


"Some say Hegel used the method of: thesis-antithesis-synthesis, and others deny this. Who is correct?


"The most vexing and devastating Hegel legend is that everything is thought in 'thesis, antithesis, and synthesis.' [...] The actual texts of Hegel not only occasionally deviate from 'thesis, antithesis, and synthesis,' but show nothing of the sort. 'Dialectic' does not for Hegel mean 'thesis, antithesis, and synthesis.' Dialectic means that any 'ism' -- which has a polar opposite, or is a special viewpoint leaving 'the rest' to itself -- must be criticized by the logic of philosophical thought, whose problem is reality as such, the 'World-itself.'


"Hermann Glockner's reliable Hegel Lexikon (4 volumes, Stuttgart, 1935) does not list the Fichtean terms 'thesis, antithesis, synthesis' together. In all the twenty volumes of Hegel's 'complete works' he does not use this 'triad' once; nor does it occur in the eight volumes of Hegel texts, published for the first time in the twentieth Century. He refers to 'thesis, antithesis, and synthesis' in the Preface of the Phenomenology of Mind, where he considers the possibility of this 'triplicity' as a method or logic of philosophy. According to the Hegel-legend one would expect Hegel to recommend this 'triplicity.' But, after saying that it was derived from Kant, he calls it a 'lifeless schema,' 'mere shadow' and concludes: 'The trick of wisdom of that sort is as quickly acquired as it is easy to practice. Its repetition, when once it is familiar, becomes as boring as the repetition of any bit of sleigh-of-hand once we see through it. The instrument for producing this monotonous formalism is no more difficult to handle than the palette of a painter, on which lie only two colours....' (Preface, Werke, II, 48-49).


"In the student notes, edited and published as History of Philosophy, Hegel mentions in the Kant chapter, the 'spiritless scheme of the triplicity of thesis, antithesis, and synthesis' (geistloses Schema) by which the rhythm and movement of philosophic knowledge is artificially pre-scribed (vorgezeichnet).


"In the first important book about Hegel by his student, intimate friend and first biographer, Karl Rosenkranz (Hegels Leben, 1844), 'thesis, antithesis, synthesis' are conspicuous by their absence. It seems Hegel was quite successful in hiding his alleged 'method' from one of his best students.


"The very important new Hegel literature of this century has altogether abandoned the legend. Theodor Haering's Hegels Wollen und Werk (2 vol., Teubner, 1929 and 1938) makes a careful study of Hegel's terminology and language and finds not a trace of 'thesis, antithesis, synthesis.' In the second volume there are a few lines (pp.118, 126) in which he repeats what Hegel in the above quotation had said himself, i.e., that this 'conventional slogan' is particularly unfortunate because it impedes the understanding of Hegelian texts. As long as readers think that they have to find 'thesis, antithesis, synthesis' in Hegel they must find him obscure -- but what is obscure is not Hegel but their coloured glasses. Iwan Iljin's Hegel's Philosophie als kontemplative Gotteslehre (Bern, 1946) dismisses the 'thesis, antithesis, synthesis' legend in the Preface as a childish game (Spielerei), which does not even reach the front-porch of Hegel's philosophy.


"Other significant works, like Hermann Glockner, Hegel (2 vols., Stuttgart, 1929), Theodor Steinbüchel, Das Grundproblem der Hegelschen Philosophie (Bonn, 1933), and Theodor Litt, Hegel: Eine Kritische Erneuerung (Heidelberg, 1953), Emerich Coreth, S.J., Das Dialektische Sein in Hegels Logik (Wien, 1952), and many others have simply disregarded the legend. In my own monographs on Hegel über Offenbarung, Kirche und Philosophie (Munich, 1939) and Hegel über Sittlichkeit und Geschichte (Reinhardt, 1940), I never found any 'thesis, antithesis, synthesis.' Richard Kroner, in his introduction to the English edition of selections from Hegel's Early Theological Writings, puts it mildly when he says: 'This new Logic is of necessity as dialectical as the movement of thinking itself.... But it is by no means the mere application of a monotonous trick that could be learned and repeated. It is not the mere imposition of an ever recurring pattern. It may appear so in the mind of some historians who catalogue the living trend of thought, but in reality it is ever changing, ever growing development; Hegel is nowhere pedantic in pressing concepts into a ready-made mold (sic). The theme of thesis, anti-thesis, and synthesis, like the motif of a musical composition, has many modulations and modifications. It is never "applied"; it is itself only a poor and not even helpful abstraction of what is really going on in Hegel's Logic.'


"Well, shall we keep this 'poor and not helpful abstraction' in our attic because 'some historians' have used it as their rocking-horse? We rather agree with the conclusion of Johannes Flügge: 'Dialectic is not the scheme of thesis, antithesis, and synthesis imputed to Hegel.'


"In an essay by Nicolai Hartmann on Aristoteles und Hegel, I find the following additional confirmation of all the other witnesses to the misinterpretation of Hegel's dialectic: 'It is a basically perverse opinion (grundverkehrte Ansicht) which sees the essence of dialectic in the triad of thesis, antithesis, and synthesis.' The legend was spread by Karl Marx whose interpretation of Hegel is distorted. It is Marxism superimposed on Hegel. Thesis, antithesis, synthesis, Marx says in Das Elend der Philosophie, is Hegel's purely logical formula for the movement of pure reason, and the whole system is engendered by this dialectical movement of thesis, antithesis, synthesis of all categories. This pure reason, he continues, is Mr. Hegel's own reason, and history becomes the history of his own philosophy, whereas in reality, thesis, antithesis, synthesis are the categories of economic movements. (Summary of Chapter II, Paragraph 1.) The few passages in Marx's writings that resemble philosophy are not his own. He practices the communistic habit of expropriation without compensation. Knowing this in general, I was also convinced that there must be a source for this 'thesis, antithesis, and synthesis,' and I finally discovered it.


"In the winter of 1835-36, a group of Kantians in Dresden called on Heinrich Moritz Chalybäus, professor of philosophy at the University of Kiel, to lecture to them on the new philosophical movement after Kant. They were older, professional men who in their youth had been Kantians, and now wanted an orientation in a development which they distrusted; but they also wanted a confirmation of their own Kantianism. Professor Chalybäus did just those two things. His lectures appeared in 1837 under the title Historische Entwicklung der speculativen Philosophie von Kant bis Hegel, Zu näherer Verständigung des wissenschaftlichen Publikums mit der neuesten Schule. The book was very popular and appeared in three editions. In my copy of the third edition of 1843, Professor Chalybäus says (p.354): 'This is the first trilogy: the unity of Being, Nothing and Becoming...we have in this first methodical thesis, antithesis, and example or schema for all that follows.' This was for Chalybäus a brilliant hunch which he had not used previously and did not pursue afterwards in any way at all. But Karl Marx was at that time a student at the university of Berlin and a member of the Hegel Club where the famous book was discussed. He took the hunch and spread (it?) into a deadly, abstract machinery. Other left Hegelians, such as Arnold Ruge, Ludwig Feuerbach, Max Stirner, use 'thesis, antithesis, synthesis' just as little as Hegel.


"{Quoted from the article of Gustav E. Mueller: 'The Hegel Legend of "Thesis-Antithesis-Synthesis"', in Journal of the History of Ideas, Volume XIX, June 1958, Number 3, Page 411. The article is still as valid today as it was in 1958.}" [This can be found here. Quotation marks have been altered to conform to the conventions adopted at this site; US spelling also altered to conform to UK English. The full article is Mueller (1958).]


This suggests that Marx and all subsequent Marxists who use this 'schema' are not reliable interpreters of Hegel. [However, it is arguable that Marx was being ironic in The Poverty of Philosophy.]


If so, then, according to Lenin, that must mean that Marx didn't understand Das Kapital!

"It is impossible to understand Marx's Capital, and especially its first chapter, without having thoroughly studied and understood the whole of Hegel's Logic. Consequently, half a century later none of the Marxists understood Marx!!" [Lenin (1961), p.180. Emphases added.]


Naturally, this implies that understanding Hegel (even if that were possible) is not integral to Marxism, or we would be faced with the ridiculous conclusion that Marx did not understand the central text of Marxism (depending, of course, on how we read The Poverty of Philosophy)!


Dialectical Inanities


[This also forms part of Note 23.]


Nevertheless, to return to the DM-fable that there are just three principles underlying FL; in fact, there are countless principles underpinning MFL --, as many as there are authors prepared to set them up. As we will see, too, this fable is not even true of AFL!


[FL = Formal Logic; MFL = Modern Formal Logic; AFL = Aristotelian Formal Logic; LOC = Law of Non-contradiction;  LOI = Law of Identity; LEM = Law of Excluded Middle.]


Dialecticians who pontificate on this topic seldom (if ever) substantiate their innovative attempts to re-write the history and foundations of FL with quotations from, or citations to a single logic text. In fact, their weak efforts to come to grips with FL -- which, in my experience, is a far more challenging subject than, say, advanced Group Theory --, bear an uncanny resemblance to the lame attempts of Creationists to summarise Evolutionary Theory (in their literature or on their websites).


Piss-poor caricatures like this will only ever impress the ignorant, which seems to be the aim. Anyone who knows any MFL will see them for what they are. Those who do not will be led astray accordingly, and if experience of debating this on the internet is anything to go by, such benighted comrades refuse to be told, preferring instead to believe what Engels, Plekhanov or Trotsky tell them about AFL, or logic in general.


This is the only explanation I can come up with to account for the fact that seemingly intelligent comrades (who are otherwise quite knowledgeable in science, economics, history, current affairs, etc. etc.) constantly produce descriptions of FL that are not only demonstrably incorrect, they aren't even coherent in their own terms -- as will be demonstrated presently. [I examine the reasons for this self-inflicted nescience in Essay Nine Parts One and Two.]


It is to be hoped that long exposure to DL hasn't completely destroyed the critical faculties of such comrades -- although in what follows it will become painfully clear that the case for the defence is considerably weakened with the publication of each new book or article on dialectics.


Below, I reproduce just a few of the crass things dialecticians have said about AFL (and FL in general), much of which is highly repetitive, anyway. Again, it is to be hoped that having read through what follows, the conclusion that dialecticians simply copy these allegations off one another without bothering to check them, or devote much thought to them, will also have occurred to the reader, and not just the present writer.


Apologies are due once again to the hardy souls who have to wade through what follows for my having to inflict yet more of this sorry material on them -- but they can spare a thought for yours truly who has had to read this stuff, and very much more, over and over again for over twenty-five years, in order to try to make some sort of sense of it.


Recall, too, that the quotations reproduced here are only a tiny fraction of those that could have been listed.


A particularly egregious example of this type of confusion can be found in Novack's book on DL:


"There are three fundamental laws of formal logic. First and most important is the law of identity. This law can be stated in various ways such as: A thing is always equal to or identical with itself. In algebraic terms: A equals A.


"...If a thing is always and under all conditions equal to or identical with itself, it can never be unequal to or different from itself. This conclusion follows logically and inevitably from the law of identity. If A always equals A, it can never equal non-A.


"This conclusion is made explicit in the second law of formal logic: the law of contradiction. The law of contradiction states: A is not non-A. This is no more than the negative formulation of the positive assertion expressed in the first law of formal logic. If A is A, it follows, according to formal thinking that A can't be non-A. Thus the second law of formal logic, the law of contradiction forms the essential supplement to the first law.


"Some examples: a man can't be inhuman; a democracy can't be undemocratic; a wageworker can't be a non-wageworker.


"The law of contradiction signifies the exclusion of difference from the essence of things and of thought about things. If A is necessarily always identical with itself, it can't be different from itself. Difference and identity are, according to these two rules of formal logic, completely different, utterly disconnected, mutually exclusive characteristics of both things and thoughts.


"This mutually exclusive quality of things is expressly taken note of in the third law of formal logic. This is the law of the excluded middle. According to this law, everything is and must be either one of two mutually exclusive things. If A equals A, it can't equal non-A. A can't be part of two opposing classes at one and the same time. Wherever two opposing statements or states of affairs confront each other, both can't be true or false. A is either B or it is not B. The correctness of one judgement invariably implies the incorrectness of its contrary, and vice versa." [Novack (1971), pp.20-21.]


The LOI will be discussed in considerable detail in Essay Six, but the reader will note that Novack -- except in one instance (discussed below) -- nowhere attempts to substantiate these wild assertions with a reference to a single FL-text. To be sure, he paraphrases Aristotle from time to time, but it is quite clear that he mastered little of what he read.


Let us be clear then what Aristotle himself said:


"So it must be possible to deny whatever anyone has affirmed. Thus it is clear that for every affirmation there is an opposite negation, and for every negation an opposite affirmation. Let us call an affirmation and a negation which are opposite a contradiction. I speak of statements as opposite when they affirm and deny the same thing of the same thing -- not homonymously, together with all other such conditions that we add to counter the troublesome objections of sophists....


"I call an affirmation and a negation contradictory opposites when what one signifies universally the other signifies not universally, e.g. every man is white -- not every man is white, no man is white -- some man is white. But I call the universal affirmation and the universal negation contrary opposites, e.g. every man is just -- no man is just. So these can't be true together, but their opposites may both be true with respect to the same thing, e.g. not every man is white -- some man is white.


"Of contradictory statements about a universal taken universally it is necessary for one or the other to be true or false; similarly if they are about particulars, e.g. Socrates is white -- Socrates is not white. But if they are about a universal not taken universally it is not always the case  that one is true and the other false. For it is true to say at the same time that a man is white and that a man is not white, or that a man is noble and that a man is not noble.... This might seem absurd at first sight, because 'a man is not white' looks as if it signifies also at the same time that no man is white; this, however, does not signify the same, nor does it necessarily hold at the same time." [Aristotle (1984b), pp.27-28. Emphasis added.]


In the above passage, Aristotle was alluding to an early version of his famous "Square of Opposition" (this links to Parsons (2012):



Figure Three: The 'Square Of Opposition'


[On this, see also here.]


Readers will, I hope, note the sophistication apparent in Aristotle's first attempts to say clearly how he intends to use certain words, just as they will note how little the musings of comrade Novack correspond with them. In fact, Aristotle says the opposite of what Novack attributes to both him and FL.


Moreover, I can find no reference to the LOI in Aristotle's work. [On that, see here.]


Since this Essay was originally posted, however, the above reference has been edited; the one I linked to earlier can be found here.


The original Wikipedia article asserted that no occurrence of the law of identity could be found in anyone's work prior to that of St Thomas Aquinas in the 13th century; however, the comments page asserts that the first instance of it occurs in John Locke.


The editorial change doesn't alter much (it just loses that useful fact), but it does locate a use of identity in Aristotle (but as far as I can see, Aristotle neither uses that word, nor that 'Law'). And even then, Aristotle doesn't connect identity with his logic.


Anyway that article quotes Aristotle as follows:


"Now 'why a thing is itself' is doubtless a meaningless inquiry; for the fact or the existence of the thing must already be evident (e.g. that the moon is eclipsed) but the fact that a thing is itself is the single formula and the single cause to all such questions as why the man is man, or the musical musical, unless one were to say that each thing is inseparable from itself; and its being one just meant this. This, however, is common to all things and is a short and easy way with the question." [Aristotle (1984e), p.1643; Book VII, Part 17. I have used a more modern translation than seems to have been used by the author of the Wikipedia article. This is available here; scroll down to Part 17. This is clearly the source the author of the said article used.]


So, far from basing his logic on this notion, Aristotle seems quite dismissive of it.


Indeed, he seems to be making a totally different point, as I noted on the 'Talk' page:


And the quotation takes this 'law' out of context, for not only does Aristotle not mention 'identity', he specifically talks about predication (and since identity is a relation, he can't be talking about identity):


"Let us state what, i.e. what kind of thing, substance should be said to be, taking once more another starting-point; for perhaps from this we shall get a clear view also of that substance which exists apart from sensible substances. Since, then, substance is a principle and a cause, let us pursue it from this starting-point. The 'why' is always sought in this form -- 'why does one thing attach to some other?' For to inquire why the musical man is a musical man, is either to inquire -- as we have said why the man is musical, or it is something else. Now 'why a thing is itself' is a meaningless inquiry (for (to give meaning to the question 'why') the fact or the existence of the thing must already be evident -- e.g. that the moon is eclipsed -- but the fact that a thing is itself is the single reason and the single cause to be given in answer to all such questions as why the man is man, or the musician musical', unless one were to answer 'because each thing is inseparable from itself, and its being one just meant this'; this, however, is common to all things and is a short and easy way with the question). But we can inquire why man is an animal of such and such a nature. This, then, is plain, that we are not inquiring why he who is a man is a man. We are inquiring, then, why something is predicable of something (that it is predicable must be clear; for if not, the inquiry is an inquiry into nothing). E.g. why does it thunder? This is the same as 'why is sound produced in the clouds?' Thus the inquiry is about the predication of one thing of another. And why are these things, i.e. bricks and stones, a house? Plainly we are seeking the cause. And this is the essence (to speak abstractly), which in some cases is the end, e.g. perhaps in the case of a house or a bed, and in some cases is the first mover; for this also is a cause. But while the efficient cause is sought in the case of genesis and destruction, the final cause is sought in the case of being also." [Quoted from here. Bold emphases added.]


There is, however, another site on the Internet that does manage to trace the history of this 'Law' (and it isn't to Aristotle, but to Medieval Roman Catholic Logicians), but since that site is run by an overt fascist, I won't cite it. [A Google search will soon find it, though -- that is, if you can stomach the rest of the material you will find there!]


Now, it may be that Novack consulted a particularly poor logic text (and, alas, there are plenty of those about), or none at all and just made things up. But, if he did either of these, he wisely kept that shameful secret to himself. [In fact, as we will see in Essay Twelve, Novack was relying largely on Hegel (and possibly on a few other traditional 18th or 19th Century logicians, who made similar mistakes).]


[Readers are encouraged to read the rest of De Interpretatione; the above gives just a hint of the sophistication Aristotle attempted to bring to the subject all those years ago, something Hegel either did not appreciate, or tried his best to undo. DM-fans have simply compounded this major step backward, and in an age when logic is far better understood than at any other time in history.]


Now, as far as specifics are concerned, it turns out that Aristotle says the opposite of what Novack attributes to FL:


"...For example, the negation of 'to be a man' is 'not to be a man', not 'to be a not-man', and the negation of 'to be a white man' is 'not to be a white man', not 'to be a not-white man'....


"...For it is possible for the same thing to be and not to be: such statements are not contradictories of one another...." [Ibid., p.34. Emphases added.]


Here, it is pretty clear that Aristotle wouldn't have accepted Novack's use of "non-A" as the contradictory of "A", for instance.


The sort of negation Aristotle is alluding to above (where he rejects expressions containing "not-man" as contradictories of those that contain "man") is called "predicate-term negation". [On that see here.]


The failure to notice the difference between predicate negation and predicate-term negation has clearly confused dialecticians like Novack (and, once again, this error is almost universal among DM-theorists). And yet, this is something Aristotle understood over two millennia ago!


Naturally, logic has moved on considerably since Aristotle's day, as have mathematics and science in general. No one (that is, other than traditionalists and confused dialecticians) would be happy with his characterisation of contradictions (etc.) today. However, it is nonetheless apparent from what Novack and the other DL-fans quoted below say that they are significantly less logically advanced than Aristotle was 2400 years ago! It is equally clear that Novack didn't consult Aristotle's writings before he simply made up the above comments, just as it is apparent that the same can be said for the other comrades quoted below. For example, Novack pointedly confuses the LOI 'stated negatively', with the LOC:


"This conclusion is made explicit in the second law of formal logic: the law of contradiction. The law of contradiction states: A is not non-A. This is no more than the negative formulation of the positive assertion expressed in the first law of formal logic. If A is A, it follows, according to formal thinking that A can't be non-A. Thus the second law of formal logic, the law of contradiction forms the essential supplement to the first law.


"Some examples: a man can't be inhuman; a democracy can't be undemocratic; a wageworker can't be a non-wageworker.


"The law of contradiction signifies the exclusion of difference from the essence of things and of thought about things. If A is necessarily always identical with itself, it can't be different from itself. Difference and identity are, according to these two rules of formal logic, completely different, utterly disconnected, mutually exclusive characteristics of both things and thoughts.


"This mutually exclusive quality of things is expressly taken note of in the third law of formal logic. This is the law of the excluded middle. According to this law, everything is and must be either one of two mutually exclusive things. If A equals A, it can't equal non-A. A can't be part of two opposing classes at one and the same time. Wherever two opposing statements or states of affairs confront each other, both can't be true or false. A is either B or it is not B. The correctness of one judgement invariably implies the incorrectness of its contrary, and vice versa." [Novack (1971), pp.20-21.]


As I will show in Essay Eight Part Three, there is no connection at all between the LOI 'stated negatively' and the LOC. The same comments apply to Novack's attempt to drag the LEM into this.


To be sure, Aristotle makes many mistakes; for example, he often confuses propositions with what he calls "terms" (e.g., almost all the way through Prior Analytics), and he criss-crosses between talk about talk and talk about things, running both of these together at times, but he does at least try to be scrupulously careful. He was, after all, starting almost from scratch. Anyone who reads his work (and who doesn't rely on comrades like Novack to put them off) will soon see why Marx thought so highly of him.


However, Novack does at least try to make some sort of a weak attempt to support what he says in the following with a direct reference to Aristotle (his only one in fact, as far as I can determine):


"Let me cite an interesting example of this kind of thinking from Aristotle's writings. In his Posterior Analytics (Book 1; ch.33, p.158 -- this is in fact pp.146-47 in the edition I have used; RL), Aristotle says that a man can't simultaneously apprehend first, that man is essentially animal, i.e., can't be other than animal -- and second, that man is not essentially animal, that is, may assume that he is other than animal. That is to say, a man is essentially a man and can never be thought of as not being a man." [Novack (1971), p.21.]


Now, if we check what Aristotle actually says, we see things aren't quite as Novack would have us believe (which is perhaps why Novack chose to paraphrase, but not to quote the passage in question):


"Similarly there is both knowledge and opinion of the same thing. For the one is of animal in such a way that it can't not be an animal, and the other in such a way that it can be -- e.g. if the one is just what is man, and the other of man but not of just what is man. For it is the same because man is the same, but the manner is not the same.


"It is also evident that it is not possible to opine and to understand the same thing at the same time. For one would at the same time hold the belief that the same thing can be otherwise and can't be otherwise, which is not possible. For in different men it is possible for there to be each of these attitudes with regard to the same thing, as has been said; but in the same man it is not possible even in this way; for he will at the same time hold a belief, e.g. that a man is just what is an animal (for this is what it was for it not to be possible for something not to be an animal), and that a man is not just what is an animal (for let that be what it is for it to be possible)." [Aristotle (1984d), pp.146-47. Bold emphases added.]


Admittedly, this passage is not the clearest that has ever been committed to paper, but it nowhere mentions "essence", and although it contains allusions to the LOC, it is couched in such terms as to make Novack's 'paraphrase' prejudicial, if not misleading, to say the least. The sections in bold bring this out. Hence, Aristotle's position is far more complex than Novack will allow, but he is happy to misrepresent him nonetheless.


Finally, on Novack: Aristotle says that "It is also evident that it is not possible to opine and to understand the same thing at the same time....", and with reference to Novack, at least, I think we can agree with Aristotle on that one. Indeed, just like other DM-fans, Novack shows that not only has he not grasped the basics of FL, but he is nonetheless quite happy to pontificate/"opine" about it.


Nevertheless, a measure of the sophistication modern logicians attempt to bring to the subject can be judged from the content of even introductory textbooks on the Philosophy of Logic. For example: one that takes a very 'Oxford' view is Wolfram (1989); a different slant can be found in Haack (1979). Now, dialecticians like to call such attention to detail shown in books like this "pedantry", but it is abundantly clear that their own relaxed attitude to what is a very difficult topic allows them to indulge in some easy, but eminently sloppy, thought.


[Bertrand Russell once said: "Most people would rather die than think, in fact they do." He didn't have dialecticians in mind when he said this, but he perhaps should have.]


More challenging material can be found in, say, Goble (2001), Jacquette (2002, 2006), Quine (1970) and Shapiro (2005). [This links to a PDF.]


As we will see in Essay Six, the LOI does not preclude change; however, in Essays Five, Seven Part One and Eight Parts One, Two and Three, it will be shown that it is dialecticians themselves who can't account for motion or change.


[As far as Aristotle and change are concerned, see here.]


As an excellent historian of science one would have expected Clifford Conner to know better, but as an avowed pupil of George Novack, he plainly doesn't. In fact he happily emulates the master, making all the usual mistakes -- except he is content to make do with just one basic law of FL:


"The central principle on which formal logic is built can be expressed in a simple formula that at first glance appears to be a self-evident truth 'A equals A'....


"Beginning with this law you can derive all of formal logic. One important corollary is the law of exclude of middle. That is, if 'A equal B' is a true statement, then 'A is not equal to B' must be a false statement. A is either identical to B or it is not. It's one or the other; there is no middle ground." [Conner (1992), p.22.]


[The above comments appeared in a section entitled Aristotle's Formal Logic, leaving the reader in no doubt that the author associated them with Aristotle's logic.]


Of course, Conner offered his readers no evidence in support of these allegations (we have already seen they can't be found in Aristotle), nor did he explain how the LEM can be derived from the LOI. Of course, if the LEM is correct, then what Connor says is the case, but then the LEM can't be a corollary of the LOI, since what he says follows only on the basis of both 'laws'. Neither takes precedence.


Be this as it may, it would be interesting to see Conner derive all of FL from the LOI -- including disjunctive and conjunctive normal forms, to say nothing of consistency and completeness proofs. [On these, see Lemmon (1996), pp.75-91, 189-200, and Hunter (1996), pp.137-215.]


Equally, if not more wide of the mark are comrades Woods and Grant:


"According to formal logic, the whole is equal to the sum of its parts....


"Let us examine the matter more closely. The basic laws of formal logic are:


1) The law of identity ('A' = 'A').


2) The law of contradiction ('A' does not equal 'not-A').


3) The law of the excluded middle ('A' does not equal 'B')....


"The law of contradiction merely restates the law of identity in a negative form. The same is true of the law of the excluded middle. All we have is a repetition of the first line in different ways. The whole thing stands or falls on the basis of the law of identity ('A' = 'A'). At first sight this is incontrovertible, and, indeed, the source of all rational thought. It is the Holy of Holies of Logic, and not to be called into question. Yet called into question it was, and by one of the greatest minds of all time....


"Similarly with the law of the excluded middle, which asserts that it is necessary either to assert or deny, that a thing must be either black or white, either alive or dead, either 'A' or 'B'. It can't be both at the same time. For normal everyday purposes, we can take this to be true. Indeed, without such assumptions, clear and consistent thought would be impossible. Moreover, what appear to be insignificant errors in theory sooner or later make themselves felt in practice, often with disastrous results. In the same way, a hairline crack in the wing of a jumbo jet may seem insignificant, and, indeed, at low speeds may pass unnoticed. At very high speeds, however, this tiny error can provoke a catastrophe. In Anti-Dühring, Engels explains the deficiencies of the so-called law of the excluded middle:


"'To the metaphysician,' wrote Engels, 'things and their mental images, ideas, are isolated, to be considered one after the other and apart from each other, fixed, rigid objects of investigation given once for all. He thinks in absolutely unmediated antitheses. 'His communication is "yea, yea; nay, nay"; for "whatsoever is more than these cometh of evil." For him a thing either exists or does not exist; a thing can't at the same time be itself and something else. Positive and negative absolutely exclude one another; cause and effect stand in a rigid antithesis one to the other.'" [Woods and Grant (1995), pp.57, 91-93. Quotation marks altered to conform to the conventions adopted at this site.]


[We will have occasion to note later that Engels was not afraid of drawing his own hard and fast antitheses, but that will have to pass for now. And what these two comrades have to say about the LOI will be dealt with in detail in Essay Six.]


I have made several comments about the sophomoric errors in Woods and Grant's book here, and at the end of this note, but for present purposes it is worth pointing out that (like other DM-fans) these two comrades referenced no logic texts as a basis for their 'definitions'. To be sure, here and there they used a few ideas lifted from two introductory logic books (i.e., those written many years ago by Luce, and Cohen and Nagel), but they failed to reveal from which lamentably poor textbook they dredged these prize specimens:


"1) The law of identity ('A' = 'A').


 2) The law of contradiction ('A' does not equal 'not-A').


 3) The law of the excluded middle ('A' does not equal 'B')...." [Ibid., p.91.]


Quite what the LOC has to do with whether "A" can or can't equal "not-A", Woods and Grant failed to say. As we will also find is the case with Hegel (and Novack above), these two have confused the LOC (which is about the truth-functional connection between a proposition and its negation, it is not about objects like "A", still less is it about "equality") with the LOI "stated negatively". This is discussed in detail in Essay Eight Part Three.


[On the LOC in general, see Horn (2006). Unfortunately, Professor Horn alleges, without textual support, that the LOI was a foundational axiom for Aristotle's logic. I have e-mailed him about this (January 2009). For his reply, see here.]


Readers will note, too, that Aristotle, for example, can only be made to say such inane things if what he actually says (reproduced above) is ignored, and his words are altered so that they say the opposite of what he intended.


In that case, clearly, "Aristotle does not equal Aristotle", according to Woods and Grant. The important thing is not to interpret Aristotle but to change him.


Indeed, while they are happy to tell us that according to FL "the whole is equal to the sum of its parts", what Aristotle in fact said was this:


"In the case of all things which have several parts and in which the totality is not, as it were, a mere heap, but the whole is something beside the parts...." [Aristotle (1984e), p.1650. I have used the on-line version, here.]


Even for those blinded by dialectics, this is hardly an "equal to".


Moreover, their characterisation of the LEM is laughable. What, it may be wondered, has "A is not equal to B" got to do with whether concerning proposition "p", "either p is true or p is false" (or in some versions "p v ¬p" -- "¬" being the sign for negation)? Do these two honestly believe that an intellect of the stature of Aristotle believed that their version of the LEM was one of his foundational principles? [Indeed, the long quotation from De Interpretatione given above explicitly contradicts what these two assert.] Or, that there are any other logicians (who are not still in the "care of the community") who would accept this caricature of the LEM? No wonder they failed to provide a reference for their fictional 'version' of it.


But, there is worse to come:


"Even the simplest judgement, as Hegel points out, contains a contradiction. 'Caesar is a man,' 'Fido is a dog,' 'the tree is green,' all state that the particular is the universal. Such sentences seem simple, but in fact are not. This is a closed book for formal logic, which remains determined to banish all contradictions not only from nature and society, but from thought and language itself. Propositional calculus sets out from exactly the same basic postulates as those worked out by Aristotle in the 4th century B.C., namely the law of identity, the law of (non-) contradiction, the law of excluded middle, to which is added the law of double negation. Instead of being written with normal letters, they are expressed in symbols thus:


"a) p = p


"b) p = ~p


"c) p V = ~p (sic)


"d) ~(p ~ p) (sic)


"All this looks very nice, but makes not the slightest difference to the content of the syllogism." [Ibid., pp.97-98. This material has now been dropped form the Second Edition.]


This is what a)-d) translate out as:


a) p is equal to p


b) p is equal to not-p


c) p or equals not-p (sic)


d) not both p not-p (sic)


a) and b) would be syntactically viable if "p" were an object, but it isn't.


[But, if "p" were an object, it could not be used to say anything. This is precisely the mistake Hegel made, which error dialecticians have simply copied; more on that here.]


c) and d) are just plain gibberish.


Clearly, these two comrades didn't obtain these prize examples of syntactical confusion from a logic text written anywhere on this planet -- which could mean that they simply made them up. At any rate, this shows that they made no serious effort to comprehend much of what they constantly deride. Witness the way that they confuse the Propositional Calculus with Aristotelian Syllogistic. The former was invented by the Stoics (and then largely forgotten until the middle of the 19th century); Aristotle knew nothing of it, as far as we know.


[Fortunately, the syntactic confusion above has been removed from the second edition of their book -- probably because a supporter of this site e-mailed Alan Woods about it several years ago. Having said that, many other errors that were pointed out to him have not been corrected, and the confused syntax quoted above still remains in the on-line version.]


Of course, the comment these two make about the contradictions allegedly implicit in simple predicative propositions is itself based on a novel piece of grammar (also lifted from Hegel, who borrowed it from Medieval Roman Catholic Logicians). "Caesar is a man" (W1) does not say the particular is the universal, and can only be made to say so by imposing on it a grammatical theory that these two comrades failed to justify. [Indeed, it can't be justified; on that see Essay Three Part One.] And even if W1 could be construed in this way, Woods and Grant failed to say why this is a contradiction, as opposed to it being a simple falsehood -- or, indeed, just plain unvarnished nonsense.


Exactly who they are seeking to influence with these blatant fibs is clear enough (i.e., those as ignorant of FL as they are), but the fact that they link Marx's great name and reputation to this rubbish is something for which they should hang their heads in shame. [The fact that they won't just about says it all.]


We also read something similar, and no less inventive, at the Socialist Party's website:


"The formal logician operates within the limitation of three laws:


"The Law of Identity -- where A is equal to A


"The Law of Contradiction -- where A can't be equal to non-A


"The Law of Excluded Middle -- where A must be equal to A, or must not be equal to A." [Quoted from here.]


It looks like the split between Woods and Grant and what later became the Socialist Party hasn't improved either side's grasp of logic.


[The lack of any connection between the LOC and the supposed negation of the LOI is discussed here.]


Not to be outdone in this respect, other comrades have vied to be crowned 'The Worst Expositor of Traditional Logic' in modern times. Here is Plekhanov's impressive bid:


"The 'fundamental laws of thinking' are considered to be three in number: 1) The law of identity; 2) the law of contradiction, and 3) the law of the excluded middle.


"The law of identity...states that 'A is A' or 'A = A'.


"The law of contradiction... -- 'A is not A' -- is merely a negative form of the first law.


"According to the law of the excluded middle...two opposing judgements that are mutually exclusive can't both be wrong. Indeed, 'A is either B or non-B'. The truth of either of these two judgements necessarily means the falseness of the other, and vice versa. There is not, neither can there be, any middle." [Plekhanov (1908), pp.89-90. Italics in the original. The online version translates this differently.]


And how does Plekhanov counter the garbled ideas he attributes to FL?


"Let us examine the matter from another angle.


"The motion of matter lies at the root of all natural phenomena. But what is motion? Here we have what seems to be a contradiction. If you are asked whether a body that is in motion is located at a particular place at a particular moment, you will be unable, however hard you try, to give an answer using [the above rules].... A moving body is at a particular place, and at the same time it is not there." [Ibid., p.90. Italics in the original.]


As we will see in Essay Five, this move was unwise (no irony or pun intended). The contradiction Plekhanov alleges is in fact no contradiction.


Even so, Plekhanov's own formulation of the LOC is fraught with problems: "A is not A" is merely the (alleged) negative form of his own ill-defined version of the LOI! He would be hard-pressed to find a logician not the worse for drink or drugs who would recognise it  as the LOC (not the least, once more, because it confuses -- a là Hegel -- objects with propositions). Small wonder then that Plekhanov (like other DM-fans) failed to refer his readers to a single logic text to substantiate this example of pure fiction.


[To be sure, Plekhanov does reference Überweg's Logic, but not in support of this particular 'definition' of the LOC. We will see later that Hegel was the source of this odd idea: that the LOI "stated negatively" yields the LOC.


Added on edit: In fact, as far as I can determine, this error can be traced back as far as Leibniz -- a vastly superior logician!]


Moreover, it is equally clear that Plekhanov confused the LEM with Aristotle's definition of contraries (see above), and then later with a semi-classical version of the LOC (that is, one that confuses propositions with "judgements"). As to whether there can be any 'middle' "judgements": clearly there can, since someone can judge in error. But, whether the LEM allows for these will depend on the examples chosen, and on how one characterises a proposition. [On this see Geach (1972c).]


[Readers should once again compare Aristotle's carefully worded prose with the sloppy use of language offered up by comrade Plekhanov.]


Here is Joseph Dietzgen:


"The first principle [the 'Law of Identity' -- RL] , then, declares that A is A, or to speak mathematically, every quantity is equal to itself. In plain English: a thing is what it is; no thing is what it is not....


"[The old logic] insists on its first, second and third law, on its identity, its law of contradiction and excluded third, which must be either straight or crooked, cold or warm and excludes all intermediary conceptions." [Dietzgen (1906), pp.386-89.]


Is it really the case that Aristotle knew nothing of warm weather, warm clothing or a warm smile?

For the UK-SWP, this is how John Molyneux manages to get things hopelessly wrong:


"Dialectics is the logic of change....


"To understand the significance of this compare it with what is know as 'formal logic' (originally developed by Aristotle and usually thought of as the rules of sound thinking). The basic idea of formal logic is that something either is the case or is not the case, but that it can't be both at the same time. For example, the cat is on the mat or it is not on the mat.


"For many purposes formal logic is useful and necessary. But as soon as you take movement and change into account, it ceases to be adequate. A cat moving goes through a moment when it is in the process of passing onto the mat or in the process of passing off it -- when it is both on and off the mat. Dialectics is in advance of formal logic because it enables us to grasp this contradiction." [Molyneux (1987), pp.49-50.]


Precisely how DL manages to help anyone "grasp" this spurious contradiction Molyneux left his readers to guess. But, what is there especially difficult about a cat being partially on or off a mat? Clearly, if the said cat falls asleep half on, half off the said mat we would still have the same 'contradiction', but no motion. In which case, this 'contradiction' has nothing to do with the ambulatory habits of furry mammals.


However, as we shall see in Essay Five, DL can't even account for the motion of domestic pets, mat or no mat; Diamat or no Diamat. And, as far as their capacity to "grasp" 'contradictions' like these is concerned -- as seems plain -- dialecticians are content merely to label such ambiguous states of affairs "contradictions", and move on. Exactly how this helps anyone "grasp" anything is left entirely mysterious. In what way does it help us comprehend motion to be told it is contradictory?


But, don't even think to ask, let alone to complain, or you risk being accused of "not understanding" dialectics.


And does Molyneux really believe that logicians/scientists (of the calibre of, say, Aristotle) failed to spot that things change?


In fact, Aristotle himself tells us he did:


"...A able to receive contraries. For example, an individual man -- one and the same -- becomes pale at one time and dark at another, and hot and cold, and bad and good.


"...Suppose, for example, that the statement that somebody is sitting is true; after he has got up this same statement will be false. Similarly with beliefs.... However, even if we were to grant this, there is still a difference in the way contraries are received. For in the case of substances it is by themselves changing that they are able to receive contraries. For what has become cold instead of hot, or dark instead of pale, or good instead of bad, has changed (has altered); similarly in other case too it is by itself undergoing change that each thing is able to receive contraries.... [I]t is because the actual thing changes that the contrary comes to belong to them...." [Aristotle (1984f), p.7. Italics in the original; bold emphases added. The on-line versions renders this passage slightly differently.]


Admittedly, the above work of Molyneux's is an introductory text; when he raised this point with a supporter of this site in private correspondence, he recommended that critics like those of us who post at this site should concentrate on the DM-classics, and ignore the writings of relatively minor figures like himself. As should now seem plain, the situation there is no better, and, in some cases, it is far worse.


However, the above passage at least scotches the myth that Aristotle's logic can't accommodate change. [See also Aristotle (1984f), pp.23-24, where he analyses six different types of change; this passage can be found here, but scroll down to Part 14.]


Unfortunately, Molyneux repeated these serious misconceptions at his blog:


"This matters because the dominant mode of thinking, based on the logic developed by Aristotle, is not founded on the principle of universal change, rather it deals with fixed states or 'things'. Its basic axioms are that A = A (a thing is equal to itself) and A does not = non-A (a thing is not equal to something other than itself), from which are derived sequences of sound reasoning known as syllogisms." [The Marxist Dialectic.]


Molyneux failed to show how a single syllogism follows from these illusory principles.


["A thing is not equal to something other than itself"?!? What the dialectics does that mean? And, what precisely has it got to do with FL?]


As this Essay has shown, the above paragraph contains nearly as many errors as it does words. I have posted a suitable reply here (which, as we can now see from his new book -- Molyneux (2012) --, sailed right over his head).


He also argues as follows:


"This formal logic was, and is, all well and good and very necessary for practical human affairs but it is limited -- it excludes change. Dialectical logic moves beyond formal logic by starting not with 'things' but with processes, processes of coming into being and passing out of being. The moment processes of change are fed into the equation it becomes necessary to deal with contradiction. If state A (e.g. day) changes into state B (night) it passes through a phase of A not being A or being both A and B (twilight)." [The Marxist Dialectic.]

But, twilight looks pretty much like a "state" (certainly as much a "state" as night and day are). Even so, it can't be a unity of twilight and not-twilight -- which it should be if all things, including twilight, is a UO. On the other hand, if it isn't a UO, then it can't change!


And, of course, if day is no longer day, but is twilight, then the above "A" (interpreted as "day" in Molyneux's example) is not in fact "A and not A", it is "C" (twilight); in which case, it isn't "A and B" either, as Molyneux asserts -- it is "A and C"!


To be sure, it might be possible to get around this by defining twilight as a combination of both day and night, but that would make Molyneux's assertions stipulatively true, and would as such have been imposed on nature.


As we will see in Essay Seven Part Three, none of this makes sense even in DM-terms. Night does not "struggle" with day to produce twilight, so exactly how this alleged 'contradiction' makes anything change is a mystery. And, if this alleged contradiction does not/can't cause change, how is it a 'dialectical contradiction' (even if we knew what one of these odd entities was)?


Also worth asking: What exactly is the 'internal opposite' of day that makes it change into night? Molyneux failed to say, and it isn't difficult to see why; day has no 'internal opposite'. Its alleged opposite is night, but that is manifestly external to day. So, unless we believe that the future can change the present (arguing perhaps that the fact that night is hours away allows it to 'back-cause' day to change into night!), Molyneux's own example can't be an instance of dialectical change to begin with!


Now, Aristotle certainly believed that during change something must remain the same (but precisely what that "something" was is subject to controversy among Aristotle scholars) -- for example, in Aristotle (1984e), p.1595. But, he also claimed that:


"...since it is impossible that contradictories should be at the same time true of the same thing, obviously contraries also can't belong at the same time to the same thing.... If, then, it is impossible to affirm and deny truly at the same time, it is also impossible that contraries should belong to a subject at the same time, unless both belong to it in particular relations, or one in particular relation and one without qualification." [Aristotle (1984e), p.1597.]


Here Aristotle allows contrary predicates to belong to a subject providing they attach to it "in particular relations"; presumably this means they could belong to parts of that subject separately (when say a poker is cold at one end, hot at another, or when a man is half wet, half dry, for example), and not 'essentially'. Nevertheless, it is clear from this, as it is from Aristotle's other writings, that he continually switches back and forth without warning between talk about talk and talk about things. In so doing, he generates no little confusion himself, which is, of course, one of the reasons modern logicians have had to re-think the whole subject from the ground floor up over the last 150 years. But, having said that, as confused as he was, Aristotle is a model of clarity compared to dialecticians. [On that, see here.]


Alas, in subsequent writings, Molyneux failed to correct these serious errors (even though he had been informed him of them); if anything, he succeeded in compounding them:


"Accompanying the development of practical human knowledge and science..., there was also developed (by Aristotle and his successors) a system of logic, i.e., rules of sound thinking. Logic was meant to tell you whether or not what you were saying, writing or thinking, made sense. A proposition that was logical was not necessarily true (in fact), but it had the possibility of being true. A proposition that was not logical, i.e., broke the rules of logic, could not possibly be true." [Molyneux (2012), p.43. Some punctuation marks modified to conform the conventions adopted at this site.]


But, what does Aristotle himself tell us is the point of his logic? Wonder no more:


"First we must state the subject of the enquiry and what it is about: the subject is demonstration and it is about demonstrative understanding. Next we must determine what a proposition is, what a term is, and what a deduction is (and what sort of deduction is perfect and what is imperfect); and after that, what it is for one thing to be or not to be in another as a whole, and what we mean by being predicated of every or of no." [Aristotle (1984c), p.39.]


The on-line version renders this passage as follows:


"We must first state the subject of our inquiry and the faculty to which it belongs: its subject is demonstration and the faculty that carries it out demonstrative science. We must next define a premiss, a term, and a syllogism, and the nature of a perfect and of an imperfect syllogism; and after that, the inclusion or noninclusion of one term in another as in a whole, and what we mean by predicating one term of all, or none, of another." [Quoted from here.]


[By "demonstration" Aristotle means "proof". (On this, see Lear (1980), p.1.)]


Not much there about logic being the study of what makes sense. A bad start, for sure, but things only get worse:


"The basic principles of this Aristotelian of formal logic were the 'law of identity' and the 'law of non-contradiction'. The 'law of identity' stated, in symbolic terms, that A is equal to A, or that an ounce of gold equals an ounce of gold, or, taking a unique object..., Leonardo da Vinci's Mona Lisa is equal to Leonardo da Vinci's Mona Lisa. The 'law of non-contradiction' stated that A can't be equal to non-A, it makes not sense to say that an ounce of gold is not an ounce of gold or the Mona Lisa is not the Mona Lisa. On the basis of these apparently 'obvious' propositions a system of logic or sound reasoning was erected, exemplified by the syllogism." [Molyneux (2012), p.43. Quotation marks altered to conform the conventions adopted at this site. Italic emphases in the original.] 


Once again, just like the other DM-fans discussed in these paragraphs, Molyneux neither quotes nor cites even so much as a single sentence from Aristotle in support of these clichéd accusations. As we have seen, the LOI was a Medieval invention, and the LOC doesn't concern itself with what does or does not equal something else, or even itself. [See also below.]


A few pages earlier, Molyneux added this not unreasonable comment:


"Marxist materialism is repeatedly attacked by the method of oversimplifying and caricaturing it to the point where it is obviously false...." [Molyneux (2012), p.36.]


And yet this is precisely what he and other DM-fans regularly do when they attempt to discuss or criticise FL.


I will add a few more comments about Molyneux's book in a later re-write of this Essay.


Next, we turn to the 'definitions' advanced by comrade Mandel:


"Dialectics, or the logic of motion, is distinct from formal or static logic. Formal logic is based on three fundamental laws:


"(a) The law of identity: A is equal to A; a thing is always equal to itself.


"(b) The law of contradiction: A is different from non-A; A can never equal non-A.


"(c) The law of exclusion: either A, or non-A; nothing can be neither A nor non-A.


"A moment's reflection will allow us to conclude that formal logic is characterised by the thought processes which consist of putting motion, change, into parenthesis. All the laws enumerated above are true, so long as we abstract from motion. A will remain A so long as it does not change. A is different from non-A so long as it is not transformed into its opposite. A and non-A exclude each other so long as there is no movement which combines A and non-A, etc. These laws are obviously insufficient if we consider the transformation of the chrysalid (sic) into the butterfly, the passage of the adolescent into the adult, the movement of life into death, the birth of a new species or a new social order, the combination of two cells into a new one, etc." [Mandel (1979), pp.160-61. Italics in the original.]


Once more, we are not told from which spoil heap these 'logical gems' had been retrieved (but notice how similar they are to the 'definitions' we have already met). To be sure, a stoically orthodox comrade like Mandel would rightly feel peeved if an opponent of Marxism simply made stuff up like this. Apparently, though, it is quite alright for 'scientific socialists' to indulge in a little fabrication themselves.


[Detailed criticism of Mandel's more substantive claims can be found in Essays Five and Seven Part One.]


From an earlier generation, this is what we find in David Hayden-Guest's book on DM:


"The 'logic' that we have been discussing is very different from what commonly passes for logic, the formal logic which deals with syllogisms and is to be found in the text book. Formal logic is necessary for dealing with the abstractions which are formed in the first stage of thinking.... The essence of its technique is to keep apart, to prevent from confounding the distinctions which have been made. It is therefore based on a development of certain very fundamental principles about identity and contradiction, principles such as the famous 'law of the excluded middle' which states that a thing must be one thing (say 'A') or not that thing (say 'not A'). It can't be both 'A' and 'not A' at the same time.


"This logic, which may be termed the 'logic of common sense,' is perfectly justified and indeed essential within certain limits -- the same limits within which the abstractions it deals with are valid.  But just because it is based on taking these abstractions, for the time being, as absolute, and because it necessarily overlooks their inter-connections, and the development of one quality or thing into another, formal logic is unable to grasp the inner process of change, to show its dialectical character. For this we require dialectical logic...." [Guest (1939), pp.71-72. Italics in the original.]


More repetition, precious little substantiation. [Notice once again the confused idea that the LEM is about things, and not propositions.]


And now this from comrade Thalheimer, whose intent was clearly to show that whatever Trotskyists (like Mandel and Novack) could misconstrue, he could garble better:


"The science of the laws of thought, formal logic, reached its highest point with Aristotle....


"The laws of logic are based on two main propositions. The first is that of identity or of self-conformity. The proposition very simply states: 'A is A,' that is every concept is equal to itself. A man is a man, a hen is a hen, a potato is a potato. This proposition forms one basis of logic. The second main proposition is the law of contradiction, or as it is also called, the law of excluded middle. This proposition states: 'A is either A or not A.' It can't be both at the same time. For example: Whatever is black is black; it can't at the same time be black and white. A thing -- to put it in general terms -- can't at the same time be itself and its opposite...." [Thalheimer (1936), pp.88-89. Italics in the original.]


To his credit, Thalheimer manages to get by with just two misrepresentations of AFL, all the while confusing the DM-version of the LOC with the DM-version of the LEM.


And then there is this gem from Fred Casey:


"First there is the law of identity, by which we say A is A; second, the law of contradiction which says that A is not B, and third, the law of excluded middle which says that A is not part of B. According to the first of these rules, a thing is what it is; according to the second, no thing is what it is not; and, according to then third, no thing is part of what it is not." [Casey (1927), p.123.]


This is one of the worst examples of dialectical confusion I have ever seen. What the LEM has got to do with whether or not 'a thing' is part of another 'thing' is a total mystery. Casey can only have made this stuff up, he certainly can't have found it in a logic textbook.


Even so, we see yet again the confused use of the letter "A" to stand for whatever takes a particular DM-theorist's fancy.


This is how John Somerville summed things up (and he should have known better!):


"The Aristotelian conception of the laws basic to correct thinking may be stated as follows:


"1. Law of Identity: Each existence is identical with itself. A is A.


"2. Law of Noncontradiction: Each existence is not different from itself. A is not non-A.


"3. Law of Excluded Middle: No existence can be both itself and different from itself. Any X is either A or non-A, but not both at once." [Somerville (1967), pp.44-45. Italics in the original.]


To be fair to Somerville, he did try to qualify the second point above in a footnote on p.205, where he made some attempt to understand Aristotle (but, even then, this 'in depth analysis' was compressed into a hundred words or so). However, the fact that it was tucked away right at the end of his book, when the body of this work confuses "what is said" (which is how Aristotle puts things) with "each existence" (Somerville's odd rendition), just about says it all.


The above had appeared in a slightly different form in an early work of Somerville's:


"The Law if Identity is usually expressed in the form, A is A. That is, each thing is identical with itself. The Law of Non-Contradiction states that A is not Non-A. That is, each thing is not different from itself. The Law of Excluded Middle states that X is either A or Non-A. That is, any third alternative or middle ground in addition to A and Non-A is excluded. The same thing cannot be both A (or itself) and Non-A (or different from itself) at the same time." [Somerville (1946), p.183.]  


I will add several comments about the next few pages of Somerville's book (where he seriously compounds the above errors) to a later re-write of this Essay.


We need simply note here the fact that Somerville plainly copied Hegel's amateurish attempt to equate the 'negation' of the LOI with the LOC, subjecting this 'derivation' to no scrutiny at all. This shows that HCDs, just like LCDs, are logical incompetents and ignoramuses. That, of course, accounts for their fondness for Hegel, an Olympic Gold Standard Logical Incompetent.


Many more examples of the same wild allegations can be found on the Internet, for example, here:


"Dialectics is a way of studying the phenomena of the world in a way that is quite a bit different than formal logic. Logic is undoubtedly very useful in many instances, but it has its limitations. Even the fundamental axioms of logic, which often seem intuitively obvious to western thinkers (e.g. A = A), only really hold when looking at the world at fixed moments in time." [Quoted from here.]


A quick Google search will reveal how widespread this dialectical weed has become:


[Although the last author is merely paraphrasing Somerville.]


The same old myths and fabulations, almost word for word!


DM, repetitive? The very idea!


And here is one of my favourites:


"Note that Hegel uses the word contradiction to mean the conflict between two opposing sides. (page 431, Hegel's Science of Logic) He does not mean simply a logically contradictory statement such as, 'That object is a horse and a television.'" [Quoted from the 'Dialectics For Kids' Website.]


Now, "That object is a horse and not a horse" might be a contradiction (it would depend on whether or not there are any hidden ambiguities buried in the quoted sentence, as well as on the meaning of the demonstrative "that"), but "That object is a horse and a television" would only be a contradiction if this were the case: "No horse is a television"; but logic can't legislate here.


It might be argued that the meaning of the word "horse" precludes it from being a television, but if that were the case "That object is a horse and a television" would be a misuse of language, and would thus be nonsensical, not contradictory.


As noted earlier, dialecticians are quite happy to pontificate about logic, but do not seem to know the first thing about it.


Here is HCD-theorist, Sean Sayers:


"In Frege-Russell logic there are valid equivalents for the traditional Aristotelian logical laws: the law of identity (A = A), the law of excluded middle (A v ~A), and the law of non-contradiction (~(A & ~A)).  For this reason, the Frege-Russell system is often referred to as 'standard logic'." [Sayers (1992); quoted from here.] 


The sloppy approach adopted by DM-theorists when it comes to all matters logical (exposed in this Essay) surfaces yet again in Sayers's article above. In the LOI, the letter "A" stands for singular terms (for example Proper Names and Definite Descriptions), so it can't feature in the LEM or the LOC; for example, "It is not the case that (Socrates and not Socrates)" -- if we interpret the letter "A" in Sayers's "(~(A & ~A))" as a Proper Name variable -- is unvarnished nonsense. [If we are charitable, Sayers probably meant to write: "the law of excluded middle (P v ~P), and the law of non-contradiction (~(P & ~P))."] He will search long and hard (and to no avail) through Frege's work (or Russell's) for such DM-gibberish.


We find similar confusion in the work of another HCD, Hyman R Cohen (here criticising an article written by Mark Mussachia):


"Engels showed as early as his writing of Dialectics of Nature that he meant nothing more than this: the opposites he had in mind were simultaneously existing tendencies, existing in the one object or process, comprising its unity as a whole. Mussachia assumes that Engels made the error of believing that A and not-A must always be of the 'direct line' kind, otherwise he (Mussachia) would not be trying so hard to prove Engels wrong. But if he wants to use the Law of Non-Contradiction (nothing can be both A and not-A) to deny that dialectically opposing tendencies can exist within one thing or process, then I must remind him of his previous argument about the Law of Identity which applies to complex things, in which he argued for a broader interpretation of the concept A = A. Engels had already shown that science had undermined the narrow 'old metaphysical' concept of the Identity Law. So, why cannot a given entity, A, have dialectically opposing elements constituting it, and still be a given A?" [Cohen (1980), p.119. Italic emphases in the original; quotations marks altered to conform to the conventions adopted at this site.]         


As usual, Cohen fails to tell us what these "A"s stand for -- are they name, predicate, property, or sentential variables? Once again, in the LOI, "A" operates as a singular term (standing for names or definite descriptions), but it can't function this way in the LOC. In the latter, "A" is a propositional, sentential or predicate letter, but it can't be any of these in the LOI. [Why this is so has been covered in detail in Essay Eight Part Three, but see below.


Even so, in the final sentence "A" now becomes an "entity"! It is no longer a variable standing for an entity, nor yet its name, but the "entity" itself. It might be news to DM-fans, but "entities" feature neither in the LOI nor the LOC, only letters/variables do.


Perhaps worse still, we are told that "A = A" is a concept, as opposed to a law -- and later that there is such a thing as the "concept of the Identity Law", which must mean that we have here the concept of a concept!


A few pages earlier "A" becomes a proposition (but note, not a propositional variable) or a "condition":


"[For Marxists] a contradiction [has the following nature]: the proposition A contradicts the proposition or condition not-A...." [Ibid., p107.]


We aren't told how a "condition" can be contradicted by a proposition, or why using the word "contradiction" is at all apposite in relation to such "conditions". We can only conclude for this that for Cohen, the operator "not-" (that is, if that is what this is!) is capable of turning "A" into a condition! [Since we are told that "not-A" is now a "condition".]


DM vague and confused? Whatever was I thinking!


In most of the above the reader will no doubt have noticed that the LOI is defined as "A = A", "A is equal to A" -- or even "A is A" (on this see Essay Six) --, and it is said to imply that "A can't be other than A" (which is incorrect, the LOI does not preclude change; again, on this see Essay Six). The LOC is similarly characterised as "A can't at the same time be A and not be A" (or even "A can't be non-A"), which is said to follow from the LOI (but with no proof that it does), whereas the LEM is depicted rather loosely as "Everything must be A or not A", or even worse, "A does not equal B". In every case, dialecticians confuse objects (or the names thereof) with propositions -- among a host of other things. These confusions have been dissected here, where, I point out the following (slightly edited):


However, as noted above, the real problem here is that if the negative particle attaches to singular terms (such as a Proper Name), so that it is interpreted as an operator mapping singular terms onto 'negative' singular terms, then it can't also be a sentential operator mapping a sentence or proposition onto its negation, which it has to be in the LEM and the LOC.


That is:


P1: N*(A) º ¬*A.


Or even:


P2: N*(A) = ¬*A.


[Where "N*" is a 'negative' operator, "A" is a name variable, and "¬*" is a 'negative' particle in logic. I have added a "*" here to distinguish these 'operators' from the more usual ones.]


Of course, given the above syntax and semantics, P1 is ill-formed, since neither "N*(A)" or "¬*A" are propositions/sentences. 'Neg(Socrates) if and only if Not(Socrates)' is unvarnished nonsense (just as 'Neg(Socrates) is identical with Not(Socrates)' is, too).


On the other hand, if the negative particle is a sentential operator mapping a sentence or proposition onto its negation, then it can't also be an operator mapping names in the above manner.


P3: N(A) º ¬A.


P4: N(A) = ¬A.


[Where "N" is a 'negative' operator, "A" is now a propositional variable, and "¬" is the negative particle in logic.]


But, in this case, it is P4 that is ill-formed, since "=" can only be flanked by singular terms, not propositions. 'Neg (Paris is in France) is identical to it is not the case that Paris is in France' is no less nonsensical.


P3, on the other hand, seems to be alright: 'Neg (Paris is in France) if and only if it is not the case that Paris is in France' is certainly odd, but it is not nonsense, but that is only because "N" now works as a surrogate for sentential negation.


Recall, Hegel thought he could derive the LOC from the LOI by claiming that the LOI "stated negatively" is, or implies, the LOC. To that end, he tells us that the LOI is "A = A", and hence that it is also "A can't at the same time be A and not A" -- or: "¬(A & ¬A)".


[Of course, there are other ways than this of viewing the 'negative form' of the LOI; for example, it could be "¬[(A = A) & (A = ¬A)]". However, the latter version presents its own problems; these are explored partly below, and partly in Note 2.]

But, in the LOC and the LEM, "A" clearly stands for a proposition, a declarative and/or indicative sentence, or a statement (again, depending on one's philosophical logic) -- i.e., it goes proxy for expressions that could be true or false.


By way of contrast, in the LOI, "A" goes proxy for singular terms; it isn't a propositional or sentential variable. But, "Caesar" on its own is not capable of being true or false. So, if "¬" is taken to be a propositional or sentential operator (mapping truths onto falsehoods, and vice versa), "¬A" would make no sense --  "It is not the case that Caesar" is, once more, nonsensical.


Alternatively, if "A" is a sentential or propositional variable, "¬(A & ¬A)" would become "It is not the case that (Caesar is identical with Caesar and Caesar is not identical with Caesar" (where, for instance, "A" stands for "Caesar is identical with Caesar", rather than just "Caesar" on its own), which seems to make sense, but only if one is questioning the LOI.


The other form mentioned above (i.e., "¬[(A = A) & (A = ¬A)]") fares little better: "It is not the case that ((Caesar is identical with Caesar) and (Caesar is identical with not Caesar))" -- that is, if "¬" is still functioning as a sentential or propositional operator. But, who exactly is this "not Caesar"?

On the other hand, if "¬" operates on names, or singular terms, then "¬(A & ¬A)" would make no sense, either. In that case, "¬(A & ¬A)" would become "Not (Caesar and not Caesar)". But, what does that mean? It isn't even a proposition. "Not Caesar" isn't an expression that is capable of being true or false, nor is "Not (Caesar and not Caesar)". In which case, given this use of "¬", "¬(A & ¬A)" can't be the LOC. "Not (Caesar and not Caesar)" isn't the LOC; it is either plain gibberish or it isn't even a proposition.


The other form (i.e., "¬[(A = A) & (A = ¬A)]") is even worse, as we have just seen -- it becomes "Not ((Caesar is identical with Caesar) and (Caesar is identical with not Caesar))".


[This isn't to suggest that the negative particle can't attach to names (on this, see here), only that when it does, it must assume a different role (and thus a different meaning) from that which it occupies when it is sentential/propositional operator. Indeed, as we have seen here, when the negative particle attaches to a name (in what appear to be relational expressions (e.g., "Paris is no Vienna", or "Brutus is not Caesar")), its role changes dramatically.]


The dilemma is thus quite stark:


(1) If "¬" operates on names, or singular expressions, and if "A" is a singular term variable, then "A = A" certainly seems to make sense. But, in that case, the 'negative form' of the LOI -- "¬(A & ¬A)" (or even "¬[(A = A) & (A = ¬A)]") -- turns out to be plain and unvarnished nonsense: "Not (Caesar and not Caesar)" -- (or "Not ((Caesar is identical with Caesar) and (Caesar is identical with not Caesar))"!


(2) On the other hand, if "¬" operates on sentences or propositions, mapping them onto their negations, and if "A" is a sentential or propositional variable, then the LOI ("A = A") would become, for example: "Caesar is identical with Caesar is identical with Caesar is identical with Caesar" (interpreting "A" here as the proposition "Caesar is identical with Caesar", again), which isn't even the LOI!


[Recall, given option (2), "A" has to go proxy for a proposition or sentence, not a name.]


Exception might be taken to the use of "A" to stand for the proposition "Caesar is identical with Caesar". [DM-fans can't in fact lodge this objection since, as we have seen, these "A"s can be interpreted to be anything we please!)]


In that case, if we take any other randomly chosen proposition to replace each "A" in the LOI, not much improves: "Paris is in France is identical with Paris is in France". [Interpreting the "A" here as "Paris is in France". Remember this doesn't yield "'Paris is in France' is identical to 'Paris is in France'", but  "Paris is in France is identical to Paris is in France".] Is anyone prepared to accept that as an example of the LOI?


In case someone is prepared to so accept, I will consider that desperate (and unwise) move presently.

So, Hegel was only able to 'derive' the LOC from the LOI by allowing these "A"s to slide effortlessly between the two semantic categories mentioned above, between denoting singular terms and denoting propositions/'judgements'/sentences (and, in fact, denoting a whole host of other things into the bargain -- such as, processes, concepts, relations, relational expressions, etc. -- on that, see an earlier section of this Essay). But, as soon that is done, the negative particle changes its meaning in the above manner -- that is, it changes from a sentential operator to a name modifier, and we end up with nonsense.


Now, do dialecticians really think that a philosopher of Aristotle's stature and sophistication actually believed that, say, "Everything must be rat or 'non-rat'" --, or, "Rat does not equal cat"? [Interpreting here the 'dialectical definition' of the LEM literally, replacing "A" with "rat", and "B" with "cat".]


If they do, we might wonder why Marx thought so highly of him.


Of course, anyone familiar with Aristotle's thought (or who bothers to check!) will know he never puts things this way. Indeed, I have been unable to find a sentence remotely like any of the above in his work.


Another, and much more sophisticated dialectician (who is probably also a card-carrying member of the HCD fraternity, and who should know better) presents us with the following 'definition':


"The method of dealing with contradictions in two-valued logic conforms with the laws of classical logic: a thing can't be contrary to itself (law of noncontradiction) and a thing can't be both itself and contrary to itself at the same time in the same respect (law of excluded middle)." [Marquit (1982), p.76. (This article appeared earlier in Science & Society, which only goes to show that if that redoubtable journal employs a peer review system, those reviewers, it seems, will pass any old rubbish!)]


This not only confuses contraries with contradictories, it commits many of the errors that have already been highlighted.


Nevertheless, even if their (collective) analysis of the LOC were correct, and it was true that "A is A and at the same time non-A", it would be impossible for dialecticians to begin to express their criticisms even of their own garbled AFL-principles. That is because it would be impossible to state the following:


B1: "A is A and at the same time non-A".


If it were indeed true that "A" is at the same time "non-A", then the first half of B1 would have to be re-written as:


B2: "Non-A is non-A".


Or, more accurately, the whole of B1 would become:


B3: "Non-A is non-A and at the same time non-(non-A)".


That is, if each "A" in B1 is replaced with what it is supposed at the same time to be (i.e., "non-A"), B1 would 'dialectically disintegrate' into B3. Or, perhaps worse, into the following:


B3a: "A and non-A is A and non-A and at the same time non-(A and non-A)".


Depending on how radically we interpret this dialectical re-write of the LOC.


[In B3a, I have replaced each occurrence of "A" with an "A and non-A", since we have been told that each "A" is at the same time "A and non-A".]


This fatal outcome can only be avoided by those who reject the DM-inspired version of the LOC (i.e., those who reject the dictum: "A is at the same time non-A"), and who thus do not think that the first half of B1 is false, or both false and true -- or even that "It depends...".


B3: "Non-A is non-A and at the same time non-(non-A)".


Even worse still, if every "A" is at the same time "non-A", then these would surely follow from B3:


B4: "Non-(non-A) is non-(non-A) and at the same time non-(non-(non-A))."


B5: "Non-(non-(non-A)) is non-(non-(non-A)) and at the same time non-(non-(non-(non-A)))."


And so on, as each successive "A" in B3, and then B4, is replaced with the "non-A" that dialecticians insist they (at the same time) are. Once more, this untoward result can only be avoided by those who reject standard DM-criticisms of the LOC.


Or even worse:


B4a: "A and non-A and non-(A and non-A) is A and non-A and non-(A and non-A) and at the same time non-(A and non-A and non-(A and non-A))".


[B3a: "A and non-A is A and non-A and at the same time non-(A and non-A)".]


Replacing each "A" in B3a with "A and non-A" once more. I won't even attempt B5a!


[Of course, it won't do to claim that all these "non-"s cancel out (an odd notion in itself; on that see here), since if they did we would have to reject the idea that each "A" was at the same time a "non-A". Thus, if each "A" were at the same time a "non-A", then, when we formed a "non-(non-A)" from a "non-A" in the above manner, and if this could be 'cancelled' back to an "A", the "A" in "non-A" would no longer be a "non-A", since these two "non-"s would ex hypothesi have cancelled, wiping out that "non-A"!]


As should now be apparent, the LOC has an annoying way of hitting back in a most un-dialectical fashion when challenged. In which case, as noted above: it is impossible for dialecticians to say what they mean!


The same problems afflict other DM-inspired criticisms of principles dialecticians claim to have found in textbooks of FL (while unwisely keeping the references to themselves).


In addition, as noted above, DM-theorists are invariably unclear what the "A"s in these alleged FL-'laws' are supposed to stand for. Based on the quotations we have already seen, and on other passages posted elsewhere at this site, it is plain that DM-theorists regularly confuse "A" with one or more of the following: propositions, judgements, properties, qualities, words, objects, processes, predicates, statements, terms, assertions, type-sentences, token-sentences, concepts, ideas, beliefs, thoughts, phrases, clauses, relations, relational expression, indexicals, places, times, names, 'entities' --, and now, in the case of Somerville, "existences"!


The significance of logical disorder of this magnitude lies not so much in the unmitigated confusion it creates, but in the fact that the vast majority of the DL-faithful have not even noticed it!


And that indictment includes HCDs!


Indeed, when this confusion is brought to their attention, they just complain about "pedantry", or "semantics"!


As has already been pointed out: 2400 years ago (and despite his own confusions) Aristotle was far clearer about such things than all these 'dialectical logicians' put together.


But, far worse: are we really supposed to believe that this sub-Aristotelian, syntactical rat's nest encapsulates ideas that lie at the very cutting edge of modern science?


Now, anyone tempted to respond to the above on the lines that it gets the DM-view of contradictions (etc.) wrong, and that dialectical contradictions are really X, or they are in effect Y, or they are…whatever (readers can insert their own favourite DM-definition here -- call it Z), need only reflect on the fact that according to the DM-inspired criticism of the LOC, that criticism itself must be X or Y, or even Z, while at the same time being not X or not Y, or not Z -- if we here interpret the "A"s above as "X or Y, or even Z", since, on sound dialectical-principles, these letters can be interpreted in any which way we fancy.


Let's see those who accuse careful logicians of "pedantry" and "semantics" try to squirm their way out of that one!


[In Essay Eight Part Three, we shall see that serious difficulties like this afflict, and thus neutralise, the best account there is (or, at least, the best account I have ever read) of the nature of 'dialectical contradictions', written by a Marxist.]


In that case, the radically imprecise nature of the DM-inspired criticism of the LOC (which sees everything as "X or Y, or even Z, and not X or not Y, or even not Z" -- where each "X or Y, or even Z" is just left undefined, so it can be anything dialecticians please) must itself be "both a criticism and not a criticism" of the LOC. This must be so unless, of course, criticisms are themselves exempt from their own criticism -- and can't thus ever aspire to become one of these wishy-washy dialectical letter "A"s.


Alas, this means that dialecticians' own criticism of the LOC must now self-destruct. So, for example, any attempt made by DL-fans to define the LOC must be "a definition and not a definition" -- if their own 'analysis' of the LOC and the LOI is invoked against any such attempt.


Hence, using "D" to stand for "the DM-'definition' of the LOC" (whatever that 'definition' is, and whatever it means, if we are ever told), it must be the case that "D is at the same time non-D". Clearly, that would mean that the DM-inspired criticism of the LOC undermines its own definition of it! Or, at least, it does and it doesn't.


It is at this point that even DL-fans might just begin to see how devilish Diabolical Logic really is.


[BAD = Buddhist Dialectics/Dialecticians; MAD = Materialist Dialectics/Dialectician, depending on context.]


However, long experience 'debating' with comrades who think Hegel is the best thing since sliced Aristotle suggests that one should never underestimate a dialectician's capacity for ignoring anything he or she does not like. 'Debating' with those whose brains have been compromised by this Hermetic virus is like debating with Buddhists -- except the latter are at least respectful and non-abusive. However, with respect to both sets of mystics (the MAD and the BAD), whatever is argued against their system simply doubles back and serves to prove their case. The fact that the BAD-ies can tell us absolutely nothing about 'Nirvana' phases them not (since it is 'Nothing'!), just as it scarcely registers with the MAD-ies that they can't say what their "Totality" is, either.


And it is little use pointing out to MAD-ies -- or BAD-ies -- that their belief in universal contradiction is self-contradictory, for to do so would be to feed this monster, and thus to lend it strength.


[This is especially true of MAD-Mystics found on internet discussion boards -- a recent and extreme example of which can be found here; check out the abusive ramblings of comrade "Wangwei".]


Now, it could be objected once more that DM-theorists do not object to the use of the LOC, the LOI or the LEM in their proper field of application (as several comrades pointed out above). However, as the argument proceeds, these principles fall short when they are applied to processes in the real world, to change and movement. This hackneyed response will be tested to destruction in Essays Five, Six and Eight Parts One, Two and Three (where consideration will be given to Engels's 'analysis' of motion, Hegel's and Trotsky's attempts to criticise the LOI, and the claim that change is the result of 'internal contradictions').


In the meantime, it is worth reminding ourselves that these DM-inspired criticisms of FL are themselves phenomenal/material objects (i.e., they have to be written in ink on a page somewhere (etc.), or propagated in the air as sound waves at some point, just as they have to be apprehended by human beings), and as such they are surely subject to change (if everything is). In that case, they "are never equal to themselves". If so, the above DM-inspired criticisms of FL must apply to each and every material copy of such DM-inspired criticisms of FL.


Hence, no materially-configured DM-criticism of the LOC is equal to itself, and so each and every phenomenal example of a DM-criticism of the LOC is at the same moment both "a criticism and not a criticism".


The rest follows as before.


The counter-argument to this (that dialecticians only need to appeal to the 'relative stability' of material objects/processes to make their point) is neutralised in Essay Six. The other counter-argument -- that this ignores Hegel's use of identity to derive the alleged fact that everything is related to, or 'reflects', its 'own other', and not merely to everything that it is 'not' --, is defused in Essays Seven and Eight Part Three.


However, in an attempt perhaps to forestall the objections posted above, James Lawler argued as follows:


"Looking one step further into this matter, Hegel suggests that the relation of A to not-A is doubly negative. Identity is established (not immediately given) through a negative relation to not-A. A is itself in not being not-A. But this negative relation to not-A is itself negated. That is, the identity of A does not consist solely in its being not-A, there is a 'return' to A again -- which Hegel calls 'reflection.' Thus 'A is A' is not a tautologous (sic) repetition of A (as 'abstract understanding' would have it) but an affirmation that has been made possible only through a doubly negative movement, a 'negation of the negation.'" [Lawler (1982), p.22. Italic emphases in the original.]


"It is necessary to ask, first of all, whether and in what sense the fact that A necessarily relates to what is not-A permits us to insert not-A in A. Hegel is quite explicit that this relation is not to be understood in such a way that the results would be the blurring of all identities in a single monistic being -- as he accuses Spinoza of doing: 'Substance, as the universal negative power, is as it were a dark shapeless abyss which engulfs all definite content as radically null, and produces from itself nothing that has a positive substance of its own.'" [Ibid., p.32, quoting Hegel (1975), p.215, in the edition I have used, which seems to be different from Lawler's. Italic emphases in the original. Quotation marks altered to conform to the conventions adopted at this site.]


Quite how the incomprehensible passage from Hegel helps clear this up I will leave to those fluent in Martian to decide, but Lawler continues:


"If we grant that A's identity involves its necessary relation to what is not-A, and that this not-A is 'its own other' -- a definite other being and not any being whatsoever -- and that this relation to some definite other is necessary for the existence of A or is essential to the constitution of A (A's identity), it seems reasonable to look for some 'imprint' of this 'other' in A, so that in some sense not-A is internally constitutive of A.... In other words, to understand the internal nature of A it is necessary to study the determinate not-A not only as a necessary external condition but as 'reflected' in A. This is not to say that one should expect to find in A some direct and immediate duplication of not-A. The direct identity of A and not-A would constitute the annihilation of the beings involved." [Ibid., pp.32-33. Italic emphases in the original. Quotation marks altered to conform to the conventions adopted at this site.]


We have already had occasion to note that dialecticians are hopelessly confused about what they mean by the sub-logical symbols they use, and Lawler is, as we will see, up there with the best of them -- confusing these "A"s one minute with propositions and sentences, the next with properties, predicates, 'beings', indexicals, relations and/or nominalised relational expressions, among other things.


Exactly how Lawler's comments are of preventing the logical explosion we witnessed earlier -- which follows from Hegel's brilliant insight that "A is identical with, but at the same time different from, not-A" (I paraphrase!) -- is somewhat unclear. Even if it were correct that "A = not-A, but at the same time A ≠ not-A" (which is a slightly shorter version of "A is identical with, but at the same time different from, not-A"), we would still obtain the following from B1 (modified):


B1: "A is A and at the same time non-A".


B1b: "A = A and at the same time not-A".


However, if we begin with the more 'orthodox' version suggested by Lawler, encapsulated in B1c, the situation is even worse:


B1c: "A = A and A = not-A and A ≠ not-A".


Here I am taking "A is A and at the same time A is not-A, and A is also not-not-A" to have the same 'dialectical' content as "A = A and A = not-A and A ≠ not-A".


If we take the underlined part of this formula of 'genius' (i.e., "A and A = not-A and A ≠ not-A", which we are assured it is 'dialectically' equal to "A") and substitute it for each "A" in B1c (but parsed by means of brackets to make it 'easier' on the eye), we obtain the following monstrosity:


B6: "(A and A = not-A and A ≠ not-A) = (A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) = not-(A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) ≠ not-(A and A = not-A and A ≠ not-A)".


If we now do the same with B6, we end up with this can of 'dialectical' spaghetti:


B7: "((A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) = not-(A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) ≠ not-(A and A = not-A and A ≠ not-A)) = ((A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) = not-(A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) ≠ not-(A and A = not-A and A ≠ not-A)) and ((A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) = not-(A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) ≠ not-(A and A = not-A and A ≠ not-A)) = not-((A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) = not-(A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) ≠ not-(A and A = not-A and A ≠ not-A)) and ((A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) = not-(A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) ≠ not-(A and A = not-A and A ≠ not-A)) ≠ not-((A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) = not-(A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) ≠ not-(A and A = not-A and A ≠ not-A))".


In the above, each "A" has been replaced successively by what Lawler assures it is identical with, namely "A and A = not-A and A ≠ not-A".


Alas, my computer might not have enough memory to do B8!


[That pleasant task is left for readers who have more time on their hands than is perhaps good for them to attempt. Good luck with B999!]


Of course, if we throw the full weight of DL at this, the entire theory [DM] will decay onto gibberish even quicker, for if "A" is never equal to "A", but is always equal to "not-A", then no other symbol can remain unscathed. In which case each and every word DM-fans use to criticise FL much be subject to these crazy strictures. Consider again B1:


B1: "A is A and at the same time non-A".


This soon 'dialectically-develops' into the following:


B1a: "Non-A non-is non-A non-and non-at non-the non-same non-time non-non-non-A".


And then:


B1b: "Non-non-non-A non-non-non-is non-non-non-A non-non-non-and non-non-non-at non-non-non-the non-non-non-same non-non-non-time non-non-non-non-non-non-non-A".


And so on...


Hence, the same fate must befall every word that DM-fans themselves use (including "non"!) -- since words are just as material as any "A" that either they or Hegel ever thought to employ. In which case. if we apply their own 'logic', dialecticians will end up with unvarnished gibberish in place of sentences that make sense, leaving them in the unenviable position of not being able to say anything at all. [This is just an elaboration of a point Aristotle made 2400 years ago!]


And, it is no good complaining that this is unfair; dialecticians' sloppy use of ill-defined letters like these invites such parody.


So, Lawler's 'solution' is in fact a major step backward, even when compared with the implications of the crass definitions of lesser LCD souls.


[Lawler's attempt to derive, a là Hegel, a "not-A" from an "A" is demolished here. It is worth pointing out again that in all of this the distinction between "not A" (predicate negation) and "not-A"/"non-A" (predicate-term negation) has been ignored, since Lawler and other DM-fans seem to be unaware of it, or they ignore it, too. More on that here.]


On a more general note, Woods and Grant make other assertions about FL that reveal just how little they know about a subject they seem quite happy to misrepresent:


"It is an astonishing fact that the basic laws of formal logic worked out by Aristotle have remained fundamentally unchanged for over two thousand years." [Woods and Grant (1995), p.89.]


This is so manifestly (and demonstrably) untrue that these two comrades have had to ignore and distort the major advances that have been made in logic since the 1850s to make it 'work':


"In the 19th century, there were a number of attempts to bring logic up to date (George Boyle (sic), Ernst Schröder, Gotlob (sic) Frege, Bertrand Russell and A. N. Whitehead). But, apart from the introduction of symbols, and a certain tidying up, there is no real change here. Great claims are made, for example by the linguistic philosophers, but there are not many grounds for them...." [Ibid., p.97.]


We have already had occasion to note the many errors this passage contains -- for example, Woods and Grant confuse George Boole with a fictional character, "George Boyle"; they also mis-spell Gottlob Frege's name --, sure, these are relatively minor issues (even though they underline how careless these two are when it comes to matters logical). The fact that these comrades can see no difference between the old logic of subject and predicate, and the newer logics of function and argument, quantifiers and predicates of different levels, of relations and sets, tensed functors, and so on, merely underlines their self-inflicted ignorance.


Traditional (Aristotelian) logic not only ignored complex inferences inexpressible in syllogisms, it dramatically failed to cope with relational expressions, quantifiers expressing multiple generality -- these are used in mathematics all the time: for example, "If every number has a successor then there is no prime larger than every other number" --, internal and external negation coupled with scope ambiguity. [This links to a PDF.] That was partly because of the way that quantifier expressions had been interpreted by earlier logicians, who, with their slavish adherence to the traditional grammar of subject and predicate, crippled logic for over two thousand years.


[On the origin of some of these confusions, see Barnes (2009). The impact of this new logic, and why it was crucially important for advances in mathematics, is detailed in Giaquinto (2004), and Grattan-Guinness (1970, 1997, 2000a, 2000b). See also Kitcher (1984), pp.227-71. On Frege's importance, see Dummett (1981a), pp.665-84.


On the general background, see Beaney (1996). Concerning the superiority of MFL over AFL, see Dummett (1981a), pp.8-33, Noonan (2001), pp.25-28, 39-43, and here. The superiority of Frege's logic is brought out admirably well in Geach (1961). See also, Zalta (2008).]


Wittgenstein himself addressed some of the confusions and limitations of the old logic in Wittgenstein (1913). Indeed, what Wittgenstein had to say about the work of one particular logician (i.e., Coffey (1938a, 1938b)) could have be addressed with equal justification at our DM-brethren:


"In no branch of learning can an author disregard the results of honest research with so much impunity as he can in Philosophy and Logic. To this circumstance we owe the publication of such a book as Mr Coffey's Science of Logic: and only as a typical example of the work of many logicians of to-day does this book deserve consideration. The author's Logic is that of the scholastic philosophers, and he makes all their mistakes -- of course with the usual references to Aristotle. (Aristotle, whose name is taken so much in vain by our logicians, would turn in his grave if he knew that so many Logicians know no more about Logic to-day than he did 2,000 years ago). The author has not taken the slightest notice of the great work of the modern mathematical logicians -- work which has brought about an advance in Logic comparable only to that which made Astronomy out of Astrology, and Chemistry out of Alchemy....


"The worst of such books is that they prejudice sensible people against the study of Logic." [Wittgenstein (1913), pp.2-3.]


However, Woods and Grant continue:


"Using a superficial and inexact analogy with physics, the so-called 'atomic method' developed by Russell and Wittgenstein (and later repudiated by the latter) tried to divide language into its 'atoms.' The basic atom of language is supposed to be the simple sentence, out of which compound sentences are constructed. Wittgenstein dreamed of developing a 'formal language' for every science -- physics, biology, even psychology. Sentences are subjected to a 'truth test' based on the old laws of identity, contradiction and the excluded middle. In reality, the basic method remains exactly the same. The 'truth value' is a question of 'either…or,' 'yes or no,' 'true or false.' The new logic is referred to as the propositional calculus. But the fact is that this system can't even deal with arguments formerly handled by the most basic (categorical) syllogism. The mountain has laboured, and brought forth a mouse." [Woods and Grant (1995), p.97.]


Again, the errors in this passage are exposed here. However, Woods and Grant nowhere reference a single passage from Wittgenstein that supports the idea that he wanted to set up "a 'formal language' for every science -- physics, biology, even psychology"; in fact, these two have plainly confused Wittgenstein with Rudolph Carnap and other members of the Vienna Circle. Nor do they show how or why the new logic can't handle syllogistic inferences, when it manifestly can. [On that, for example, see Lemmon (1993), pp.168-79.]


Not finished, these two continue:


"The introduction of symbols into logic does not carry us a single step further, for the very simple reason that they, in turn, must sooner or later be translated into words and concepts. They have the advantage of being a kind of shorthand, more convenient for some technical operations, computers and so on, but the content remains exactly as before. The bewildering array of mathematical symbols is accompanied by a truly Byzantine jargon, which seems deliberately designed to make logic inaccessible to ordinary mortals, just as the priest-castes of Egypt and Babylon used secret words and occult symbols to keep their knowledge to themselves. The only difference is that they actually did know things that were worth knowing, like the movements of the heavenly bodies, something which can't be said of modern logicians." [Ibid., pp.97-98.]


On a similar basis, therefore, algebraists must have been unwise to introduce symbols into mathematics. And yet, how many ordinary people understand algebra? Does that mean algebra is "elitist"? More revealingly, Woods and Grant's jibe about the esoteric nature of modern logic hides, one feels, the fact that these two comrades have found even elementary Symbolic Logic far too difficult to grasp. [Exhibit A for the prosecution was presented earlier.]


To be sure, MFL is unbelievably difficult. As I noted above, in my own study of University Mathematics and Postgraduate Logic, I found, for example, that advanced Abstract Algebra (Group Theory) was far easier to follow than advanced MFL (especially if we throw in the Philosophy of Logic, surely one of the most difficult subjects yet devised by the human brain). Others, of course, may find that the reverse is true. But, that no more maligns MFL than it does, say, Group Theory, or Lie Algebra.


Readers will however have noticed these two threw in another snide remark about ancient priests, whose knowledge, we are told, involved certain practicalities -- unlike those supposedly displayed (or not) by modern logicians. This from comrades who sing the praises of a logical 'theory' (DL) which has no known practical applications (other than that of thoroughly confusing its acolytes and, of course, crippling Soviet Agriculture), but who nevertheless endlessly snipe at an entire discipline that has countless.


And, as far as "Byzantine jargon" is concerned, anyone who reckons they can learn something (anything) from Hegel's Logic, as these two certainly seem to do, has little room to accuse others of an excessive devotion to jargon. The technical terms in MFL are there for the same reason they are there in modern mathematics. No such grounds exist for excusing the seemingly endless pages of terminally obscure jargon and tortured prose one finds in Hegel's Logic; quite the reverse, as we shall see.


Unfortunately, there is more:


"Terms such 'monadic predicates,' 'quantifiers,' 'individual variables,' and so on and so forth, are designed to give the impression that formal logic is a science to be reckoned with, since it is quite unintelligible to most people. Sad to say, the scientific value of a body of beliefs is not directly proportionate to the obscurity of its language. If that were the case, every religious mystic in history would be as great a scientist as Newton, Darwin and Einstein, all rolled into one." [Ibid., p.98.]


The new terminology employed in MFL was introduced simply because the old logic of subject and predicate failed to do justice to inferences found in everyday life, to say nothing of the complex deductions made by mathematicians and scientists. Moreover, the above reference to religious mystics is a little rich in view of the Hermetic writings from which Woods and Grant caught such a virulent dose of dialectics.


"In Moliere's comedy, Le Bourgeois Gentilhomme, M. Jourdain was surprised to be told that he had been talking prose all his life, without realising it. Modern logic merely repeats all the old categories, but throws in a few symbols and fancy-sounding terms, in order to hide the fact that absolutely nothing new is being said. Aristotle used 'monadic predicates' (expressions that attribute a property to an individual) a long time ago. No doubt, like M. Jourdain, he would have been delighted to discover that he had been using Monadic Predicates all the time, without knowing it. But it would not have made a scrap of difference to what he was actually doing. The use of new labels does not alter the contents of a jar of jam. Nor does the use of jargon enhance the validity of outworn forms of thought.


"The sad truth is that, in the 20th century formal logic has reached its limits. Every new advance of science deals it yet another blow. Despite all the formal changes, the basic laws remain the same. One thing is clear. The developments of formal logic over the past hundred years, first by propositional calculus (p.c.), then by lower predicate calculus (l.p.c.) has carried the subject to such a point of refinement that no further development is possible. We have reached the most comprehensive system of formal logic, so that any other additions will certainly not add anything new. Formal logic has said all that it has to say. If the truth were to be told, it reached this stage quite some time ago." [Ibid., pp.98-99.]


I have been unable to find the term "Monadic predicate" in Aristotle, but that doesn't mean he didn't use monadic predicates. But so what? Ancient mathematicians used ideas and abbreviations that are analogous to the symbols employed by modern mathematicians; does that mean that modern mathematics is full of "fancy-sounding terms", and thus fit only for ignorant derision? Or, that modern formalism is no advance over ancient mathematical terminology?


And, of course, a monadic predicate (such as "ξ is a confused dialectician") can apply to more than one individual (as in "Anyone who reads RIRE, and believes everything they read, is a confused dialectician"); so it isn't true that 'monadic predicates' are expressions that "attribute a property to an individual". Plainly, it applies to the lot of them.


The question whether or not MFL has been usurped by advances in science will be dealt with elsewhere at this site (however, see Harrison (1983, 1985) and Slater (2002)), on the LEM and QM); but, as far as the allegation that MFL has reached the end of the line is concerned, only someone who knows nothing of the subject will think of saying this. Even a cursory look along the relevant shelves in a University Library will soon reveal how the subject is continuing to blossom --, as will a cursory Google search.


[LEM = Law of Excluded Middle; QM = Quantum Mechanics.]


In fact, this by-now-familiar 'head in the sand' approach -- perfected by these two comrades -- is somewhat reminiscent of the stance taken toward Galileo's work by Catholic Theologians: "Stick to Dialectical Dogma comrades (it is safe), and under no circumstances look down that telescope!"


One last comment by Woods and Grant is worth noting:


"Another type of syllogism is conditional in form (if...then), for example, 'If an animal is a tiger, it is a carnivore.' This is just another way of saying the same thing as the affirmative categorical statement, i.e., all tigers are carnivores. The same in relation to the negative form -- 'If it's a fish, it's not a mammal' is just another way of saying 'No fishes are mammals.' The formal difference conceals the fact that we have not really advanced a single step." [Ibid., p.86.]


Alas, Woods and Grant seriously expose their ignorance here; a hypothetical proposition -- such as: 'If an animal is a tiger, it is a carnivore' -- isn't an argument of any sort, so it can't be a syllogism.


On the other hand, if the above were a conditionalised argument (i.e., an argument that has been transformed into a conditional proposition), the original argument must have had a suppressed premiss (as in, "No fish is a mammal", in relation to 'If it's a fish, it's not a mammal'). Either way, these aren't syllogisms.


Nevertheless, Woods and Grant have clearly missed the point of hypothetical deduction in MFL (a facility that was in fact foreign to AFL, but present in Stoic Logic). We can surely reason from premisses whose truth-status is unknown to us (as scientists often do), in order to try to establish their truth-values. Indeed, it is no less important for us to find out whether or not any of our beliefs are false, and we can often do that by drawing out their consequences. This can't be done with categorical reasoning -- unless the hypothetical mode is used implicitly.