Essay Eight Part Three -- 'Dialectical Contradictions'
Readers need to make note of the fact that this Essay does not represent my final view on any of the issues raised. It is merely 'work in progress'.
If you are viewing this with Mozilla Firefox, you might not be able to read all the symbols I have used.
(1) This Essay began life as a footnote to Essay Eight Part Two ("Forces and 'Contradictions'"), and as such it assumes the results of that Essay, and those of Essay Eight Part One ("Change Through Internal Contradiction"); (2) The central concern of this Essay largely revolves around the arguments found in the best article I have ever read on this topic (written by James Lawler). (3) The ideas of other dialecticians in this area are covered in other Essays published at this site (but their comments are nowhere near as clear and comprehensive as Lawler's). (4) Hegel's actual arguments will be considered in Essay Twelve Parts Five and Six (but they differ little from those reproduced below, as far as I can tell).
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Anyone using these links must remember that they will be skipping past supporting argument and evidence set out in earlier sections:
(1) Well, What Are 'Dialectical Contradictions'?
(a) The Best Article I Have Read
(b) Yet Another Syntactic Mess
(e) Law Of Identity Mis-Identified
(f) More Dark Sayings From Hegel's Dialectical Dungeon
(g) 'Difference' Made Unrecognisable
(h) The Fog Thickens
(k) The Magical Use Of 'Negation'
(l) Hegel's Hermetic House Of Horrors
(m) Acid Corrodes Hegel's 'Logic'
(n) Two Senses Of "Independent" Confused
(o) Threadbare
(p) What A Dialectical Dog's Dinner!
(2) References
Abbreviations Used At This Site
Well, What Are 'Dialectical Contradictions'?
The Best Article I have Ever Read
Easily the best account of 'dialectical contradictions' I have come across in my trawl through the wastelands of 'dialectical logic' is to be found in Lawler (1982). Having said that, I should immediately qualify it by adding that Lawler's essay is the best of the worst, for his analysis of this terminally obscure piece of Hegelian jargon is no better than was his analysis of Bertrand Russell's criticism of Hegel for confusing the "is" of identity with that of predication, discussed in Essay Three Part One.
In fact, there are so many logical errors in Lawler's article that any conclusions he draws are not really worth the paper they were printed on.
First of all, running through the entire article is the Hegelian confusion of logic with the 'science of thought', which Lawler nowhere tries to defend, and upon which he does not even comment. Indeed, he quotes Engels in support of this very idea:
"Modern materialism is essentially dialectical.... What independently survives of all former philosophy is the science of thought and its laws -- formal logic and dialectics." [Engels (1976), p.31, quoted in Lawler (1982), p.14; Lawler's added italic emphasis here.]
Lawler then adds:
"In view of this passage, in which the distinction between formal logic and dialectics could hardly have been made more clearly, it is difficult to see how Marx and Engels could have confused elsewhere undoubtedly, formal logic with dialectics or, more seriously, rejected formal logic altogether." [Lawler (1982), p.14.]
However, the passage from Engels seems to identify formal and dialectical logic (indeed, he lumps them together as "the science of thought and its laws -- formal logic and dialectics"). In that case, far from making the said distinction so plain that it could not have been clearer, had Engels actually said they were distinct, that would have been clearer.
Hence, it is obvious from the beginning that Lawler's aim is to defend a view consonant with tradition, rather than read even Engels with any accuracy.
As noted in Essay Two, when it comes to Philosophy, dialecticians are as studiously traditional as they are demonstrably conservative. Indeed, they are happy to recapitulate all the errors committed by aristocratic Greek (and now modern-day Hermetic) thinkers, and spin their a priori webs of Jabberwocky-lore with obscure jargon they struggle even now to explain to the rest of us.
[How they do the above is the subject of Essay Three Parts One and Two, and Essay Twelve Part One. Why they do it is outlined in Essay Nine Part Two and Essay Fourteen (summary here).]
Sure, we have no evidence that Marx himself was similarly confused about the nature of logic, but there is enough in Engels's writing to indicate that he was no clearer than Hegel -- indeed, Hegel was less clear than Aristotle (who tended to confuse logical with psychological and ontological issues far less than did this modern-day, Hermetically-confused 'genius') --, which makes the logical views of both these dialecticians totally worthless.
And, as we have already seen (in Essay Four), Logic cannot be counted as a science of thought, for if it were, logicians would perform brain scans, psychometric testing and surveys (etc.), and not waste their time with all those useless definitions, rules of inference and proofs.
Nevertheless, we should not let these relatively minor errors detract from the worse ones to come.
Lawler now tackles this topic with a consideration of Hegel's criticism of the LOI, which he regards as central to understanding the nature of 'dialectical contradictions'. But, as we have seen (and will see later), Hegel's criticism of the LOI is worthless, since he confused predication with the relation of identity, which then 'allowed' him to conjure his Ideal universe out of a reconfiguration of the diminutive verb "to be", a stunning trick even David Blaine could not match.
[LOI = Law of Identity, which Lawler calls "the principle of Identity".]
[Lawler's own misguided attempt to have the charges of logical ineptitude against Hegel dropped were ruled out of court in Essay Three Part One.]
We have also seen that Trotsky's attack on the LOI was even more inept, and while Hegel cannot be implicated with the latter's misconceptions, these two shared enough confusion in this area to make it difficult for us to tell which one of these two jokers was the Stan Laurel and which the Oliver Hardy of Logic.
[However, since Hegel got us into this mess, I reckon he's Stan.]
Be that as it may, if we turn to more substantive issues, we find Lawler is just as slip-shod in his use of 'logical' terms as other dialecticians are. Indeed, this is the only way he and they can make Hegel's 'logic' seem to work.
First of all, as we have already seen with respect to other DM-fans, Lawler is decidedly unclear about the denotation of the letter "A"s he uses.
For example, on pages 18-19, in reference to Hegel's discussion of Identity, Lawler has this to say:
"Hegel's critique of formal-logical principles begins with consideration of the principle of identity, A = A, or a thing or a concept is itself." [Ibid., pp.18-19. Italic emphasis in the original.]
We have already shown that this is a thoroughly inadequate way to characterise identity (either in logic or in ordinary language), but the point at issue here is the fact that Lawler views these "A"s as the names of objects and concepts, or perhaps even as those entities themselves, three different kinds of 'things'.
[LEM = Law of Excluded Middle.]
But then in the very same paragraph he goes on to say:
"The other principles follow from this basic one. The principle of noncontradiction, Hegel argues, is the principle [of Identity, RL] stated negatively. 'A is A' implies 'A cannot at the same time be A and not be A,' or one cannot assert something to be true and at the same time, and in the same respect, assert it to be false. The principle of excluded middle is that something must either be A or not be A: there is no third possibility. By extension, the law of noncontradiction implies that 'A cannot be non-A', where 'non-A' is something that is not A, or some part or property of A." [Ibid., p.19. Italic emphasis in the original; quotation marks in all the passages taken from Lawler have been altered to conform to the conventions adopted here. The middle set of quotation marks here (around the LEM) are missing in the original.]
As we will soon see, the principle of identity does not imply what Hegel says it does (or even what Lawler himself says it does -- since he nowhere corrects Hegel), but that is not of immediate concern here. However, when Lawler qualifies what he takes Hegel to mean, he clearly views these "A"s as propositions:
"'A cannot at the same time be A and not be A,' or one cannot assert something to be true and at the same time, and in the same respect, assert it to be false." [Ibid.]
So, they are no longer the names of objects or concepts, they are (the names of, or proxy letters for) propositions. That's now four different 'kinds' of things.
Of course it could be argued that Lawler is merely saying that such things cannot be asserted (etc.) of A, making A an object, or perhaps its name (but that is hardly likely; Lawler and/or Hegel were not bothered to discover alleged truths about names, one supposes). But even if this were so, in the above passage, "A" itself would be an object and what can be asserted of an object (i.e., a predicate expression, say). So, this response would be at once to defend Lawler and convict him.
Despite that, his wording does not support this contention. Lawler pointedly says:
"…one cannot assert something to be true and at the same time, and in the same respect, assert it to be false." [Ibid.]
As opposed to:
"…one cannot assert something to be true of A and at the same time, and in the same respect, assert it to be false of A."
If Lawler had meant his "A"s to be named objects, say, then he would have used the latter phrasing.
[Anyway, as we shall soon see, later on in Lawler's Essay these accommodating letters are unambiguously propositions.]
In addition, as pointed out above, it is worth noting that these "A"s (or at least, these "not-A"s) appear to be properties, or predicates (perhaps?); that's now six different 'kinds' of things:
"The principle of excluded middle is that something must either be A or not be A: there is no third possibility. By extension, the law of noncontradiction implies that 'A cannot be non-A', where 'non-A' is something that is not A, or some part or property of A." [Ibid.]
Of course, it could be that Lawler is merely adopting a tradition in ancient/early modern logic that treats all logical expressions equally sloppily (which, as it turns out, is the tradition that presided over the creation of the bowdlerised version of AFL that Hegel was taught at University (the kind of sloppy 'formalism' one finds in Kant's Logic, for example), and which he then put to no good), which seems to be the most likely explanation for Lawler's confusion here, given the other things we are about to discover (and to which we have already drawn attention, in Essay Three Part One, and Essay Four).
[AFL = Aristotelian Formal Logic.]
Nevertheless, it is this slip-shod approach to logic that 'allowed' Hegel (and now Lawler) to construct some rather 'innovative' metaphysics. Indeed, as Bertrand Russell noted:
"This illustrates an important truth, namely, that the worse your logic, the more interesting the consequences to which it gives rise." [Russell (1961), p.715.]
And this is somewhat reminiscent of the sort of word-juggling which allowed, say, St Anselm to concoct his famous 'proof' of the existence of 'God'.
[For more on Hegel's confused logic, the reader should consult Rosenthal (1998), pp.111-36, and Rosenthal (2001).]
This is all so quintessentially traditional as it is thoroughly confused.
But, after another flip, on page 21, Lawler now says:
"Putting the concept of identity into practical application, as it is interpreted by abstract understanding. We are compelled to say that a cow is a cow, a man is a man, white is white, spirit is spirit, etc. In attempting to express the principle of identity according to the spirit of abstract understanding, we end up paradoxically speaking of an endless number of different things." [Ibid., p21. Italic emphasis in the original.]
Although Lawler does not mention those "A"s here, they have now clearly become "things" once again. However, on page 22, they quickly transmogrify into "entities":
"'A is A' implies that A is not some other entity which is not-A." [Ibid., p.22. Italic emphases in the original.]
And, in the same paragraph, they soon morph into "beings":
"…in the abstract, undialectical understanding of identity, the relation of A to not-A (beings that are not A as well as A's own nonbeing) seems to 'vanish.'" [Ibid., p.22. Italic emphasis in the original.]
Here, not only has one of these "A"s been confused with a "being", "not-A" becomes its "non-being" (in fact, and to be more precise, it seems that these "A"s might also be predicates, once more, or even the subjects to which "being" is attributed; who can say?). At any rate, so far this makes the letters eight different kinds of 'things'.
[The reader should now convince herself that if someone says "Bush is not Bush" or even "Blair is not Bush", this does not imply Bush no longer exists. Anti-imperialists would surely have consigned one or both of these war-mongers and mass murderers to 'non-being' had their sticky end been quite so easy to engineer. To be sure, in the quirky world of Hermetic Hegelianism, negation might indeed be the same as 'non-being', but in the material world, one has to do much more to one's enemies than merely wish them away -- or simply glue a "non" or a "not" onto their names.]
On page 24, these chameleonic "A"s now change into "terms", and perhaps even propositions again:
"The point we have argued is that Hegel is attempting to establish identity, not destroy it. A term 'to be itself,' requires a negative relation to another term…. Does Colletti [an Italian Marxist, who Lawler is criticising in this article, RL] deny Hegel's point that asserting 'A' is equivalent to saying 'not-not-A'" [Ibid., p.24. Italic emphases in the original.]
If something is capable of being asserted, it must be an indicative sentence, or a clause, at the very least (and thus perhaps a proposition). To be sure, predicates can be asserted of named individuals (etc.) -- or perhaps better: true or false sentences can be formed if predicative expressions are completed with names, or with other singular terms (or indeed with the linguistic equivalents of the bound variables of quantifiers). As should seem obvious to any language-user, it is not possible just to assert a bald "term", predicate or concept. Uttering "ξ is a cat" (or "...is a cat", or even "is a cat") is to assert nothing (i.e., it is to make no assertion) -- and the same is true of merely uttering the word "cat".
Of course, one can point at an animal and utter this word, but that is the equivalent of saying "That is a cat". Without the pointing gesture, the use of that word would be to assert nothing. And one can utter the phrase "a cat" in answer to a question, such as, say, "What animal seems to know more logic than Hegel?"
To be sure, Hegel appears to think that objects/'concepts' can be true:
"In common life the terms truth and correctness are often treated as synonymous: we speak of the truth of a content, when we are only thinking of its correctness. Correctness, generally speaking, concerns only the formal coincidence between our conception and its content, whatever the constitution of this content may be. Truth, on the contrary, lies in the coincidence of the object with itself, that is, with its notion. That a person is sick, or that some one has committed a theft, may certainly be correct. But the content is untrue. A sick body is not in harmony with the notion of body, and there is a want of congruity between theft and the notion of human conduct. These instances may show that an immediate judgment in which an abstract quality is predicated of an immediately individual thing, however correct it may be, cannot contain truth. The subject and predicate of it do not stand to each other in the relation of reality and notion." [Hegel (1975), p.237, §172.]
Unfortunately, detailed consideration of the above will take us into areas that discussed in Essay Twelve (when it is finally published); suffice it to say here that Hegel's confusions on this score have clearly arisen out of his conflation of predicate expressions with singular terms, compounded by the adoption of the Medieval Identity Theory of Predication. [More on that here.]
The conflation of "terms" with "things", and then with linguistic expressions that can be asserted of named individuals (or once again perhaps better: the formation of true or false sentences by the completion of predicative expressions with names, or with other singular terms (or indeed with the linguistic equivalents of the bound variables of quantifiers, etc., etc.)), 'allows' Lawler (just as it 'allowed' Hegel) to derive the sort of "interesting" results we have come to know and loathe.
So, that is nine sorts of things that these "A"s are.
On page 26, these impressively Heraclitean (if not worryingly Cratylean) letter "A"s now morph into relations (as far as can be ascertained, that is), or perhaps named relational expressions(!):
"Hegel's main objective is to show an integral connection between A and not-A, or, in categorical terms, between 'identity' and what is supposed to be the contradictory of identity, 'difference.'" [Ibid., p.20.]
"In view of the criticisms made of Hegel, it is quite significant that Hegel recognises the force of logical contradiction as a weapon of criticism of his philosophical opponents. First they say, Hegel maintains, that identity has nothing to do with difference. Then they say that identity is different. They assert 'A' and then 'not A'" [Ibid., p.26.]
The only way to understand these passages is to read the "A" above as standing for "identity" and the "not-A" for "difference" (i.e., "not-identity", one presumes). Of course, this could be to misread what Lawler says --, but then he simply invites it.
That is now ten, or possibly eleven, different denotations for these semantically-dithering letters.
And it will not do to say that Lawler is merely reporting what Hegel's opponents might say, since he nowhere tries to pull these miscreants up for their syntactical sins.
At the very least these morphoholic letter "A"s now stand for propositions again, since here Lawler says they can be asserted once more. This interpretation is confirmed in the next-but-one paragraph:
"The contradiction is not any kind of contradiction. For example, first they [the said critics, RL] affirm that all swans are white and then they deny that all swans are white." [Ibid., p.26.]
Well, if two hundred years ago Hegel was indeed faced with such simple-minded opponents, then no wonder he got away with so many logical howlers. But even so: What is so contradictory about someone changing his/her mind (if that is what one of these 'simpletons' did)?
[In fact, this is the only way to read this example that does not treat Hegel's opponents as sub-literate morons.]
Nevertheless, Lawler's "A"s have been transmuted once more into either propositions or predicates -- or perhaps even into properties(?) --, or maybe all three(?).
On the very next page (but in the same paragraph), it becomes a little clearer that these plastic "A"s are indeed relations, or nominalised relational expressions (or maybe nominalised relational phrases(?)); in fact it is quite plain that this is indeed what they are:
"The law of noncontradiction holds, for if 'identity held aloof from difference' (A) is false, then the contradictory 'not identity held aloof from difference' (not-A) is true." [Ibid., p.27. Italic emphases in the original.]
Since phrases can neither be true nor false, Lawler's reasoning is, shall we say, 'innovative'. Nevertheless, these busy little "A"s have plainly had yet another denotational make-over, and now stand for "identity held aloof from difference".
[The phrase "identity held aloof from difference" might appear to make sense to some, but that is only because they too have become inured to this odd way of talking -- perhaps as a result of reading far more Hegel, or "systematic dialectics", than is good for any denizen of this planet --, a use which pretends that relational expressions can be named and still remain relational. (This ancient ploy was exposed for what it is in Essay Three Part One.)]
The mercurial career of these infamous "A"s continues apace; on page 28 they metamorphose into indexical or token-reflexive terms(!):
"Hegel's statement is made in response to Zeno's famous paradox. Zeno's paradox, according to Hegel, is that since motion involves both A and not-A, and since this violates the principle of noncontradiction, it follows that motion is impossible. What should probably be called 'Hegel's paradox' is the assertion that since motion occurs, there must in some sense both the A and not-A of Zeno's position. It is clear that this assertion cannot be taken in the sense of a strict contradiction. Not-A in a purely formal sense means only the denial of A, and is compatible with saying that the object is both 'here' and 'anywhere else,' perhaps also on the moon. Not-A can also mean the simple denial of 'here' -– an assertion that clearly leaves us nowhere….
"…Hegel's line of thought here is similar to his approach to the problem of 'abstract identity' or 'identity held aloof from difference.' The paradox arises if we begin with an abstract notion of place, a 'here' which is totally discrete and unrelated to any other place. The common-sense definition of motion as 'change of place' or as a passage of an object through a succession of places runs into insuperable intellectual difficulties if 'place' is understood in this manner. For one thing 'place' is defined as 'fixed place,' i.e., as motionless place. Can motion be explained in terms of a concept which excluded motion? On the other hand, it does not seem possible to eliminate some notion of definite place from our concept of motion, but such a notion must be that of a 'relative place,' a place which is both 'here' and 'there' or, paradoxically, 'here' and 'not-here." [Ibid., pp.28-29. Italic emphases in the original.]
In this passage, Lawler's "A"s and "not-A"s now plainly stand for "here" and "not-here", respectively. A change of identity perhaps, but no less an example of lamentably poor logic for all that.
That is now at least thirteen different identities for these impressively fluid letters!
However, we saw in Essay Five that the above 'analysis' of motion had more holes in it than a lorry load of Polo Mints. There is no 'common sense definition' of the items Lawler mentions; ordinary language (let alone 'common sense') easily allows for the sorts of motion in the material world that Idealists like Hegel ignored --, and both of these (i.e., the vernacular and 'common sense') do this with relative ease, too.
Nevertheless, on page 32, these change-oholic "A"s go into morphological hyper-drive as they become parts (or perhaps 'reflected' parts) of one another:
"One might readily grant that the definition of A includes A's relating to something that is not A (some non-A which is not-A). This does not mean that non-A or what is not-A is a part of A or part of A's identity….
"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….
"…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." [Ibid., p.32. Italic emphases in the original.]
These denotationally-profligate letter "A"s, it seems, can take on any form whatsoever in order to make this Hermetic Hodgepodge seem to work. I have been able to identify at least fourteen different denotations for them in this article. This means that Lawler is a verbal-trickmeister to rank with some of the best.
In the Summary of Essay Two, the following was baldly asserted:
"For over two thousand years traditional Philosophers have been playing on themselves and their audiences what can only be described as a series of complex verbal tricks. Since Greek times, metaphysicians have occupied themselves with deriving a priori theses solely from the meaning of a few specially chosen (and suitably doctored) words. These philosophical gems have then been peddled to the rest of humanity, dressed-up as profound truths about fundamental aspects of reality, peremptorily imposed on nature -- often without the benefit of a single supporting experiment….
"Even before the first dialecticians put pen to misuse, they found themselves surrounded on all sides by ideas drawn from this ancient tradition. Clearly, they faced a serious problem: if they imposed their ideas on nature in like manner, they could easily be accused of constructing a comparable form of Idealism. On the other hand, if they didn't do this, they wouldn't have a 'philosophical' theory of their own to lend weight to, and provide a bedrock for, their claim to lead the revolution. Confronted thus by traditional styles-of-thought (which they had no hand in creating, but which they were only too happy to appropriate), DM-theorists found there was no easy way out of this traditional minefield -- or at least none that managed to keep their theory the right side of immaterialism.
"Their solution was simple and effective: ignore the problem.
"This is not to deny that dialecticians are aware of the Idealism implicit in traditional thought; on the contrary, but their excuse for ignoring its pernicious influence on their own ideas is that the materialist flip they allegedly inflicted on Hegel was capable of changing such theoretical dirt into philosophical gold. However, flip or no flip, their own thought is still thoroughly traditional in style: it is dogmatic, a priori, and couched in jargon lifted straight from the Philosophers' Phrase Book. Even though few DM-theorists deny that traditional Philosophy is largely Idealist, not a single one has avoided copying its conservative approach to a priori knowledge.
"So, despite the fact that dialecticians constantly claim that DM has not been forced on nature -- for that would surely brand their theory "Idealist" -- they all invariably end up doing exactly that, imposing their theory on reality. In so doing, they merely underline the fact that traditional thought has found a new batch of converts among erstwhile radicals."
We are now (partly) in a position to see why this was asserted quite so forcefully back then. Lawler's defence of Hegel depends solely on such a sloppy use of words, where predicate expressions are turned into names, objects, terms, indexicals and possibly relations themselves -- and which can thus stand in some relation to other similarly deformed linguistic expressions, or suitably processed objects.
Indeed, this is the only way that those spooky Hegelian "internal relations" can be generated (as Bertrand Russell correctly noted), which "relations" to this day still defy scientific detection. [Not that anyone in the dialectical fraternity (or beyond) is searching for them with much urgency.]
But, without this 'innovative' use of language, Lawler's explanation of 'dialectical contradictions' falls completely flat, as we will see.
Now it could be argued that these syntactical niggles are not really all that important; after all, it is quite clear what Hegel and Lawler meant. Anyway, it might prove possible to repair both accounts so that they pass such 'pedantic' hurdles with ease.
That, of course, remains to be seen. But since Lawler's article is by far and away the best defence of this incomprehensible Hegelian notion (i.e., 'dialectical contradiction') I have so far seen, this should indicate to the reader just how bad things are in this back-water of traditional myth-making. In that case, a dialectical rescue is highly unlikely from this wing of Idealism. Even academic dialecticians regularly make serious errors of this sort, and worse -- and they all fail to notice them, let alone acknowledge them, even after they have been exposed. That is how logically purblind this ruling-class gobbledygook has rendered them.
[This was the outcome with respect to Rosenthal (1998, 2001), which also fell upon deaf dialectical ears. The above allegations, however, will be substantiated in Essay Twelve, where Hegel's work in this area (along with that of his 'Marxist' groupies) will be taken apart.]
Naturally, I exclude Graham Priest's work from these impertinent indictments since it is far from clear whether the 'contradictions' he considers are 'dialectical' to begin with (even if we could tell!), or even contradictions to begin with -- and he is generally very careful with his syntax. Nevertheless, as far as I am aware, he has not yet noticed the logical blunders I have exposed in this Essay.
However, to those who think that this sort "pedantry" can be ignored it is worth pointing out that that would be the only way they could excuse their own sloppy thinking, and the only way they could make their ideas appear to work.
This sort of attitude would not be tolerated for one second in the sciences, or in any other branch of genuine knowledge. Can you imagine the fuss if someone were to argue that it does not matter what the Magna Carta said, or when the Battle of the Nile was fought, or what the Declaration of Independence actually contained, or what the exact wording of Newton's Second Law was, or whether "G", the Gravitational Constant, was 6.6742 x 10-11 or 6.7642 x 10-11 Mm2kg-2, or indeed something else? Would we accept this sort of excuse from someone who said it did not matter what the precise wording of a contract in law happened to be? Or, that it did not really matter what Marx meant by "variable capital", or that he "pedantically" distinguished use-value from exchange-value -- or more pointedly, the "relative form" from the "equivalent form" of value --, we should be able to make do with anyone's guess? And how would we react if someone said, "Who cares if there are serious mistakes in that policeman's evidence against those strikers"? Or if someone else retorted "Big deal if there are a few errors in this or that e-mail address/web page URL, or in that mathematical proof! And who cares whether there is a difference between rest mass and inertial mass in Physics! What are you, some kind of pedant?"
You can be sure such 'anti-pedants' will be examining these Essays with well-focussed magnifying glasses, nit-picking with the best, having turned their selectively pedantic eyes on all I have written in order to locate the tiniest of assumed errors --, all the while refusing to examine anything in the DM-Grimoire with a tiny fraction of such attention to detail. [In fact, they already have.]
With such a sloppy regard for logic and a fondness for Mickey Mouse Science, is it any wonder that genuine ruling-class theorists regard Dialectical Marxists with undisguised contempt, and workers in their billions ignore Marxism?
Nevertheless, in order to consider every option open to Dialectical Mystics to say what they mean by 'dialectical contradictions', Lawler's argument will be considered on its own merits, and his syntactical sins will be put to one side for now -- that is, where they can.
Notwithstanding this, Lawler tries to revamp Hegel's criticism of the LOI by arguing thus:
"Hegel's critique of formal-logical principles begins with consideration of the principle of identity, A = A, or a thing or a concept is itself." [Ibid., pp.18-19. Italic emphasis in the original.]
"A thing or concept is itself"? Is this meant to be serious? Not only is it a caricature of the LOI, it ropes in "concepts" which are not objects, and so cannot be related to themselves. We saw the difficulties traditional thinkers got into over precisely this in Essay Three Part One, and Essay Four.
[LOI = Law of Identity; FL = Formal Logic.]
To be sure, Hegel was writing at a time when little work had been done on this 'law', but Lawler isn't. And yet he refers his readers to no modern work in this area; had he done so Hegel's 'definition' would have been seen for the mystical joke that it is. [On this, see here, and here.]
Again, putting this to one side, Lawler now goes on to argue as follows:
"The other principles follow from this basic one. The principle of noncontradiction, Hegel argues, is the principle [of Identity, RL] stated negatively. 'A is A' implies 'A cannot at the same time be A and not be A,' or one cannot assert something to be true and at the same time, and in the same respect, assert it to be false. The principle of excluded middle is that something must either be A or not be A: there is no third possibility. By extension, the law of noncontradiction implies that 'A cannot be non-A', where 'non-A' is something that is not A, or some part or property of A." [Ibid., p.19. Italic emphasis in the original; middle set of quotation marks (around the LEM) missing in the original.]
This is so full of errors it is difficult to know where to begin. Lawler (following Hegel) tells us that the other principles of FL follow from the LOI, or rather from its denial (i.e., stated "negatively"). The latter principles comprise the LOC and the LEM –- but notice once again the common error dialecticians make (exposed in Essay Four) of thinking that FL has just three fundamental principles.
It seems in this regard therefore that academic Marxists (HCDs) are just as benighted as their more lowly LCD brethren were shown to be (here). Naturally this sorry state of affairs is itself not unconnected with the fact that both wings of Dialectical Darkness think that, to a greater or lesser extent, sane and sober sections of humanity can learn something useful from Hegel.
[LOC = Law of Noncontradiction; LEM = Law of Excluded Middle; HCD = High Church Dialectician; LCD = Low Church Dialectician. MFL = Modern Formal Logic.]
Hegel (and now Lawler) offers no proof of this 'inference', nor could he (they). The LOI concerns the relation that is supposed to hold between an object and itself (or perhaps between its names, depending on how one reads this 'law'); it is not about the truth-functional properties of propositions, which is what concerns these other 'laws'.
Lawler thus reports the following:
"The principle of noncontradiction, Hegel argues, is the principle [of Identity, RL] stated negatively. 'A is A' implies 'A cannot at the same time be A and not be A,' or one cannot assert something to be true and at the same time, and in the same respect, assert it to be false." [Ibid.]
But this 'derivation' only works because of the aforementioned confusion over the denotation of these letter "A"s (which explains why I went into all that 'pedantic' detail making this very point!).
Now, in relation to the LOC, if these letters refer to propositions, no problem. The above would at least be a passable 'definition' of the LOC; but under no stretch of the imagination can these letters refer to propositions when they appear in the LOI. That 'law' is not about the identity of a proposition with itself (which means that, with respect to propositions, the LOI is not a tautology), but even if it were, that would have no implications for the LOC. The LOC does not rule out propositions being non-identical (but see below), since it doesn't concern the identity of propositions to begin with. So, it neither rules them in nor rules them out. Indeed, if a proposition lacked identity it would not be a proposition in the first place. And if it possessed identity it would be an object, not a proposition.
To be sure, we can speak about two propositions saying the same thing, but that would not be to relate them, but to predicate something of one or both. Any attempt to go further than this stands in danger of confusing a propositional sign (i.e., the physical marks on the page, or the sounds involved when it is spoken) with what a proposition expresses. [On this, see below.]
We have already seen (here, here and here) that the LOI cannot be about the alleged identity between concepts, or even between predicates (since if it were, the latter would be objects too, and cease to be predicative), so the LOI can only apply to objects (or perhaps to their names), if it applies anywhere. This means that identity statements are at best 'necessary truths' (although I should want to call them "grammatical propositions"), not tautologies.
This is partly because they are not molecular --, that is, they relate objects to themselves, and so they do not contain sub-clauses, or simpler propositions. (On this, see Glock (1996), pp.164-69.) And even in predicative sentences, tautologies (at a discursive level) merely "say the same thing", or involve the use of synonyms. They do not involve identity statements, since they are not predicative, but relational. At best, a proposition expressing identity contains a relational expression which is both symmetrical and reflexive (among other things).
In short, identity statements cannot be tautological (in the sense of "saying the same thing") because both halves do not "say the same thing" (since they do not say anything at all). "A", if it is a name, or other singular term, does not say the same thing as "A", since "A", if it is a name (etc.), says nothing. Only clauses, propositions or sentences can be used to do that. And if "A" is a proposition, or clause, it cannot be put into a relation with itself, since it is not an object.
Discursively, an example of a tautology would be something like "A vixen is a female fox", which expresses a rule of language, and so cannot be true or false (this was argued at length in Essay Twelve Part One). On the other hand "A vixen is a vixen" is not a rule of language. However, if it is taken predicatively, "ξ is a vixen" cannot be saying the same thing as "A vixen", for the latter is plainly not of the form "ξ is a vixen". Moreover "A vixen" is not saying anything determinate, so "A vixen is a vixen" cannot be saying 'the same thing'. And "'ξ is a vixen' is a vixen" is not a tautology.
Of course, it could be objected here that the above would mean that "A vixen is a female fox" is not a tautology since "A vixen" and "ξ is a female fox" are not 'saying the same thing' (in the strict sense meant in the previous paragraph), which is absurd.
Indeed, and that is why this sentence was called a rule, since it expresses a pattern for replacing synonymous terms in English, so that anyone who used "a vixen" in a sentence" would be saying the same as anyone using "a female fox" (in non-opaque contexts).
[MFL = Modern Formal Logic; wff (pronounced "woof") = well formed formula .]
It could be argued that an identity statement is predicative, or could be put into predicative form; for example "ξ is identical with ξ", which always gives the value true for any substitution instance. Maybe so, and in that sense, it would be a tautology in MFL (if that is defined as any wff that always maps onto the true). But this is not a necessary adjunct to logic, as Wittgenstein showed. In a properly constructed formal language, identity would be expressed by the use of the same sign, so we do not in fact need this formal relation. [More on this, here.]
And it is certainly not what Hegel and Lawler are talking about.
Anyway, even as predicative propositions, they would still not be tautologies in the discursive sense Lawler and Hegel need (i.e., in the sense of "saying the same thing"). This is because the predicate here would be a two-place linguistic function "ζ is identical with ξ" (it cannot be "ξ is identical with ξ", for that prejudges the substitutional instances allowed), which is in no way tautological. [Once more, "...is identical with ξ" does not "say the same thing" as "ζ is identical with...".]
[The term "linguistic function" is explained in Geach (1961). Basically, such functions are analogous to mathematical functions, except in this case, they map linguistic expressions (of a certain sort) onto linguistic expressions (of another sort) -- although, in Frege's sense, they map such expressions onto the "True" or the "False". (The latter sense is not intended here.)]
But, even if the predicate were "ξ is identical with ξ", this would be no use, either, for "...is identical with ξ" does not "say the same thing" as "ξ is identical with...".
The Law Of Identity Mis-Identified
But, even if we were to concede that the LOI were the following:
L1a: p = p
[Where "p" denotes a proposition, statement or spoken token indicative sentence, (etc.), depending on one's philosophy of logic.]
or perhaps:
L1b: ∀(x) [Fx = Fx]
[where "∀(ξ)" is the universal quantifier, and "F(ξ)" a one-place, first-level predicate expression], neither of these would have any bearing on the relation they are supposed to have with their alleged negative/'opposite', as might be the case with the following:
L2: p cannot at the same time be p and not be p.
Nor would either have anything to do with so-called "assertibility conditions":
L3: One cannot assert that p is true and at the same time, and in the same respect, assert that p is false.
This is because there are no rules for deriving either L2 or L3 from L1a or L1b (or from the less formal versions of these two), or indeed from something analogous. And it is not hard to see why. [More on this presently.]
[Of course, L3 could itself be correct (I will pass no opinion on it here), but L2 and L3 certainly do not follow from L1a or L1b, or from their alleged negations (or from the less formal versions of these two).]
Now, if L2 had been:
L2a: p cannot at the same time be identical with p and not be identical with p,
the problems associated with Hegel's 'derivation' would have been a little easier to see. Quantifying across propositions (if that were possible, and if we could make sense of the use of "=" between propositional variables/tokens), we might be able to obtain this:
L4: ∀(p) [(p = p) ® ¬(p ≠ p)].
If not, then perhaps just this:
L4a: [(p = p) ® ¬(p ≠ p)].
But, exactly how this implies the LOC is still rather obscure.
Perhaps the following will work? From L4a we can obtain:
L5: ¬(p = p) v ¬(p ≠ p),
and thus (by De Morgan's rules):
L6: ¬[(p = p) & (p ≠ p)],
and if we now replace "(p = p)" with "Γ" and "(p ≠ p)" with "¬Γ" we could derive the following from L6:
L7: ¬(Γ & ¬Γ).
But, we have as yet no rules for parsing the identity sign in the required manner, i.e., so that (p ≠ p) º ¬(p = p). Until we do, this derivation cannot work.
[On the rules we do have, see Bostock (1997), pp.323-33, Lemmon (1993), pp.159-67, and Quine (1974), pp.221-26.]
Even if we did have such rules, in order to obtain L7, the alleged LOI (i.e., "p = p") had to be combined with its supposed Hegelian 'other' (i.e., "¬(p = p)") [or is it "(p ≠ p)"?]), and then with its double negation (i.e., "¬(p ≠ p)") in a conditional. But, as we have seen, it is not too clear how L7 can be derived from "p = p" on its own, or even from its 'negation'.
However, it is worth pointing out again that if a proposition is not 'identical with itself', it cannot be a proposition (at least, not one with a determinate content). In that case, nothing could follow from it. And if it is 'identical with itself', it would be an object -- and, plainly, nothing follows from an object.
Either way, we hit another brick wall.
Nevertheless, it could be argued that in stencils like, say:
L9: ∀(x) [Fx = Fx]
and:
L10: (∀x)(∀y)(∀F)((Fx º Fy) ® (x = y))
there is an unambiguous identity sign between propositions, or at least between their signs. So the earlier claims cannot be correct.
But, logicians who use either the equal or the equivalence sign between propositional tokens do not imagine that these physical objects on the page are identical. They do have eyes! They variously interpret them as expressing a truth-functional relationship between the results of applying F(ξ), for example, to names or to objects (depending on the philosophy of logic to which they adhere), yielding an identity (or as expressing an equivalence relation) of some sort between abstract objects (i.e., sets, courses of values, graphs, ranges, classes, and the like), or between the truth values of the interpreted sentences that finally emerge as a result, and so on.
So, these signs in effect express rules that are applicable to other signs/symbols; they do not express an identity between lifeless marks on the page, or between propositions that exist in an ethereal realm somewhere.
[To be sure, some philosophers have held this view, but they too confused propositions with objects.]
Indeed, the second of the above (L10) shows that this is so by implicitly interpreting the equivalence sign as one expressing an identity between objects of some sort. In that case, stencils like L9 and L10 do not contradict what was maintained earlier, which was that where the sign for identity (etc.) is used, it expresses a relation between objects (or an object and itself -- or between its names), not between concepts, predicates or propositions.
Moreover, in L10, the "=" sign appears between quantified variables (the interpretation of which will depend on the domain of quantification, so this might not even be an example of the use of that sign between propositional tokens).
Now, whether this employment of signs captures the full range of meanings available in scientific contexts, or even in ordinary language, I will leave to one side for the present (but, it is worth adding here that Essay Six delivers a negative judgement in this regard).
[Of course, in stencils like L9, the "=" sign would be replaced by an "º", that is, by a biconditional sign. This is because "=" is a sign for two-place predicate/linguistic function (i.e., "ξ = ζ"), which can only take names or singular terms as arguments.]
Nevertheless, one thing is clear: MFL and ordinary language succeed in capturing the full range of words we have for identity (etc.) far better than the syntactical mess we find in DL. In fact, as Essays Three through Seven show, DL cannot handle the simplest of ideas/objects (such as a bag of sugar!), let alone anything more complicated.
[DL = Dialectical Logic.]
Hence, once more, the suggested Hegelian 'derivation' of the LOC (i.e., the one expounded by Lawler) cannot work if these "A"s are read as objects (since objects cannot be true or false), nor, indeed, if propositions are viewed as objects (and, for the same reason).
This is why it is so important to be clear about the denotation of these letters, and (once more!) why such a fuss was made earlier.
Alas, there is not much that can be done with this:
"The principle of excluded middle is that something must either be A or not be A: there is no third possibility. By extension, the law of noncontradiction implies that 'A cannot be non-A', where 'non-A' is something that is not A, or some part or property of A." [Ibid.]
Here, the letter "A" oscillates between predicative and naming roles (it seems), and if so, the LEM as stated above cannot be correct. [Even Aristotle saw through that one!]
[Nevertheless, as with most topics in logic, things are not quite so simple. We need to distinguish between sentential negation (i.e., "not p"), predicate negation (i.e., "not F") and predicate-term negation (i.e., "not-F" or "non-F"). It is unclear which form Lawler intends to use in the above passage (but his indiscriminate employment of "not A" and "not-A" suggests he is either unaware of this distinction, or he considers it unimportant -- the same unfortunately seems to be true of Hegel and his many groupies), so I have not dwelt on this difference in this Essay (nor on its alleged double negated form --, as in "non-non-F"). This topic will, however, loom large in Essay Twelve, where the deleterious effects of suicidally sloppy syntax like this will be exposed.
More details on this distinction can be found in Horn (1989) and Wansing (2001).]
If the "A" in the above passage were a predicate expression or property token (as the latter part of the last sentence in the quoted passage reproduced below clearly indicates) this version of the LOC could only be interpreted, for example, as "…is red" cannot be "…is non-red" (if viewed traditionally --, but as "ξ is red" cannot be "ξ is non-red", otherwise).
"The principle of excluded middle is that something must either be A or not be A: there is no third possibility. By extension, the law of noncontradiction implies that 'A cannot be non-A', where 'non-A' is something that is not A, or some part or property of A." [Ibid. Bold emphasis added.]
As we saw earlier, this would only be 'true' if these expressions were interpreted as names (or objects?), and not as predicate expressions or properties -- or, perhaps, as the names of whatever predicates allegedly designate.
And in that case, Lawler's "A cannot be non-A" would yield "C cannot be D". This is because Lawler clearly sees these "A"s here as the names of properties (and if these are expressed as predicate expressions, then the latter will become names once more). So using "C" for the name of whatever "...is red" is supposed to stand for, and "D" for whatever "...is non-red" is supposed to designate, we obtain "C cannot be D". And that is because, "...is red" must name something different from "...is non-red".
Of course, this will be so unless "…is red" is viewed as the same name (say "E") as "…is non-red" (also "E"). If so, Lawler's 'definition' would become "E cannot be E"!
Either way, we hit yet another brick wall, hence it is impossible to make sense of what Lawler is trying to say here.
[This is because Lawler's 'definition' tried to relate a term to its negated 'other', but his own (sloppy) syntax prevents this. The reader will note that at the beginning of this passage, "A" is a predicate letter, but by the end it has become a name! That is clear from Lawler's own paraphrase: "where 'non-A' is something that is not A, or some part or property of A." This is the confusion I have tried to highlight above.]
Now, there might be a way of reading these predicate expressions that allows them to be grafted into the LEM in the way Lawler imagines; I cannot say since he does not say. [And no one else has.]
Moreover, when Lawler says that "non-A is something that is not A", it is unclear what he means. It seems it might be either:
P1: Non-A is not A,
or:
P2: Non-A is B which is not A.
Where B is the "something" that is not A. But Lawler immediately qualifies this by saying that "non-A" is "something that is not A, or some part or property of A". In which case he might mean:
P3: Non-A is not some part or property of A,
or perhaps:
P4: Non-A is some part or property of A.
It is impossible to decide which of these represents his view. And this lack of clarity is, once again, a direct result of the impoverished conceptual and logical tools Hegel passed on to the unfortunates who look to him for inspiration.
So, as things stand, this 'logical' sow's ear cannot be made even into a plastic purse, whatever is done with it.
More Dark Sayings From Hegel's Dialectical Dungeon
Now Lawler moves on to consider several other dark sayings he rescued from Hegel's Manichean Mausoleum:
"Recognition that the principle of noncontradiction is the principle of identity stated negatively, or is implied in the principle of identity, is central to Hegel's dialectical analysis." [Ibid., p.19.]
If so, Hegel's analysis is a non-starter, since it can only 'work' if propositions, predicates and objects are confused one with another, as we have seen. This means that we can only make sense of 'dialectical contradictions' if we pretend that the denotation of words and letters does not matter. In which case, we should openly remove the word "logic" from its already precarious presence in Hegel's corpus, and rename it perhaps "Dialectical Licence".
However, Lawler continues:
"Hegel's main objective is to show an integral connection between A and not-A, or, in categorical terms, between 'identity' and what is supposed to be the contradictory of identity, 'difference.' Hegel approaches this objective by considering the claim that 'identity' is 'held aloof from difference.' This is the claim that 'identity' is a concept that stands by itself and does not require its opposite or contradictory, 'difference,' in order to acquire its meaning." [Ibid., p.20. Italic emphases in the original.]
But why do we need to refer to "difference" in order to speak of, or give meaning to, "identity"? More to the point, why do we have to nominalise relational expressions in the first place?
As we saw in Essay Three Part One, this was an inept trick the ancient Greeks tried to pull: nominalise anything and everything in sight. In fact, they had to do this to try to make their a priori 'theories' work (and this in turn was prosecuted for ideological reasons, explored in Essay Twelve (summary here)).
The problem is that this move changes propositions into lists, which destroys their capacity to say anything at all. [Why that is so is demonstrated here.] Any 'contradiction', or, indeed, conclusion that 'follows' from this Stone Age segue is thus entirely bogus, since nothing can legitimately follow from a named abstract object like "identity". [Conclusions can only follow from propositions, or clauses.]
Well, perhaps Hegel meant that the practice of referring to identity statements tended to exclude those that expressed difference; in other words, he was merely speaking elliptically about one or both.
If so, this still won't work since there is no such thing as Identity (i.e., it is not an object, but a relation), and yet it is quite plain that both Hegel and Lawler need this 'abstraction' to be an object so that it can serve as the denotation of those annoyingly plastic letter "A"s we met earlier. However, if identity isn't an object (abstract or otherwise), then neither of these two can extract a contradiction from even their idiosyncratic version of the LOI:
"Hegel's main objective is to show an integral connection between A and not-A, or, in categorical terms, between 'identity' and what is supposed to be the contradictory of identity, 'difference.'" [Ibid.]
Here, plainly, "A" stands for "identity" and "not-A" for "difference". But, once again, we see that it is only sloppy syntax that allows this argument to gain even so much as a pretend toehold. If so, and without it, no contradiction can follow, as we have seen.
The problems this now creates for Lawler's interpretation of Hegel become clearer if we consider the latter half of the passage quoted earlier, along with what follows:
"Hegel approaches this objective by considering the claim that 'identity' is 'held aloof from difference.' This is the claim that 'identity' is a concept that stands by itself and does not require its opposite or contradictory, 'difference,' in order to acquire its meaning. This is also the claim that the identity of something can be determined without contrast to something that is not the thing we wish to define." [Ibid, p.20.]
Here identity is many things all at once: a property (as in "identity of something"), a concept (as in "'identity' is a concept"), a word (as in "in order to acquire its meaning") as well as an object (as in "'identity' is 'held aloof…'"). So it is no wonder that Hegel can derive all sorts of 'interesting' results from logical goulash of this (in)consistency. But there is more:
"According to this 'philosophy of abstract identity,' meanings and objects (including processes, relations, etc.) are independently identifiable, standing on their own, atomistically. Against this claim, Hegel argues that it is impossible to say what one means by identity without bringing into the definition what it as supposed to exclude, namely difference." [Ibid., p.20.]
However, if this is correct, and if Hegel were the genius we have been led to believe, he should have pointed out what seems obvious to his straw opponents: 'abstract identity' can only be conjured into existence if relational expressions are changed into names (in a way that is analogous to the linguistic atomism found in the theories of those he was criticising).
How could he possibly have missed this obvious response?
[Hint: Hegel was a logical incompetent.]
Insults aside, can any sense be made of this?
Not much, it seems, since the whole topic (indeed, the whole of Hegel's work) is a direct result of a crass misuse of language, on a grand scale, and nothing less.
And, of course, it is possible to identify something (in the sense of the LOI) without having to involve "difference". Consider the following:
[1] (∀x)(∀y)((x = y) º (Fx ® Fy)).