Summary Of Essays Four, Five And Six


Essay Four: Formal Logic Meets Wilful Ignorance


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In this Essay I expose the woeful ignorance of FL generally displayed by DM-theorists. Few dialecticians can resist making ill-informed and unsubstantiated criticisms even of AFL, while fewer still appear to know anything of MFL.


[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.]


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. Sixty years ago Burnham tried to tell Trotsky that his knowledge was badly out-of-date, but he might as well have been talking to the cat for all the good it did.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 idea that appears to have escaped the Heraclitean flux.


Even to this day, the 'news' that logic underwent a profound revolution in the late 19th century (easily of the same order that Physics underwent in the 17th century) has yet to penetrate most dialectical skulls. Still, they refuse to be told. In fact, I raised this with John Rees at Marxism 1990 -- in front of a large audience -- 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.


Furthermore, based on what DM-theorists themselves write, it is clear that the majority of them do not appear to have opened a single logic text ever, especially before they began pontificating on the subject -- at least, not one written since Hegel misnamed his own particular work Logic. And, of the tiny minority who have, few seem to have understood much of what they rapidly skimmed. The hackneyed definitions that DM-theorists give of the three allegedly fundamental 'laws' of logic are hopelessly confused; their 'research' in this area has clearly been confined to copying these 'non-definitions' off of one another.


However, in most of the above the LOI is defined as "A = A", "A is equal to A" -- or even "A is A" (on this see Essay Six) --, which is said to imply that "A cannot be other than A" (which is incorrect). The LOC is similarly characterised as "A cannot at the same time be A and not be A" (or even "A cannot be non-A"), which is said to follow from the LOI (but with no proof that it does), whereas the LEM is depicted rather loosely as "Everything must be A or not A", or even worse, "A does not equal B". [These confusions are dissected here.]


Do dialecticians really think that a philosopher of Aristotle's stature and sophistication actually believed that, say, "Everything must be rat or not rat" (sic), or that "rat does not equal cat"? [Interpreting here the 'dialectical definition' of the LEM literally, replacing "A" with "rat", and "B" with "cat", respectively.]


If they do, we might wonder why Marx thought so highly of him.


Of course, anyone familiar with Aristotle's style of writing (or who bothers to check!) will know that he never expresses himself this way. Indeed, I have been unable to find a sentence remotely like any of these in his work. And he does not even so much as mention the LOI.


Nevertheless, even if their analysis of the LOC were correct, and it was true that "A is A and at the same time non-A", it would be impossible for DM-theorists to give voice to their criticisms of these alleged AFL-principles. This is because it would be impossible to state the following:


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


Hence, if it were true that "A" is at the same time "non-A", then sentence B1 would have to be re-written as:


B2: "Non-A is non-A".


Or even worse:


B3: "Non-A is non-A and at the same time non-(non-A)".


That is, if each "A" in B1 is replaced with what it is supposed at the same time to be (i.e., "non-A"). B1 thus dialectically disintegrates into B3.


Now, this fatal result can only be denied by someone who also rejects the DM-inspired version of the LOC, and who thinks B1 is false.


Even worse still, 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" dialecticians insist that they are. Once more, this could only be denied by those who reject standard DM-criticisms of the LOC.


As should now seem apparent, the LOC has an annoying way of hitting back in a most un-dialectical way when challenged; it thus becomes impossible for dialecticians to say what they mean. The same problems afflict other DM-inspired criticisms of principles dialecticians claim to have found in textbooks of FL.


Perhaps worse, DM-theorists are invariably unclear what the "A"'s in these alleged FL-laws are supposed to stand for. Based on what they say (the details are given in Essay Four), 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, phrases, clauses, relations, relational expression, indexicals, places, times, names and "existences".


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 have not even noticed it!


As will be shown in Essay Four, 2400 years ago (and despite his own confusions in this area) Aristotle was far clearer about such things than the vast majority of DL-fans are.


And this set of doctrines represents ideas we are told lie at the very cutting edge of modern science?


Now, anyone tempted to respond to the above on the lines that it gets the DM-view of contradictions (etc.) wrong, and that dialectical contradictions are really 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 DL-principles, these letters can be interpreted in any which way we fancy.


Thus 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 not defined) must itself be seen as "both a criticism and not a criticism" of the LOC. This is 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 "A"s).


Alas, this means that DM's own criticism of the LOC must now self-destruct. So, for example, any attempt made by DM-'logicians' to define the LOC must be "a definition and not a definition" -- if their own 'analysis' of the LOC and LOI is itself invoked against any such attempt.


Hence, using "D" to stand for the DM-'definition' of the LOC (whatever that 'definition' is, and whatever it means, if we are ever told), it must be the case that "D is at the same time non-D". Clearly, that would mean that the DM-inspired criticism of the LOC undermines its own definition of it! Or, at least, it does and it doesn't.


It is at this point that even DM-advocates might just begin to see how devilish their own Diabolical Logic really is.


Now, it could be objected once more that DM-theorists do not object to the use of the LOC, the LOI and the LEM in their proper field of application; where these principles fall short is 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 and Two (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 (etc.), or propagated in the air as sound waves at some point), and as such they are surely subject to change (if everything is). In that case, they "are never equal to themselves". If this is so, the above DM-inspired criticisms of FL must apply to each material copy of such DM-inspired criticisms 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) will be examined in Essay Six. The other counter-argument that this ignores Hegel's use of identity to derive the alleged fact that everything is related, or 'reflects' to its 'own other', but not to everything that it is 'not', is defused in Essays Seven and Eight, Part Two.


However, in order to refute the claim that FL cannot account for change (a charge DM-theorists make as often as they fail to substantiate it), I demonstrate how even AFL (never mind modern Temporal Logic, for example) can easily cope with change. By way of contrast, I reveal that DL cannot even handle a simple bag of sugar!


Moreover, given that DL is supposed to be applicable to the practical affairs of the material world, the surprising fact is that so far there have been no discernible practical or technological applications of DL. This contrasts unfavourably with the many real applications there already are of MFL, not the least of which are those that have enabled the development of computers. Every standard processor, for example, operates with rules drawn from modern-day Propositional Calculus.


Once more, 'dialectics' meets its worst enemy: practicalities. MFL is eminently practical; DL is practically useless.



Essay Five:  Dialectics, The 'Doctrine Of Change' Cannot Account For Movement


This material is now badly out-of-date. Visitors are encouraged to read the updated version of this Essay summary, here.


In Essay Five I demolish Engels's alarmingly brief 'analysis' of motion:


"[A]s soon as we consider things in their motion, their change, their life, their reciprocal influence…[t]hen we immediately become involved in contradictions. Motion itself is a contradiction; even simple mechanical change of place can only come about through a body being both in one place and in another place at one and the same moment of time, being in one and the same place and also not in it. And the continual assertion and simultaneous solution of this contradiction is precisely what motion is." [Engels (1976), p.152.]


There are many problems with this passage, not the least of which is Engels's claim that the alleged contradiction here has something to do with its "assertion" and "solution". This is not easy to square with his other belief that matter is independent of mind. Who, for example, "asserted" this alleged contradiction before humanity evolved? And who did the "solving"?


Or, are we to assume that things only began to move when sentient beings capable of making assertions appeared on the scene?


In fact, Engels's 'analysis' itself was based solely on a very brief thought experiment, one motivated by a superficial consideration of a limited number of words associated with movement. Indeed, Engels was quite happy to derive a set of universal truths about motion -- applicable everywhere in the entire universe for all of time -- from the alleged meaning of a few simple phrases. Clearly, the concepts Engels used cannot have been derived by 'abstraction' from his (or from anyone else's) experience of moving bodies since no conceivable experience could confirm that a body is in two places at once, only that it moves between at least two locations in a finite interval of time. To be sure, that is why Engels not only had to indulge in flights of fancy to make his case, he had to impose his views on reality.


Leaving this aside, even if Engels's claims were correct, they can't account for movement (and hence they can't explain change). Clearly, Engels failed to notice (just as subsequent dialectical-copiers of the above passage have failed to notice) that the way he depicts motion does not distinguish moving from stationary bodies. Stationary bodies can be in two places at once, and they can be in one place and not in it at the same time. For example, a car can be in a garage and not in it at the same time (having been left parked half-in, half-out); and it can be in two places at once (in the garage and in the yard), and stationary with respect to some inertial frame, all the while. Not only that, it can be in and not in the same place at the same time (in the garage but not fully in the garage, being half-in and half-out of it).


The only way this and similar awkward counter-examples can be neutralised is to re-define the relevant terms in ways that make Engels's 'analysis' inapplicable to material bodies, in that it would then only apply to immaterial, mathematical points. Unfortunately, in that case, Engels's thought experiment would not then pick out what is unique to moving material bodies.


Of course, mathematical points themselves cannot move by occupying still other points, hence they cannot move. Since points are not containers, no point can occupy another point. Points have no physical dimensions or rigidity, so they cannot even 'push' each other out of the way as they try to 'move'. Certainly, there are mathematicians who talk as if they believe points can move, but, beyond a certain way of speaking (i.e., figuratively), there is nothing to support the idea that they can (and everything to suggest they can't -- not the least of which is that such points do not exist in space and time to move anywhere).


Indeed, if certain ways of speaking could make things move, then more of us would believe in magic.


Moreover, Engels's claim that motion is contradictory only follows if a body cannot logically be in two places at once, or if it cannot be in one place and not in it at the same time (otherwise he would not have called it a logical contradiction, and he could not have used it to illustrate the alleged limitations of FL). Engels just assumed the truth of this premiss; he nowhere tried to justify it (and no one since seems to have bothered to fill in the gaps).


However, because an ordinary stationary material body can be in two places at once, and in one place and not in it at the same time (as we have just seen), Engels's key premiss is not even empirically true; hence it certainly can't be a logical/conceptual truth restricted only to moving bodies. If it is true that stationary objects can also do what Engels says, then it cannot be a contradiction when moving bodies do it -- or it can't be a contradiction true only of moving bodies. In that case, it cannot be something that accounts for motion, or that distinguishes motion from rest.


Now, Engels needed to be able to show that if someone asserts that their car is both in the garage and in the yard at the same time, and it is in the garage and not in it (being half in, half out) they must be contradicting themselves. Clearly, since no one else would think this of anyone who asserted such things, if dialecticians still insist on depicting these as contradictions, then they must be using this word in a new and as yet unspecified sense. Otherwise, the word "contradiction" must lose the sense it has, and Engels's claim would be devoid content (for we would not then know what he was ruling in or out -- just as we would not know what on earth he was talking about).


Engels's use of "contradiction" is thus based on ambiguities in language, ones that are easily eliminated once the details are filled in. In Essay Five I list many other examples where ordinary language seemingly allows everyday miracles to happen if it is interpreted in a similarly crude manner.


For instance, it is possible to show that some things move while staying still: worker NN is second in line in a queue, and rooted to the spot. Worker MM, at the front of the queue, drops out. At that moment, NN will have moved to the front of the queue without necessarily moving a muscle. Similarly, some things can move but stay in the same place: so on a train moving at 100 mph, worker NM is reading his copy of Engels (1976); miraculously the words on page 152 (quoted above) all stay in the same place on the page. So, not everything that moves needs to be in two places at once, and not everything that moves needs to change places. There are many more examples of this sort of everyday miracle.


Of course, the above examples only work because of ambiguities in language, and they can easily be removed when disambiguated. But the same applies to Engels's abstract 'analysis' of motion. So, anyone who objects to the previous paragraphs along those lines should therefore also object to Engels's equally cavalier use of language.


Furthermore, Engels's 'argument' depends on the claim that while the location of a particular body is subject to infinite divisibility (an assumption which, one presumes, is necessary to support the claim that moving bodies must be in two places at the same time, no matter how microscopically close together the latter are -- which implies that spatial locations can be given in endlessly finer-grained detail), the time interval during which that body occupies this or any other location is not subject to such a division. This is an a priori and non-symmetric restriction -- that is, it is being applied to time but not to space -- which is impossible to justify either on empirical or logical grounds.


If this constraint is waved (as surely it should!), it would mean that no matter how close together the two locations are that a body is supposedly in, we can always specify a time interval in which this occurs -- or, perhaps two moments isomorphic to them. The alleged 'contradiction' thus vanishes.


Again, the only way to neutralise this response is to counter-claim that a body is motionless if it is in a certain place at a certain time. In that case, if it is moving, a body must be in two places at the same time. But, that just repeats the non-symmetrical restriction noted above, for if we can divide up places more finely so that it is possible to say an object is in two of the latter while the 'instant' during which this occurs stays the same, then we can surely do the same with time, specifying two times for each of these two places.


Yet another negative response (from DM-fans) to that question needs to justify this asymmetric restriction before it can be taken seriously.


Once more, none of this is surprising since Engels's claims about motion and change date back to the a priori speculations of that ancient mystic Heraclitus -- a thinker who did not even bother to base his wild ideas on anything remotely like evidence (having derived his 'profound' conclusions about all of reality for all of time from what he thought was true about the possibility of stepping into a certain river!) --, and to an Idealist conundrum invented by Zeno.


Engels also failed to note that several other paradoxical consequences follow from his ideas. One of these is that if a moving body is anywhere, it must be everywhere, all at once. This is because Engels's argument depends on the idea that a moving body must be in two places at the same time --, i.e., in, say, P1 and P2 --, otherwise it would be stationary. This allows him to derive his 'contradiction': a moving body must be in two places at once and both be in and not in at least one of these at the same moment.


But, clearly, if the said body is in P2 it must also be in P3 in the same instant. If this is denied, then the assumption that a moving body must be in one place and not in it at the same instant, and in another place at the same instant, will have to be dropped. However, if it is still true to say that at one and the same instant a moving body is in one place and not in it, and that it is in another place at that instant (otherwise it would be stationary), then it must be in P3 at the same instant that it is in P2, or it would not be moving while at P2, and would be stationary at P2.


So, assuming that the said body is still moving while at P2, then by the application of a sufficiently powerful induction, it can be shown that any moving body must be everywhere if it is anywhere, all at the same instant!


Now that is even more absurd than Zeno's ridiculous conclusion.


But that's Diabolical Logic for you.



Essay Six: Trotsky Is  Equally Confused About Identity


This material is now badly out-of-date. Visitors are encouraged to read the updated version of this summary, here.


In this Essay, Trotsky's radically misconceived criticism of the LOI is analysed in detail and shown to be patently wrong at best, incomprehensible at worst. [Comments on Hegel's 'analysis' of Identity, which is marginally better than Trotsky's, will appear in Essay Twelve.]


For example, the 'definition' Trotsky uses (viz., "A is equal to A" ) -- and one reproduced identically by his followers -- is in fact an example of the principle of equality, not of identity:


"The Aristotelian logic of the simple syllogism starts from the proposition that 'A' is equal to 'A'…. But in reality 'A' is not equal to 'A'. This is easy to prove if we observe these two letters under a lens -- they are quite different from each other. But, one can object, the question is not the size or the form of the letters, since they are only symbols for equal quantities, for instance, a pound of sugar. The objection is beside the point; in reality a pound of sugar is never equal to a pound of sugar -- a more delicate scale always discloses a difference. Again one can object: but a pound of sugar is equal to itself. Neither is true (sic) -- all bodies change uninterruptedly in size, weight, colour etc. They are never equal to themselves. A sophist will respond that a pound of sugar is equal to itself at 'any given moment'…. How should we really conceive the word 'moment'? If it is an infinitesimal interval of time, then a pound of sugar is subjected during the course of that 'moment' to inevitable changes. Or is the 'moment' a purely mathematical abstraction, that is, a zero of time? But everything exists in time; and existence itself is an uninterrupted process of transformation; time is consequently a fundamental element of existence. Thus the axiom 'A' is equal to 'A' signifies that a thing is equal to itself if it does not change, that is if it does not exist." [Trotsky (1971), pp.63-64.]


From this poor start Trotsky's 'analysis' deteriorates rapidly. Neither he nor his epigones quote classical versions of the LOI (for example, that of Leibniz), and the latter seem to be unaware of more recent, technical definitions of this 'Law'. Clearly, these major interpretive blunders fatally compromise DM's claim to be a science, let alone a philosophical theory that merits serious attention.


Identity and equality are relatively easy to distinguish (so much so that even the children of workers can grasp the difference). For example, in elementary mathematics the equation 2x + 1 = 7 is true if and only if x = 3, but no one supposes that x is identical to 3, otherwise it could never equal any other number (as it does in, say, 3x – 2 = 19).


In contrast, the "º" sign that appears in, say, 2sinxcosx º sin2x expresses identity, for this rule yields the true for all defined values of x. Worse still: two or more identicals can be equal to, but different from, the same identical; for instance, even though 0 = 0, it is also true that 0 + 0 = 0, even while it is also true that 0 + 0 is not identical to 0.


In MFL, the distinction between these two is even more profound. "=" is a relational expression (and can be flanked only by names (or other singular expressions)), whereas "º" and is a truth-functional operator (and can be flanked only by propositions, and the like). [Of course, these distinctions are not the same as those applied in ordinary language (no irony intended), nor yet those in Traditional Philosophy -- more on this below.]


[MFL = Modern Formal Logic.]


Some might object to these and other examples on the grounds that they are "abstract"; but even if this were correct, there would still be a clear difference between abstract identity and abstract equality, something Trotsky also failed to notice.


Furthermore, in ordinary material language the difference is even clearer. So, we can say things like "The author of What is To Be Done? is identical to Lenin" (whereas, it would be odd to say "The author of What is To Be Done? is equal to Lenin"), just as we can say that "The number of authors of What is To Be Done? is equal to one" (but not, "The number of authors of What is To Be Done? is identical to one"). And, since counting objects is just as material a practice as weighing them is, no dialectician can consistently take exception to these and other such awkward material examples of the difference between identity and equality, while accepting uncritically Trotsky's point about weighing bags of sugar.


Not only that, two equal things can fail to be identical, and vice versa. For example, two distinct comrades could be equally first in two separate lists (and the material embodiment of this fact could alter either greatly or hardly at all without affecting their status -- so, for example, their names could be written in neon signs that flashed on and off every second, and out of sequence, or, one could do handstands while the other read a book, but they would still both be equal first, and non-identical for all that).


Moreover, two items can be identical as well as equal in certain respects but not in others; for example two workers could be identically placed in two unequal queues -- for instance, both second from the front. And some things can be equal and identical, or not, as the case may be. For example, the letter "T" can occur identically in first place in two different words (such as "Trotsky" and "teamster") even though neither letter nor word is equal or identical in size or shape. And, two letters, which are identically first in the alphabet (namely two "A"s) can be non-identically positioned in two unequal words (such as "target" and "Antarctic"). Indeed, careful optical examination will fail to show that those two "T"s were not identically positioned at the front of the two quoted words (nor equally first in each), or that the two numerically different "A"s are not identically the opening letter of the alphabet. This sort of identity is clearly not sensitive to empirical test, eyeglass or no.


And we needn't concentrate on examples that some might consider "abstract"; two physical ink marks on a page (two letter "A"s, say) which are not identical in shape or size (i.e., "a" and "A") could be identically positioned between other non-identical letters. So, in "Pat" and "PAT" each letter "A" is identically sandwiched between two other non-identical letters. Now the physical position of material ink marks on a page, or even that of these electronically produced pixels on your screen, is not abstract, it is eminently material --, so much so that it can be obliterated by the non-dialectical application either of Tippex or the delete key.


This non-dialectical deletion would not be deleting an abstraction.


Ordinary material language is in fact almost limitless in the possibilities it allows those who refuse to be led astray by the obscure jargon employed by Idealist philosophers (like Hegel) to express sameness, equality, identity and difference. It is a pity that Trotsky's otherwise brilliant mind failed to notice such banalities, ones indeed the children of workers are capable of grasping. Many other examples are given in Essay Six -- so many that many non-identical readers might all be in danger of becoming equally bored perusing the same list on their non-identical screens.


[The triteness of some of these examples should provide no reason for anyone to cavil; after all Trotsky it was who advised his readers to consider bags of sugar and letter "A"s.


It could be objected that the above examples do not address the classical problem, which concerns the entire set of predicates "true of" an object, or indeed of some 'substance'. This is undeniable, but then DM-theorists do not consider these either (fixated as they are on "A = A"), and neither did Hegel. As soon as they do, I will address what they have to say.]


Moreover, some things can change even while they stay the same; for example, it is easy to transform 1/√n into √n/n thus: 1/√n x √n/√n = √n/n. But, 1/√n does not even look like √n/n, even though the two are identical: 1/√n º √n/n. So, here we have change with no change! [Recall: the signs used here are eminently material. Also, note that I am using the "º" sign mathematically here, not logically.]


Again, it is possible to choose other non-'abstract' examples here: an actor can change costume while playing identically the same role in a play (say the Prince in Hamlet -- indeed such a change might actually define that character's identity, not necessarily in this particular play, but a different one), just as a passenger can change buses while still on identically the same holiday (i.e., two weeks in Bognor), and a worker can change jobs while occupying identically the same position (as Treasurer) in her local Stop the War! branch.



Trotsky Refutes Himself -- Again In Practice


Even if it had have been correctly worded and targeted, Trotsky's attack on the LOI would still backfire. This is because his argument depends on the LOI being true of instants in time so that he can criticise it when it is applied to bags of sugar. Hence, his criticism depends on, say, a bag of sugar being non-self-identical during the same moment in time, and yet moments in time are just as capable of being measured as bags of sugar are. In that case, Trotsky cannot consistently use "same moment" while criticising "same weight"; both are legitimate examples of identity. In that case, Trotsky needs the LOI to be true of instants in time so that he can criticise it as false when it is applied to bags of sugar!


Again, if time can be measured (just as sugar can be weighed), the above objection of mine to Trotsky's 'analysis' cannot be neutralised by claiming that time and/or temporal moments are "abstractions". Even if they were, Trotsky cannot argue that a bag of sugar changes in the same instant, for there could be no such thing (if he were right) -- unless the LOI can be applied validly to them (as abstractions). So he has to be able to refer to the same 'abstract moment'.


And Trotsky (or one of his epigones) can't use the fall-back option that bags of sugar are the "same, yet different" (employing the "identity-in-difference" gambit) since Trotsky had already torpedoed that response, declaring that all things are never the same:


"Again one can object: but a pound of sugar is equal to itself. Neither is true (sic) -- all bodies change uninterruptedly in size, weight, colour etc. They are never equal to themselves." [Ibid., p.64. Emphasis added.]


Hence, if objects and processes are never the same, they cannot be the "same, yet different", they can only be "different, yet different". Of course, if it is true that they are the "same, yet different" then it cannot be true that they are never the same. Either way, Trotsky's criticism backfires.


Moreover, Trotsky also ignored clear examples of identity that are not subject to his strictures on equality. For example: the number of volumes of Das Kapital in 1917 is identical and equal to the number of volumes of Das Kapital in 2005, namely three. This is true even though copies of the books in question could differ radically, and be changing diachronically all the while. As already noted, since counting and weighing are both physical activities carried out in the material world, no DM-apologist can complain that this is an "abstract" example (indeed, when comrades refer to Volume Three of Kapital, they are not referring to an abstraction!). Moreover, the 'concept' of "abstract identity" (where any sense can be made of it, that is) itself requires reference be made to material identity to give it some content (as we will see); in that case, "abstract identity" is based on notions of sameness and difference already present in material language.


In fact, just to consider one such use: any two dialecticians who fancy they have the same idea of "abstract identity" must either accept that a material version of the LOI applies to their two distinct ideas of "abstract identity" (so that they can confirm they are talking about the same thing in this material world), or they must concede that they are talking about two different things, and stop their blather.


[And any response from the DM-community that the above two are and are not doing the aforementioned must suffer the same fate.]


Furthermore, the idea that ordinary identity (or even the misconstrued version of it that Trotsky used) only really approximates to abstract identity (so that no two concrete things in material reality are exactly the same, even if they are approximately (abstractly) identical, or are only approximately (abstractly) self-identical), is equally misconceived.


We are surely no further forward unless we can be told with what it is that our ordinary terms for identity are supposed to approximate (if anything), for if these terms do not approximate to anything specifiable, they must be empty notions. On the other hand, if DM-apologists can say with what it is that our words for identity do in fact approximate, then they must have a clear idea of abstract identity which cannot itself be subject to Trotsky's criticisms, since their idea of abstract identity (situated here and now in this world) must be materially identical to abstract identity itself. On the other hand, if this idea is not identical to abstract identity, then what they say about identity (ordinary or abstract) can safely be ignored, for it won't be about identity, but about something different.


Furthermore, Trotsky's appeal to the hypothetical weighing of bags of sugar is no less misplaced. Since weighing devices are just as susceptible to change as bags of sugar are, Trotsky had no way of knowing whether the different weights he predicted were genuine effects (because the weight of the sugar (etc.) alters) or merely artefacts of changing machinery -- or the result of a locally variable gravitational field, or even the changing eyesight of the experimenter, or indeed a host of other factors.


In fact, this latest objection can only be neutralised if weighing machines, experimenters and the rest of the universe (other than bags of sugar) are all exempted (from consideration) as changeless beings. In such circumstances it would then be safe to assume that differing measurements were solely the result of changes in the items being weighed. Short of that, Trotsky could only be 100% confident that subsequently detectable differences were always and only the result of changes to the weight of the sugar because of an a priori stipulation to that effect. In that sense, Trotsky would have imposed dialectics on nature, contrary to what he elsewhere said should never be done:


"Dialectics cannot be imposed on facts; it has to be deduced from facts, from their nature and development…." [Trotsky (1973), p.233.]


On the other hand, if Trotsky had been faced with someone who claimed that at least two of their weighings gave identical results, he could only have responded in one of the following ways: (1) Insisting that this experimenter must have been mistaken; (2) Complaining that the machines used were not accurate enough; (3) Claiming that his instructions had not been carried out exactly as prescribed; (4) Arguing that identically the same experiments had not been performed each time. In other words, in the absence of a mistake (and if the same results were recorded on more accurate scales), Trotsky would only be able to criticise the above reported experimental verification of the LOI (i.e., one which reported identical weights for the same bag) by an appeal to that very same law, but now applied to his own instructions!


Hence, in order to counter results that disconfirmed his forecast, he would have to argue that only those who followed his instructions identically and to the letter could disprove the LOI!


The irony is thus quite plain: identically performed experiments are required in order to prove that nothing is identical with anything else (including experiments)!


Of course, anyone who only roughly followed instructions (who was perhaps content with a wishy-washy, "approximate-within-certain-limits" dialectical-sort-of-equality) would probably find that many (if not most) of their measurements gave identical results for the weights of bags of sugar.


In which case, Trotsky's predictions about the weight of sugar varying would end up being refuted by anyone who adopted this diluted version of the LOI, since they would quite often obtain identical weights.


Such experimenters would succeed in confirming the absolute version of the LOI by adopting a weaker variant of it!


Conversely, the more exactly the experimenters adhered to Trotsky's instructions, the more likely they would be to detect non-identical weights. In that case, they would succeed in disconfirming the absolute version of this 'law' (applied to sugar) by applying an exact copy of Trotsky's instructions! So, by converse irony, they would refute Trotsky in practice by doing exactly as instructed, using the LOI applied to instructions to disconfirm it as applied to bags of sugar!


Finally, and most damningly, Trotsky (and Hegel) failed to notice that if anything changes then whatever is identical with it must change equally quickly. In that case, identity is no enemy of change.


With that observation, much of classical DM falls apart.


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© Rosa Lichtenstein 2016


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