Essay 16-04 -- Summary Of Essay Four Part One: Formal Logic And Change

 

Preface

 

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This is an Introductory Essay, which has been written for those who find the main Essays either too long, or too difficult. It doesn't pretend to be comprehensive since it is simply a summary of the core ideas presented at this site. Most of the supporting evidence and argument found in each of the main Essays has been omitted. Anyone wanting more details, or who would like to examine my arguments in full, should consult the Essay for which this is a summary. [In this particular case, that can be found here.]

 

As is the case with all my work, 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.

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

 

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

 

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

 

[Latest Update: 05/04/17.]

 

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1) Formal Logic Meets Wilful Ignorance

 

2) Dialectical Mayhem

 

3) Logic And Change

 

4) DL -- A Superior Form Of Logic?

 

5) Accounting For Change

 

Summary Of My Main Objections To Dialectical Materialism

 

Abbreviations Used At This Site

 

Return To The Main Index Page

 

Contact Me

 

Formal Logic Meets Wilful Ignorance

 

In Essay Four, I expose the woeful ignorance of FL displayed by the vast majority DM-theorists. Few dialecticians seem able to resist making ill-informed and unsubstantiated criticisms even of AFL, while even fewer clearly know anything at all about MFL.

 

[DM = Dialectical Materialism/Materialist, according to context; FL = Formal Logic; MFL = Modern Formal Logic; LOI = Law Of Identity; AFL = Aristotelian Formal Logic; LOC = Law of Non-Contradiction; LEM = Law of Excluded Middle; TAR = The Algebra of Revolution (i.e., Rees (1998); DL = Dialectical Logic.]

 

One particularly egregious aspect of this self-inflicted ignorance is the fact that most DM-theorists seem to think that FL began and ended with Aristotle, despite being told repeatedly that they are wrong. In fact, as any reasonably decent history of logic would have told them (had they bothered to check), 95% of FL is less than 130 years old. Seventy odd years ago Burnham tried to tell Trotsky that his knowledge was badly out-of-date, but he might as well have been talking to the cat for all the good it did.

 

This is one idée-fixe that appears to have escaped the clutches of the Heraclitean Flux.

 

Even to this day, the 'news' that logic underwent a profound revolution in the late 19th century, at the hands of Frege (which revolution was easily of the same order of magnitude that science underwent in the 17th century) has yet to penetrate most dialectical skulls. They still refuse to be told -- preferring the comforting mantras repeated in their DL-bubble, rather like US Republicans and Donald Trump supporters prefer to live inside an 'alternative fact' bubble --, even though there are now literally scores of sites on the Internet that introduce this new logic to any willing to learn (for example, here and here).

 

In fact, a friend of mine raised this very point with John Rees at Marxism 1990 (an annual gathering of the UK-SWP), but there is no evidence in TAR that the message got through. Similar attempts posted on Internet discussion boards are an equal waste of time.

 

Dialecticians, it seems, are happy to wear this particular badge of ignorance with pride.

 

Indeed, based on what DM-theorists themselves write about logic, it is pretty clear that the vast majority of them don't appear to have opened a single logic text, ever -- but that doesn't stop them pontificating about it and its supposed 'limitations' -- at least, other than Hegel's badly misnamed book, "Logic" (although there is precious little evidence that many of them have read that either!). And, of the tiny minority who have opened a logic textbook, few seem to have grasped much of what they read. The egregiously defective definitions of the three alleged 'laws' of logic, which virtually all DM-theorists present their readers, are hopelessly confused; their 'research' in this area has clearly been confined to copying these 'non-definitions' off of one another for several generations.

 

Just to take one example (there are plenty more here) -- the following is among the worst I have seen in what follows when I use, or simply mention, variables used in FL I will highlight them in bold to distinguish them from ordinary letters; but when I quote other authors who use such terms, I will leave the text unaltered):

 

"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 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 assert that is necessarily either to assert or deny, that a thing must be either black or white either alive or dead, either 'A' or 'B'. It cannot 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 cannot 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 have been altered to conform with the conventions adopted here.]

 

It is worth pointing out that these two comrades referenced no logic text in support of these 'definitions'. They were happy however to quote Engels -- who wrote before the aforementioned revolution in logic (so he at least had an excuse) -- as if he were an expert, when it is obvious from his writings that Engels was hardly even a novice in this area.

 

To be sure, here and there Woods and Grant lift a few ideas from two introductory works (i.e., those written many years ago by Luce, and Cohen and Nagel), but they failed to reveal from which lamentably poor logic textbook they dredged-up 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.]

 

Quite what the LOC has to do with whether A can or cannot equal not-A, Woods and Grant failed to say. As we will also find was the case with Hegel, these two have confused the LOC -- which concerns the truth-functional relation between a proposition, or indicative clause, and its negation; it is not about objects like A, still less is it about "equality") with the LOI supposedly "stated negatively".

 

[The lack of any connection between the LOC and the alleged negative version of the LOI is discussed here. On the LOC in general, see here. "Truth-functional" is technical term that relates to the logical relation between propositions, the alteration of which changes the conditions under which they are true or false. See my comments over at Wikipedia on this.]

 

Readers will no doubt note, too, if they check, that these characterisations cannot be found in Aristotle, and he can only be made to say such inane things if what he actually says is ignored, or his words are altered so that they say the opposite of what he intended. In this case, clearly, "Aristotle does not equal Aristotle", according to Woods and Grant. For example, while Woods and Grant 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 (1984b), p.1650. I have used the on-line version, here.]

 

This is hardly an "equal to".

 

Moreover, their characterisation of the LEM is, to be frank, laughable. What, it may be wondered, has "A is not equal to B" got to do with the LEM? It is worth reminding ourselves that the LEM merely states that of proposition p, either p is true or p is false (or, more formally, p v ¬p -- "¬" standing for negation, and "v" for the inclusive "or").

 

But, there is much 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 from the Second Edition, although it remains in the on-line version.]

 

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) would be syntactically viable if "p" stood for an object, or operated as a singular term variable (going proxy for a Proper Name or Definite Description). However, in b), it isn't clear what role "not-" occupies. Is it an operator mapping a name onto a 'negative name' (whatever that is!), or is it an operator mapping a propositional variable onto its negation? If the latter is the case, then "p" can't be operating as a singular term, as it is in a). If the former, then it would be pertinent to ask W&G what "not-Socrates" could possibly mean -- turning b) into "Socrates is equal to not-Socrates". Even supposing some sense could be made out of that, what sense can be made of c) and d)?

 

c1) Socrates or equals not-Socrates (sic).

 

d1) Not both Socrates not-Socrates (sic). 

 

c1) and d1) are just plain gibberish.

 

[I have covered these points in more detail below.]

 

Furthermore, if "p" were an object (as opposed to standing for the name of an object), it couldn't be used to say anything. This is precisely the mistake Hegel made, which error W&G have simply compounded. [More on that here.]

 

If, on the other hand, "p" were a propositional variable (standing for something like "Lenin is the author of 'What is to be done?'", then c) and d) would become:

 

c2) Lenin is the author of 'What is to be done?' or equals not Lenin is the author of 'What is to be done?'

 

d2) Not both Lenin is the author of 'What is to be done?' not Lenin is the author of 'What is to be done?'

 

Which, if anything, seem even worse!

 

Clearly, these two comrades didn't find these prize examples of syntactical confusion in a logic text written anywhere on this planet -- which can only mean they simply made them up. At any rate, this shows that they, too, made no serious attempt to comprehend much of what they constantly deride and denigrate. [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 was removed from the second edition of W&G's book -- probably because a supporter of this site e-mailed Alan Woods about it several years ago. Having said that, many of the other errors that had been pointed out to him at the time haven't been corrected, and the confused syntax quoted above still remains in the on-line version -- or it did so up until at least June 2015, the last time I checked.]

 

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 in turn borrowed it from Medieval Theologians Logicians). "Caesar is a man" (W1) does not say the particular is the universal, and can only be made to do so by imposing on it a grammatical theory that these two comrades failed to justify. [Indeed, it cannot be justified; on that see Essay Three Part One (summary here).] And even if W1 could be construed in this way, Woods and Grant failed to tell us why this would be a contradiction, as opposed to it being a simple falsehood --, or just plain unvarnished nonsense.

 

As we can now see, their book should be re-named more accurately: Reason In Remission.

 

Dialectical Mayhem

 

However, in most DM-texts, the LOI is defined as "A = A", "A is equal to A" -- or even "A is A" (but on this see Essay Six) --, and said to imply that "A cannot be other than A" (which is incorrect; again on that see Essay Six, here).

 

[LOI = Law Of Identity; FL = Formal Logic; AFL = Aristotelian Formal Logic; LOC = Law of Non-Contradiction; LEM = Law of Excluded Middle.]

 

The LOC is similarly characterised as "A cannot at the same time be A and not A" (or even "A cannot be non-A"), which is said to follow from the negative form of the LOI (but with no proof that it does; on that see here), whereas the LEM is depicted rather loosely as "Everything must be A or not A", or even worse, "A does not equal B"! [These confusions are dissected here and here. Again, see my comments over at Wikipedia on this.]

 

Be this as it may, it turns out that it is impossible to say what it is that DL commits its adherents:

 

"The principles of difference: 'All things are different....' 'A is also not A....'

 

"And then -- Hegel says wittily -- it is said that there is no third. There is a third in this thesis itself. A itself is the third, for A can be both +A and -A. 'The Something thus is itself the third term which was supposed to be excluded.'" [Lenin (1961), p.135-38. Italic emphases in the original; bold added.]

 

"And it is just as impossible have one side of a contradiction without the other, as it is to retain the whole of an apple in one's hand after half has been eaten." [Engels (1891), p.496.]

 

"Let us now consider the matter from the standpoint of a higher doctrine of thought, from the standpoint of dialectics. Let us take the first law which we have developed as the foundation of logic: A is A. A thing is always the same thing. Without testing this law, let us consider another one which we have already mentioned, the law of Heraclitus which says 'Everything is in flux,' or 'One cannot ascend the same river twice.' Can we say that the river is always the same? No, the law of Heraclitus says the opposite. The river is at no moment the same. It is always changing. Thus one cannot twice nor, more exactly, even once ascend the same river. In short: the law 'A is A' in the last analysis is valid only if I assume that the thing does not change. As soon as I consider the thing in its change, then A is always A and something else; A is at the same time not-A. And this in the last analysis holds for all things and events." [Thalheimer (1936), pp.88-89. Bold emphasis added.]

 

"This law of identity of opposites, which so perplexes and horrifies addicts of formal logic, can be easily understood, not only when it is applied to actual processes of development and interrelations of events, but also when it is contrasted with the formal law of identity. It is logically true that A equals A, that John is John…. But it is far more profoundly true that A is also non-A. John is not simply John: John is a man. This correct proposition is not an affirmation of abstract identity, but an identification of opposites. The logical category or material class, mankind, with which John is one and the same is far more and other than John, the individual. Mankind is at the same time identical with, yet different from John." [Novack (1971), p.92. Bold emphasis added.]

 

If this analysis of the LOC were correct, and it were true that "A is A and at the same time non-A", or that "A is both A and non-A" (that is, if what DM-theorists say about the LOI were correct), it would be impossible for DM-theorists to begin to express their criticisms even of their bogus AFL-principles. That is because it wouldn't be possible to state the following:

 

B1: "A is A and at the same time non-A".

 

Again, if it were indeed true that "A is A and not A/non-A" or "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"), and if we unwisely followed the advice of DM-'logicians'. Plainly, B1 would 'dialectically disintegrate' into B3 -- or, perhaps even 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 the 'dialectical' re-write of the LOC.

 

Now, this fatal result can only be rejected by those who also renounce the DM-inspired version of the LOC (i.e., those who repudiate the following: "A is at the same time non-A").

 

Furthermore, if every A is also 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 B4 is replaced by the non-A that dialecticians insist they are.

 

Once more, this disintegration can only be rejected by those who repudiate standard DM-criticisms of the LOC and the LOI.

 

As should now seem apparent, the LOC has an annoying way of hitting back in a most un-dialectical fashion when challenged. Hence, as noted above: it is impossible for dialecticians to say what they think they mean.

 

The same problems afflict other DM-inspired criticisms of principles dialecticians claim to have found in FL-textbooks.

 

In addition, DM-theorists are invariably unclear what the As in these alleged FL-'laws' are supposed to stand for. Based on the above, and on other passages quoted elsewhere at this site (for example, here), it is obvious that DM theorists regularly confuse these letters with one or more of the following: propositions, judgements, properties, qualities, words, objects, processes, predicates, statements, assertions, type-sentences, token-sentences, concepts, ideas, beliefs, thoughts, categories, phrases, clauses, relations, relational expressions, indexicals, places, times, names, and, in one case, "existences" (i.e., anything in the universe!).

 

The significance of logical disorder of this magnitude lies not so much with the unmitigated confusion it creates, but with the fact that the vast majority of the DL-faithful haven't even noticed it!

 

And, even when this is pointed out to them, they complain about "pedantry", or "semantics"! [On my alleged 'pedantry', see here.]

 

Welcome to grown-up logic, comrades. Sloppy thought is left at the door. As Bertrand Russell once said (sarcastically):

 

"This illustrates an important truth, namely, that the worse your logic, the more interesting the consequences to which it gives rise." [From here.]

 

[DM-fans confronted with this quote often focus on the word "interesting" and ignore "worse".]

 

2400 years ago (and despite his own confusions) Aristotle was far clearer about such things than all these 'dialectical logicians' put together.

 

Are we really supposed to believe that this sub-Aristotelian jumble encapsulates ideas that lie at the very cutting edge of modern philosophy and science?

 

Now, anyone tempted to respond to the above along the lines that it gets the DM-view of contradictions (etc.) wrong, and that dialectical contradictions are really this, or they are in effect that, or they are…whatever, need only reflect on the fact that according to the DM-inspired criticism of the LOC, that criticism itself must be this or that, or whatever, while at the same time being not this or that, or whatever -- if we here interpret the "A"s above as "this or that, or whatever", since, on sound DM-lines, these letters can be interpreted in any which way we like.

 

Let's see those who accuse careful logicians of "pedantry" try to squirm their way out of that one!

 

[In Essay Eight Part Three, we shall see that this serious difficulty afflicts, and thus neutralises, the best (Marxist) account there is (or, at least, the best account I have so far seen in over thirty years) of the nature of 'dialectical contradictions'.]

 

In that case, the radically imprecise nature of the DM-inspired criticism of the LOC (which sees everything as "this or that, or whatever, and not this or that, or whatever" -- where each "this or that, or whatever" is left undefined so it can be anything you like) must itself be "both a criticism and not a criticism" of the LOC. That must be so unless, of course, criticisms are themselves exempt from their own criticism -- and cannot thus ever aspire to become one of those wishy-washy dialectical letter "A"s.

 

Alas, that means this Hegel-inspired criticism of the LOC now self-destructs. Hence, 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 with any clarity or consistency), it must be the case that:

 

A1: 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 perhaps that even DL-fans might begin to see how devilish their own Diabolical Logic really is.

 

[MAD = Materialist Dialectics/Dialecticians, depending on context; BAD = Buddhist Dialectics/Dialecticians; DL = Dialectical Logic.]

 

However, long experience 'debating' with comrades who think Hegel is the best thing since sliced Aristotle suggests that one should never underestimate their capacity for ignoring anything they do not like, or haven't even thought about. 'Debating' with those whose brains have been compromised by this Hermetic virus is like debating with Buddhists -- except the latter do not generally resort to abuse. With respect to both sets of mystics (the BAD and the MAD), whatever argument is deployed against their system simply doubles back to prove their case. After all "That's dialectics for you. To attack it is to confirm it!"

 

[The fact that BAD-ies can tell us absolutely nothing about 'Nirvana' phases them not one iota (since it is Nothing!), just as it scarcely registers with MAD-ies that they can't say what their "Totality" is, either.]

 

And it is no use pointing out to MAD-ies (or BAD-ies) that their belief in universal contradictions is self-contradictory, for to do so would merely be to feed this monster, and thus lend it strength.

 

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 sphere of application. These principles fall short when they are applied to processes in the 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 and Trotsky's attempt to criticise the LOI, and the claim that change is the result of 'internal contradictions').

 

In the meantime, it is worth pointing out 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, or propagated in the air as sound waves), 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 material copy of a DM-inspired criticism of FL.

 

In that case, no materially-configured DM-criticism of the LOC is equal to itself, and hence each phenomenal example of a DM-criticism 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 related to everything that it is 'not' --, is defused in Essays Seven and Eight Part Three.]

 

 

Logic And Change

 

Now, it is exceptionally rare to find a dialectician who fails to say something like the following:

 

"Formal logic regards things as fixed and motionless." [Rob Sewell.]

 

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

 

"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 equals A, it can never equal non-A." [Novack (1971), p.20.]

 

Once again, the bemused reader will search long and hard, and to no avail, to find a reference to a single logic text in the writings of such dialecticians that supports these rather odd allegations.

 

In fact, Formal Logic uses variables -- that is, it employs letters to stand for named objects, designated expressions (some of these are called "predicates"), and the like -- all of which can and do change.

 

This handy device was invented by Aristotle, who experimented with variables approximately 1500 years before the same tactic was extended into mathematics by Muslim Algebraists -- who in turn used them several centuries before René Descartes (1596-1650) began employing them in the 'West'.

 

This is what 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.]

 

Now, Engels himself admitted that the introduction of variables into mathematics allowed mathematicians to depict change:

 

"The turning point in mathematics was Descartes' variable magnitude. With that came motion and hence dialectics in mathematics, and at once, too, of necessity the differential and integral calculus…." [Engels (1954), p.258.]

 

But, if variables allow mathematicians to handle change, why can't this be allowed of logicians?

 

Nevertheless, a few counter-examples (to the claim that FL cannot cope with change) should at least give neutral observers pause for thought (though not dialecticians, who ignore awkward details like these, and continue to make the same baseless assertions about FL and change whatever awkward facts are lobbed in their general direction).

 

In the following examples, I have deliberately kept the arguments very simple (this is a summary, after all!):

 

Argument One:

 

Premiss One: All dialecticians are human beings.

 

Premiss Two: All human beings age.

 

Conclusion: All dialecticians age.

 

Argument Two:

 

Premiss One: All dialecticians believe Formal Logic cannot cope with change.

 

Conclusion: The refutation of a dialectician is the refutation of someone who believes Formal Logic cannot cope with change.

 

[A refutation is a form of change.]

 

Argument Three:

 

Premiss One: For all objects/processes x, for some time t, and for some time t' (where t'>t), if Fx(t) and ¬Fx(t'), then x has changed.

 

Premiss Two:  Fa(t) and ¬Fa(t'),

 

Conclusion: a has changed.

 

[Argument Three merely says (if we translate the whole of it into a more colloquial conditional sentence): if something is true of an object which isn't true of it at a later time, then it must have changed. Several more example can be found in Essay Four. The above are, of course, largely taken from Informal Logic, but it wouldn't be difficult to translate them into FL proper.]

 

Now, the above examples are highly unlikely alter the minds of dialecticians (who, unlike formal logicians, cannot cope with a change of opinion), perhaps since they seem rather trite. But they were introduced specifically to show that FL can handle change, and they were kept simple since most DM-fans find it hard to follow complex arguments expressed in modern logic, anyway. If the full range devices available to modern logicians had been used, and other branches of logic had been employed (of which dialecticians seem unaware -- such as Modal and Temporal Logic), countless complex examples could be wheeled out to show how MFL can cope with change, and rather easily.

 

[However, on this, see the last section of this Essay, below.]

 

Moreover, when it is remembered that DL itself cannot cope with change (the proof of that controversial allegation can be found here), the bankruptcy of at least this area of Modern-Day Hermeticism should be apparent to all but DM's very own True Believers.

 

 

DL -- A Superior Form Of Logic?

 

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. On the other hand, it would appear equally clear that a different logical system based on the opposite view of reality -- as it is also claimed of DL -- should have countless practical applications in science and technology.

 

Oddly enough, the exact opposite of this 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 still: DL has made no contribution to technological innovation. [The usual arguments to the contrary are neutralised in Essay Four: here, here and here.]

 

In stark contrast, FL has played a key role in 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 of FL on technology is the development of computers. Their origin goes back many centuries, but advances in control technology (in the 18th century) and 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 in general, the principles of Propositional Calculus govern the operation of all standard processors.

 

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, or to, 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 never tire of telling us that their 'logic' is superior to FL when it is applied to the material world.

 

Now, only the terminally naive will imagine that any of the above will have the slightest effect on dialecticians, or stop them saying the same erroneous things about FL, year in, year out.

 

As we noted above, the Heraclitean Flux has no control over these, its most inconsistent progeny.

 

Accounting For Change

 

When faced with the sorts of points made above, dialecticians have often responded as follows: "Well, how do you account for change, then?" Here is my reply:

 

1) Historical Materialism (minus Hegelian jargon) is well able to account for change. So we don't need DL.

 

[Concerning the difference between HM and DM, see here.]

 

2) Ordinary language contains countless words that can be used to depict every conceivable form of change imaginable (especially if it is augmented with words taken from HM, mathematics and science). Hence, Hegelian jargon is surplus to requirements.

 

And this is no mere dogma; it is easily confirmed. Here is a greatly shortened list of ordinary words (restricted to modern English) that allow speakers to refer to changes of unbounded complexity:

 

Vary, alter, adjust, adapt, amend, make, produce, revise, rework, advise, administer, allocate, improve, enhance, deteriorate, depreciate, edit, bend, straighten, weave, merge, dig, plough, cultivate, sow, twist, curl, turn, tighten, fasten, loosen, relax, ease, tense up, slacken, fine tune, 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, glide, ring, differentiate, integrate, multiply, divide, add, subtract, simplify, complicate, partition, unite, amalgamate, fuse, mingle, connect, link, brake, decelerate, 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, sink, 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, gobble, chew, gnaw, digest, ingest, excrete, absorb, join, resign, part, sell, buy, acquire, prevent, avert, avoid, forestall, encourage, invite, appropriate, 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, abduct, abandon, leave, abscond, many, more, less, fewer, steady, steadily, jerkily, intermittently, 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, limp, swim, fly, hover, drown, submerge, immerse, break, abrogate dismiss, collapse, shatter, split, interrupt, charge, retreat, assault, squash, adulterate, purify, filter, raze, crumble, erode, corrode, rust, flake, demolish, dismantle, pulverise, atomise, disintegrate, dismember, destroy, annihilate, extirpate, flatten, lengthen, shorten, elongate, crimple, inflate, deflate, terminate, initiate, instigate, replace, undo, redo, analyze, synthesise, articulate, disarticulate, 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, object, challenge, confirm, deny, repudiate, reject, expel, eject, repel, attract, remove, overthrow, expropriate, scatter, distribute, surround, gather, admit, acknowledge, 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...

 

[In each case, where there is a noun form of the word listed, its verb form is intended. So, where you see "ring", for example, think of the verb "to ring" and its cognates -- like "ringing", for instance.]

 

It wouldn't be difficult to extend this list until it contained literally tens of thousands of words all capable of depicting countless changes in limitless detail (especially if it is augmented in the manner suggested above). It is only a myth put about by Hegel and DM-theorists that ordinary language cannot express 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.

 

Word count: 6,990

 

Latest Update 05/04/17

 

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