Refuting A Weak Attempt At Refutation -- Part One

 

Preface

 

If you are using Internet Explorer 10 (or later), you might find some of the links I have used won't work properly unless you switch to 'Compatibility View' (in the Tools Menu); for IE11 select 'Compatibility View Settings' and then add this site (anti-dialectics.co.uk). I have as yet no idea how Microsoft's new browser, Edge, will handle these links.

 

Quick Links

 

Anyone using these links must remember that they will be skipping past supporting argument and evidence set out in earlier sections.

 

If your Firewall/Browser has a pop-up blocker, you will need to press the "Ctrl" key at the same time or these and the other links here won't work!

 

I have adjusted the font size used at this site to ensure that even those with impaired vision can read what I have to say. However, if the text is still either too big or too small for you, please adjust your browser settings!

 

(1) Background

 

(2) Opening Shots

 

(3) Formal Logic

 

(4) Temporal Logic

 

(5) Motion -- Contradictory Or Not?

 

(6) Bibliography

 

Summary Of My Main Objections To Dialectical Materialism

 

Abbreviations Used At This Site

 

Return To The Main Index Page

 

Contact Me

 

Background

 

In 2015, I posted the following comment on a YouTube page which was devoted to introducing prospective viewers to a highly simplified version of DM:

 

Alas for this video, I have demolished this dogmatic theory (from a Marxist angle) at my site:

http://anti-dialectics.co.uk/index.htm

Main objections outlined here:

http://anti-dialectics.co.uk/Why%20I%20Oppose%20DM.htm

 

I have posted many similar comments on other pages at YouTube that are devoted to this theory and received little or no response. But, the producer of this film (whose on-screen name used to be Marxist-Leninist-Theory [MLT], but which has now changed to The Finnish Bolshevik -- henceforth, TFB) did respond (and to which I replied, here and here).

 

Not long afterwards, another video appeared on YouTube, which was also produced by MLT (but posted to his other site) -- entitled: "Refuting a Trotskyite Attack on Dialectics" -- although after being asked to drop the derogatory term "Trotskyite", MLT has agreed to stop using it:

 

 

Video One: The 'Case' For The Prosecution

 

After having viewed this video, it is quite clear that it closely resembles the attempts made by several others who have tried to show that my work is thoroughly misguided, if not mendacious (I will highlight the basic errors of interpretation that litter this production as this response unfolds), and it succeeds about as much as all the rest have, too -- , i.e., not even close!

 

However, this video is unlike the other responses MLT has thought to make in that it contains down-right lies about my ideas. [There is no other word I can think of that better describes MLT's new tactic -- as the reader will soon see for herself.] They will also be exposed as this response progresses.

 

As I note on the opening page of my site (referring readers to a page where I have listed most of the attempts made by DM-supporters to challenge my work):

 

How Not To Argue 101

 

The above page contains links to forums on the web where I have 'debated' this creed with other comrades. For anyone interested: check out the desperate 'debating' tactics used by Dialectical Mystics in their attempt to respond to my ideas. You will no doubt notice that the vast majority all say the same sorts of things, and most of them pepper their remarks with scatological and abusive language. They all like to make things up, too, about me and my beliefs.

 

[I have now added MLTs video as a particularly egregious example of the lies DM-fans are prepared to spin.]

 

30 years (!!) of this stuff from Dialectical Mystics has meant I now take an aggressive stance toward them every time -- I soon learnt back in the 1980s that being pleasant with them (my initial tactic) didn't alter by one jot their abusive tone, their propensity to fabricate, nor reduce the amount of scatological language they used.

 

So, these days, I generally go for the jugular from the get-go.

 

Apparently, they expect me to take their abuse lying down, and regularly complain about my "bullying" tactics.

 

These mystics can dish it out, but they plainly cannot take it.

 

Given the damage their theory has done to Marxism, and the abuse they all dole out, they are lucky this is all I can do to them. [Bold added.]

 

MLT's language seems not to have descended to this level (yet!), but he certainly follows a well-trodden DM-path of preferring to make stuff up about my work in order to 'take down' a straw man.

 

~~~~~~oOo~~~~~~

 

I had wanted this reply to be confined to one page only, but MLT has included new criticisms of my work not contained in his other responses. This has meant that my reply will, alas, once more stretch over several pages! Indeed, in order to do justice to this video (it is after all over 40 minutes long!), anything less would be an insult.

 

[I have also included a word-for-word transcript of this (somewhat garbled and repetitive) video, which has added at least 15-20% to the length of this response.]

 

Opening Shots

 

In the first couple of minutes of this video, MLT makes a handful of points that are easily disposed of:

 

[DM = Dialectical Materialism/Materialist, depending on context; HM = Historical Materialism.]

 

(1) MLT assumes my attack on this theory is an attack on Marx, Engels and Lenin (I have omitted Stalin and Mao's names here since, as a Trotskyist, I do not hold them in any esteem -- quite the opposite, in fact), but he neglected to quote me to this effect. Indeed, I say the opposite (and at the very beginning of the Introductory Essay which is the main focus of this video):

 

Nothing said below is aimed at undermining Historical Materialism [HM] -- a theory I fully accept -- or, for that matter, revolutionary socialism. My aim is simply to assist in the scientific development of Marxism by helping to demolish a dogma that has in my opinion seriously damaged our movement from its inception: Dialectical Materialism [DM] -- or, in its more political form, 'Materialist Dialectics' [MD].

 

Naturally, these are highly controversial allegations, especially since they are being advanced by a Marxist; the reason why I am publishing them is partially explained below, and in far more detail in my other Essays. Exactly why I began this project is explained here.

 

Some readers might wonder how I can claim to be both a Leninist and a Trotskyist given the highly critical things I have to say about philosophical ideas that have been an integral part of these two traditions from their inception. However, to give an analogy: we can surely be highly critical of Newton's mystical ideas even while accepting the scientific nature of his other work. The same applies here.

 

I count myself as a Marxist, a Leninist and a Trotskyist since I fully accept, not just HM (providing Hegel's baleful influence has been fully excised), but the political ideas associated with the life and work of Marx, Luxembourg, Lenin and Trotsky. Some might think that this must compromise HM itself, in that HM would then be like a "clock without a spring". The reverse is the case. As I aim to show below: if DM were true, change would in fact be impossible.

 

[MLT attempts, somewhat sarcastically, to malign me for the words I posted in the first paragraph; I will deal with his comments in Part Two.]

 

In which case, this is no more a personal attack on Marx, Engels or Lenin than would be a similar criticism of Newton for allowing mystical ideas to corrupt his scientific work. Nor is this an attempt to show that Marx, Engels and Lenin were completely wrong (or "idiots" to use MLT's term -- this is a class, not an individual, issue).

 

For one thing, as is relatively easy to show, Marx didn't accept this theory, and had abandoned Philosophy root-and-branch by the late 1840s. [On that, see here, here, and here.] For another, as I note above, I am in 100% agreement with Marx, Engels and Lenin over the nature of revolutionary socialism, and since these three great revolutionaries wrote far more on that particular subject than they ever devoted to DM, this means I am in agreement with the vast bulk of their work.

 

[One of the problems arguing with DM-supporters is that they tend to skim read my work looking for things to attack, and that means they almost invariably miss key parts of it, which then, naturally, prompts them into mis-interpreting what they think they have read. It looks like MLT has done this, too. Indeed, we will see him do precisely this many times over as this reply unfolds, which error, in his case, has been compounded by an unwise propensity to tell (easily exposed) fibs.]

 

(2) MLT confuses my claim to have demolished DM with what he interprets as arrogance on my part:

 

"Our Trotskyist seems to think highly of themselves...god I really admire the modesty here". [Approximate video time: 1:30.]

 

In fact, as I also note elsewhere, my demolition depends as much on Marx's own ideas as it does on that of others, to whom I give credit at every turn. The only originality in my work lies in (a) the use to which I have put these ideas, (b) their mode of presentation and (c) my endeavour to keep as much of my work as possible accessible to those with little or no knowledge of technical issues. That is why I asserted that this was a demolition from a "Marxist angle", not my own! I claim Marx's authority as the main inspiration for my Essays. MLT might find this particular point risible, but it is based on Marx's own words, and for these reasons:

 

(a) My work is systematically and consistently anti-philosophical, as was Marx's:

 

"Feuerbach's great achievement is.... The proof that philosophy is nothing else but religion rendered into thought and expounded by thought, i.e., another form and manner of existence of the estrangement of the essence of man; hence equally to be condemned...." [Marx (1975b), p.381. I have used the on-line version, here. Bold emphasis and link added.]

 

"One has to 'leave philosophy aside'..., one has to leap out of it and devote oneself like an ordinary man to the study of actuality, for which there exists also an enormous amount of literary material, unknown, of course, to the philosophers." [Marx and Engels (1976), p.236. Bold emphasis added. Quotation marks altered to conform to the conventions adopted at this site.]

 

[I have summarised my reasons for adopting this approach, here.]

 

(b) It re-directs our attention to ordinary, as opposed to philosophical language, again taking its cue from Marx:

 

"One of the most difficult tasks confronting philosophers is to descend from the world of thought to the actual world. Language is the immediate actuality of thought. Just as philosophers have given thought an independent existence, so they were bound to make language into an independent realm. This is the secret of philosophical language, in which thoughts in the form of words have their own content. The problem of descending from the world of thoughts to the actual world is turned into the problem of descending from language to life.

 

"We have shown that thoughts and ideas acquire an independent existence in consequence of the personal circumstances and relations of individuals acquiring independent existence. We have shown that exclusive, systematic occupation with these thoughts on the part of ideologists and philosophers, and hence the systematisation of these thoughts, is a consequence of division of labour, and that, in particular, German philosophy is a consequence of German petty-bourgeois conditions. The philosophers have only to dissolve their language into the ordinary language, from which it is abstracted, in order to recognise it, as the distorted language of the actual world, and to realise that neither thoughts nor language in themselves form a realm of their own, that they are only manifestations of actual life." [Marx and Engels (1970), p.118. Bold emphases alone added.]

 

And there are excellent reasons for doing this, too, over and above Marx's clear advice -- on that, see here and here.

 

(3) MLT has concentrated his attention on an introductory work of mine -- indeed, I emphasised this point at the top of the Essay in question:

 

Please note that this Essay deals with very basic issues, even at the risk of over-simplification.

 

It has only been ventured upon because several comrades (who weren't well-versed in Philosophy) wanted a very simple guide to my principle arguments against DM.

 

In that case, it isn't aimed at experts!

 

Anyone who objects to the apparently superficial nature of the material presented below must take these caveats into account or navigate away from this page. The material below isn't intended for them.

 

It is worth underlining this point since I still encounter comrades on Internet discussion boards who, despite the above warning, still think this Essay is a definitive statement of my ideas. It isn't!

 

So, And To repeat: this Essay is aimed solely at novices

 

As noted above, those who want more detail should consult Essay Sixteen or the relevant Essays published at the main site.

 

Any who still find this Essay either too long or too difficult might prefer to read two much shorter summaries of my ideas: here and here.

 

Attempting to 'refute' my attack on DM using only (or mainly) the above Essay would be like trying to refute Das Kapital by concentrating solely on Wage Labour and Capital!

 

[Not at I am comparing myself to Marx! The point is that if comrades want to refute my work, they should concentrate on the core Essays, not work aimed at novices! Indeed, MLT makes the mistakes he does simply because he hasn't done this. By way of contrast, I have consulted (and studied, many times), stretching over several decades, the work of the DM-classics and countless 'lesser' DM-works. Anything less than this would be to treat Marx, Engels, Lenin and all the rest with contempt.]

 

I have also listened to and watched the above video many times over -- not only in order to transcribe it as accurately as I can, but also in order to do justice to MLT's criticisms.

 

MLT says he hasn't the time or inclination to read my work -- fine, no one is forced to read anything I have written. But, only a fool would presume to attack another's work based on approximately 2% of it (my site now stretches to well over 2.75 million words -- the Essay in question is approximately 43,500 words long), and it's an Essay aimed only at novices, too!

 

(4) Although this doesn't feature as part of his 'refutation', MLT laments the fact that my site is rather difficult to navigate around, and he seems to connect this with all the links I have inserted (which take to reader to other Essays, and around in a circle sometimes).

 

Well, it is rather odd being criticised by a DM-supporter for linking things when it seems to be a fundamental DM-thesis that everything is interlinked!

 

However, one of the reasons I have done this is to help prevent readers from drawing the wrong conclusions about my work. Since it isn't possible (or even desirable) to make every single point one should like to make, or list all the caveats one would like to include, in a single sentence or paragraph, I have had to link many of the things I assert to other parts of my work where I have either argued the point more fully, or have supplied the necessary evidence in support of whatever it is that I had said. As we will see, MLT clearly failed to follow many of these links, and hence advanced numerous false or misleading accusations about my ideas (examples will be given below).

 

And sure, my site isn't easy to follow, but here is the reason why (this comes from the opening page of my site):

 

These Essays represent work in progress; hence they do not necessarily reflect my final view.

 

I am only publishing this material on the Internet because several comrades whose opinions I respect urged me to do so back in 2005 -- even though the work you see before you is less than half complete. Many of my ideas are still in the formative stage and need considerable attention devoted to them to mature.

 

I estimate this project will take another ten years to complete before it is fit to publish either here in its final form or in hard copy.

 

All of these Essays will have radically changed by then.

 

This work will be updated regularly -- edited and re-edited constantly --, its arguments clarified and progressively strengthened as my research continues (and particularly as my 'understanding' of Hegel develops).

 

So, visitors are encouraged to check back often.

 

It is because this work appeared long before I considered it ready that it is in the state it is. Hence, in its present form it more closely resembles a Rube Goldberg machine than it does a finely-tuned Ferrari -- this also partially explains all those links (which hold the site together like sticking plaster!) -- a 'machine' cobbled together in a piece-meal fashion over the last ten years. I can only apologise to the reader for this, but there was no way round it given the above considerations.

 

Formal Logic [FL]

 

About 3 minutes into the video, MLT attempts to tackle a subject about which he claims not to be an expert: FL -- whereas I have a mathematics degree, and have studied logic to postgraduate level. I say this neither to brag nor to 'pull rank', but I am heartily tired of being told what is or is not the case with respect to FL by those who seem to know very little about it, but who could have easily found out (on-line) that what they had to say about FL in fact became obsolete over 140 years ago. Indeed, much of it was obsolete when Aristotle was alive!

 

In the Essay under review by MLT, I assert the following:

 

Dialecticians tell fibs about Formal Logic [FL], and they persist even after they have been told -- many times -- that what they have to say about logic is woefully inaccurate.

 

Indeed, they regularly say things like the following:

 

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

 

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

 

"There are three fundamental laws of formal logic. First and most important is the law of identity....

 

"…If a thing is always and under all conditions equal or identical with itself, it can never be unequal or different from itself." [Novack (1971), p.20.]

 

However, I have yet to see a single quotation from a logic text (ancient or modern) that supports these allegations -- certainly dialecticians have so far failed to produce even so much as one.

 

And no wonder; they are completely false.

 

FL uses variables -- that is, it employs letters to stand for propositions, objects, processes and the like, all of which can and do change.

 

This handy formal device was invented by the very first logician we know of (in the 'West'), Aristotle (384-322BC). Indeed, Aristotle experimented with the use of variables approximately 1500 years before they were imported into mathematics by Muslim Algebraists, who in turn employed them several centuries before French mathematician and philosopher, René Descartes (1596-1650), introduced them into the 'West'.

 

Engels himself said the following about that particular innovation:

 

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

 

Now, no one doubts that modern mathematics can handle change, so why dialecticians deny this of FL -- when it has always used variables -- is somewhat puzzling.

 

It is even more puzzling when we realise that if DM itself were true, change would be impossible.

 

[Moreover, as we will see in the next section, the 'Law of Identity' [LOI] doesn't preclude change.]

 

So, what does MLT offer by way of proof that FL deals with 'static' objects/concepts/categories? -- This:

 

"It [FL] is generally perceived as dealing with static objects which exist in a vacuum and not with..., you know..., real things." [Approx 03:10 seconds. Bold added.]

 

Ouch! That has me put in my place, and no mistake.

 

But, by whom is this "generally perceived"?

 

By dialecticians!

 

Which is why MLT could find not one single FL-textbook (other than perhaps that badly misnamed book written by Hegel) that says this!

 

Indeed, just as I alleged (in the very Essay under review): Dialecticians tell fibs about FL!

 

Unfortunately, MLT digs himself deeper into a hole:

 

"They [meaning me -- RL] don't even attempt to explain how Formal Logic deals with change." [Approx 04:03.]

 

But, in the clip showing the section of the Essay in question, the viewer can clearly see a link to another page at my site where I do precisely this -- Essay Four Part One! So, the above quotation from this video should now be altered to read (more honestly) as follows:

 

"I made no attempt to find out how Ms Lichtenstein explains how Formal Logic deals with change. The onerous task of clicking on a link was far too much effort for me!" 

 

MLT now switches into full sarcasm mode:

 

"I for one can't figure it out.... I guess our Trotskyite revisionist has some brilliant theory about this which is just beyond the minds of us mere mortals..." [Approx 04:19.]

 

1) I don't have a theory; nor do I want one (which is a point I made in the Introductory Essay to my site).

 

Indeed, we don't need one (on why that is so, see Essay Twelve Part One). All it would take for MLT (and his happy band of 'mere mortals') to grasp this simple point is: click on a link, read a few sections of Essay Four Part One, and all will become clear to him/them.

 

2) Anyway, what is so wrong with 'revisionism'?

 

Were the DM-classicists infallible? Were they possessed of semi-divine wisdom, so that they never, ever made a theoretical or factual mistake? Or never, ever lacked sufficient information to develop an informed opinion?

 

If, according to Lenin, human knowledge isn't absolute, but relative and incomplete, then this must also be true of DM. Or was Lenin wrong? Does the only absolute knowledge in existence belong to Marxist-Leninist parties?

 

Has (genuine) science changed at all in the last two millennia? If it has, why can't DM change?

 

How come the only thing in the entire universe not subject to change is DM itself?

 

Temporal Logic [TL]

 

Relying on memory alone, and hence failing to quote me on this (however, what I said is easy to find; here it is), MLT now tries to make a point in response to something I said on a different YouTube page:

 

"...They argue that modern temporal logic, for example, copes with change rather well.... So, judging from this talk about math and temporal logic I think this person misunderstands what people mean when they say formal logic can't handle change. It's not that some change cannot be represented in terms of formal logic -- for example, you can use time as a variable and then say, for example, 'Now A is x and after one hour A is y', or something like that [sic!] -- however, that doesn't change the fact that this is purely theoretical, that these are only static objects that have no connection to reality, whereas things in the real world are interconnected and being affected by each other, changing and creating change elsewhere, almost as if they were in a dialectical relationship [said with a slightly funny voice! -- RL]. What do you know! That said, even if the claims of this Trotskyite were true...it still wouldn't be an argument against dialectics, because it's only a defence of formal logic." [Approx 05:03-06:08.]

 

Well, there are nearly as many errors and misconceptions in the above as there are words.

 

1) In fact, there was no misunderstanding on my part, since DM-theorists themselves are entirely unclear what they mean when they tell us FL can't cope with change, just as they are even less clear how their own theory manages to do the opposite of this. The very best they can do is assert (again, without even a cursory attempt to provide any evidence) that FL deals with "static" objects -- when, of course, it deals with no objects (or concepts) at all!

 

We can see this confusion in miniature form in the above comments. After telling us (or rather, after summarising something MLT substituted for TL, not having checked what that branch of logic actually has to tell us -- his "something like that" is the give-away, here!) -- after telling us that TL focuses on sentences like, "Now A is x and after one hour A is y" (all the while failing to inform us what these letters stand for, thus following on in yet another well-established DM-tradition of posting garbled schematic sentences as supposed examples of FL/TL! -- on that, see here), he then informs us that "these are only static objects", when he has just shown us they change! "A used to be x, now it is y". Is this an example of change or not? It sure looks like one. This perhaps tells us that MLT doesn't actually know what a "static object" is (in FL or anywhere else, perhaps).

 

2) As noted above, MLT's in depth research into TL amounted to...making up a sentence supposedly drawn from it. [What was that I said earlier about dialecticians telling fibs about FL? The very idea!] There are plenty of sites on the Internet that would have told him what TL is. Here is one, and here is another -- and, of course, there is always good old Wikipedia.

 

3) Next, MLT informs us that these TL-sentences are "purely theoretical", and "have no connection to reality". Now, it might come as a surprise to, say, Physicists, that they, too, have a theory -- called Relativity [RT] -- that it is "purely theoretical" and thus has "no connection to reality".

 

"Not fair!" I hear someone say. "RT does deal with processes in the real world, so it isn't 'purely theoretical'". Indeed, but that is only when the Pure Mathematics and the Theoretical Physics (in which RT is usually expressed) have been interpreted, and then re-shaped as a series of "real world" models. Left as uninterpreted Pure Mathematics and Theoretical Physics, RT would suffer from all the supposed/alleged 'weaknesses' of FL/TL.

 

Here is how I have addressed this issue in Essay Four Part One:

 

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

 

L1: Premiss 1: No As are B.

 

L2: Premiss 2: All Cs are B.

 

L3: Ergo: No As are C.

 

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

 

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

 

What FL supplies us with are the conceptual tools that enable us to theorise about change.

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

"Formal categories, putting things in labelled boxes, will always be an inadequate way of looking at change and development…because a static definition can't cope with the way in which a new content emerges from old conditions." [Rees (1998), p.59. Added on edit: I have quoted this since Rees and MLT agree on this point, as do many other DM-supporters, whether they are Trotskyists, like Rees, or Stalinists or Maoists.]

 

But, as a criticism of FL, this is entirely misguided. FL doesn't put anything in "boxes", and its practitioners don't deny change as a result. DM-theorist have yet to quote a single textbook of logic (other than Hegel's!) that supports this allegation.

 

Added in a footnote:

 

With respect to this argument schema, the only condition validity requires is the following: if, for a given interpretation, the premisses are true then the conclusion is true. That claim isn't affected by the fact that schematic premisses themselves can't be true or false, since such schema express rules, and are hypothetical. [A clear explanation of this can be found here.]...

 

One interpretation of L1 that might illustrate this is the following:

 

Premiss 1: No moving object is stationary.

 

Premiss 2: All objects with zero velocity are stationary.

 

Ergo: No moving object is one with zero velocity.

 

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

 

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

 

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

 

Premiss 1: All human beings are aging.

 

Premiss 2: All Londoners are human beings.

 

Ergo: All Londoners are aging.

 

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

 

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

 

Premiss 2: All Londoners are human beings.

 

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

 

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

 

Finally, here is an argument that depends on change:

 

Premiss 1: All rivers flow to the sea.

 

Premiss 2: The Mississippi is a river.

 

Ergo: The Mississippi flows to the sea.

 

A couple of points are worth making about the above argument:

 

1) In order for the conclusion to follow, the premisses of an argument do not have to be true -- clearly Premiss 1 is false.

 

2) The above argument isn't of the classic syllogistic form, although it parallels it.

 

3) Anyone who understands English will already know that rivers are changeable, and that they flow; this example alone shows that logic can not only cope with changeable 'concepts', it actually employs them. Hence, logic is capable of utilising countless words that express change in a far more varied and complex form than anything Hegel (or his latter-day DM-epigones) ever imagined. [On that, see here.]

 

Here is another example:

 

Premiss 1: All fires release heat.

 

Premiss 2: I have just lit a fire.

 

Ergo: My fire will release heat.

 

Or, even:

 

Premiss 1: All sound waves transmit energy.

 

Premiss 2: Thunder is a sound wave.

 

Ergo: Thunder transmits energy.

 

The above examples are perhaps more akin to argument forms found in Informal Logic, but that is also true of most interpretations of argument forms drawn from FL, too.

 

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

 

[DL = Dialectical Logic; MFL = Modern Formal Logic.]

 

Some might object that while the above examples might appear to cope with some changes in reality, but they ignore conceptual change, and as such show once again that FL is inferior to DL. I deal with conceptual change later in this Essay.

 

There is an excellent account of Aristotelian Logic in Smith (2015). And there is an equally useful account of MFL (i.e., now confusingly called "Classical Logic") in Shapiro (2013).

 

In the above, I specifically chose an example drawn from AFL to show that even it could cope with change; had I employed all the techniques available to us in MFL, it would have become even clearer how FL more easily copes with change. [Readers are directed to Essay Four Part One for more details.]

 

Also from Essay Four Part One:

 

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

 

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


http://plato.stanford.edu/entries/logic-modal/

http://plato.stanford.edu/entries/logic-epistemic/

http://plato.stanford.edu/entries/logic-manyvalued/

http://plato.stanford.edu/entries/logic-deontic/

 

http://earlham.edu/~peters/courses/logsys/nonstbib.htm

 

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

 

The point is that when we supply the formal schemas studied in MFL (or even in AFL) with an interpretation -- just as we do in Physics -- those schemas do in fact relate to the "real world" -- contradicting MLT.

 

Hence, once they have been interpreted, these terms can (and often do) express change.

 

This means that what MLT alleges of FL is misguided in the extreme. [Well, he did say he wasn't an expert!]

 

[It is important to note that "Interpretation" doesn't mean the same in logic as it does in the vernacular; it relates to the substitution instances that result from the systematic replacement of variable letters with what they supposedly mean (often these are derived from ordinary language, but they can also be taken from scientific or mathematical languages), according to the syntax and/or the semantics of formal system involved.]

 

4) My argument wasn't a defence of FL; FL needs no more defending than mathematics does. It was aimed at showing that DM-theorists and supporters make things up about FL and they do so from a position of almost total ignorance, repeating the same things they have uncritically picked up from one another, or have read in other books on DM (which were similarly supported by not one single quotation from an FL-textbook) -- as we have seen is the case with MLT.

 

Earlier in the video (at approximately 03:35), MLT asserted that logic is different from mathematics. This was aimed at countering the analogy I drew between the variables used in FL and the variables used in Mathematics. Well, this argument might have carried some weight (but very little) two hundred years ago, but it carries none at all since the revolution in MFL that took place 140 years ago (with the work of Frege). As a result, we now have a thriving discipline called Mathematical Logic [ML]. Naturally, this discipline can cope with change just as well as Mathematics can.

 

[On ML, see Hinman (2005 ), and Mendelson (1979).]

 

Motion -- Contradictory Or Not?

 

MLT's next point concerns the alleged contradictory nature of motion -- a dogmatic idea DM-theorists have imported into Marxism from the speculative theories of assorted Idealists and Mystics, in support of which there isn't a shred of physical evidence -- just a few trite, badly-worded, verbal arguments (compounded by the use of garbled concepts drawn from 18th century calculus).

 

[MLT seems to have a problem with my accusation that Engels, Lenin, Mao and Stalin (but, note, not Marx) adopted and then promoted a "dogmatic" theory -- DM. In fact, not two weeks after making the above video, he posted another entitled "Dogmatism in Marxism". I will deal with that 'issue' in Part Two.]

 

So, what does MLT have to say? First of all he attempts to summarise Zeno's argument for the impossibility of motion, and he then adds:

 

"Our Trotskyite brings up this paradox, and roughly..., you know, explains it, but doesn't really deal with it in any way; but just points out 'Oh, this is a paradox, blah, blah, blah.... Therefore something....'" [Approx 07:46.]

 

Ok, so let's see how accurate the above 'summary' of my argument is; here is what I actually wrote (a small fraction of which was posted on-screen in the video) itself:

 

This is an age-old confusion derived from a paradox invented by an Ancient Greek mystic called Zeno (490?-430?BC).

 

In fact, as should seem obvious, all objects (which aren't mathematical points) occupy several places at once, whether or not they are moving. So, for example, while you are sat reading this Essay your body isn't compressed into a tiny point! Unless you have suffered an horrific accident, your head won't be in exactly same location as your feet, even though both of these body parts now (pre-accident!) occupy the same place -- i.e., where you are sat. So, occupying several points at the same time isn't unique to moving bodies. In which case, this 'paradox' has more to do with linguistic ambiguity than it has with anything 'contradictory'. [The ambiguity here is plainly connected with words like "place" and "location", the meanings of which Engels seems to think are perfectly obvious; more on that presently.]

 

Notice, I nowhere try to "explain" this paradox, so I am not too sure what the above "Blah, blah, blah" is all about. And, can anyone see a "Therefore something" in the above?

 

As seems clear, DM-supporters don't just tell fibs about FL.

 

But, am I allowed to be this cavalier with MLT's words in return?

 

I think not...

 

MLT then refers his viewers to another page (over at the Soviet Empire Forum), where another comrade attempted to refute my case against DM, after which MLT states:

 

"The interesting thing here is that the comments exchanged [MLT's words aren't clear here - RL] that is cited doesn't actually fare too favourably for the Trotskyite. The person challenging them gives a completely sufficient refutation of their arguments to which they don't respond with anything, and instead just, you know, just gloat here to have demonstrated how this theory apparently leads to 'even more ridiculous conclusions'. So, the refutation that the person challenging our Trotskyite's views [again this part isn't too clear -- RL] is based on Physics and is the following (also got to love the fact that (garbled) the explanation by this Trotskyite...they're so vague, it's like...couple, multiple times it seems like they're just saying 'Oh, this is a contradiction, therefore it's wrong', even though, of course, it's a contradiction, that's the whole point...):

 

'when a body is in motion its velocity is not zero and therefore...v = dx/dt =/= 0

 

'What we’re discussing are fundamental facts of physics which you have to understand prior to attempting to understand philosophical theories involving them....

'During motion, the position of a body in physical terms is defined by x and yet it is not defined by x but is defined by dx. When in motion a body is at one point x and yet it is at two points whose difference is dx. The same applies to time -- you can define the body in motion at time t and yet there is a difference of two times, dt, which also characterizes temporally a body in motion. These are obviously contradictory conditions of motion, coexisting. Motion is a constant resolution of these contradictions. This is what physics says....'

 

"And the Trotskyite counter-argument is...seems to be..., er... 'This is silly, hah hah hah' ..., like, that's not an argument. 'Yeah, I mean, physics is kind of funny sometimes', that's not an argument. The rest of their counter-arguments are just silly. Instead of contesting the fact that things in motion exist in multiple places at the same time, they turn around and argue that really all physical bodies exist in multiple places, for example, beans exist inside a tin and inside a store. or your head and your feet exist in different places despite being your body. However, this is simply word-play. The point they're making is that things don't exist in a single point but in an area, but that has no impact on the argument whatsoever on Engels nor anyone that the Trotskyite is arguing against has (sic) ever claimed that humans, beans or tin cans exist in a single point. It's obvious that wasn't hat Engels was arguing about. Besides, this kind of talk is metaphysical. And then they proceed to say that 'You know, this is an...um.., mistake by Engels because this kind of idea applies to things that are not in motion, for example, you know..., beans in tin cans. But as I just pointed out, that's not what Engels was talking about at all because, yeah..., well, you get the point. It's just, er..., word games to say 'Oh, beans exist inside a tin can inside a warehouse..., that's.. obviously it's not the same location, it's not the same point existing inside a tin and also inside a factory or a warehouse, whatever, doesn't mean they exist in two different points." [Approx 07:50-11:50.]

 

Once again, there are nearly as many errors in there as there are words.

 

1) However, I am genuinely amazed by the blatant lies in the above passage! Did MLT imagine that no one would check my answers to the critic he quoted -- while he [MLT] failed to quote (or summarise) any of my responses? Did he honestly think that when others read what I posted they would summarise my words as follows: "This is silly, hah hah hah"? In fact, I rather suspect he was hoping no one would visit the Soviet Empire Forum and check this for themselves -- and from the comments posted below this video, it looks like he was right; no one bothered to check his downright lies!

 

Ok, so here's is part of what I posted in reply to this individual (who wrote under the name 'Future World' [FW]) -- see if you think any of it amounts to "Yeah, I mean, physics is kind of funny sometimes!" -- or even "This is silly, hah hah hah":

 

Well, this isn't my objection (and I note you do not quote me to this effect). My objection is far more complex than this. Here, in fact, is just one of my core objections to Engels and Hegel:

 

From this point on it will be assumed that the difficulties with Engels's account noted in the previous section can be resolved, and that there exists some way of reading his words that implies a contradiction, and which succeeds in distinguishing moving from motionless bodies.

Perhaps the following will suffice:

L10: For some body b, at some time t, and for two places p and q, b is at p at t and not at p at t, and b is at q at t, and p is not the same place as q.

This looks pretty contradictory. With suitable conventions about the use of variables we could abbreviate L10 a little to yield this slightly neater version:

L11: For some b, for some t, for two places p and q, b is at p at t and not at p at t, and b is at q at t.

This latest set of problems revolves around the supposed reference of the "t" variable in L11 above.

It's always possible to argue that L11 really amounts to the following:

L12: For some b, during interval T, and for two 'instants' t1 and t2 [where both t1 and t2 belong to T, such that t2 > t1], and for two places p and q, b is at p at t1, but not at p at t2, and b is at q at t2.

[In the above, t1 and t2 are themselves taken to be sets of nested sub-intervals, which can be put into an isomorphism with suitably chosen intervals of real numbers; hence the 'scare' quotes around the word "instant" in L12.]

Clearly, the implication here is that the unanalysed variable "t" in L11 actually picks out a time interval T (as opposed to a temporal instant) -- brought out in L12 -- during which the supposed movement takes place. This would licence a finer-grained discrimination among T's sub-intervals (i.e., t1 and t2) during which this occurs. Two possible translations of L12 in less formal language might read as follows:

L12a: A body b, observed over the course of a second, is located at point p in the first millisecond, and is located at q a millisecond later.

L12b: A body b, observed over the course of a millisecond, is located at point p in the first nanosecond, and is located at q a nanosecond later.

And so on…

Indeed, this is how motion is normally conceived: as change of place in time -- i.e., with time having advanced while it occurs. If this were not so (i.e., if L12 is rejected), then L11 would imply that the supposed change of place must have occurred outside of time -- or, worse, that it happened independently of the passage of time --, which is either incomprehensible, or it would imply that, for parts of their trajectory, moving objects (no matter of how low their speed) moved with an infinite velocity! This was in fact pointed out earlier.

And yet, how else are we to understand Engels's claim that a moving body is actually in two places at once? On that basis, a moving body would move from one place to the next outside of time -- that is, with time having advanced not one instant. In that case, a moving body would be in one place at one instant, and it would move to another place with no lapse of time; such motion would thus take place outside of time (which is tantamount to saying it does not happen, or does not exist).

Indeed, we would now have no right to say that such a body was in the first of these Engelsian locations before it was in the second. [That is because "before" implies an earlier time, which has just been ruled out.] By a suitable induction clause, along the entire trajectory of a body's motion it would not, therefore, be possible to say that a moving body was at the beginning of a journey before it was at the end! [The reasons for saying this will be provided on request.]

Despite this it would seem that this latest difficulty can only be neutralised by means of the adoption of an implausible stipulation to the effect that whereas time is not composed of an infinite series of embedded sub-intervals -- characterised by suitably defined nested sets of real numbers --, location is.

This would further mean that while we may divide the position a body occupies as it moves along as finely as we wish -- so that no matter to what extent we slice a body's location, we would always be able to distinguish two contiguous points allowing us to say that a moving body was in both of these places at the same time --, while we can do that with respect to location, we cannot do the same with respect to time.

Clearly, this is an inconsistent approach to the divisibility of time and space -- wherein we are allowed to divide one of these (space) as much as we like while this is disallowed of the other (time). [It could even be argued that this is where the alleged 'contradiction' originally arose -- it was introduced into this 'problem' right at the start by this inconsistent (implicit) assumption, so no wonder it emerged at a later point -- no puns intended.]

This protocol might at first sight seem to neutralise an earlier objection (i.e., that even though a moving body might be in two places, we could always set up a one-one relation between the latter and two separate instants in time, because time and space can be represented as equally fine-grained), but, plainly, it only achieves this by stipulating (without any justification) that the successful mapping of places onto (nested intervals of) real numbers (to give them the required density and continuity) is denied of temporal intervals.

So, there seem to be three distinct possibilities with these two distinct variables (concerning location and time):


(1) Both time and place are infinitely divisible.

(2) Infinite divisibility is true of location only.

(3) Infinite divisibility is true of either but not both (i.e., it is true of time but not place, or it is true of place but not time).


Naturally, these are not the only alternatives, but they seem to be the only three that are relevant to matters in hand.

Of course, one particular classical response to this dilemma ran along the lines that the infinite divisibility of time and place implies that an allegedly moving body is in fact at rest at some point; so, if we could specify a time at which an object was located at some point, and only that point at that time, it must be at rest at that point at that time. [This seems to be how Zeno at least argued.]

Nevertheless, it seemed equally clear to others that moving bodies cannot be depicted in this way, and that motion must be an 'intrinsic' (or even an 'inherent' property) of moving bodies (that is, we cannot depict moving bodies in a way that would imply they are stationary), so that at all times a moving body must be in motion, allowing it to be in and not in any given location at one and the same time. [This seems to be Hegel's view of the matter -- but good luck to anyone trying to find anything that clear in anything he wrote about this!]

If so, one or more of the above options must be rejected. To that end, it seems that for the latter set of individuals 1) and 3) must be dropped, leaving only 2):


(2) Infinite divisibility is true of location only.


However, it's worth pointing out that the paradoxical conclusions classically associated with these three alternatives only arise if other, less well appreciated assumptions are either left out of the picture or are totally ignored -- i.e., in addition to those alluded to above concerning the continuity of space and the (assumed) discrete nature of time. As it turns out, the precise form taken by several of these suppressed and unacknowledged premisses depends on what view is taken of the allegedly 'real' meaning of the words like "motion" and "place".

The above is taken from Essay Five at my site (where I detail several other fatal objections to Engels and Hegel).

http://anti-dialectics.co.uk/page%2005.htm

 

[Added on edit -- the above passage has been re-written extensively -- in order to make my argument even clearer -- since this comment was posted at the aforementioned site. Despite this, readers are encouraged to visit this site and see for themselves to what extent MLT is a 'stranger to the truth'.]
 

So, I hope readers spotted my "This is silly, hah hah hah", and my "Yeah, I mean, physics is kind of funny sometimes!" in there somewhere.

 

Furthermore, in the thread in question, I responded to FW's supposedly 'mathematical arguments' (which response MLT ignored); here is part of it. First of all I quote Engels:

 

"As 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. Bold emphasis added.]

 

I did this as part of my reply to the passage MLT quoted:

 

"When a body is in motion its velocity is not zero and therefore...v = dx/dt =/= 0

 

"What we’re discussing are fundamental facts of physics which you have to understand prior to attempting to understand philosophical theories involving them....

"During motion, the position of a body in physical terms is defined by x and yet it is not defined by x but is defined by dx. When in motion a body is at one point x and yet it is at two points whose difference is dx. The same applies to time -- you can define the body in motion at time t and yet there is a difference of two times, dt, which also characterizes temporally a body in motion. These are obviously contradictory conditions of motion, coexisting. Motion is a constant resolution of these contradictions. This is what physics says...."

 

I then pointed out the following:

 

Here, he [Engels] is quite clear: a body is "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", that is, it moves with no time having lapsed.

If he had meant this:

E1: For some b, for two instants t(1) and t(2), b is at p at t(1) and not at p at t(2), and b is at q at t(2).

where t(1) and t(2) both belong to some time interval T (such that dt =/= 0), there would be no contradiction. His [Engels's] 'contradiction' depends on the time difference between t(1) and t(2) being zero.

Which is why he [Engels] argued elsewhere as follows:

 

"How are these forms of calculus used? In a given problem, for example, I have two variables, x and y, neither of which can vary without the other also varying in a ratio determined by the facts of the case. I differentiate x and y, i.e., I take x and y as so infinitely small that in comparison with any real quantity, however small, they disappear, that nothing is left of x and y but their reciprocal relation without any, so to speak, material basis, a quantitative ratio in which there is no quantity. Therefore, dy/dx, the ratio between the differentials of x and y, is dx equal to 0/0 but 0/0 taken as the expression of y/x. I only mention in passing that this ratio between two quantities which have disappeared, caught at the moment of their disappearance, is a contradiction; however, it cannot disturb us any more than it has disturbed the whole of mathematics for almost two hundred years. And now, what have I done but negate x and y, though not in such a way that I need not bother about them any more, not in the way that metaphysics negates, but in the way that corresponds with the facts of the case? In place of x and y, therefore, I have their negation, dx and dy, in the formulas or equations before me. I continue then to operate with these formulas, treating dx and dy as quantities which are real, though subject to certain exceptional laws, and at a certain point I negate the negation, i.e., I integrate the differential formula, and in place of dx and dy again get the real quantities x and y, and am then not where I was at the beginning, but by using this method I have solved the problem on which ordinary geometry and algebra might perhaps have broken their jaws in vain." [Engels (1976), p.175. Bold emphasis added.]

 

As he [Engels] notes, it is the alleged "disappearance" of these 'quantities' (when they equal zero, when dy/dx or dx/dt =0) that creates/constitutes the 'contradiction'.

And why he asserted:

 

"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." [Bold added.]
 

According to him, a moving body is in one place and not in it at the same time. In other words it has moved while time hasn't.
 

http://tinyurl.com/ndvzx6r

 

Much of the rest of the discussion in the thread in question revolved around this point, and how FW's interpretation of this part of DM differed from Engels's view of his own theory, and of the Calculus. Now, there might be some readers who still agree with FW (but, it isn't too clear how they could possibly do that if they want to defend Engels), but how many who have read the above will think my words can be summarised as follows: "This is silly, hah hah hah", or by "Yeah, I mean, physics is kind of funny sometimes!"?

 

And yet, MLT seems to be able to see words like this in there. Which suggests he either didn't read my response to FW, or he prefers to tell lies -- or both.  

 

I also go on to point out (to FW) that his ideas are based on an obsolete 18th century view of the calculus -- a point I don't expect MLT to be able to grasp, since he, unlike me, hasn't got a degree in mathematics. Again, I add this comment not to brag, or to 'pull rank', but merely to note that the only reason MLT is impressed with FW's argument is that he knows rather too little mathematics (and seems not to have read Engels too carefully, either!) -- as if dx/dt is a division! [Which is how MLT depicts this symbol in the video.] It was a division for 18th century mathematicians, but no one since Riemann or Weierstrass has argued this way (except perhaps the ignorant).

 

Moreover, the points FW makes are mathematical, not physical. It isn't possible to conduct an experiment (or imagine one that could be conducted -- even in an ideal world, and the experimenter were possessed of 'god'-like powers of perception) to test and thus verify what he (or Engels, or Hegel) had to say about motion; so it can't be Physics, can it?

 

In fact, if anything is "'purely theoretical' and thus has 'no connection to reality'", this argument of FW's is!

 

How come MLT failed to spot this?

 

2) Similarly, I defy MLT to find anywhere at the above Forum, or even at my site, where I say anything that is remotely like this: "Oh, this is a contradiction, therefore it's wrong".

 

It would be very easy for me to 'refute' MLT by deliberately making stuff up (and patently ridiculous stuff, too) about his ideas, wouldn't it? In fact, in an earlier exchange, MLT pointed out that I had misrepresented him (even though, unlike him, I didn't attribute to him a ridiculous or totally fictitious set of beliefs), so I apologised.

 

Will he do the same?

 

3) But, what about this?

 

"The person challenging them gives a completely sufficient refutation of their arguments to which they don't respond with anything, and instead just, you know, just gloat here to have demonstrated how this theory apparently leads to 'even more ridiculous conclusions'."

 

Ok, so let's go back to the original Essay where I supposedly said this -- only part of which was quoted by MLT -- but this time, restoring the part he omitted:

 

One comrade has recently sought to challenge me on this; the details can be found here. In fact, I have shown that Hegel and Engels's ideas about motion lead to even more ridiculous conclusions than this. The reader is once again directed to Essay Five for more details -- here, here, and here.

 

Notice the three occurrences of "here" at the very end? They are links to my site where I reveal what these "even more ridiculous conclusions" are; and, what is more, I actually quoted one of these in full in the thread where I discussed this with FW -- both of which MLT ignored, or preferred not to see.

 

Here is one of them (this has again been taken from Essay Five, but slightly edited -- many of the points I raise below depend on a detailed argument to be found in the previous section of the Essay; I have also left the text the same size as these remarks to save me having to re-size all those subscripts!):

 

The absurdity in L34b (below) is quite plain for all to see and needn't detain us any longer. However, the ludicrous nature of L17a isn't perhaps quite so obvious. It may nevertheless be made more explicit by means of the following argument:

 

[L17a: Since a body can't be at rest and moving at one and the same time in the same inertial frame, a moving body must both occupy and not occupy a point at one and the same time.

 

L34b: Despite appearances to the contrary, all bodies are at rest.]

 

(L35 below is an abbreviated version of Engels's theory.)

 

L35: Motion implies that a body is in one place and not in it at the same time; that it is in one place and in another at the same instant.

 

L36: Let A be in motion and at (X1, Y1, Z1), at t1.

 

L37: L35 implies that A is also at some other point -- say, (X2, Y2, Z2), at t1.

 

L38: But, L35 also implies that A is at (X2, Y2, Z2) and at another place at t1; hence it is also at (X3, Y3, Z3), at t1, otherwise it would be at rest at (X2, Y2, Z2).

 

L39: Again, L35 further implies that A is at (X3, Y3, Z3) and at another place at t1; hence also at (X4, Y4, Z4), at t1., otherwise it will be at rest at (X3, Y3, Z3).

 

L40: Once more, L35 implies that A is at (X4, Y4, Z4) and at another place at t1; hence also at (X5, Y5, Z5), at t1....

 

By n successive applications of L35 it is possible to show that, as a result of the 'contradictory' nature of motion, A must be everywhere in its trajectory if it is anywhere, and all at t1!

 

But, that is even more absurd than L34b!

 

L34b: Despite appearances to the contrary, all bodies are at rest.

 

The only way to avoid such an outlandish conclusion would be to maintain that L35 implies that a moving body is in no more than two places (i.e., less than three places) at once. But, even this wouldn't help, for if a body is moving and in the second of those two places, it can't then be in motion at this second location -- unless, that is, it were in a third place at the very same time (by L15 and L35). Once again, just as soon as a body is located in any one place it is at rest there, given this way of viewing things. The proposed dialectical derivation outlined above required that very assumption to get the argument going, repeated here:

 

L15: If an object is located at a point it must be at rest at that point.

 

L35: Motion implies that a body is in one place and not in it at the same time; that it is in one place and in another at the same instant.

 

Without L15 (and hence L35), Engels's conclusions wouldn't follow. So on this view, if a body is moving, it has to occupy at least two points at once, or it will be at rest. But, that is precisely what creates this latest 'problem': if that body is located at that second point, it must be at rest there, unless it is also located at a third point at the same time.

 

This itself follows from L17 (now encapsulated in L17b):

 

L17: A moving body must both occupy and not occupy a point at one and the same instant.

 

L17b: A moving object must occupy at least two places at once.

 

Of course, it could be argued that L17b is in fact true of the scenario depicted in L35-L40 -- the said body does occupy at least two places at once namely (X1, Y1, Z1) and (X2, Y2, Z2). In that case, the above objection is misconceived.

 

Or, so it might be maintained.

 

[For those not too familiar with phrases like "at most two" or "at least two"; if we remain in the set of positive integers, the former means the same as "less than three" (i.e., "two or less"), while the latter means the same as "two or more".]

 

The above objection would indeed be misconceived if Engels had managed to show that a body can only be in at most two (but not in at least two) places at once, which he not only failed to do, he couldn't do:

 

L17c: A moving object must occupy at most two places at once.

 

That is because, between any two points there is a third point, and if the body is in (X1, Y1, Z1) and (X2, Y2, Z2), at t1, then it must also be in any point between (X1, Y1, Z1) and (X2, Y2, Z2), at t1 --, say (Xk, Yk, Zk). But, as soon as that is admitted, there seems to be no way to avoid the conclusion drawn above: if a moving body is anywhere, it is everywhere at the same time.

 

[And that is why the question was posed earlier about the precise distance between the points at/in which Engels says a body performs such 'contradictory' marvels.]

 

Anyway, it would be unwise to argue that Engels believed this (or even that DM requires it) -- that is, that a moving body occupies at most two points at the same time -- since, as we have seen, if that body occupies the second of these two points, it must be at rest at that point unless it also occupies a third point at the same time. Given L15 (reproduced below), there seems no way round this.

 

On the other hand, the combination here of an "at least two places at once" with and an "at most two places at once" would amount to an "exactly two places at once".

 

L17d: A moving object must occupy exactly two places at once.

 

L15: If an object is located at a point it must be at rest at that point.

 

However, any attempt made by DM-theorists to restrict a moving body to the occupancy of exactly two places at once would once again only work if that body came to rest at the second of those two points! L15 says quite clearly that if a body is located at a point (even if this is the second of these two points), it must be at rest at that point. In that case, the above escape route will only work if DM-theorists reject their own characterisation of motion, which was partially captured by L15. [This option also falls foul of the intermediate points objection, outlined earlier.]

 

In that case, if L15 still stands, then at the second of these two proposed DM-points (say, (X2, Y2, Z2)), a moving body must still be moving, and hence in and not in that second point at the same instant, too.

 

It is worth underling this conclusion: if a body is located at a second point (say, (X2, Y2, Z2)) at t1, it will be at rest there at t1, contrary to the assumption that it is moving. Conversely, if it is still in motion at t1, it must be elsewhere also at t1, and so on. Otherwise, the condition that a moving body must be both in a certain place and not in it at the very same instant will have to be abandoned. So, DM-theorists can't afford to accept L17d.

 

Consequently, the unacceptable outcome --, which holds that as a result of the 'contradictory' nature of motion, a moving body must be everywhere along its trajectory, if it is anywhere, at the same instant -- still follows.

 

Again, it could be objected that when body A is in the second place at the same instant, a new instant in time could begin. So, while A is in (X2, Y2, Z2) at t1, a new instant, say t2, would start.

 

To be sure, this ad hoc amendment avoids the disastrous implications recorded above. However, it only succeeds in doing so by introducing several serious problems of its own -- for this option would mean that A would be in (X2, Y2, Z2) at t1 and  t2, which would plainly entail that A was located in the same place at two different times, and that in turn would mean that it was stationary at that point!

 

It could be objected, once more, that A-like objects occupy two places at once, namely (X1, Y1, Z1) and (X2, Y2, Z2), so the above argument is defective. Indeed, this is why the 'derivation' that purports to show that a moving body must be everywhere along its trajectory, if it is anywhere at the same instant can't work. We can perhaps clarify this objection by means of the following:

 

L38: L35 also implies that A is at (X2, Y2, Z2) and at another place at t1, hence it is also at (X3, Y3, Z3) at t1.

 

[L35: Motion implies that a body is in one place and not in it at the same time; that it is in one place and in another at the same instant.]

 

The idea here is that if we select, pair-wise, any two points that a body occupies in any order (either (X1, Y1, Z1) and (X2, Y2, Z2), or (X1, Y1, Z1) and (X3, Y3, Z3)..., or (X1, Y1, Z1) and (Xn, Yn, Zn), and so on), then L17c will still be satisfied:

 

L17c: A moving object must occupy at most two places at once.

 

Unfortunately, this seemingly promising escape route turns into yet another annoying cul-de-sac.

 

Here is why:

 

The 'DM-reply' proffered above held that Engels only needed a body to be in any two places at once. But, the third place above -- (X3, Y3, Z3) -- isn't implied by his description of the 'contradiction' involved. L38 (repeated below) only works by ignoring the fact that the other place that in which A is located is precisely (X1, Y1, Z1); so, it can't be in (X3, Y3, Z3) at that time --, or it doesn't have to be, which is all that is needed. So, when A is in (i) (X1, Y1, Z1) and (X2, Y2, Z2), and (ii) (X1, Y1, Z1) and (X3, Y3, Z3), and so on, it can't be in at most two places at once, since it is in this case in more than two. The use of "and" scuppers this line-of-defence.

 

[It also falls foul of an earlier response that if a moving object is in at most two places at once, it must be stationary at the second of these locations.]

 

L38: L35 also implies that A is at (X2, Y2, Z2) and at another place at t1, hence it is also at (X3, Y3, Z3) at t1.

 

[L35: Motion implies that a body is in one place and not in it at the same time; that it is in one place and in another at the same instant.]

 

It could be objected that the above response only works because an "and" has been surreptitiously substituted for an "or". The original response in fact argued as follows:

 

R1: If we select pair-wise any two points a body occupies in any order (either (X1, Y1, Z1) and (X2, Y2, Z2), or (X1, Y1, Z1) and (X3, Y3, Z3)..., or (X1, Y1, Z1) and (Xn, Yn, Zn), and so on), then L17c will be satisfied. [Underlining added.]

 

[L17c: A moving object must occupy at most two places at once.]

 

But not:

 

R2: If we select pair-wise any two points a body occupies in any order (i.e., (a) (X1, Y1, Z1) and (X2, Y2, Z2), and (b) (X1, Y1, Z1) and (X3, Y3, Z3)..., and (c) ((X1, Y1, Z1) and (Xn, Yn, Zn), and... (d)..., and so on), then L17c will be satisfied.

 

Unfortunately, once more, this reply simply catapults us back to an earlier untenable position, criticised above, as follows:

 

That is because, between any two points there is a third point, and if the body is in (X1, Y1, Z1) and (X2, Y2, Z2), at t1, then it must also be in any point between (X1, Y1, Z1) and (X2, Y2, Z2), at t1 --, say (Xk, Yk, Zk). But, as soon as that is admitted, there seems to be no way to avoid the conclusion drawn above: that if the body is anywhere, it is everywhere at the same time.

 

In that case, the reply encapsulated in L38/R1 fails, too. So, if a body is in (X1, Y1, Z1) and (X2, Y2, Z2) at t1, it must also be in at least one of the intermediate points -- say, (Xk, Yk, Zk) -- also at t1. Hence, R2 is still a valid objection.

 

In order to see this, a few of the subscripts in R2 need only be altered, as follows:

 

R3: If we select pair-wise any two points a body occupies in any order (i.e.,  (a) (X1, Y1, Z1) and (X2, Y2, Z2), and (b) (X1, Y1, Z1) and (Xk, Yk, Zk)..., and (c) (X1, Y1, Z1) and (Xi, Yi, Zi)..., and so on), then L17c won't be satisfied.

 

It is surely philosophically and mathematically irrelevant whether we label points with iterative letters (i.e., "k" or "i") or with numerals ("1", "2", or "3"). [Recall, the variables labelled with iterative letters (i.e., "k" or "i") are intermediate points.]

 

In which case, R3 implies that if a body is in, say, (X1, Y1, Z1) and (X2, Y2, Z2), at t1, it must also be in at least one of the intermediate points, say, (Xk, Yk, Zk), at the same moment. R3 thus implies that L17c is false.

 

L17c: A moving object must occupy at most two places at once.

 

Since there is a potentially infinite number of points between any two points, there is no way that L17c could be true.

 

Moreover, it is also worth asking the following in relation to L38: Is A at (X2, Y2, Z2), at  t1? If it is, then it must be elsewhere at the same time, or it will be stationary, once more. So much is agreed upon. In that case, the only way to stop the absurd induction (i.e., the one that derived the conclusion that if a moving body is anywhere it must be everywhere at the same time) would be to argue as follows:

 

L38a: L35 also implies that A is at (X2, Y2, Z2) and at another place at t1, hence it is also at (X1, Y1, Z1), at t1, but not at (X3, Y3, Z3), at t1.

 

[L38: L35 also implies that A is at (X2, Y2, Z2) and at another place at t1, hence it is also at (X3, Y3, Z3), at t1.

 

L35: Motion implies that a body is in one place and not in it at the same time; that it is in one place and in another at the same instant.]

 

However, this 'straw', once clutched, has unfortunate consequences that desperate dialecticians might want to think about before they claw at it too frantically:

 

L38b: If A is at (X2, Y2, Z2) and (X1, Y1, Z1), at t1, but not at (X3, Y3, Z3), at t1, then it must be at (X3, Y3, Z3), at t2.

 

L38c: If so, A will be at two places -- (X2, Y2, Z2) and (X3, Y3, Z3) -- at different times (i.e., (X2, Y2, Z2), at t1, and (X3, Y3, Z3), at t2).

 

L38d: In that case, between these two locations (i.e., (X2, Y2, Z2) and (X3, Y3, Z3)), the motion of A will cease to be contradictory -- since it will not now be in these two places at the same time, but at different times.

 

So, it seems that dialecticians can only escape from the absurd consequence of their theory -- that a moving object is everywhere at the same time -- by abandoning their belief in the contradictory nature of motion at an indefinite number of intermediate locations in its transit -- for example, right after it leaves the first two places it occupied in that journey!

 

Now, if the conclusions above are valid (that is, if dialectical objects are anywhere in their trajectories, they are everywhere all at once), then it follows that no moving body can be said to be anywhere before it is anywhere else in its entire journey! That is because such bodies are everywhere all at once. If so, they can't be anywhere first and then later somewhere else.

 

In the dialectical universe, therefore, when it come to motion and change, there is no before and no after!

 

In that case, according to this 'scientific theory', concerning the entire trajectory of a body's motion, it would not only be impossible to say it was at the beginning of its journey before it was at the end, it would be incorrect to say that! In fact, it would be at the end of its journey at the same time as it sets off! So, while you might foolishly think, for example, that you have to board an aeroplane (in order to go on your holidays) before you disembark at your destination, this 'path-breaking' theory tells us you are sadly mistaken: you not only must get on the plane at the very same time as you get off it at the 'end', you do!

 

Whether or not the reader agrees with the above arguments, one thing I hope is clear: I do not "gloat" over anything; I attempt to substantiate what I allege with detailed argument. Would that DM-supporters did the same!

 

4) But what about the following?

 

"The rest of their counter-arguments are just silly. Instead of contesting the fact that things in motion exist in multiple places at the same time, they turn around and argue that really all physical bodies exist in multiple places, for example, beans exist inside a tin and inside a store. or your head and your feet exist in different places despite being your body. However, this is simply word-play. The point they're making is that things don't exist in a single point but in an area, but that has no impact on the argument whatsoever on Engels nor anyone that the Trotskyite is arguing against has (sic) ever claimed that humans, beans or tin cans exist in a single point. It's obvious that wasn't hat Engels was arguing about. Besides, this kind of talk is metaphysical. And then they proceed to say that 'You know, this is an...um.., mistake by Engels because this kind of idea applies to things that are not in motion, for example, you know..., beans in tin cans'. But as I just pointed out, that's not what Engels was talking about at all because, yeah..., well, you get the point. It's just, er..., word games to say 'Oh, beans exist inside a tin can inside a warehouse..., that's.. obviously it's not the same location, it's not the same point existing inside a tin and also inside a factory or a warehouse, whatever, doesn't mean they exist in two different points."

 

It is reasonably clear from this that MLT has missed the point. Here it is again:

 

Finally, as noted above, this 'contradiction' is a direct consequence of the glaring ambiguities built into Zeno's (and thus Hegel and Engels's) account of motion -- that is, in their use of certain words (like "moment", "move", and "place"). This means that when these equivocations have been resolved, the 'contradictions' simply disappear. [Once again, that disambiguation has been carried out here.]

 

And we can see for ourselves this ambiguity and equivocation in the way MLT struggles to make himself clear:

 

"It's just, er..., word games to say 'Oh, beans exist inside a tin can inside a warehouse..., that's.. obviously it's not the same location, it's not the same point existing inside a tin and also inside a factory or a warehouse, whatever, doesn't mean they exist in two different points."

 

Does MLT mean by "point" (and/or "location") a mathematical point? Or does he intend some other meaning? If he means a mathematical point, then he can't be referring to physical objects (of the sort that Engels was referring to -- i.e., those that exist in the "real world" (to use MLT's own phrase, here). Gross bodies in the "real world" do not occupy "a point" (or even an "area" (as MLT also says(!) -- unless they have been flattened into a two-dimensional manifold), but a volume interval, or sub-space of 3-space.

 

And it is little use telling us what Engels meant, since he was equally unclear; and that is why I raised the issues I did. Of course, they were deliberately simplified, since the Essay MLT was criticising was aimed "at novices"!

 

However, in Essay Five, I enter into this very topic in considerable detail; here is just a brief excerpt (slightly edited):

 

Engels tells us that a body must be:

 

"[B]oth 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." [Engels (1976), p.152.]

 

Here, he appears to be claiming two separate things that do not immediately look equivalent:

 

L1: Motion involves a body being in one place and in another place at the same time.

 

L2: Motion involves a body being in one and the same place and not in it.

 

L1 asserts that a moving body must be in two places at once, whereas L2 says that it must both be in one place and not in it, while leaving it unresolved whether it is in a second place at the same or some later time -- or even whether it could be in more than two places at once. To be sure, it could be argued that it is implicit in what Engels said that these events occur in the "same moment of time"; however, I am trying to cover every conceivable possibility, and it is certainly possible that he not only did not say this, he didn't even intend it. [The significance of these comments will emerge as the Essay unfolds.]

 

It is also far from easy to see how a moving body can be "in one place and not in it", and yet still be in two places at once. If moving object M isn't located at X  -- that is, if it is not in X --, then it can't also be located at X (contrary to what Engels asserts). On the other hand, if M is located at X, then it can't also not be at X! Otherwise, Engels's can't mean by "not" what the rest of us mean by that word. But, what did he mean?

 

At this point, we might be reminded that there is a special sort of 'dialectical' "not" [henceforth "notD"] which can also mean, it seems, "Maybe this isn't a 'not' after all; indeed, it's the exact opposite of 'not'". And yet, if the meaning of "not" is so malleable, how can we be sure we know what "motion" and "place" mean, let alone "dialectical". If "notD" can mean the opposite of the everyday, ordinary "not", then perhaps "motion" can also mean "stationary", and "dialectical" can mean "metaphysical" (in the sense of this word as it was used by Hegel and Engels).

 

But, when a DM-theorists tells us that "notD" does not mean "not", what are we to say of the "not" in the middle (the one coloured red)? If "not" can slide about effortlessly in this manner, then perhaps this red "not" might do likewise, and mean its opposite, too? If so, when a DM-theorist tells us that "notD" does not mean "not", who can say whether or not he/she actually means the following: "'NotD' does not not (sic) mean 'not'" -- which pans out as "'NotD' means 'not'"; at which point the 'dialectical "not" collapses back into an ordinary "not". A rather fitting 'dialectical inversion' if ever there was one.

 

Until DM-theorists come up with non-question-begging criteria that inform us unambiguously which words don't 'dialectically' develop into their opposites and which do, the above 'reminder' can be filed away in that rather large box labelled "Dialectical Special Pleading".

 

[Anyone who objects to the above argument hasn't read the DM-classics, where we are told that everything in the universe -- and that must include words, which, it seems, do exist in this universe -- struggles with and then turns into its opposite.]

 

On the other hand, if this theory can only be made to work by fiddling with the meaning of certain words, how is that different from imposing this theory on the facts, something that Engels, at least, disavowed?

 

Be this as it may, if M is in two places at once -- say in X and Y at the same time --, then it can't just be in Y but must be in Y and another place -- otherwise it will be stationary at Y!

 

[That point was developed in greater detail above.]

 

Returning to the main feature: it is important to be clear what Engels meant here because L1 is actually compatible with the relevant body being at rest! This can be seen if we consider a clear example: where an extended body is motionless relative to an inertial frame. Such a body could be at rest and in at least two places at once. Indeed, unless that body were itself a mathematical point, or maybe discontinuous in some way, it would occupy the entire space between at least two distinct spatial locations (i.e., it would occupy a finite volume interval -- or more colloquially, it would take up some space). But since all real, material bodies are extended in this way, the mathematical point option seems irrelevant, here. [Anyway, it, too, will be considered again, below.]

 

[Added on edit: the above comments (as well as those below) should be of interest to MLT since he seems to prefer it if we concentrate on objects and processes that have a genuine "connection to reality", and which aren't "purely theoretical" -- and real material bodies take up space. Only mathematical points do not do this.]

 

A commonplace example of this sort of situation would be where, say, a train is at rest relative to a platform. Here, the train would be in countless places at once, but still stationary with respect to some inertial frame. [There are innumerable examples of this everyday phenomenon, as I am sure the reader is aware.]

 

[In this and subsequent paragraphs I will endeavour to illustrate the alleged ambiguities in Engels's account by an appeal to everyday situations (for obvious materialist reasons). However, these can all be translated into a more rigorous form using vector algebra and/or set theory. In the last case considered below, just such a translation will be given to substantiate that particular claim. (That has been done here.)]

 

Unfortunately, even this ambiguous case could involve a further equivocation regarding the meaning of the word "place" -- the import of which Engels clearly took for granted. As seems plain, "place" could either mean the general location of a body (roughly identical with that body's own topological shape, equal in volume to that body --, or, on some interpretations of this word, very slightly larger than its volume so that the body in question can fit 'inside' its containing volume interval). Alternatively, it could involve the use of a system of precise spatial coordinates (which would, naturally, achieve something similar), perhaps pinpointing its centre of mass and using that to locate the body, etc.

 

Of course, as noted above, Engels might have been referring to the motion of mathematical points, or point masses. But, even if he were, it would still leave unresolved the question of the allegedly contradictory nature of the motion of gross material bodies, and how the former relate to the latter.

 

It is Engels's depiction of motion that is unclear; because of that, I will concentrate on ordinary material bodies. Anyway, since DM-theorists hold that their theory can account for motion in the real world, the motion of mathematical points -- even where literal sense can be made of such 'abstract points, or, indeed, of the idea that they can move (after all, if such points do not exist in physical space, they can hardly be said to move) -- won't in general be entered into here.

 

Moving on to L2 (no pun intended): this sentence also involves further ambiguities that similarly fail to distinguish moving from motionless bodies. Thus, a body could be located within an extended region of space and yet not be totally inside it. In that sense, it would be both in and not in that place at once, and it could still be motionless with respect to some inertial frame.

 

Here, the equivocation would centre on the word "in". To be sure, it could be objected that "in" has been illegitimately replaced by "(not) totally or wholly inside/in". Even so, it is worth noting that Engels's actual words imply that this is a legitimate, possible interpretation of what he said:

 

L2: Motion involves a body being in one and the same place and not in it.

 

If a body is "in and not in" a certain place it can't be totally in that place, on one interpretation of these words. So, Engels's own words allow for his "in" to mean "not wholly in".

 

A mundane example of this might be where, say, a 15 cm long pencil is sitting in a pocket that is only 10 cm deep. In that case, it would be perfectly natural to say that this pencil is in, but not entirely in, the pocket -- that is, it would be both "in and not in" the pocket at the same time (thus fulfilling Engels's definition) --, but still at rest with respect to some inertial frame. L2 certainly allows for such a situation, and Engels's use of the word "in" and the rest of what he said plainly carry this interpretation.

 

Hence, it seems that Engels's words are compatible with a body being motionless relative to some inertial frame.

 

This is still the case even if L1 and L2 are combined, as Engels intended they should:

 

L3: Motion involves a body being in one place and in another place at the same time, and being in one and the same place and not in it.

 

An example of L3-type -- but apparently contradictory -- 'lack of motion' would involve a situation where, say, a car is parked half in, half out of a garage. Here the car is in one and the same place and not in it ("in and not in" the garage), and it is in two places at once (in the garage and in the grounds of a house), even while it is at rest relative to a suitable inertial frame.

 

In which case, the alleged contradiction that interested Engels can't be the result of motion (since his own words are compatible with a body being at rest -- that is, what he alleged isn't unique to moving bodies); it is in fact a consequence of the vagueness or the ambiguity of his description.

 

Objects at rest relative to some inertial frame can and do display the same apparent 'contradictions' as those that are in motion with respect to the same inertial frame. Naturally, if things at rest share the very same vague or ambiguous features (when they are expressed in language) as those that are in motion, Engels's description clearly fails to pick out what is unique to moving bodies.

 

This isn't a good start. We still lack a clear and unambiguous DM-description of motion!

 

At best, L3 depicts the necessary, but not the sufficient conditions for motion. [But, as we will see later, not even this is true.] In that case, the alleged contradictory nature of L3 has nothing to do with any movement actually occurring, since the same description could be true of bodies at rest, which share the same necessary conditions. As already noted, alleged paradoxes like this arise from the ambiguities implicit in the language Engels himself used -- and, as it turns out, in language he misused. [This will also be discussed in greater detail below (that is, "below" in Essay Five; this material hasn't been reproduced here).]

 

Nevertheless, in the next few sections several attempts will be made to remove and/or resolve these equivocations in order to ascertain what, if anything, Engels might have meant by the things he tried to say about moving bodies. Alas, all of them fail....

 

In which case, it isn't at all clear what Engels meant by the terms he used, and to drive this point home, I added these comments (to Essay Five):

 

Many of the ambiguities mentioned above (in relation to Engels's analysis of "motion") actually depend on systematic vagueness in the meaning of the word "place" and its cognates. Even when translated into the precise language of coordinate algebra/geometry, the meaning of this particular word doesn't become much clearer (when used in such contexts).

 

Of course, this isn't to criticise the vernacular; imprecision is one of its strengths. Nor is it to malign mathematics! However, when ordinary words are imported into Philosophy, where it is almost invariably assumed they have a single unique (or 'essential') meaning, problems invariably arise....

 

Indeed, as it turns out, there is no such thing as the meaning of the word "place" -- or, for that matter, of "move".

 

This lack of clarity carries over into our use of technical terms associated with either word; the application of coordinate systems, for example, requires the use of rules, none of which is self-interpreting. [The point of that comment will emerge presently.]

 

Nevertheless, it is relatively easy to show (by means of the sort of selective linguistic 'adjustment' beloved of metaphysicians, but applied in areas and contexts they generally fail to consider, or, rather, choose to ignore) that ordinary objects and people are quite capable of doing the metaphysically impossible. The flexibility built into everyday language actually 'enables' the mundane to do the magical, and on an alarmingly regular basis. Such everyday 'prodigies' do not normally bother us -- well, not until some bright spark tries to do a little 'philosophising' with them.

 

[Added on edit: it needs underlining that I am being ironic here!]

 

If the ordinary word "place" is now employed in one or more of its usual senses, it is easy to show that much of what Engels had to say about motion becomes either false or uninteresting. Otherwise, we should be forced to concede that ordinary people and objects can behave in extraordinary -- if not miraculous -- ways.

 

Consider, therefore, the following example:

 

L41: The strikers refused to leave their place of work and busied themselves building another barricade.

 

Assuming that the reference of "place" is clear from the context (that it is, say, a factory), L41 depicts objects moving while they remain in the same place -- contrary to what Engels said (or implied) was possible. Indeed, if this sort of motion is interpreted metaphysically, it would involve ordinary workers doing the impossible -- moving while staying still!

 

Of course, an obvious objection to the above would be that L41 is a highly contentious example, and not at all the sort of thing that Engels (or other metaphysicians) had in mind by their use of the word "place".

 

But, Engels didn't tell us what he meant by this term; he simply assumed we'd understand his use of it. If, however, it is now claimed that he didn't mean by "place" a sort of vague "general location" (like the factory used in the above example), then that would confirm the point being made in this part of the Essay: Engels didn't say what he meant by "place" since there was nothing he could have said that wouldn't also have ruined his entire argument. Tinker around with the word "place" and the meaning of "motion" can't fail to be compromised (as noted above). This can be seen by considering the following highly informal 'argument':

 

L42: Nothing that moves can stay in the same place.

 

L43: If anything stays in the same place, it can't move.

 

L44: A factory is one place in which workers work.

 

L45: Workers move about in factories.

 

L46: Any worker who moves can't stay in the same place (by L42, contraposed).

 

L47: Hence, if workers move they can't do so in factories (by L44 and L45).

 

L48: But, some workers stay in factories while they work; hence, while there they can't move (by L43).

 

L49: Therefore, workers work and do not work in factories, or they move and they do not move.

 

As soon as one meaning of "place" is altered (as it is in L44), one connotation of "move" is automatically affected (in L45), and vice versa (in both L47 and L48). In one sense of "place", things can't move (in another sense of "move") while staying in one place (in yet another sense of "place"). But, in another sense of both they can, and what is more, they can typically do both. Failure to notice this produces 'contradictions' to order, everywhere (as in L49).

 

Even so, who believes that workers work and do not work in factories? Or, that they move and do not move while staying in the same place?

 

Perhaps only those who "understand" dialectics...?

 

Clearly, Engels's 'theory' of motion has to be able to take account of ordinary objects if it is to apply to the real world and not just to abstractions, or to physically meaningless mathematical 'points'. But, this is precisely what his 'theory' can't do, as we are about to see.

 

It could be objected that it would be possible to understand what Engels and Hegel were trying to say if "place" is defined precisely without altering the meaning of "move", contrary to the points raised in the last few sections of this Essay. In that case, it could be argued that if "place" is defined by the use of precise spatial coordinates (henceforth, SCs), Engels's account of motion would become viable again.

 

Or, so some might like to think.

 

Of course, the problem here is that in the example above (concerning those contradictory mobile/stationary workers), if we try to refine the meaning of the word "place" a little more precisely, it will come to mean something like "finite (but imprecise) three-dimensional region of space large enough to contain the required object". Well, plainly, in that sense things can and do move about while they remain in the same region (i.e., "place") -- since, by default, any object occupies such a region as it moves -- that is, it must always occupy a three-dimensional region of space large enough to contain it as it moves; it certainly doesn't occupy a larger or a smaller space (unless it expands/contracts)! Moreover, objects occupy finite regions as they move in relation to each other (or they wouldn't be able to move).

 

Hence, if defined this way, moving objects always occupy the same space, and hence they don't move! That is, if they always stay in the same space, they can't move -- if we insist on defining motion the way Engels and Hegel thought they could.

 

As we have seen, objects always occupy the same space, even as they move. So, they both move and don't move! Plainly we need to be more precise.

 

Of the many problematic options there are before us, the following seem to be most relevant to the points at hand:

 

(1) If an object always occupies the same space (which fits it like a glove, as it moves), then it can't actually move!

 

(2) If it occupies a larger space as it moves, it must expand.

 

(3) If it moves about in the same region of space (such as a factory), it still can't move!

 

(4) If it successively occupies spaces equal to its own volume as it moves, the situation is even worse, as we will soon see.

 

Hence, if the 'regions' mentioned above are constrained too much, nothing would be able to move -- this is Option (1). Put each worker in a tightly-fitting steel box that exactly fits him or her and watch all locomotion grind to a halt.

 

On the other hand, put that worker in a larger region of space, and he/she still won't be able to move -- this is Option (3). That is because if we define motion as successive occupancy of regions of space within a broader region, then this worker can't move since he/she is always in the same broader region, the same space.

 

The difficulty here is plainly one of relaxing the required region (that an object is allowed to occupy) sufficiently enough to enable it to move from one place to another without stopping it moving altogether -- that is, preventing Option (3) from undermining Option (4) --, all the while providing an account that accommodates the movement of medium-sized objects in the real world. But, once this has been done the above difficulties soon re-appear, for it is quite clear that objects still move while staying in the same place -- if the place allowed for this is big enough for them to do just that!

 

Indeed, this fact probably accounts for, or permits, most (if not all) of the locomotion in the entire universe. Clearly, in the limit, if anything moves in nature it must remain in the same place, i.e., it must remain in the universe! Unless an object travels beyond the confines of the universe, this must always be the case: the said object moves while remaining in the same place -- i.e., the universe! Of course, this relaxes the definition of "same place" far too much. But, the problem now is how to tighten the definition of "place" so that objects aren't put in straight-jackets once more. [I.e., Option (1).]

 

At first sight, the above objection (concerning a precise enough definition of "place") seems reasonable enough. Engels clearly meant something a little more precise than a vague or general sort of location (like a factory). But, if so, what? He didn't say, and his epigones haven't, either -- indeed, it is quite clear that they don't even recognise this as a problem, so sloppy has their thought become. [Good luck finding a clear definition in Hegel!]

 

It might seem possible to rescue Engels's argument if tighter protocols for "place" are prescribed --, perhaps those involving a reference to "a (zero volume) mathematical point, in three-dimensional space, located by the use of precise SCs". But, this option would embroil Engels's account in far more intractable problems. That is because such an account would (plainly!) relate to mathematical point locations, or the movement of mathematical points themselves -- and we saw earlier that that was a non-starter.

 

[SC = Spatial Co-ordinate.]

 

Clearly, things cannot move about in such points -- but this has nothing to do with the supposed nature of reality. These 'entities' do not (and could not) exist in nature for them to contain anything. That is because mathematical points aren't containers. They have no volume and are made of nothing. If this weren't the case, they wouldn't be mathematical points, they'd be regions.

 

As noted above, if Engels meant something like this by his use of "place", his account would fail to explain or accommodate the movement of gross material bodies in nature, for the latter do not occupy mathematical points.

 

And, it is no use appealing to larger numbers/sets of such points located by SCs (or other technical devices); no material body can occupy an arbitrary number of points, since points aren't containers.

 

Perhaps we could define a region (or a finite volume interval) by the use of SCs? Maybe so, but this would merely introduce another classical conundrum (which is itself a variation on several of Zeno's other paradoxes): how it is possible for a region (or a volume interval) to be composed of points that have no volume. Even an infinite number of zero volume mathematical points adds up to zero. Now, there are those who think this conundrum has a solution (just as there are those who think it doesn't), but it would seem reasonably clear that the difficulties surrounding Engels's 'theory' aren't likely to be helped by importing several more of the same from another set of paradoxes -- especially when these other paradoxes gain purchase from the same linguistic ambiguities and vagaries about "space", etc.

 

Be this as it may, it is far more likely that Engels's use of the word "place" is an implicit reference to a finite three-dimensional volume interval (whose limits could be defined by the use of well-understood rules in Real and Complex Analysis, Vector Calculus, Coordinate Algebra and Differential Geometry, etc.).

 

Clearly, such volume intervals must be large enough to hold (even temporarily) a given material object. If so, this use of the phrase "volume interval" would in principle be no different from the earlier use of "place" to depict the movement of those workers! If they can move about in locations big enough to contain them, and who remain in the same place while doing so, Engels's moving objects can do so, too -- except they would now have a more precise "place"/region in which to do it.

 

However, and alas, this sense of "place" is no use at all, for when such workers move, they will, by definition, stay in the same place! So, it seems must be the case with Engels's moving objects, if we depict "place" this way. [This is just Option (3), again!]

 

Naturally, the only way to avoid this latest difficulty would be to argue that the location of any object must be a region of space (i.e., volume interval) equal to that object's own volume. This is in effect one of the classical definitions. In that case, as the said object moves, its own exact volume interval would move with it, too; the latter would follow each moving object around more faithfully than its own shadow, and more doggedly than a world-champion bloodhound. But, plainly, if that were the case, it would mean that such objects would still move while staying in the same place -- since, plainly, any object always occupies a space equal to its own volume, which would, on this view, travel everywhere with it, like a sort of metaphysical glove. [Option (1), again!]

 

As should now seem plain: in this case we now have two problems where once there was just one, for we should now have to explain not only how bodies move, but how it is also possible for volume intervals to move so that they can faithfully shadow the objects they contain!

 

Moreover, and far worse: in this instance, not only would we have to explain how locations (i.e., volume intervals) are themselves capable of moving, we would also have to explain what on earth they could possibly move into!

 

What sort of ghostly regions of space could we appeal to, to allow regions of space themselves to move into them?

 

Even worse still: these 'moving volume intervals' must also occupy volumes equal to their own volume, if they are to move (given this 'tighter' way of characterising motion). And, if they do that, then these new 'extra' locations containing the volume intervals themselves must now act as secondary 'metaphysical containers', as it were, to the original 'ontological gloves' we met earlier. Metaphorically speaking, this theory, if it took such a turn, would be moving backwards, since an infinite regress would soon confront us, as spatial mittens inside containing gloves, inside holding gauntlets, piled up alarmingly to account for each successive spatial container, and how each of them could possibly move. As seems reasonably clear, we would only be able to account for locomotion this way if each moving object were situated at the centre of some sort of 'metaphysical onion', each with a potentially infinite number of 'skins'! [Iterated Option (1)!]

 

It could be countered that even though objects occupy spaces equal to their own volumes, as they move along they then proceed to occupy successive spaces of this sort (located in the surrounding region, for example), all of which are of precisely the right volume to contain the moving object that now occupies them, and which can be located/defined precisely. On this revised scenario, moving objects would leave their old locations (their old containers) behind as they barrelled along.

 

This now brings us to a consideration of Option (2), and/or Option (4) -- now modified to (4a) --, from earlier:

 

(2) If an object occupies a larger space as it moves, it must expand.

 

(4a) An object successively occupies spaces (or volume intervals) equal to its own volume as it moves.

 

I will reject (2) as absurd. If anyone wants to defend it, they are welcome to all the headaches it will bring in its train.

 

Considering, now, Option (4a):

 

Even if (4a) were a correct interpretation of what Engels meant, and it were also a viable option -- and, indeed, if sense could be made of these new, and accommodating successive locations without re-duplicating the very same problem noted in the previous few paragraphs --, no DM-theorist could afford to adopt it. That is because dialecticians claim that moving bodies occupy at least two such "places" at the same time, being in one of them and not in it at the same moment. Clearly, if motion were defined in such terms (that is, if it were characterised as involving objects successively occupying spaces equal to their own volumes), then moving objects would occupy at least two of these volume intervals at once.

 

In that case, 'dialectical objects' would not so much move as stretch or expand! [Modified Option (2)!]

 

To see this point more clearly (no pun intended!), it might be useful to examine the above argument a little more closely.

 

If the centre of mass (COM) of a 'dialectically moving' object, D, were located at, say, (Xk, Yk, Zk) and (Xk+1, Yk+1, Zk+1), at the same time (to satisfy the requirement that moving bodies occupy at least two such "places" at the same time, being in one of them and not in it), it would have to occupy a space larger than its own volume while doing so.

 

Let us call such a space "S", and let the volume interval containing (Xk, Yk, Zk) and (Xk+1, Yk+1, Zk+1) be "δV1", leaving it open for the time being whether S and δV1 are the same or are different. Thus, if the COM of D is in two such places (i.e., (Xk, Yk, Zk) and (Xk+1, Yk+1, Zk+1)) at once, D would plainly be in S, and would occupy δV1. But, once again, that would mean that D would move while remaining in the same place -- i.e., it would remain inside S, or inside δV1 (whichever is preferred), as its COM moved from (Xk, Yk, Zk) to (Xk+1, Yk+1, Zk+1), in the same instant. [Option (3), again!]

 

[Except, we can't speak of a 'dialectal object' moving from one point to the next since that would imply it was in the first before it was in the second, and that it was in the second after it was in the first. As we have seen, if such an object is in both places at the same time, there can be no "before" and no "after", either.]

 

Now, the only way to avoid the conclusion that D moves while occupying the same place/space S and/or δV1 --, and hence that it appears to stay still while it moves, just like the 'mobile/stationary' workers we encountered earlier -- would be to argue that such spaces remain where they are while D moves into successively new locations, or new spaces. This seems to be the import of Option (4a):

 

(4a) An object successively occupies spaces (or volume intervals) equal to its own volume as it moves.

 

But, as D moves it still occupies δV1, only we would now have to argue that as it does so it also moves into a new δV each time, say, δV2 -- except that δV2 must now contain (Xk+1, Yk+1, Zk+1) and (Xk+2, Yk+2, Zk+2) -- otherwise it wouldn't be a new containing volume interval that satisfied the requirement that moving bodies occupy at least two such "places" at the same time, being in one of them and not in it.

 

Plainly, all objects have to occupy some volume interval or other at all times (or they would 'disappear'). However, in D's case it has to do this while also occupying new volume intervals at the same time as it moves along (otherwise, as we saw, it would move while being in the same place, which would imply that it didn't move, after all!).

 

So, if D occupies only one S or only one δV at once, it would be at rest in either. [Options (1) and (3).] Hence, it must occupy at least two of these at the same time (if, that is, we accept the 'dialectical' view of motion).

 

If so, the only apparent way of avoiding the conclusion that D-like objects move while staying still is to argue that they occupy two successive Ss, or two successive δVs (perhaps these partially 'overlap', perhaps they don't), at once. Unfortunately, this would now mean that D-like objects would have to occupy a volume/volume interval bigger than either of S or δV at once, and hence: they must expand or stretch.

 

It could be objected that two successive δVs would contain (Xk, Yk, Zk) and (Xk+1, Yk+1, Zk+1) each between them -- that is, δV1 would contain (Xk, Yk, Zk) and δV2 would contain (Xk+1, Yk+1, Zk+1) --, so the above objection is misguided. Maybe so, but the point is that dialectical objects must occupy two δVs at once, and if that is so, both δVs must contain (Xk, Yk, Zk) and (Xk+1, Yk+1, Zk+1), jointly or severally, otherwise such moving objects couldn't occupy two spaces (two δVs) at the same time.

 

But, if that is so, and D isn't stationary while it occupies δV2 -- and as we saw above in an analogous context -- it must also occupy δV3 at the same time, and so on. Successive applications of this argument would have D occupying bigger and bigger volume intervals (i.e., δV1 + δV2 + δV3 + δV4 +...,+ δVn), all at the same time. In the limit, D could fill the entire universe (or, at least, the entire volume interval encompassing its own trajectory), all at the same time -- if it moves, and if Hegel is to be believed!

 

There thus seems to be no way to depict the motion of D-like objects that prevents them from either (i) moving while staying still, or, from (ii) expanding alarmingly like some sort of metaphysical Puffer Fish....

 

Either way, Engels's theory finds itself in yet another Hermetic Hole.

 

The reader should now be able to see for herself what mystical mayhem is introduced into our reasoning by this cavalier use of (contradictory) metaphysical language. When one sense of "move" is altered, one sense of "place" can't remain the same, nor vice versa.

 

Of course, no one believes the above ridiculous conclusions, but there appears to be no way to avoid them using the radically defective and hopelessly meagre conceptual and/or logical resources DL supplies its unfortunate victims....

 

Despite this, it could be argued that if the ordinary word "place" is so vague then it should be replaced by more precise concepts; those defined in terms of SCs, once more. But, as the following argument shows, that would be another backward move (no pun intended!):

 

L50: A place or location can be defined by the use of SCs.

 

L51: SCs are composed of ordered real number 3-tuples (i.e., number triples, defined precisely -- see L52) in R3.

 

[R3 is just a mathematical shorthand for three-dimensional Cartesian Space.]

 

L52: However, when written correctly, the elements in such 3-tuples must occupy their assigned places (by the ordering rules). Consider then the following ordered triplet: <x1, y1, z1>. Each element in such an SC must be written precisely this way, with xi, yi, and zi (etc.) all in their correct places.

 

L53: But, the situating of such elements can't itself be defined by exact SCs, otherwise an infinite regress will ensue.

 

L54: Consequently, this latter sense of "place" (i.e., that which underlies the ordering rules for SCs) can't be defined (without circularity) by means of SCs.

 

[SC = Spatial Coordinate.]

 

This means that the definition of "place" by means of SCs is itself dependent on a perfectly ordinary meaning of "place", and, further, that the latter sense of "place" must already be understood if a co-ordinate system is to be set-up correctly.

 

Therefore, the ordinary word "place" can't be defined without circularity by means of a coordinate system.

 

In short, the precision introduced by means of SCs is bought at the expense of presupposing mundane linguistic facts such as these.

 

Of course, this isn't to malign or depreciate coordinate geometry, it merely serves to remind us that any branch of human knowledge (even one as technical and precise as modern mathematics) has to mesh with ordinary language and everyday practice (at some point), if it is to be set-up to begin with, and if human beings (or machines programmed by human beings) are to use it. Everyday facts like these are soon forgotten (in the course of one's education), since, as Wittgenstein pointed out, we are taught to quash or dismiss such simple questions very early on. As a result we inherit the mythological structures that previous generations have built on top of unexamined foundations like this.

 

If, on the other hand, a typographically identical word (viz.: "place") were to be defined in this way, and then used in mathematics or physics, it wouldn't be the same word as the ordinary word "place" upon which the definition itself was predicated. And, if this new term, "place", is used to define the movement of objects in DM, then the motion of gross bodies in the material world would still be unaccounted for.

 

It could be objected here that it is surely possible to disambiguate the ordinary word so that it could be employed in a DM-analysis of motion --, meaning that it was no longer confused with the less precise phrase "general location".

 

Since this has yet to be done (even by DM-advocates, who, up until now, have shown that they aren't even aware of this problem!) it remains to be seen whether this promissory note is redeemable. However, even if it were, it would still be of little help. As we have seen, and will see again, the word "place" (even as it is used in mathematics) is itself ambiguous, and necessarily so. [There is more on this in Note 25.]

 

Moreover, Engels's account requires motion to be depicted by a continuous variable, while one or both of time or place is/are held to be discrete, otherwise a contradiction wouldn't emerge (which is, of course, something even Hegel recognised). This trick is accomplished either by (1) The simple expedient of ignoring examples of discrete forms of motion (several of which are given below -- this material from Essay Five has been omitted -- RL), and/or by (2) Failing to consider instances where both time and place are continuous -- all the while imagining that the relevant ordinary words used to depict both have been employed in their usual senses, and haven't been altered by these new uses/contexts.

 

Even assuming a stricter sense of "place" could be cobbled-together somehow, it would still be of little help. That is because it would either make motion itself impossible -- or, if possible, incomprehensible -- since, given Engels's account, a moving object would have to be everywhere if it is anywhere, and, it wouldn't so much move as expand or stretch, as noted earlier.

 

So, my argument isn't about tins of beans as such (that was my way of simplifying the above rather complex arguments so that novices could appreciate the point), but about what Hegel, Engels or Lenin could possibly have meant by their use of such language. Unfortunately, MLT is absolutely no help in this regard. Indeed, from what little he has said about locations and points, for example, he is perhaps even more confused than Engels!

 

5) It's a little rich of MLT asserting that I am playing "word games" here, when Hegel and Engels's argument is precisely this! Both of them attempt to derive what seem to them to be fundamental theses about every example of motion in the entire universe, for all of time, based on what they took to be the 'real' meaning of a handful of words, none of which they defined clearly (or at all)! In which case, MLT has no valid reason to cavil if I use language to expose such sloppy thought.

 

Indeed, as George Novack pointed out:

 

"A consistent materialism can't proceed from principles which are validated by appeal to abstract reason, intuition, self-evidence or some other subjective or purely theoretical source. Idealisms may do this. But the materialist philosophy has to be based upon evidence taken from objective material sources and verified by demonstration in practice...." [Novack (1965), p.17. Bold emphasis added.]

 

But, that is precisely what Hegel, Engels and Lenin did.

 

More to follow...

 

Bibliography

 

Engels, F. (1954), Dialectics Of Nature (Progress Publishers).

 

--------, (1976), Anti-Dühring (Foreign Languages Press).

 

Goble, L. (2001) (ed.), The Blackwell Guide To Philosophical Logic (Blackwell).

 

Haack, S. (1979), Philosophy Of Logics (Cambridge University Press).

 

--------, (1996), Deviant Logic. Fuzzy Logic (University of Chicago Press).

 

Hinman, P. (2005), Fundamentals Of Mathematical Logic (A K Peters).

Hintikka, J. (1962), Knowledge And Belief (Cornell University Press).

 

Hughes, G., and Cresswell, M. (1996), A New Introduction To Modal Logic (Routledge).

 

Jacquette, D. (2006) (ed.), A Companion To Philosophical Logic (Blackwell).

 

Marx, K. (1975a), Early Writings (Penguin Books).

 

--------, (1975b), Economical And Philosophical Manuscripts, in Marx (1975a), pp.279-400.

 

Marx, K., and Engels, F. (1970), The German Ideology, Students Edition, edited by Chris Arthur (Lawrence & Wishart).

 

--------, (1976), The German Ideology, MECW, Volume 5 (Lawrence & Wishart).

 

Mendelson, E. (1979), Introduction To Mathematical Logic (Van Nostrand, 2nd ed.).

 

Novack, G. (1965), The Origins Of Materialism (Pathfinder Press).

 

--------, (1971), An Introduction To The Logic Of Marxism (Pathfinder Press, 5th ed.).

 

Priest, G. (2000), Logic. A Very Short Introduction (Oxford University Press).

 

--------, (2008), An Introduction To Non-Classical Logic (Cambridge University Press, 2nd ed.).

 

Prior, A. (1957), Time And Modality (Oxford University Press).

 

--------, (1967), Past Present And Future (Oxford University Press).

 

--------, (2003), Papers On Time And Tense (Oxford University Press, 2nd ed.).

 

Read, S. (1994), Thinking About Logic (Oxford University Press).

 

Rees, J. (1998), The Algebra Of Revolution (Routledge). [This links to a PDF.]

 

Shapiro, S. (2013), 'Classical Logic', The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta (Winter 2013 Edition).

 

Smith, R. (2015), 'Aristotle's Logic' The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta (Summer 2015 Edition).

 

Trotsky, L. (1971), In Defense Of Marxism (New Park Publications).

 

Von Wright, G. (1957), Logical Studies (Routledge)

 

--------, (1963), Norm And Action (Routledge).

 

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