Essay Five: Why Motion Isn't Contradictory

 

This Essay should be read in conjunction with Essays Four and Eight Parts One, Two and Three.

 

Preface

 

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As is the case with all my Essays, nothing here should be read as an attack either on Historical Materialism [HM] -- a theory I fully accept --, or, indeed, on revolutionary socialism. I remain as committed to the self-emancipation of the working class and the dictatorship of the proletariat as I was when I first became a revolutionary nearly thirty years ago.

 

The difference between Dialectical Materialism [DM] and HM, as I see it, is explained here.

 

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

 

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

 

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

 

It is also worth pointing out that a good 50% of my case against DM has been relegated to the End Notes. Indeed, in this particular Essay, most of the supporting evidence and argument is to be found there. This has been done to allow the main body of the Essay to flow a little more smoothly. In many cases, I have added numerous qualifications, clarifications, and considerably more detail to what I have to say in the main body. In addition, I have raised several objections (some obvious, many not -- and some that will have occurred to the reader) to my own arguments -- which I have then answered. [I explain why I have adopted this tactic in Essay One.]

 

If readers skip this material, then my answers to any qualms or objections readers might have will be missed, as will my expanded comments and clarifications.

 

[Since I have been debating this theory with comrades for over 25 years, I have heard all the objections there are! Many of the more recent on-line debates are listed here.]

 

Update 07/03/2014: I have just received a copy of Burger et al (1980), the existence of which I had been unaware until a few weeks ago. One of the contributors to this book, Hyman Cohen [Cohen (1980)] seems to have anticipated (and answered) one or two of the points I have raised in this Essay. Unfortunately, Cohen's 'answers' also fail miserably; I will attempt to explain why that is so in a future re-write of this Essay.

 

Update: 29/11/2016: I have now added to Essay Four Part One a few thoughts about Cohen's egregious logical confusions.

 

Finally, anyone puzzled by the unremittingly hostile tone I have adopted toward DM/'Materialist Dialectics' [MD] in these Essays might do well to read this first.

 

As of December 2016, this Essay is just under 82,500 words long; a much shorter summary of some of its main ideas can be found here, and a more recent summary, here.

 

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

 

[Latest Update: 12/12/16.]

 

 

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(1)  Introduction

 

(2)  Initial Problems

 

(a) "Asserted" By Whom?

 

(b) "Solved" In What Way? And By Whom?

 

(c) Yet More Vagueness

 

(d) Yet More Dogmatism?

 

(e) Motion 'Itself'

 

(3)  Do Contradictions Explain Motion? Or Merely Re-Describe It?

 

(a) The Problem Stated

 

(b) Are Contradictions Causes?

 

(c) 'Internal Contradictions' And Motion

 

(d) An Indistinct Note

 

(4)  Is Engels's Theory At All Comprehensible?

 

(a) Minimum Requirement

 

(b) An Initial Ambiguity

 

(c) First Attempt At Disambiguation

 

(d) Second Attempt At Disambiguation

 

(e) Fatal Ambiguity

 

(5)  The Classical Response To Zeno

 

(a) Inconsistent Division

 

(6)  Back to The Drawing Board

 

(a) The Devil In The Detail

 

(b) Space To Let

 

(7)  Further Problems

 

(a) The Background To Engels's Argument?

 

(b) Pick Your Contradiction

 

(c) Theatre Of The Absurd

 

(d) Samuel Beckett Eat Your Heart Out

 

(8)  No Word Is An Island -- Philosophers Ignore Ordinary Language

 

(a) For Whom The Bell Tolls

 

(b) Ordinary Language And Paradox

 

(c) Lack Of Imagination

 

(d) Ordinary Objects Regularly Do The Impossible

 

(9)  Dialectical Objects Do The Oddest Things

 

(a) Moving While Remaining Still

 

(b) Do They Move Or Simply Expand?

 

(c) Or Do They Concertina?

 

(d) Coordinates To The Rescue?

 

(10)  Everyday Miracles?

 

(a) Ordinary Objects Behave 'Miraculously'

 

(11) Inferences From Language To The World

 

(a) Thought Experiment In Place Of Scientific Investigation

 

(b) Metaphysical Con-Trick

 

(c) Exclusively Linguistic

 

(12) Dialectical 'Contradictions'

 

(13) Conclusion

 

(14) Notes

 

(15) References

 

Summary Of My Main Objections To Dialectical Materialism

 

Abbreviations Used At This Site

 

Return To The Main Index Page

 

Contact Me

 

Introduction

 

In this Essay I aim to examine critically the role that 'contradictions' are supposed to play in explaining motion and change.1

 

[DM = Dialectical Materialism/Materialist, depending on context; FL = Formal Logic.]

 

DM-theorists in general attempt to illustrate the 'contradictory' nature of reality by appealing to a handful of examples, some of which are based on variations of Zeno's Paradoxes. For instance, in order to highlight the limitations of FL, Engels directed our attention to the 'contradictory' nature of motion, depicting it in the following way:2

 

"[S]o long as we consider things as at rest and lifeless, each one by itself, alongside and after each other, we do not run up against any contradictions in them. We find certain qualities which are partly common to, partly different from, and even contradictory to each other, but which in the last-mentioned case are distributed among different objects and therefore contain no contradiction within. Inside the limits of this sphere of observation we can get along on the basis of the usual, metaphysical mode of thought. But the position is quite different as soon as we consider things in their motion, their change, their life, their reciprocal influence on one another. Then we immediately become involved in contradictions. Motion itself is a contradiction: even simple mechanical change of position can only come about through a body being at one and the same moment of time both in one place and in another place, being in one and the same place and also not in it. And the continuous origination and simultaneous solution of this contradiction is precisely what motion is." [Engels (1976), p.152.]3

 

As is well-known, Engels lifted these ideas from Hegel; in the above comments he also connects change with motion, and then both with "contradictions" supposedly in nature and society (elsewhere in the same book).

 

However, before this passage is examined in detail, there are several problems it poses which will need to addressed first since they influence the overall interpretation placed on the conclusion Engels seems to have reached; indeed, left unresolved they threaten to undermine completely what he has to say.

 

 

Initial Problems

 

There are in fact five initial, general difficulties with the above passage.

 

 

(1) "Asserted" By Whom?

 

Engels's closing sentence is rather odd:

 

"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." [Ibid. Bold emphasis added.]

 

Exactly who is supposed to do the "asserting", and who the "solving", here? Of course, it could be argued that these words were meant to be taken metaphorically. But, if that is so, what is the force of Engels's use of "precisely"?

 

Even more to the point: if Engels was speaking figuratively what has "assertion and simultaneous solution" got to do with motion? This isn't even a good metaphor!

 

Perhaps Engels intended to say that these phrases merely pertain to the description of motion? In that case, his conclusions must have been restricted to language about motion, not 'motion itself'.4

 

 

(2) "Solved" In What way?

 

How exactly are contradictions "solved"? Are they like puzzles, riddles and mysteries? If they are, do they disappear once they have been "solved"? Puzzles and mysteries cease to be puzzles or mysteries when they have been resolved. Is this the same with these contradictions?4a If so, do new contradictions immediately take their place? Is each "solved" contradiction then replaced by the 'same' contradiction, or by an entirely new one? How might any of this be confirmed? And, how do we know if there is only one contradiction present, or countless thousands for each unit of time involved? If there is more than one contradiction, how are they all connected with a given body in motion? Does each contradiction arise and fall as that body moves? Or is there a single, extended contradiction spread out, as it were, right across its entire trajectory? Is this 'extended contradiction' then perhaps this: that a moving body is "here and not here, in general", so to speak?

 

More puzzling still: Are these contradictions "solved" by some mind or other comprehending them first? If not, what sense can be given to the word "solved"? And, what precisely is there to understand in a contradiction so that a 'solution' is required in the first place, but which now mysteriously still helps further propel the moving object along (if it does)? On the other hand, if a 'solution' is required, how was this engineered before human beings evolved?

 

At first sight, Engels appears to be arguing that it is only our understanding of motion that is contradictory:

 

"[A]s soon as we consider things…then we…become involved in contradictions…." [Ibid., p.152. Bold emphasis added.]

 

This might help explain why the passage refers to the "continual assertion" of contradictions, since it is evident that only human beings can assert anything. If so, it looks like Engels thought that human observers can't avoid "asserting" such contradictions whenever they attempt to describe motion, and that might itself be a result of their partial understanding of the 'absolute truth' about motion. On the other hand, this conundrum could be a fault of logic, or even of language, both of which are said by some to be inadequate to the task. But, that would fail to explain how and why contradictions, upon being "asserted", are immediately "solved", and then promptly re-asserted.

 

Anyway, and worse, this would mean that it is only human understanding (of motion) that is contradictory, not 'reality itself' -- unless, of course, we are to suppose that nature is Mind -- or, maybe even: that it is the 'self-development of Mind' that propels bodies along. But, the former alternative suggests that when reality is fully understood all such contradictions will disappear. If so, this in turn implies that motion might one day cease, all contradictions having been 'solved'! Moreover, if contradictions actually 'cause' motion, then their complete resolution should, it seems, freeze nature in its entirety. Or, is it that motion will just stop being (or appearing to be) contradictory, but will otherwise carry on as normal? Or, does it mean that nature will just slow down as it is better understood (i.e., if what we know about motion and change becomes less and less contradictory)? Who can say? Certainly, in the 140 years since Engels wrote these enigmatic words, DM-fans have been more content merely to repeat them than they have been concerned to raise, let alone consider, these glaringly obvious questions.

 

Admittedly, DM-theorists distinguish between subjective and objective dialectics -- the former relating to our (perhaps decreasingly) partial grasp of the 'nature of reality', the latter referring to processes in the 'objective world' independent of our will or our knowledge. Even so, it is still unclear how this helps answer the above questions. If the human mind "solves" the contradictions involved in motion, wouldn't this mean that things actually stop moving? And wouldn't it indicate, too, that movement only seems to be contradictory because of the partial nature of knowledge -- implying that motion isn't really contradictory? Plainly, that is because these 'subjective contradictions' ought to disappear as knowledge grows, which in turn means that (in the limit) reality isn't 'contradictory', after all. In that case, it is only our 'one-sided knowledge' of nature that fools us into concluding otherwise.

 

Well, perhaps this merely implies that we don't really understand these 'contradictions' to begin with. But, then again, that would fail to explain why contradictions are promptly reasserted upon being "solved"; nor is it at all clear how they could be "solved" if no one understands them, or if no one understands nature fully. More alarmingly, this might mean that the objects in question aren't really moving, as Zeno originally contended.

 

Why then does Engels declare the following?

 

"…the continual assertion and simultaneous solution of this contradiction is precisely what motion is…." [Ibid., p.152. Bold emphasis added.]

 

This seems to confirm the conclusion that motion isn't really a 'contradictory-in-itself', that it is simply our 'one-sided' perspective that misleads us. After all, Engels tells us that the "continual assertion" and "solution" of this contradiction is "precisely what motion is". Why then does Engels say that this reveals "precisely" what motion is, as opposed to arguing that it merely depicts what we subjectively think it is?

 

An appeal to "objective dialectics" can't help us comprehend what Engels means here, either, since neither assertions nor solutions occur in nature (apart, that is, from the intelligent beings who make or who provide them). And, if that is so, these non-objective assertions and solutions can't have been reflected in the mind of observers as part of an objective scientific theory, or, indeed, as part of 'objective dialectics'. If assertions and solutions don't exist in the world independent of the individuals involved, there would be nothing there (in the material world) for the minds of scientists or dialecticians to reflect.

 

And, if that is so, what has assertion and solution got to do with motion in the real world? And why did Engels think they were at all relevant?

 

So many questions -- so few answers...

 

 

(3) More Vagaries

 

As we have seen, Engels informs us that:

 

"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." [Ibid. Bold emphasis added.]

 

More specifically, in relation to moving bodies, it is pertinent to ask: How far apart are the two proposed "places" that a moving object is supposed to occupy while at the same time not occupying one of them? Is there a minimum distance involved? The answer can't be "It doesn't matter; any distance will do." That is because, as we will see, if a moving object is in two places at once, then it can't truly be said to be in the first of these before it is in the second (since it is in both at the same time). So, unless great care is taken specifying how far apart these "two places" are, the DM-view of motion would have, say, an aeroplane landing at the same time as it took off! If any distance will do, then the distance between the two airports involved is as good as any. [I return to this topic, and discuss it in much more detail, later in this Essay.]

 

Indifference in this respect would have you arriving at your destination at the same time as you left home!

 

Anyway, whatever the answer to that annoying conundrum happens to be -- as is well known -- between any two locations there is a potentially infinite number of intermediary points (that is, unless we are prepared to impose an a priori limitation on nature by denying this).

 

Does a moving body, therefore, (i) occupy all of these intermediate points at once? Or, (ii) does it occupy each successively?

 

If the former is the case, does this imply that a moving object can be in an infinite number of places at the same time, and not just in two, as Engels asserted? On the other hand, if Engels is correct, and a moving body only occupies (at most) two places at once, wouldn't that suggest that motion is discontinuous? That is because such an account seems to picture motion as a peculiar stop-go sort of affair, since a moving body would have to skip past (but not occupy, somehow?) the potentially infinite number of intermediary locations between any two arbitrary points (the second of which it then occupies), if it is restricted to being in at most two of them at any one time, and is therefore stationary at the second of these two points. [That is what the "at most" qualifier implies, here.] But, that itself appears to run contrary to the hypothesis that motion is continuous and therefore contradictory -- or, it runs counter to that hypothesis in a straight-forward sense, at the very least. It is surely the continuous nature of motion that poses problems for a logic (i.e., FL), which is allegedly built on a static, discontinuous view of reality, this being the picture that traditional logic is supposed to have painted --, or, so we have been told by generations of dialecticians.

 

It could be argued that no matter how much we 'magnify' the path of a moving body, it will still occupy two points at once, being in one of them and not in it at the same time. And yet, that doesn't solve the problem, for if there is indeed a potentially infinite number of intermediary points between any two locations, a moving body must occupy more than two of them at once, contrary to what Engels seems to be saying:

 

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

 

Hence, between any two points, P and Q -- located at, say, (Xp, Yp, Zp) and (Xq, Yq, Zq), respectively -- a moving object, M, occupies (at the same "moment in time", T1), there are, for example, the following intermediary points: (X1, Y1, Z1), (X2, Y2, Z2), (X3, Y3, Z3),..., (Xi, Yi, Zi),..., (Xn, Yn, Zn) -- where n itself can be arbitrarily large. Moreover, the same applies to (X1, Y1, Z1) and (X2, Y2, Z2): there is a potentially infinite number of intermediate points between these two, and so on.

 

So, if Engels is right, M must occupy not just P and Q at the same instant, it must occupy all these intermediary points, as well -- again, all at T1. That can only mean that M is located in a potentially infinite number of places, all at the same "moment". It must therefore not only be in and not in P at T1, it must be in and not in each of (X1, Y1, Z1), (X2, Y2, Z2), (X3, Y3, Z3),..., (Xi, Yi, Zi),..., and (Xn, Yn, Zn) at T1, just as it must be in all the intermediary points between (X1, Y1, Z1) and (X2, Y2, Z2), if it is also to be in Q at the same "moment".

 

And, what is worse: M must move through (or be in) all these intermediate points without time having advanced one instant!

 

That is, M will have achieved all this in zero seconds!

 

M must therefore be moving with an infinite velocity between P and Q!

 

Unless, of course, we decide to re-define "velocity" so that it is no longer the expression of a functional link between distance and time -- calculated by dividing the former by the latter.

 

But, if not, what then is it?

 

[An appeal to the Calculus here -- or, rather, to a DM-interpretation of the Calculus -- would be to no avail, as we will see in Essay Seven Part One. See also this sub-section of the present Essay.]

 

Of course, we could always claim that by "same moment" Engels meant "same temporal interval", but as we will also see, this scuppers his theory even faster. [No pun intended.] That is because if by "same moment" Engels meant "same temporal interval", then there is no reason why "same point" can't also mean "same spatial interval", at which point the alleged 'contradiction' simply vanishes. [Again, no pun intended!]

 

[Why that is so will be explained below. Indeed, we will also see that this alternative (i.e., that a moving body occupies all the intermediate points between any two points, all at the same time) poses even more serious problems for Engels's theory than this --, that is, over and above implying that 'dialectical' objects move with infinite velocities.]

 

However, if M moves from P to Q in temporal interval, T, comprised of sub-intervals, T1, T2, T3, ..., Tn, each of which is also comprised of its own sub-intervals, then M will be located at P at T1 and then at Q at Tn, which will, of course, mean that M won't be in these two places at the same time, although it will be located at these two points in the same temporal interval. The 'contradiction' Engels claims to see here would in that case have vanished. Few theorists, if any, think it is the least bit contradictory to suppose that M is in P at one moment and then in Q a moment later. Consider a car travelling north across Texas during a three-hour temporal interval. Let us suppose it is in the centre of Lubbock at 08:00am and in the centre of Amarillo (approximately 124 miles away) at 11:00am. In that case, it will have been in two locations during the same temporal interval (lasting three hours), but not in two places in the same moment in time. In this case, the alleged contradiction has disappeared. Indeed, this car won't even be in Lubbock and not in it at, say, 08:01, even while it is moving -- since it will be in Lubbock for several minutes (until it reaches the city boundary). So, in this instance, the car isn't in one place and not in it in this sub-section of the interval. If that is so, only a very short-sighted DM-fan will want to take advantage of this escape route (no pun intended) -- i.e, referring to temporal intervals as opposed to 'moments in time'. This is probably why Engels didn't refer to temporal intervals, and, as far as can be ascertained, no DM-theorist has done so since. 

 

On a different tack: Do these contradictions increase in number, or stay the same, if an object speeds up? [This is a problem that, for example, exercised Leibniz; more on this below.] Or, are the two locations depicted by Engels (i.e., the "here" and the "not here") just further apart? That is, are the two points that M occupies at the same moment, if it accelerates, just further apart? But, if it occupies them at the same time, it can't have accelerated. That is because it hasn't moved from the first to the second, since it is in both at once. Speeding up, of course, involves covering the same distance in less time, but that isn't allowed here, nor is it even possible. In which case, it is far from easy to see how, in a DM-universe, moving bodies could accelerate (or even move!) if they are in these two locations at once.

 

[I am of course using "accelerate" here as it is employed in everyday speech, not as it is used in Physics or Applied Mathematics.]

 

Accelerated motion (in the above sense of this word) involves a body being in (or passing through) more places in a given time interval than had been the case before it accelerated. But, if M is in these two places at the same time, how can it pick up speed?

 

[For some of the complexities involved here, see Note 18c.]

 

So many more questions; even fewer answers...

 

 

(4) Yet More A Priori Dogmatics?

 

Quite apart from this, Engels's endeavour to provide an overtly linguistic, or even 'conceptual', solution to the 'problem of motion' suggests that there is more than a hint of LIE to his theory. And no wonder: he lifted this approach from Hegel, an Idealist of the worst possible kind.

 

[LIE = Linguistic Idealism; this term is explained here.]

 

This 'conceptual' approach to motion is evident from the way that Engels's depiction of it depends on a 'one-sided' consideration of just a few of the concepts that seemingly apply in this area -- expressed though by means of some rather ordinary-looking words, the meaning of which Engels simply took for granted (more on this later). So, based on thought alone, Engels imagined he could conclude what must be true of every moving body in the entire universe, for all of time, without exception. But, how could he possibly know all this with so little evidence (in fact, no evidence at all, as we will also see) to back it up?

 

"[S]o long as we consider things as at rest and lifeless, each one by itself, alongside and after each other, we do not run up against any contradictions in them. We find certain qualities which are partly common to, partly different from, and even contradictory to each other, but which in the last-mentioned case are distributed among different objects and therefore contain no contradiction within. Inside the limits of this sphere of observation we can get along on the basis of the usual, metaphysical mode of thought. But the position is quite different as soon as we consider things in their motion, their change, their life, their reciprocal influence on one another. Then we immediately become involved in contradictions. Motion itself is a contradiction: even simple mechanical change of position can only come about through a body being at one and the same moment of time both in one place and in another place, being in one and the same place and also not in it. And the continuous origination and simultaneous solution of this contradiction is precisely what motion is." [Engels (1976), p.152. Bold emphasis added.]

 

"Motion is the mode of existence of matter. Never anywhere has there been matter without motion, nor can there be…. Matter without motion is just as inconceivable as motion without matter. Motion is therefore as uncreatable and indestructible as matter itself; as the older philosophy (Descartes) expressed it, the quantity of motion existing in the world is always the same. Motion therefore cannot be created; it can only be transmitted….

 

"A motionless state of matter therefore proves to be one of the most empty and nonsensical of ideas…." [Ibid., p.74. Bold emphases alone added.]

 

Notice, Engels explicitly contrasts what we can see (when he refers to the "limits of this sphere of observation") with how things seem when we "consider things". In other words, his only 'evidence' is based on how we think about motion.

 

Clearly, Engels was the possessor of a truly remarkable skill: the ability to uncover fundamental features of reality, valid for all of space and time, from the alleged meanings of a few words or 'concepts'! Indeed, Engels's claims about motion are all the more impressive when it is recalled that he hit upon them in abeyance of any supportive evidence -- let alone a significant body of it. As it turns out (and this will also be demonstrated below), even had any been available to him (or is now extant), evidence would have been unnecessary, anyway.

 

As we have already seen (in Essay Two), all that an aspiring dialectician like Engels needs to do in such circumstances is briefly 'reflect' on the supposed meaning of a few words or 'concepts', and substantive truths about fundamental aspects of nature, valid for all of space and time, spring instantly to mind.

 

Or, to be more honest, all they have to do is read Hegel's 'Logic' (or the work of some other mystic, such as Heraclitus). This a priori approach to 'knowledge' is the thread that runs through all of ruling-class thought, unfortunately imported into the workers' movement by incautious non-workers like Engels. [On this, see Essay Nine Parts One and Two, Twelve Part One and Fourteen Part Two.]

 

The only 'evidence' that supports Engels's interpretation of motion is this highly compressed (and as we will see in later sections, rather badly formulated) argument -- or rather, 'thought experiment' --, which is itself based on a consideration of what a few innocent-looking words or 'concepts' must mean. Pressed for a justification of this line of reasoning, all that Engels could possibly have offered by would have been a rather weak claim that this is what the word "motion" really means. Clearly, such an imagined, but plausible, rejoinder gives the game away, since it would reveal that substantive truths about motion had indeed been derived from the supposed meaning of certain words, and nothing more.

 

[The significance of that observation will emerge in Essay Twelve Part One.]

 

As noted above, an appeal to evidence would be irrelevant, anyway. That is because the examination of countless moving objects would fail to confirm Engels's assertion that they occupy two places at once. That would still be the case no matter what instruments or devices were employed to carry out these hypothetical observations, and regardless of the extent of the magnification used to that end -- or, indeed, the level of microscopic detail enlisted in support. No observation could confirm that a moving object is in two places at once (except in the senses noted below), in one of these and not in it at the same time. This, of course, explains why Engels offered no scientific evidence whatsoever in support of his belief in the contradictory nature of motion. And this picture hasn't altered in the intervening years -- indeed, no book or article on DM even so much as thinks to quote or cite such evidence --, and this situation isn't ever likely to change.5

 

It could be objected to this that if, say, a photograph were taken of a moving object, it would show by means of the recorded blur, perhaps, that such a body had occupied several places at once. In that case, therefore, there is, or could be, evidence in support of Engels's claims.

 

The problem with this is that no matter how fast the shutter speed, no camera (not even this one, or this) can record an instant in time, merely a temporal interval (that is, such devices record what happens in the time interval between opening and closing the shutter, or other light permitting aperture). Clearly, to verify the claim that a moving object occupies at least two places in the same instant, a physical recording of an instant would be required. Plainly, since instants (i.e., in the sense required) are mathematical fictions, it isn't possible to record them.

 

Update December 2016: The New Scientist recently reported this:

 

"For the first time, physicists have measured changes in an atom to the level of zeptoseconds, or trillionths of a billionth of a second -- the smallest division of time yet observed. In this case, the speed demon was an electron escaping the bonds of its parent atom when struck by a photon. This electron ejection is known as the photoelectric effect, and was described by Albert Einstein in 1905. Previous experiments could only measure what happened after the electron was kicked out, says Martin Schultze at the Max Planck Institute of Quantum Optics in Garching, Germany. Now, he and his colleagues have measured the ejection of electrons from a helium atom from start to finish with zeptosecond precision (10-21 seconds), marking the smallest time slot ever measured. To do this, they fired ultraviolet laser pulses lasting 100 to 200 attoseconds (10-18 seconds) at a helium atom to start exciting its pair of electrons. By making many readings and calculating their statistical spread the team could measure events with a resolution of 850 zeptoseconds. They found the ejections took 7 to 20 attoseconds (Nature Physics, doi.org/bszd). The results are an important window into the quantum behaviour of atoms, especially how their electrons interact with each other, says Schultze." [New Scientist, 19/11/2016, p.14. Paragraphs merged to save space.]

 

Not even this measurement captures an 'instant', but an interval.

 

It could be countered that as we increase a camera's shutter speed, photographs taken will always show some blurring. This supports the conclusion that moving objects are never located in one place at one time. Despite this, it still remains the case that no photograph can catch an instant, and thus none can verify Engels's contention.

 

Again, it could be argued that it is reasonable to conclude that moving objects occupy two locations at the same moment from the above. Once more, since an instant in time is a fiction, it isn't reasonable to conclude this. Not even a mathematical limiting process could capture such ghostly 'entities' in the physical world, whatever else it might appear to achieve in theory. But, even if it could, no camera (radar device, or other equipment) could record it. Hence, even if an appeal to a mathematical limiting process was viable (or available), it would be of no assistance. No experiment is capable of substantiating any of the conclusions Engels reached about moving bodies.

 

And that explains why he and those who accept these ideas have had to force this view of motion onto nature.

 

But, as we will see later, the idea that a moving object is in two places at once possesses fatal consequences of it own (for this theory), so DM-fans had better hope that no camera will ever be able to record this alleged fact.

 

Hence, this thesis about moving bodies hasn't emerged from a consideration of the facts, but has been imposed on them, in defiance of what Engels himself said:

 

"Finally, for me there could be no question of superimposing the laws of dialectics on nature but of discovering them in it and developing them from it." [Engels (1976), p.13. Bold emphasis added.]

 

"All three are developed by Hegel in his idealist fashion as mere laws of thought: the first, in the first part of his Logic, in the Doctrine of Being; the second fills the whole of the second and by far the most important part of his Logic, the Doctrine of Essence; finally the third figures as the fundamental law for the construction of the whole system. The mistake lies in the fact that these laws are foisted on nature and history as laws of thought, and not deduced from them. This is the source of the whole forced and often outrageous treatment; the universe, willy-nilly, is made out to be arranged in accordance with a system of thought which itself is only the product of a definite stage of evolution of human thought." [Engels (1954), p.62. Bold emphasis alone added.]

 

"We all agree that in every field of science, in natural and historical science, one must proceed from the given facts, in natural science therefore from the various material forms of motion of matter; that therefore in theoretical natural science too the interconnections are not to be built into the facts but to be discovered in them, and when discovered to be verified as far as possible by experiment.

 

"Just as little can it be a question of maintaining the dogmatic content of the Hegelian system as it was preached by the Berlin Hegelians of the older and younger line." [Ibid., p.47. Bold emphasis alone added.]

 

In which case, the following characterisation of Idealism clearly applies to Engels's 'analysis' of motion:

 

"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, this is precisely what Zeno and Hegel did, just as it accurately describes Engels's approach; they all "proceed[ed] from principles which are validated by appeal to abstract reason, intuition, self-evidence or some other subjective or purely theoretical source."

 

Of course, as noted above, part of the problem here is what the word "instant" means. [I am taking this term to mean the same as the phrase "moment in time", used by Engels.] So, it might be thought that this 'problem' could be solved by means of a suitable re-definition. However, even if this were possible, such an 'adjustment' would merely represent the adoption of a new linguistic convention, and would have no bearing at all on the 'nature of reality'. It would also further confirm the suspicion that this 'theory' had been imposed on nature, not 'read from it' -- for what else is the introduction of a new linguistic convention, adopted solely in order to make a theory 'fit the facts'?5a

 

As Trotsky argued:

 

"How should we really conceive the word 'moment'? If it is an infinitesimal interval of time, then a pound of sugar is subjected during the course of that 'moment' to inevitable changes. Or is the 'moment' a purely mathematical abstraction, that is, a zero of time? But everything exists in time; and existence itself is an uninterrupted process of transformation; time is consequently a fundamental element of existence. Thus the axiom 'A' is equal to 'A' signifies that a thing is equal to itself if it does not change, that is if it does not exist." [Trotsky (1971), p.64. Bold emphasis added.]

 

Unfortunately for Engels, if motion were to take place in one of these "moments", that would mean that it couldn't exist -– that is, not unless we are also prepared to reject the a priori conclusion Trotsky expressed in the above passage, too!

 

But, if motion actually takes place -- as it surely does -- then what are we to make of the claim that if something is moving it must be in at least two places in the same instant when (according to Trotsky) the latter don't exist? Does this refute Trotsky, or Engels? Or both? Is there even a straw-sized 'contradiction' here for dialecticians to "grasp" to save their drowning theory?

 

Furthermore, pointing out that some of the conclusions drawn above are rather abstract can't rescue Engels, either. His analysis of motion is no less abstract itself! Even worse: his account can't have been derived by abstraction from all (or any) of the forms of motion hitherto experienced either by himself or by humanity in general -- or even from a finite sub-set of them, observed by scientists or philosophers down the ages. That is because Engels's thesis clearly appeals to things that, according to Trotsky, don't exist -- such as "moments" in time. And, even if they did exist, we couldn't experience or observe them, and hence we couldn't use them to confirm what Engels said. As seems plain, observations take place in time, and have a duration; "instants" do not.

 

Worse still, it isn't possible to 'abstract' from such non-existent instants in order to agree with Engels, either.6

 

Whichever way we turn we hit yet another non-dialectical brick wall.

 

 

Motion 'Itself'

 

To be sure, Engels promptly changed direction (no pun intended) in the above passage, arguing that it is motion itself that is contradictory, not just our thoughts about it that are -- declaring that:

 

"Motion itself is a contradiction…." [Engels (1976), p.152. Emphasis added.]

 

In which case, it could be maintained that Engels was merely pointing out that our thoughts about motion are contradictory because motion itself is. That is, our theories depict the world more fully and truly when they reflect its contradictory nature, and that substantive claims about the universe are justified, indeed, objective, when our ideas capture changing reality more accurately (but, only if they have been tested in practice).

 

Unfortunately, if this response were correct, it would be inimical to DM, anyway, since that would mean DM itself contains contradictions, which would imply it is a contradictory theory.7

 

[The disastrous implications that particular conclusion has for DM are outlined in Essays Seven Part One and Eleven Part One.]

 

Despite this, such a reply would give the game away, since it conforms an earlier accusation that this view has been imposed on nature because there is no way that Engels could know, or have known, that nature is contradictory in its entirety, and thus that all motion in the entire universe, for all of time, is as he says it is. The very best that Engels could claim is that our thoughts about motion are contradictory, and that this suggests that motion in nature might be, too.

 

However, as will become apparent by the end of this Essay, the real problem with the above suggested fall-back position is that our thoughts about motion aren't the least bit contradictory, either!7a

 

Be this as it may, the above response fails anyway to neutralise the fatal consequences outlined earlier. That is because Engels's philosophical thesis, which was the result of an extrapolation from what he took to be the meaning of a handful of words or 'concepts' to fundamental aspects of reality, is openly Idealist (on this see Essays Two and Twelve Part One). Indeed, Engels himself pointed this out:

 

"The general results of the investigation of the world are obtained at the end of this investigation, hence are not principles, points of departure, but results, conclusions. To construct the latter in one's head, take them as the basis from which to start, and then reconstruct the world from them in one's head is ideology, an ideology which tainted every species of materialism hitherto existing.... As Dühring proceeds from "principles" instead of facts he is an ideologist, and can screen his being one only by formulating his propositions in such general and vacuous terms that they appear axiomatic, flat. Moreover, nothing can be concluded from them; one can only read something into them...." [Marx and Engels (1987), Volume 25, p.597. Italic emphases in the original; bold emphases added.]

 

Compare (again) the above comments with those of George Novack:

 

"A consistent materialism cannot 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.]

 

Worse still, and for reasons given above, not only can this 'theory' not be confirmed, its subject matter (i.e., the thesis that a moving body occupies and does not occupy the same place in the same moment, being in two places at once) resists all attempts to make sense of it, as we will soon see.

 

Substantive philosophical 'truths' like this (about motion, for example) are ambitiously universal in intent, but are thoroughly parochial in origin. Indeed, their promulgators' epistemologically imperialist intentions (which purport to stretch across all regions of space and time) remain stubbornly unmatched by any obvious capacity to satisfy such excessive philosophical ambitions with adequate material evidence --, or, in this case, any at all.

 

More to the point, how can this thesis be 'tested in practice'?

 

As we have seen, throughout history Traditional Theorists -- like Engels, and more particularly, Hegel -- have privileged speculation ahead even of a perfunctory search for supporting evidence. Indeed, they assume that all of nature must be as their 'surgically-enhanced' words seem to depict it.

 

However, if this approach to Super-Truth were valid, it would mean that the universe is possessed of these features simply because of certain idiosyncrasies of Indo-European Grammar -- the language group in which most of this hyper-bold talk has been concocted.

 

 

(5) Explanation Or Re-Description?

 

The Problem Stated

 

Perhaps even worse still: It isn't easy to see how the 'contradictory' nature of motion could in any way explain it; nor is it easy to see how it could form part of a wider scientific account of anything at all. At best, this way of characterising motion simply re-describes it.

 

More specifically: it is difficult to see how one 'part' of this supposed 'contradiction' is capable of exercising a causal influence over any other 'part'; or indeed how one or both of these UOs (i.e., this "here" and this "not here") could actually make anything move.

 

[A more general objection to this way of seeing change has been posted here.]

 

[UO = Unity of Opposites.]

 

As Engels depicts things, both 'parts' of this UO appear to manifest themselves together; a body is "here" and "not here" all at once, as it were:

 

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

 

In that case, it looks like awkward questions concerning the proximate cause of motion (with the implied temporal concomitants these often motivate) can't be answered by anyone who accepts this way of depicting it. That is because the mere fact that a moving body is "here" doesn't appear to be capable of making it become "not here". There is no struggle going on between this "here" and this "not here", as we were told by the DM-classicists should be the case with all such 'dialectical contradictions'. Indeed, this alleged contradiction seems to lack any causal powers whatsoever, any capacity to make things happen. It isn't so much that the dialectical batteries have run down as it is that there don't appear to have been any supplied with the original item -- and there is no slot for them to fit into.

 

This probably explains why Engels didn't even attempt to construct a causal account of motion based on the contradiction he claims to have found there (and, as far as can be ascertained, no DM-theorist since has made any effort to fill in the gaps -- and that includes Graham Priest). But, even if a DM-causal account were provided (one day!), it isn't easy to see how these alleged contradictions could explain motion; after all, how does being "here" and "not here" (all at once) explain why anything actually moves? What work do such contradictions do -- even if you believe in them?

 

It could be objected that this radically misconstrues DM, for the counter-argument presented above misleadingly splits the assumed 'parts' of a contradiction from one another when DM itself requires contradictions to be constituted by (or to be based upon) interpenetrated opposites. A dialectical contradiction is a relation, not a thing. Moreover, and contrary to the above, DM doesn't depict motion or change in such mechanical, causal terms. Dialecticians' various discussions of causation are specifically aimed at countering mechanistic and reductionist accounts like this.

 

Or, so a response might go.

 

However, even if this reply were acceptable, no attempt was made in Engels's work -- and, to my knowledge, none has been made anywhere else -- to explain how contradictions can have any effect on anything at all, anywhere, anyhow, and in whatever preferred causal or mediational/dialectical language they are expressed -- that is, other than perhaps figuratively. [There is more on this in Essay Eight Parts One and Two.] And, this is quite apart from the fact that this alleged contradiction (in motion) doesn't appear to be relational at all. What precisely is being related to what? What "relation" is this particular example meant to picture or reflect? Is a body related to itself as it moves? But, even if it were, how would that make it move?

 

[One of the best 'dialectical' attempts that I have so far seen (and written by a Marxist Dialectician) to explain the rationale behind this view of motion and change has been taken apart here. In Note 18a, I am in process of doing something similar -- but on a smaller scale -- to the best account (found in Graham Priest's work), which might not actually be a 'dialectical-account', after all.]

 

Of course, it could be argued that it is the relation between bodies and processes that makes objects move and change; that response will be examined below, and in more detail in Essay Eight Part Two, as will the idea that contradictions can be accounted for in terms of "opposing forces".

 

Moreover, it is far from easy to see how a contradiction could exercise any sort of effect on anything at all unless it was translated into, or was expressed somehow in, physical or material terms (that will be attempted below). At some point, bits of matter are going to have to be moved about the place. Now, this physically inconsequential word ("contradiction") doesn't seem to have the required presence -- the necessary oomph, as it were -- that might conceivably enable it to carry out such menial tasks.8

 

[HM = Historical Materialism.]

 

Furthermore, if the volunteered DM-response above were correct (but see below), contradictions wouldn't be of much help in explaining social change, let alone changes in nature. If no causal role is assignable to contradictions in DM (with respect to motion, or, indeed, with respect to anything at all), then they certainly can't serve in such a capacity in HM. The alleged contradictions in Capitalism, for example, wouldn't, therefore, make anything actually happen; they would, at best, be the result of other things happening (for which DM-theorists would now have no explanation, since these 'other things' wouldn't themselves have been caused by contradictions), or they would be the result of certain specific social relations.

 

The cause or causes of social development would be totally obscure (given this (assumed) rejection of any causal role for contradictions). In that case, we are forced to conclude that if there are any contradictions in reality, they must play some sort of causal role, at some level, in some form, otherwise dialecticians wouldn't be able to explain why anything actually happened in nature and society.

 

[Of course, that might be the real reason why dialecticians can't actually do this; but they certainly don't see things this way, to state the obvious.]

 

Conversely, this could mean that if the development of class society is still to be accounted for in terms of the supposed contradiction between the forces and relations of production -- or even between opposing classes -- contradictions could be dispensed with at no loss to HM, since (given the above response) contradictions would do no work in HM, too -- playing no causal role there. In that case, the sooner they are pensioned-off the better. Attention could then be focussed on the genuinely causal nature of the above relations -- suitably phrased in historical and materialist terms. Naturally, this would involve a radical re-write of HM, abandoning much of the traditional, Hermetically-inspired jargon, which has up until now only succeeded in suffocating Marxist theory.

 

If so, this means that dialecticians need to specify -- as a matter of some urgency, I would suggest -- what, if anything, is so causal about the contradictions they seem to see everywhere, so that the latter can at least do some genuine work in HM. At present they don't appear to be part of the action; at best, they look merely decorative.

 

On the other hand, the assignment of a causal role to contradictions in HM or DM -- so that they cease to be merely ornamental -- would generate insuperable difficulties for both theories, as we are about to see.

 

 

Are Contradictions Causes?

 

As hinted above, even if it were possible to assign some sort of causal role to contradictions (albeit expressed in suitably acceptable 'dialectical language'), it would still fail to help DM-theorists account for motion. That is because (according to Engels) motion allegedly involves a body being in one place and not in it, all the while being in two places at one and the same 'instant', or 'moment'. The problem is: How does this actually explain motion causally -- or, indeed, in any other sense? What exactly does it add to a scientific account of the same phenomenon? All it appears to offer is a paradoxically-worded re-description.

 

In order to make the last point clearer, it is worth pondering once again the possible answer(s) to the following questions: (a) Do contradictions cause motion (i.e., do they make it happen), or (b) Does motion merely reveal the presence of contradictions as it unfolds? On one reading of Engels's account, it looks like it is motion that causes (or creates) contradictions. Hence, according to this way of reading his exact words, something must be in motion first for it to bring about contradictory, simultaneous occupancy and non-occupancy of successive locations (while time advances no one micro-second). But, as we will soon see, this would mean that one or both of the following hypotheticals would have to be true:

 

(1) If there were no contradictions, movement could still take place.

 

(2) If movement ceased, contradictions would still remain.

 

Taking each in turn:

 

(1) The relevance of the first of these alternatives is underlined by the fact that unless motion was already underway, a contradiction couldn't be inferred.

 

At the very least, this option prompts a further question: Which came first -- the movement or the contradiction? One possible answer to this might be what lay behind Engels's comments that such contradictions could be "solved", and then "re-asserted", since, on that basis, it looks like motion causes contradictions, not the other way round.

 

Of course, it could be argued that these two (i.e., contradiction and motion) go hand-in-hand; so it no more makes sense to ask which came first, movement or contradictions than it would to ask: "Which came first, counting or numbers?"

 

But, as we will see later on in this Essay, there are (in fact) examples of motion (in the real world) where no 'contradiction' is implied, directly or indirectly. So, perhaps that is the case here, too?8a

 

(2) The second option above follows from the simple observation that a stationary body can also occupy two places at once, and it can be in one place and not in it at the same time. [Examples of both of these alternatives are given below.]

 

In that case, alternative (2) suggests that contradictions aren't a sufficient cause of motion, whereas (1) indicates they aren't even necessary.

 

Furthermore, and with respect to (1), once again: Engels himself appears to have reasoned from his understanding of what motion is to its contradictory implications. In that case, it looks as if there is no causal role for contradictions to play with respect to 'motion itself', at least, as far as Engels saw things -- that is, there seems to be no way that they could make anything move. At best, a noted above, they appear to be conceptually derivative, not causative; they depend on motion, not the other way round. Hence, as things now stand, it looks like bodies first of all move, and only then do contradictions emerge -- and even then this only applies to our depiction of motion.

 

If so, it might be correct to say that contradictions operate solely at the conceptual level -- they appear to have no part to play in the physical action, on the ground, as it were.

 

Given this 'modified view', it would seem that objects in the world just move, but they don't to do so because they become embroiled in literal contradictions.

 

[So, for example, moving bodies don't argue among themselves about the occupancy or non-occupancy of this or that particular "place" --, which would be the clear implication of the ordinary, literal use of the verb "to contradict". Nor do they become entangled in 'time-and-motion' wrangles about who or what was where, when, and why. Again, they would do this if literal contradictions (as opposed to a figurative, DM-extension to this word) were operative in such cases. (On this, see Note 1, and Essay Eight Parts One and Three.)]

 

In fact, given Engels's account of motion, it seems that it is we who derive these paradoxical conclusions in our attempt to depict something that just takes place (without any such fuss) in nature.

 

In other words, according to this interpretation of Engels's views, it looks like the 'fault' lies in us, not in objects and processes.

 

However, this way of depicting motion is clearly unacceptable to DM-theorists; they insist that we must begin with material reality (or our perception of it), and not simply with a description of it. From there, according to them, we must postulate only those contradictions that actually exist in nature and society -- based perhaps on their reflection in human thought, confirmed in practice. Clearly, human beings study motion and its attendant contradictions, using whatever conceptual resources they have to hand, which, unfortunately, might not always be up to the job.

 

Or, so a counter-claim might go.

 

But, even this response is no help. That is because there seems to be nothing in reality that thought could latch onto, or reflect -- and hence, nothing for anyone to abstract from, or to, and then test in practice -- that even remotely resembles the contradictions postulated by dialecticians.

 

[Why this is so occupies the last three quarters of this Essay -- as well as this one.]

 

In relation to Engels's account of motion, as will soon emerge, there is no clearly specifiable set of possibilities -- or even actualities -- in nature and society with which his description could conceivably correspond. In fact, his words turn out not to be a depiction of the physical world in any shape or form. That isn't because he got the details wrong, or because he failed to capture nature accurately enough --, nor yet because nature is too complicated for us to describe -- it is because his words fail to be a description to begin with. Hence, Engels's 'description' of motion isn't just empty, it isn't even a description!

 

Again, it could be objected that the analysis presented in this Essay is misguided since it compartmentalises reality, distorting the account of nature presented in DM.

 

In response, it is worth pointing out that we don't have to divide the 'parts' of a contradiction, one from another (or from other relevant aspects of reality), to make the above argument work.

 

If each and every contradiction postulated by dialecticians (whether derived from "really existing material forces", or not) is given a sufficiently complex, 'dialectical background' (interconnected within the Totality, required by the theory, verified in practice, etc., etc.), that still wouldn't amount to an explanation of the causal or "mediated" links that are required by this theory. Widening the domain (to the entire Totality if need be) can't suddenly provide an explanation of how the simultaneous presence and absence of an object in one and the same place (at the same time) could possibly make it move -- or even how it could account for motion in any way at all.

 

An appeal to forces here would be to no avail, either -- as will be demonstrated in detail in Essay Eight Part Two. Unless forces are anthropomorphised, they, too, can't account for movement and change in DM-terms, either. [That cryptic comment will also be explained in Essay Eight Parts One and Two.]

 

Furthermore, the alleged reflection of contradictions 'in the mind', which might be thought capable of providing the 'conceptual connection' that supposedly exists between a cause and its effects (or between various mediated items, objects, or processes in the Totality), can't create a genuine connection if there aren't any contradictions in reality for it to reflect. Contradictions must have some sort of material basis if they are to be reflected in thought; for materialists they can't just be conceptual. And yet, what material form do these contradictions take?

 

Unless some sort of sense can be given to the idea that contradictions are capable of connecting things in the required way -- in reality and not just 'in the mind' --, in order to provide grist for the DM-causal/mediational mill to grind away at, DM-style reflections would advance the explanation of motion not one micro-metre.

 

Even assuming it could be shown that contradictions do in fact represent a material relation between objects or processes -- and which have been abstracted from (or read into) the phenomena (in an as yet unspecified way!) -- they still couldn't account for motion. That is because this would simply amount to a re-description of the phenomena, once more. We still await the explanatory punch-line: how do contradictions make things move? What is the material point to this Hegelian myth?

 

If, though, it is now claimed that a causal (mediational) link of this sort between events must to be postulated (i.e., if it is just assumed to exist to make the theory work), then that would merely provide a conceptual link between the said events, once more -- and such it would remain until the physical details had been filled in. Without the latter, the contradictory nature of motion would remain at best a conceptual, and not yet a material aspect of reality.

 

[This conclusion should surprise no one who is aware of the Idealist, nay mystical, origin of the DM-use of the word "contradiction".]

 

If, on the other hand, it is claimed that the mere presence of the said conceptual connection indicates that these causal links must exist in reality -- that is, if the complex reflection theory of knowledge is assumed to be true (wherein the human mind actively acquires knowledge in practice etc.) --, then that would still fail to explain how contradictions could actually cause motion. Precisely how do contradictions succeed in moving things about the place? It would seem that here the dialectical spade isn't just turned, it snaps in two.

 

Clearly, the above difficulties will only be resolved at some point if a clear explanation is given as to how contradictions can make things move -– or, at least, until it is shown how and in what way the above objections are misguided.

 

However, as should now seem plain, the role that contradictions supposedly play in motion is hardly helped by an account that depicts them (i) As the product, not the cause of motion (implying they are derivative, at best), or (ii) As the result of human reflection on the nature of motion (suggesting they are merely conceptual, and are thus Ideal).

 

Hitherto, DM-theorists have been content merely to label certain states-of-affairs "contradictory" without (apparently) giving any thought to the lack of explanatory role this empty ceremony assumes in their theory. Why call anything "contradictory" (and claim so much for the use of this term) if no account can be given of how this explains how or why anything actually changes or moves?

 

 

'Internal Contradictions' And Motion

 

At this point, it could be argued that the above objections are all irrelevant since DM-theorists are committed to the thesis that motion and change are caused by internal contradictions; the above account seems to be obsessed with external causes.9

 

Unfortunately, in connection with motion, there don't appear to be any internal contradictions capable of impelling objects along. No one supposes (it is to be hoped!) that an internal contradiction works like some sort of metaphysical motor, humming away inside a moving object, powering it on its way!9a And there don't seem to be any 'struggles' taking place within moving bodies that impel them onward (perhaps in the way that a drunken brawl might make a train carriage wobble from side to side, only worse). And, this would still be the case even if it were true that all bodies are in fact UOs. No matter how intense this supposed internal battle becomes, a 'metaphysical boxing match' of this sort seems incapable of generating self-propulsion.

 

Lenin's "demand", therefore, looks rather empty (if this is what he meant):

 

"Dialectics requires an all-round consideration of relationships in their concrete development…. Dialectical logic demands that we go further…. [It] requires that an object should be taken in development, in 'self-movement' (as Hegel sometimes puts it)…." [Lenin (1921), p.93. Bold emphases added. This entire topic is examined in much greater detail in Essay Eight Parts One and Two.]

 

Furthermore, there don't appear to be any identifiable contradictions situated at the leading edge of a moving body 'dragging' it along, as it were, just as there seem to be none at the back 'pushing'.

 

Worse still: both of these scenarios (even if they were remotely plausible) would clearly involve the creation of kinetic energy out of thin air. Precisely which "internal contradictions", for example, keep a billiard ball moving?

 

In that case, with regard to individual bodies, motion can't be an example of change through "internal contradiction".

 

However, as we will see in Essay Eight Part One, part of the problem here is that DM-theorists equivocate between two meanings of the phrase "internal contradiction". Sometimes it refers to (i) A dialectico-logical "internal relation" between objects and processes; sometimes it (ii) Assumes a spatial connotation. So, an "internal contradiction" of the first sort could still exist between two spatially separated bodies (they would be 'logically' connected, or would 'mediate' and/or define one another); whereas examples of the second sort would occur inside a given body, process or system (which would 'contradict' one another merely by 'struggling' with each other). In which case, it is reasonably obvious that something could be spatially-internal to an object or system without it being logically-internal, just as something can be spatially-external while also being logically-internal.

 

As I have pointed out elsewhere (slightly edited):

 

The expressions "internal contradiction" and "internal relation" (or what they supposedly represent) clearly underpin the idea that there are, or can be, internal, 'inter-penetrated' opposites. We can perhaps illustrate what an internal opposite is by recalling what DM-theorists say about the relation between the two main classes under Capitalism, the Proletariat and the Bourgeoisie. It is quite clear that for DM-theorists the Bourgeoisie and the Proletariat presuppose, inter-define and condition one another; each provides the condition for the other's existence; without the one the other not only wouldn't, it couldn't exist. They are thus internally related, not externally or accidentally connected.

 

This is what dialecticians mean by "interpenetration"; they don't mean these factors spatially interpenetrate one another, but that the one cannot exist without the other, nor vice versa; the existence of the one logically implies the existence of the other, and vice versa. And this is where the presumed "contradiction" arises; Proletariat and Bourgeoisie are logically locked together, they cannot exist independently of one another. This means that they have diametrically opposed material interests which force them into unremitting class conflict. None of this is accidental or external; the interplay between capitalist and worker is both reciprocal and inter-dependent.

 

Plainly, an external relation doesn't possess these logical properties. Concerning any two items (i.e., objects and/or processes), if they are externally related, the one can exist without the other; they do not presuppose one another, nor do they inter-define one another.

 

But, as noted above, something can be (a) spatially-internal to an object or system without it being logically-internal, just as something can be (b) spatially-external while also being logically-internal.

 

[Indeed, something can be spatially-internal to an object or system and logically-internal to it, too, just as something can be spatially-external while also being logically-external, as well.]

 

Here is an example that might illustrate (a), above: an Amazonian tribe is logically-external to capitalism (since there seem to be no internal opposites in the capitalist system that condition that tribe and which are conditioned in return by it, or which define it and which it defines in return). Capitalism can live without Amazonian tribes, but it can't live without the Bourgeoisie and the Proletariat. Even so, this tribe would still be spatially-internal to the capitalist system in that it still exists in a Capitalist country, Brazil.

 

Alternatively, to illustrate (b): consider the relation between, say, tenants and their landlords. They presuppose and inter-define one another; each is the condition for the other's existence; so they are logically-internal to one another. However, no landlord lives inside his or her tenants, nor vice versa. In that case, landlords and tenants, while being logically-internal to each other are at the same time spatially-external to one another.

 

Of course, one could always say that landlords and tenants are spatially-internal to whatever social or economic system they happen to exist within, and that is the problem. As we will see (in Essay Eight Part One), this ambiguity lies behind the equivocation mentioned above: When we consider wider economic, social, or even physical systems, it turns out that there are in the end no such things as spatially-external opposites, and hence spatially-external contradictions! Indeed, it is even arguable that there are no logically-external opposites either!

 

Be this as it may, it could be replied that since locomotion and development in a system are the result of forces acting on bodies/processes, the contradictory nature of motion can easily be accounted for on the basis of a network of internal, systematically-opposed forces. This might therefore be an example of type-(ii) "internal contradictions". That would make the unit within which contradictions (and thus motion) occur the whole, not the part, which seems to be the assumption underlying the comments made in earlier paragraphs.

 

Naturally, that response would make a mockery of the claim that all objects change through self-development, or that they barrel along because they are self-motivated. Just as it would make a mockery of Lenin's contrast between a mechanical, 'external' account of movement and change, and a dialectical version of the same. Given this modified 'theory', no object would be self-motivated -- never mind what Lenin demanded -- it would be moved by forces internal to the system of which it is a part, but external to any object in that system.

 

"Dialectics requires an all-round consideration of relationships in their concrete development…. Dialectical logic demands that we go further…. [It] requires that an object should be taken in development, in 'self-movement' (as Hegel sometimes puts it)…." [Lenin (1921), p.93. Bold emphases added.]

 

"The identity of opposites...is the recognition...of the contradictory, mutually exclusive, opposite tendencies in all phenomena and processes of nature (including mind and society). The condition for the knowledge of all processes of the world in their 'self-movement,' in their spontaneous development, in their real life, is the knowledge of them as a unity of opposites. Development is the 'struggle' of opposites. The two basic (or two possible? Or two historically observable?) conceptions of development (evolution) are: development as decrease and increase, as repetition, and development as a unity of opposites (the division of a unity into mutually exclusive opposites and their reciprocal relation).

 

"In the first conception of motion, self-movement, its driving force, its source, its motive, remains in the shade (or this source is made external -- God, subject, etc.). In the second conception the chief attention is directed precisely to knowledge of the source of 'self'- movement.

 

"The first conception is lifeless, pale and dry. The second is living. The second alone furnishes the key to the 'self-movement' of everything existing; it alone furnishes the key to 'leaps,' to the 'break in continuity,' to the 'transformation into the opposite,' to the destruction of the old and the emergence of the new.

 

"The unity (coincidence, identity, equal action) of opposites is conditional, temporary, transitory, relative. The struggle of mutually exclusive opposites is absolute, just as development and motion are absolute...." [Lenin (1961), pp.357-58. Italic emphases in the original; bold emphases added. Quotation marks altered to conform with the conventions adopted at this site.]

 

Despite this, even if systematically-opposed forces could somehow be interpreted as contradictions -- or if they could at least be regarded as constituting them -- that would still fail to show how internal contradictions could explain motion (or, rather, how they could account for a change in motion), let alone how they could initiate it. Nor would it explain the contradictory nature of motion itself. At best, all this would do is appeal to the allegedly contradictory nature of the system of forces that supposedly produced, or changed, any motion in the system. The fact that a moving body appears to be in at least two places at once (and hence contradictory in itself while moving) is in no way connected to whatever allegedly initiated that motion, or with whatever now maintains it (if anything does) -- at least not obviously so. Certainly, dialecticians have yet to connect contradictory forces themselves with the alleged fact that moving bodies appear to be in two places at once, in and not in at least one of them at the same time. Nor is it easy to see how this might be done even on their behalf.

 

Hence, whether or not it is true that movement is caused, or 'mediated', by a disequilibrium within a system of incipient forces ('internal' or otherwise), that still wouldn't affect the alleged fact that once it is moving, a body appears to do contradictory things. Even given the truth of such an 'internalist', or even 'externalist', account of contradictions and forces (i.e., assuming both (i) and (ii) above are correct), the fact that a body is in two places at once is a consequence of this setup. But, the "in two places at once" (etc.) descriptor (or its physical correlate) doesn't also cause motion in addition to the forces at work in the system. Indeed, while forces might cause a change in motion, the alleged contradictory nature of the movement that results from this has no part to play in the action.

 

So, even if the 'internalist', or the 'externalist', picture were correct, Engels's analysis of motion would still amount to nothing more than a re-description of motion; it would remain the case that motion makes bodies do allegedly contradictory things, not the other way round. Hence, the 'contradiction' that Engels highlights is still derivative, not explanatory.

 

It is worth re-emphasising this point: even if opposing forces could explain contradictory motion (which thesis is demolished in Essay Eight Part Two, anyway), the nature of the connection between the supposedly contradictory nature of motion and the forces operating on moving bodies has still to be established. All that the addition of opposing forces has achieved is to account for the origin of one contradiction (motion) in terms of another (oppositional forces). The contradictory nature of motion itself is still locked in the descriptive mode -- it does no work. Whether or not forces can explain any changes in motion isn't being questioned here -- yet. Even supposing they could, the contradictions Engels supposedly saw in moving bodies remain descriptive. We are still owed an explanation as to why a moving body being "here and not here at the same time" and "in two places at once", accounts for its motion, as opposed to merely re-describing it.

 

Of course, on this view, change in motion would be causally related to forces, but this just divorces the latter from the contradictory behaviour of moving bodies (a point Engels himself seems to have conceded -- on that, see Note 10). So, even if it were the case that opposing forces caused motion (or changed it), this still would provide no useful role for the observation that motion is itself contradictory. As far as DM is concerned (that is, on the basis of one particular interpretation that appears to be inconsistent with what Engels himself said about forces -- again, see Note 10), what seems to be important here is the alleged fact that opposing forces are contradictory; the other notion (about the contradictory nature of motion) still appears to be redundant; it serves no obvious purpose, and plays no role in the action.10

 

[As will be argued at length in Essay Eight Part Two, the appeal to oppositional forces to explain contradictions (or contradictory totalities) is no less misguided. There, it will be argued in detail that not only is there no conceivable interpretation of opposing forces that could account for contradictions (in FL or DL), there is no viable literal or figurative way of depicting contradictions as opposing forces, nor vice versa.]

 

[DL = Dialectical Logic; FL = Formal Logic.]

 

Of course, even more revealing is the fact that in Classical Physics forces are supposed to change the motion of bodies; this means that the idea that something has to maintain movement (whether this is contradictory or not) depends on an obsolete Aristotelian theory of motion. If so, the fact that contradictions can't supply a causal explanation of motion is all to the good, for if the allegedly contradictory nature of motion caused and maintained movement, much of post-Aristotelian (i.e., Newtonian) mechanics would have to be binned.11

 

But, then again, if such 'contradictions' don't, or can't, explain motion (i.e., they don't change or initiate it), why make such a fuss about them?

 

Despite the above, it could be objected that this whole line-of-attack seriously misunderstands the nature and role of contradictions in dialectics. As John Rees pointed out:

 

"[These] are not simply intellectual tools but real material processes…. They are not…a substitute for the difficult empirical task of tracing the development of real contradictions, not a suprahistorical master key whose only advantage is to turn up when no real historical knowledge is available." [Rees (1998), pp.8-9.]

 

Hence, it could be argued that the problem with the above criticism is that it substitutes an abstract analysis for one that should focus on real material forces.

 

This objection is considered in detail elsewhere at this site (here, here, here, and here), where Rees's and other dialecticians' epistemological and methodological claims are examined at length alongside a consideration of the "real material contradictions", to which most DM-theorists appeal in order to illustrate their theory -- in tandem with the claim that dialecticians don't regard their theory as a "master key" that unlocks all of reality, when they clearly do. [On that, see Essay Two.]

 

The allegation will also be revived (here and here, but, more specifically here, here and here) that material contradictions can't account for change, since they are locked in the descriptive mode (and a radically confused descriptive mode, at that).

 

 

An Indistinct Note

 

However, one further possibility hasn't yet been examined (and this involves a topic that will dominate much of the rest of this Essay): What if it is entirely unclear what Engels was trying to say in the passage under consideration? Indeed, what if it could be shown that he was in fact saying nothing at all comprehensible?

 

In that case, it would be completely beside the point whether or not there are any genuine examples of "material contradictions" in nature (at least, not as Engels viewed them). Well, no more than there would be any point in Christians, for example, trying to locate the actual Trinity somewhere in outer space. The problem here lies not so much with the search itself (in that it might be too difficult, or would take too long), but with the nature and description of something that could conceivably be looked for. If we are given nothing comprehensible to search for, plainly, no search can begin.

 

[As noted in Essay Six, you can look, say, for your keys if you don't know where they are, but not if you do not know what they are.]

 

But, is there any substance to these claims?

 

The next few sections aim to show that there is -- and plenty more than enough.

 

 

Is Engels's Theory At All Comprehensible?

 

Minimum Requirement

 

Before an empirical investigation into the 'real' cause and nature of motion can begin, we need to be clear precisely what it is we are being asked to examine. As things turns out it isn't possible to determine what Engels was trying to say when he wrote the following about motion:

 

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

 

In order to substantiate the above allegation, several further ambiguities in Engels's account will need to be examined first.

 

 

An Initial Ambiguity

 

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." [Ibid., p.152.]

 

Here, he appears to be claiming two separate things that don't 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 then 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 is the exact opposite of 'not'". And yet, if the meaning of "not" is so plastic, 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 and ever-growing cabinet 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 it on the facts, something that Engels, at least, said he 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!

 

[We will return to the above problem later in order to see if there is some way to avoid its disastrous consequences.]

 

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 doesn't seem relevant. [Anyway, it, too, will be considered below, as will the motion of 'point masses'.]

 

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

 

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 countless examples of this everyday phenomenon, as I am sure the reader is well 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 or set theory. In the last case considered below, just such a translation will be given to substantiate that particular claim.]

 

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, and 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 -- won't in general be entered into here.

 

[After all, if such points don't exist in physical space, they can hardly be said to move. And even if they could, what on earth do they move into? Other points? In passing, it is worth adding that Graham Priest's otherwise sophisticated attempt to defend Hegel and Engels (in Priest (2006)) largely depends on (a) the use of such mathematical and metaphysical idealisations (i.e., mathematical points, planes, instants in time, etc.), and (b) the material world being a rather complex mathematical object of some sort -- which makes much of what he has to say of no relevance to their defence. Quite the reverse, in fact; it would make movement itself either impossible -- or far more paradoxical than even Hegel himself imagined -- as we will see later, for example, here and here.]

 

Turning to L2: this option 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". Despite this, 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. No one would think that NN was lying if she said she had a pencil in her pocket if the above were the case. 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!

 

What is more, this is still the case even when 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 an 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 in 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 expressed in language) as those that are in motion, then 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!

 

[Of course, it might prove possible to repair Engels's attempt to describe 'dialectical motion'; I will leave that for others to decide. However, given what we will soon discover about the language associated with this topic (especially when that language has been incorporated into a 'philosophical theory' about motion), scepticism is perhaps the best policy.]

 

At best, L3 depicts the necessary, but not a sufficient condition for motion. [But, as we will also see later, not even that is true.] If so, the alleged contradictory nature of L3 has nothing to do with any movement actually occurring since it would also apply to bodies at rest, which plainly share the same necessary conditions.

 

As already noted, 'paradoxes' like this arise from the ambiguities implicit in the language Engels himself used -- and, as it turns out, in the language he misused.

 

[This topic is discussed in greater detail below.]

 

Nevertheless, in the next few sections several attempts will be made to remove, 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.

 

 

First Attempt At Disambiguation

 

As was also demonstrated in Essay Six in relation to Trotsky's (and indirectly Hegel's) attempt to analyse the LOI, Engels's account of motion is far too vague and ambiguous to be of much use.11a

 

[LOI = Law of Identity.]

 

I now propose the following disambiguation of Engels's comments about motion in order to determine if there is any sense at all to be made of what he concluded about moving bodies:

 

L5: A moving body, B, involves a change of place such that:

 

L6: B is at (X1, Y1, Z1) at t1 and at (X2, Y2, Z2) at t1.

 

L7: (X1, Y1, Z1) isn't the same place as (X2, Y2, Z2).

 

[Where, (Xi, Yi, Zi) etc., represent coordinate triples, and ti is a temporal variable. These could, of course, be combined to yield (Xi, Yi, Zi, ti).]

 

This opening set looks more promising. However, it is worth noting that this clarity has only emerged because of the introduction of the phrase "change of place", in L5. Unfortunately, if this expression succeeds in bringing out what Engels meant it would suggest that change explains motion, not the other way round. Perhaps this minor difficulty can be circumvented; again, I will leave that for others to decide.

 

[Still others, of course, might wonder exactly how the word "change" could be explicated (given DM) without an appeal being made to a definition that involved the word "motion" (a definition, it is worth remembering, that has yet to be attempted by dialecticians -- Graham Priest excepted, of course). Naturally, the use of the latter term wouldn't alter the 'truth' of L5, but it would make it eminently circular.]

 

However, even if this 'niggle' were resolvable, the initial promise L5-L7 seemed to offer soon evaporates when it is remembered that they fail to rule out cases where an extended body might move at a later time, say t2, but not at t1. That is, B could still be stationary at t1, and in two different places at once (because it is an extended object), and at rest with respect to some inertial frame, with the subsequent motion taking place at t2, not at t1 -- as we saw above with that car.

 

The significance of this observation is easily lost, but it revolves around the fact that Engels's account is compatible with an object being stationary at t1, and it is no reply to be told that this object moved later, when we are still owed a 'dialectical' description of motion that captures its necessary and sufficient conditions, not a promissory note that the said object will move at some later time. Anyway, attempts to capture the necessary and sufficient conditions of the future predicted or hypothesised motion of this object will only attract the same criticism -- that is, if L5-L7 were replaced with propositions that simply changed the temporal variable to t2, no other adjustments having been being made. This is because in that case questions will only arise as to why this minor alteration is capable of turning L5-L7 into necessary and sufficient conditions when the use of t1 had failed to do this originally. L6-L8 below attempt to fix this glitch.

 

The problem, it seems, lies with L5, since it fails to connect the motion it mentions with the same instant recorded in L6 and L7. Hence, the following emendations need to be made, it would seem:

 

L8: A moving body, B, involves a change of place only at t1, such that:

 

L6: B is at (X1, Y1, Z1) at t1 and at (X2, Y2, Z2) at t1.

 

L7: (X1, Y1, Z1) isn't the same place as (X2, Y2, Z2).

 

Of course, the same caveats could be applied to later instants so that such a description captures the movement of the body in question along its entire trajectory. That would merely entail the use of "tk" in the place of "t1" in L8 and L6. This complication will be ignored here, since it doesn't seem to affect the points at issue.

 

Unfortunately, however, L6-L8 don't appear to imply a contradiction --, that is, not unless it is clear that B is no longer at (X1, Y1, Z1) at t1, since it is possible for a (stationary) body to be in two places at once. For example, few would regard it as a contradictory feature of reality that a cake, say, could be in a box and in a supermarket all at once (hence in two places at once), and stationary with respect to some inertial frame all the while.

 

On the other hand, if a die-hard dialectician could be found who thought that the above scenario was contradictory, they would need to explain to the rest of us exactly what this alleged contradiction amounted to, and how, in virtue of its being in two such places at once, for example, the cake involved was engaged in some sort of 'struggle', and with what it was 'struggling'! As we will see in Essay Seven Part Three, the dialectical classics inform us that objects turn into their opposites -- that is, they turn into whatever they are contradicted by, or with what they 'struggle'. In the above example, that would seem to involve this cake 'struggling' with and then turning into the building that housed it! Since no one in their left mind could reasonably be expected to believe this, cakes in supermarkets can't be regarded as in anyway contradicting the bricks and mortar that surround them. Anyone who still thinks this is advised to seek professional help.

 

Of course, it could be objected that since the first location (i.e., the tin) is itself located inside the second (i.e., the building), the above isn't at all what Engels meant. But, on the basis of which of Engels's words is this objection itself predicated? Engels didn't tell us what he meant by "place", so it isn't possible to rule out the above counter-example because of anything Engels himself said. Indeed, as we will see later, the word "place" is far more complex than Engels, Hegel, and even Zeno, acknowledged.

 

In order to rectify this minor glitch, we need to replace L6 with L9, as follows:

 

L8: A moving body, B, involves a change of place only at t1, such that:

 

L9: B is at (X1, Y1, Z1) at t1 and not at (X1, Y1, Z1) at t1, and B is at (X2, Y2, Z2) at t1.

 

L7: (X1, Y1, Z1) isn't the same place as (X2, Y2, Z2).

 

Now, this set (henceforth, "") certainly looks inconsistent. The question, though, is: Can all of its constituent sentences be false at once? Only if we can rule out that eventuality is it possible to construct a contradiction from all and only elements of .

 

[At this point it is worth recalling that a set S of sentences is inconsistent just in case not all of its elements can be true at once. But, a "contradiction" requires more than this. In the simplest case, the elements of a binary sub-set of sentences taken pair-wise from elements of S are contradictory just in case (1) Those elements are inconsistent and (2) They can't also be false together. In short, they can't both be true and they can't both be false. This salient fact is invariably overlooked by DM-theorists, which, naturally, leads them into confusing contradictions with inconsistencies or contraries -- and, in many cases, with a host of other unrelated things, too. (Any who object to the 'pedantry' here should read this, and then maybe think again.)]

 

The question is, therefore: Can all of the elements of be false at once? If they can, then it won't be possible to construct a contradiction from all and only elements of . I propose to resolve this question by considering each of 's constituent sentences in turn, but in reverse order:

 

(1) L9 would be false if at least one of its conjuncts was false. But, the first part of L9 ["B is at (X1, Y1, Z1)"] could be false in several ways: for example, if B is at (X3, Y3, Z3) at t1.

 

L9: B is at (X1, Y1, Z1) at t1 and not at (X1, Y1, Z1) at t1, and B is at (X2, Y2, Z2) at t1.

 

[In fact L9 is an inconsistent sentence anyway, and hence it is false (either that, or it isn't a proposition (which is what I would maintain, anyway)11b --, depending on which branch of the Philosophy of Logic one attends to). However, since DL is based on the claim that an inconsistent sentence, or pair of sentences, can be true, I have ignored this complication because it would beg the question.]

 

(2) L8 is linked to L9 by means of a "such that" phrase, so the truth or falsehood of L8 is sensitive to the truth or falsehood of L9. Hence, when L9 is false, L8 is, too.

 

L8: A moving body, B, involves a change of place only at t1, such that:

 

(3) L7 could be false if (X1, Y1, Z1) were the same place as (X2, Y2, Z2). This would make L9 false, as well.

 

L7: (X1, Y1, Z1) isn't the same place as (X2, Y2, Z2).

 

In which case, it looks like we can imagine situations in which, while not all of 's elements could be true at once, all could be false at once. This means that it isn't possible to construct a contradiction from all and only elements of .

 

Knowledgeable readers will no doubt have noticed the illegitimate way in which some of the schematic sentences of (and others) have been interpreted here to derive this spurious result. The reason for this ploy (and what its implications are) will be commented upon presently.

 

 

Second Attempt At Disambiguation

 

From this point on it will be assumed that the difficulties with Engels's account noted in the previous section (whether or not they are legitimate) 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.

 

However, one point needs underlining here: none of the strictures dialecticians impose on the LOI can be allowed to stand if L11 is to be of any use, otherwise we would lose the ability to talk about "the same body", "the same time" or "the same place". This would also affect the application of certain conventions governing the use of terms such as "same variable", "same meaning" and "same reference". Hence, if we are to depict the contradictory nature of motion successfully we are forced to accept as valid the application of the LOI to the use of the same words and the same variables ranging over temporal instants (but, as a rule of language, not a 'logical truth' -- why this distinction is important is explained in Essay Twelve Part One). Since protracted examples of motion (plainly!) take place over very extended time periods, we can't appeal to the 'relative stability of language' to fix the reference of these variables (or the reference of their ordinary language counterparts), if the LOI isn't applicable in all cases.

 

[FL = Formal Logic; MFL = Modern FL; LOI = Law of Identity.]

 

But, if the LOI is rejected then Engels's description would become irredeemably vague. Many of the 'spurious' objections rehearsed toward the end of the previous section (in relation to ) depend on ignoring some (or all of these conventions; as a result they were entirely illegitimate. Of course, that ploy was deliberately aimed at underlining this very point: the use of variables in FL is based on conventions that DM-theorists must themselves observe (in ordinary discourse, and in logic) if Engels's analysis of motion is to be rendered at least minimally comprehensible, but which conventions in turn undermine their own criticisms of the LOI! Naturally, it is a moot point which horn of this dilemma dialecticians will want to "grasp": (i) Accept Hegel's criticisms of the LOI and thus sink Engels's analysis of motion, or (ii) Accept Engels's account and reject Hegel's criticism of the LOI.

 

It could be objected that the above comments represent a caricature of the criticisms dialecticians make of the LOI. The relative stability of both material bodies and linguistic expressions permits talk about such things as the "same body", "same word", "same place", "same variable", "same moment", and so on. Moreover, dialecticians do not flatly deny or reject the LOI; they just claim that it is true only within certain limits. In addition, they hold that objects and processes in change possess "identity-in-difference".

 

These responses are considered in extensive detail in Essay Six; the 'relative stability argument', for example, was neutralised here, here, and here. 'Dialectical contradictions' themselves have been analysed in Note 1, as well as here and here.

 

Of course, hard-nosed dialecticians might choose to ignore MFL altogether. That is, of course, their right. But, as a consequence of that they would then find it rather difficult to say what Engels actually meant in the quoted passage above. [Anyway, that rather desperate ploy will be blocked later on in this Essay.]

 

Unfortunately, however, even as it stands, and despite the foregoing considerations (that is, if the contentious claims made above about the LOI and MFL are, indeed, misconceived, and were withdrawn as a result), L11 would still fail to be a logical contradiction, and that is because of several more annoying ambiguities.

 

In fact, this new batch of vagaries turns out to be far more intractable than the relatively minor quibbles considered so far.

 

 

A Fatal Ambiguity

 

This new set of equivocations revolves around the supposed reference of the "t" variable in L11:

 

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.

 

It is 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 are elements of 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 sets of nested sub-intervals themselves, which can be put into an isomorphism with suitably chosen intervals of real numbers; hence the 'scare' quotes around the word "instant" in L12. (Incidentally, t2 > t1 means that t2 is later than t1.)]

 

Clearly, the implication here is that the unanalysed variable "t" in L11 actually represents a time interval, T (as opposed to an instant in time) -- which fact was brought out in L12 -- during which the supposed movement takes place. Plainly, this would licence a finer-grained discrimination among T's sub-intervals (e.g., t1 and t2) during which this occurs.12

 

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.

 

[Some might want to argue that the above would in fact freeze motion, since it speaks about the body in question being "located" at a certain point. But, if it is located anywhere, it can't also be moving. That is the point Hegel and Engels wanted to make. This response will be dealt with in much of the rest of this Essay.]

 

Indeed, this is how motion is normally conceived, as change of place in time -- i.e., with time having advanced while it occurs.

 

[This mustn't be confused with what Graham Priest calls "The Orthodox Account Of Motion", classically represented in Russell (1937), pp.469-74 -- Priest (2006), pp.172-75.]

 

If this weren't 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 (as even Trotsky would have admitted, see below), or it would imply that, for parts of their trajectory, moving objects (no matter how low their speed) move with an infinite velocity! [This was pointed out earlier.]

 

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.

 

L12: For some b, during interval T, and for two 'instants', t1 and t2 [where both t1 and t2 are elements of 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.

 

And yet, how else are we to understand Engels's claim that a moving body is actually in two places at once? If that were so, 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. But, according to Trotsky, that sort of motion wouldn't exist, for it wouldn't have taken place in time.

 

Indeed, if this were so, we would lose the right to say that a moving 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 in this case.] Hence, by a suitable induction clause, and in relation to the entire trajectory of a body's motion, it wouldn't be possible to say that a moving body was at the beginning of its journey before it was at the end!

 

[The exact reasons for saying this will be given below, but the above conclusion depends on an argument presented here, which readers would be wise to consult first. Trotsky's 'worries' about 'instants' are examined again, below. The contrary idea that if a body is located at a point at an instant, it must be stationary, will also be examined below.]

 

Despite this, it might seem that this latest difficulty could be neutralised by means of a stipulation to the effect that whereas time isn't composed of an infinite series of embedded sub-intervals (or, rather, our depiction of it isn't) -- given by suitably defined nested sub-sets of real numbers --, location is.

 

[Once more, such a stipulation would have to reject Trotsky's strictures on events taking place only in time.]

 

This would further mean that while we may divide the space occupied by a body (as it moves along) as finely as we wish -- so that no matter to what extent we magnify a body's location, we would always be able to distinguish two contiguous (or proximate) points in its path that allow us to say that that body was in both of these places at the same time --, while we can do that with respect to location, we can't 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 variables (space) as much as we like, we can't do that with the other (time).

 

In fact, this is actually 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 inconsistent 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 in an equally fine-grained manner), but, plainly, it only achieves this by stipulating (without any justification) that the successful mapping of occupied places onto nested intervals of real numbers (to give them the required density and continuity) is denied of temporal intervals.

 

 

The Classical Response

 

Inconsistent Division

 

Continuing from the issues raised in the previous sub-section: there seem to be three distinct possibilities with respect to these two distinct variables (i.e., 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 aren't the only alternatives, but they seem to be the only ones 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. Hence, if we could specify a time at which an object is located at a point in space, 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 -- or it is what his argument implied.]

 

Nevertheless, it seemed equally clear to others that moving bodies can't be depicted in this way, and that motion must be an 'intrinsic' (or even an 'inherent' property) of moving bodies (that is, we can't 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 topic, or any other)! It is also argued for in Priest (2006).]

 

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

 

(2) Infinite divisibility is true of location only.

 

However, it is worth pointing out that the paradoxical conclusions classically associated with these three alternatives only arise if other, less well appreciated (but often implicit) 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 supposedly 'real' meaning of words like "motion" and "place".

 

In Essays Three Part One and Twelve Part One, it was shown that philosophical 'problems' like this arise when ordinary words are twisted beyond recognition (which criticism, incidentally, was endorsed by Marx), or they are employed in contexts far removed from their ordinary use, and the new conventions or rules for the use of such terms (that emerge as a result) are then mis-interpreted as super-empirical truths, and not as (what they are) misconstrued conventions or rules.

 

[The justification for these seemingly dogmatic assertions can't be entered into in this Essay; I have discussed this topic in extensive detail in Essay Twelve Part One -- link above.]

 

In short, the 'classical' approach to this 'problem' only gets off the ground if linguistic conventions (or rules) are mistakenly interpreted as Super-Scientific, mega-empirical propositions, which reflect, or represent, 'industrial strength' facts.

 

Hence, this approach mistakes what amounts to an implicit decision to use words in novel ways as a reflection of fundamental truths about reality itself. It misconstrues the medium for the message.

 

Indeed, this is precisely how theorists (in Ancient Greece) began to misread and misconstrue the products of social relations (i.e., the aforementioned conventions and rules) as if they were, or expressed, the real relations between things, or even were those things themselves, thus fetishising language. Because of this, they imagined they could 'derive' Super-theses like these from the 'philosophical' jargon they had invented for that very purpose --, as the late Professor Havelock pointed out:

 

"As long as preserved communication remained oral, the environment could be described or explained only in the guise of stories which represent it as the work of agents: that is gods. Hesiod takes the step of trying to unify those stories into one great story, which becomes a cosmic theogony. A great series of matings and births of gods is narrated to symbolise the present experience of the sky, earth, seas, mountains, storms, rivers, and stars. His poem is the first attempt we have in a style in which the resources of documentation have begun to intrude upon the manner of an acoustic composition. But his account is still a narrative of events, of 'beginnings,' that is, 'births,' as his critics the Presocratics were to put it. From the standpoint of a sophisticated philosophical language, such as was available to Aristotle, what was lacking was a set of commonplace but abstract terms which by their interrelations could describe the physical world conceptually; terms such as space, void, matter, body, element, motion, immobility, change, permanence, substratum, quantity, quality, dimension, unit, and the like. Aside altogether from the coinage of abstract nouns, the conceptual task also required the elimination of verbs of doing and acting and happening, one may even say, of living and dying, in favour of a syntax which states permanent relationships between conceptual terms systematically. For this purpose the required linguistic mechanism was furnished by the timeless present of the verb to be --  the copula of analytic statement.

 

"The history of early philosophy is usually written under the assumption that this kind of vocabulary was already available to the first Greek thinkers. The evidence of their own language is that it was not. They had to initiate the process of inventing it....

 

"Nevertheless, the Presocratics could not invent such language by an act of novel creation. They had to begin with what was available, namely, the vocabulary and syntax of orally memorised speech, in particular the language of Homer and Hesiod. What they proceeded to do was to take the language of the mythos and manipulate it, forcing its terms into fresh syntactical relationships which had the constant effect of stretching and extending their application, giving them a cosmic rather than a particular reference." [Havelock (1983), pp.13-14, 21. Bold emphases added; quotation marks altered to conform with the conventions adopted at this site. Spelling modified to agree with UK English. Links added.]

 

As a result of this ideologically-motivated 'wrong turn' (on this, see below, and here), Traditional Philosophers reasoned that the word "motion", for example, implied some sort of 'problem', 'contradiction', or 'paradox', which needed to be resolved. Of course, they imagined they were talking about 'motion itself' and not the words we use to talk about it -- or, indeed, about what these words supposedly 'reflected' --, but as we will see, since they concentrated their attention on a limited and unrepresentative selection of terms associated with this phenomenon (which they also misconstrued), what they had to say about motion in the end depended on this misconstrual and on this limited choice of examples. Indeed, few, if any, questioned the original distortion or fetishisation that had been inflicted on ordinary words for movement, location, and change --, but which linguistic deformation had artificially created these 'philosophical problems'. As Keith Thomas pointed out in relation to 16th century magicians:

 

"It would be tempting to explain the long survival of magical practices by pointing out that they helped provide many professional wizards with a respectable livelihood. The example of the legal profession is a reminder that it is always possible for a substantial social group to support itself by proffering solutions to problems which they themselves have helped to manufacture." [Thomas (1972), p.295. Bold emphasis added.]

 

The same could be said, but perhaps with even more justification, about the 'philosophical problems' invented by Traditional Philosophers.

 

That is because these thinkers came from those sections of society that were divorced from the world of collective labour and communal life, but whose theories reflected the Ideal view of reality that this privileged life-style encouraged. This view of the world also born out of an ideologically-motivated denigration of the vernacular. [Again, these allegations will be fully-documented in Essay Twelve (summary here).] So, in the view these 'thinkers', if the world is ultimately Ideal, it would be quite 'safe' to infer Super-Scientific truths about it from language alone -- as we saw George Novack point out earlier.

 

The fact that the classical 'paradox' of motion is based solely on a set of initial (surreptitious and, as it turns out, illegitimate and unacknowledged) false linguistic moves like this is confirmed by the further fact that the acceptance or rejection of one or more of the three options listed above (repeated below) can't be (and has never been) based on evidence of any sort. Severally or collectively, each of these alternatives is founded on linguistic conventions overtly or covertly accepted by all parties to this metaphysical con-trick, conventions that appeal to what is supposed to be the 'real' meaning of the word "motion" -- or, indeed, the 'real' meaning of any of the other terms associated with it (such as "place", "same", "time" and "instant") -- to derive paradoxical or 'contradictory' conclusions.

 

Moreover, the choice of one or more of options (1) to (3) (as a way motivating any particular, favoured 'solution' to this artificially-created 'problem') also depends on the adoption of one or other of two further ideas:

 

(A) Even if the specification of the location of a moving body is in no way problematic (in that we can always and uncontroversially declare that a moving body is in two places at once), the specification of the time or times when this occurs is. So, while time can be partitioned as much as we like, location can't.

 

(B) Even if the specification of the temporal history of a moving body is in no way problematic (in that we can always and uncontroversially track a moving body and declare it to be wherever it is a particular 'moment'), the specification of its location in such moments is -- in that it is both "here and not here" at some specific time. So, while location can be divided as much as we like, time can't.

 

As far as option (A) is concerned, the identification of point instants in time is the 'problem', while the specification of points in space hardly raises a eyebrow. The obverse provides the rationale for option (B).

 

With respect to DM, we can see the tension between these two approaches to this 'problem' from the way that Trotsky, for example, failed to draw the same conclusions about locations in space that he drew about 'instants' in time. After all, how is it possible to declare that an instant in time is an abstraction, which can't actually exist, but fail to say the same about 'locations'? It can't be that objects have to be somewhere in order to exist, since they also have to be wherever they are at some time, too.12a  If, according to Trotsky, instants in time don't exist (since they are mathematical fictions), how is it possible for points in space (that is mathematical points in space) to exist? If the one can't exist, how can the other?

 

Moreover, mathematical points are problematic in other respects, too: they aren't circular, or do they have any other shape -- otherwise they would have parts and hence wouldn't be mathematical points. They thus have no radius or circumference, and so they can't be 'occupied' by moving bodies -- plainly, they aren't containers or they wouldn't be points, once more. But, which DM-theorist has ever expressed a single reservation about these obvious facts? Of course, in modern Mathematics and Physics, these issues are handled differently, where the functional relation between space and time (with respect to moving bodies) is expressed differently (in the Calculus, for example); but this can't help us resolve this 'problem'. That is because (i) It has directly arisen out of linguistic confusion, and (ii) Mathematics isn't a description of the world; if it were then nature would be Mind. [Why that is so will be explained in Essay Twelve. I return to this topic again, below.]

 

Be this as it may, it seems reasonably clear that DM-theorists have in general adopted alternative (B):

 

(B) Even if the specification of the temporal history of a moving body is in no way problematic (in that we can always and uncontroversially track a moving body and declare it to be wherever it is a particular 'moment'), the specification of its location in such moments is -- in that it is both "here and not here" at some specific time. So, while location can be divided as much as we like, time can't.

 

(1) Both time and place are infinitely divisible.

 

(2) Infinite divisibility is true of location only.

 

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

 

Nevertheless, (1)-(3) appear to be among the fundamental issues that have exercised Traditional Philosophers for millennia -- and now dialecticians. In their case, however, the preferred 'solution' appears to rule out the possibility of a moving object being in two contiguous places at two different times. This means, therefore, that DM-theorists have implicitly opted for alternative (2):

 

(2) Infinite divisibility is true of location only.

 

[With the word "indefinite" perhaps replacing "infinite", here.]

 

As has already been noted, this choice was motivated by a surreptitious exclusion: the indefinite division of time is ruled out, while that of location isn't.13

 

Finally, but more importantly, the 'solutions' on offer in Traditional Metaphysics (over the last two millennia) are similarly based on the rejection of at least one implication of the ordinary understanding of motion, which is that moving bodies occupy different places at different times. This is such a mundane connotation of our everyday grasp of certain kinds of motion that it seldom features in classical discussions, except perhaps where it is rejected out-of-hand as far too 'crude' to be worthy of consideration. [Or it is conflated with the 'Orthodox Account', mentioned earlier.]

 

However, as we shall soon see (indeed, as we will in several other Essays posted at this site), the protocols of ordinary language and common understanding aren't so easily ignored, dismissed, depreciated, or waved aside.

 

 

Back To The Drawing-Board

 

The Devil In The Detail

 

However, there are (and can be) no (a priori) empirical constraints on the length of time intervals. In fact, as was noted above, Engels's account of motion was not (and could not have been) derived from observation or experiment -- mediated or not via the naïve or the sophisticated version of the RTK. Nor could his idea of 'motion in general' -- nor, indeed, any conception of 'abstract motion' -- have been materially-grounded, either.

 

[RTK = Reflection Theory of Knowledge.]

 

That is because human beings -- aided or not by the use of microscopes, computers, cameras or lasers -- do not possess powers of discrimination sufficiently fine-grained to allow the study of movement in the detail required, so that 'reflection' (or 'abstraction') could be presented with anything useable to work with, or upon, in order to decide what does or does not happen to moving bodies in an 'instant'. Nor do the machines or devices we employ.

 

And, it is little use objecting that this or that 'must' be true of 'motion itself', for that would be to concede that a 'must' like this had been derived from the assumed 'real' meaning of a few words, the import of which, as we will soon see, is far less straight-forward than Traditional Theorists would have us believe.

 

It could be argued that the classical analysis of motion follows deductively from certain incontestable premises. There are only a handful of possibilities that the world could conceivably present to us; Engels's analysis, via Hegel, is based on one of these. So, what's the problem?

 

Once more, the problem is that the deducibility or otherwise of these conclusions also depends on the use of a handful of words the meanings of which have been artificially modified, construed or constrained -- such as "place", "move", "time", and "moment". These words have either been idiosyncratically, or narrowly, (re-)defined, or they have had their meanings (implicitly) altered in other ways. In that case, nothing reliable can follow from thee use (as I hope to show later in this Essay). This was, of course, the point Marx was trying to make.

 

Once again, as George Novack argued:

 

"A consistent materialism cannot 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 what the above proffered response achieves: it seeks to derive what seem to be substantive conclusions about fundamental aspects of the world from "abstract reason, intuition, self-evidence or some other subjective or purely theoretical source".

 

Even worse, not only does nothing legitimately follow from such distorted language, it is impossible to give a clear sense (or any sense) to the classical account of motion (nor, indeed, to more modern versions that depend upon the same defective tradition). In fact, as will be demonstrated in Essay Twelve Part One, all such accounts are non-sensical and incoherent; they not only fail to say anything comprehensible about the world, they can't.

 

In that case, if humanity does in fact possess an 'abstract' idea of motion (but even this will be contested below, and in other Essays posted at this site), it can't have been derived from 'reflection', nor could it have been based on anything ascertainable from the material world. And these observations become all the more apposite if it turns out that this 'abstract' and traditional idea of motion itself originated from (a) The inequitable constraint mentioned above -- i.e., that which was arbitrarily imposed on temporal intervals, but excused of point locations in space --, for no good reason; and (b) A ruling-class view of reality.

 

In short, Engels's theory wasn't based on reflection (howsoever this 'process' is understood), or on evidence, or even on 'abstraction', but only on 'concepts' that were themselves the product of traditional, or classical, stipulations and covert conventions -- which were then imposed on reality inequitably.

 

I would be tempted say you just can't make this stuff up, but obviously someone did!

 

 

Space To Let

 

Returning now to re-examine several earlier options; consider L11 and L12:

 

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.

 

L12: For some b, during interval T, and for two 'instants' t1 and t2 [where t1 and t2 belong to T, 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.

 

(2) Infinite divisibility is true of location only.

 

[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…]

 

However, if for some reason L12 were to be rejected as an alternative interpretation of L11 (that is, if the idea that time is continuous and indefinitely divisible is flatly denied (even while this condition is asymmetrically allowed of space) -- i.e., if Option (2) above is simply imposed on the phenomena) --, then there would seem to be no consistent way of ruling out the following as yet another possible reading:

 

L13: For some b, for just one instant t, for three places p1, p2 and p3, b is at p1 at t, but not at p2 at t, and b is at p3 at t (where p2 and p3 are proper parts of p1).

 

Here, a finer-grained discrimination of position (but not of time) means that L13 isn't contradictory after all; that is because a body can be in two places at once whether or not it moves (as we saw earlier), with no implication that it both is and isn't in any one of them.14

 

Translated, L13 could be read as follows:

 

L13a: A stationary body b, observed over the course of an instant, is at (X1, Y1, Z1) and (X3, Y3, Z3), but not at (X2, Y2, Z2), where (X3, Y3, Z3) and (X2, Y2, Z2) are both located inside (X1, Y1, Z1).

 

L13b: A moving body b, observed over the course of an instant, is at (X1, Y1, Z1) and (X3, Y3, Z3), but not at (X2, Y2, Z2), where (X3, Y3, Z3) and (X2, Y2, Z2) are both located inside (X1, Y1, Z1).14a

 

[An obvious objection to the above is neutralised in Note 14a (link above).]

 

In which case, this alternative fails to discriminate between moving and stationary bodies.

 

An everyday example of L13 might involve a case where a ship, say, enters port; here the ship could be in the water and in the port at the same time (and hence extended across several locations, and thus for it to be in at least two places at once), and be moving, but with no implication that it is entirely in any one of them at one and the same instant, or that it is fully occupying any specific part at any moment, nor yet occupying every point in this finite region (so that it need not be in other areas of that port, for example, at that time). In the latter case, while it is still inside the said port it wouldn't be in, say, the dry dock (which is also part of that port), nor in the staff canteen, or in a host of other places in that port, at that time.

 

Moreover, the same possibilities would still apply if the ship were stationary with respect to some inertial frame. Here, this ship could be in one place and not (fully) in it, in two or more places at once and stationary (or moving), without this implying a contradiction. Plainly, that is because this particular example employs a finer-grained division of place to compensate for the arbitrary imposition of the opposite convention on time.

 

In that case, the alleged contradiction vanishes once again.

 

[Any who object to my use of "not (fully) in" here in place of "in" should read this, and then maybe think again. I have given a more technical version of this scenario in Note 15.]15

 

As pointed out above, L12 and L13 may only be successfully rejected by an ad hoc stipulation to the effect that while spatial location can be divided indefinitely, time may not.

 

But, even then we have just seen that Engels's claims still don't work!

 

In which case, of course, the allegedly contradictory nature of motion is at best an artefact of convention -- which only works by constraining the divisibility of time but not of place --; hence it isn't based on 'genuine features of reality'.16

 

In fact, it is the product of a confused use of abstract, philosophical jargon.

 

Again, it could be objected that no matter how much we partition time, no moving body can be located at a certain point (i.e., at one point, and one point only) at that time, otherwise it would be stationary.

 

It is to this core idea that I now turn.

 

 

Further Problems

 

The Background To Engels's Argument?

 

It could be objected to all this that while it might not be possible to express the contradictory nature of motion in ordinary (or even technical) language,17 motion in the real world must nevertheless be contradictory.18 This might involve the acceptance of one or more of the following (but so far suppressed) assumptions:

 

L14: An object can't be in motion and at rest at one and the same time (in the same inertial frame).

 

L15: If an object is located at a point it must be at rest at that point.18a, 18b

 

L16: Hence, a moving body can't be located at a point, otherwise it wouldn't be moving, but would be at rest.18b1

 

L17: Consequently, given L14, a moving body must both occupy and not occupy a point at one and the same instant.

 

In which case, it could be argued that L14-L16 (or their 'dialectical' equivalent) capture the rationale behind Engels's analysis of motion.

 

Indeed, if this weren't so, it would suggest that motion was either (a) impossible or (b) illusory --, or even (c) that it was a sort of 'stop-go' affair.18c

 

As far as (c) is concerned, motion would be analogous to the way it is depicted in film. Here, motion on the screen only appears to be continuous when it is in fact discontinuous, being composed of rapidly sequenced 'freeze frames', as it were. When played at a certain speed, this 'fools' the human eye into 'seeing' continuous movement. Given this 'quasi-static' view of motion, a 'moving' body (in the real world, not on film!) would occupy a point and be stationary at that point, and then occupy another point an instant later, and be stationary there too, and so on. Naturally, what the said object gets up to in between such locations at such times would be, on this view, somewhat mysterious. But, on its own, that wouldn't be enough to make this picture of motion false, no more than certain quantum 'leaps' (which are discontinuous in this way) now invalidate QM -- that is, given the way that motion is depicted in Traditional Philosophy.19

 

[QM = Quantum Mechanics.]

 

[Options (a) and (b) above are obviously absurd and won't be considered any further in this Essay -- although much that will be argued later will indirectly reveal why they are absurd.]

 

In order to reject this 'quasi-static' view (i.e., option (c)), consideration might be given to one or more of the following (each defined in relation to a suitable inertial frame, as necessary -- I'm not suggesting that dialecticians have argued this way, but what follows could underpin some of the assumptions and conclusions to which they might assent, even if only after having read them here for the very first time!):

 

L18: If a body is located at a point it is at rest.

 

L19: If that body subsequently occupies another point, it must be at rest there, too.

 

L20: Hence, on this view (i.e., according to (c) above), motion is little more than successive point occupancy. This means that locomotion must be composed either of: (i) Successive states of instantaneous rest, or (ii) The sequential existence and non-existence of what only seem to be identical -- but which are in fact numerically different -- bodies at each of the said points, with that body falling into non-existence at the end of each instance of location or rest, followed by the subsequent entry into existence of a new, but seemingly identical body, at the next moment, at the new point, giving only the impression of motion.

 

[Option (ii) would resemble the way that neon lights in a complex sign, say, can be turned on and off in sequence to create the illusion of motion. It seems that for a while at least Leibniz held a version of this theory.]

 

L21: L20(i) involves a body in discontinuous motion separated by periods of instantaneous rest. L20(ii) involves a body, or series of bodies, in discontinuous existence at contiguous locations.

 

L22: L20(ii) must be rejected as absurd.

 

L23: If L20(ii) is rejected then L20(i) implies that in between each successive point occupancy a body must pass through an indefinite (possibly infinite) number of intervening locations.

 

[Of course, L23 depends on the further assumption that there is an infinite, or a potentially infinite, number of points between any two points.]

 

L24: Hence, even on the assumption that motion is discontinuous, there will still be an indefinite number of such intermediate points that a moving object has to occupy while it is passing between the points at which it is said to be at rest in consecutive instants, but which intermediate locations the body must both occupy and leave at one and the same instant. In that case, that body can't be at rest in any of these intermediate points.

 

L25: Consequently, if motion takes place -- and it is either continuous or discontinuous -- a moving body must both be located and not be located in a given place at one and the same time, namely at these intermediate points, at the very least.

 

L26: Therefore, the assumption that a body is in motion only if it occupies and is at rest in successive locations at contiguous instants is false -- for even on that assumption, a body must violate this condition for an indefinite number of intermediate points between each successive instance of 'rest', at successive instants.

 

L27: Therefore, either motion is impossible or illusory (which is absurd), or motion can't be wholly discontinuous.

 

[It is possible to strengthen L27 by means of L27a, but that option won't be pursued further here:

 

L27a: Therefore, either motion is impossible or illusory (which is absurd), or motion can't be discontinuous.]19a

 

 

Pick Your 'Contradiction'

 

However, it is worth noting that the above argument begins with the rejection of an apparent contradiction -- expressed in L14 (restated here for ease of reference, but re-numbered L28, and hence very slightly altered) alongside its supposed contradictory, L29:

 

L28: A body can't be at rest and in motion at the same time in the same inertial frame.

 

L29: A body can be at rest and in motion at the same time in the same inertial frame.

 

Naturally, that depends on whether these are genuine contradictories; I will ignore this minor complication in what follows. On the other hand, if they aren't even propositions, then they can't be contradictories to begin with.

 

Nevertheless, I will assume they are propositions for the purposes of this argument; however, their status as propositions will be questioned in Essay Twelve Part One.20

 

If these 'niggles' are now ignored, then L29 is true if L28 is false, and vice versa.

 

As is well-known, an analogous series of background assumptions motivated Zeno into trying to 'prove' that motion was either impossible or illusory. DM-theorists clearly reject Zeno's conclusion, but it seems they can only do so by accepting L28 (or its equivalent), thus rejecting L29, in order to derive their own contradiction expressed in L17, which was:

 

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

 

Plainly, if L28 were false (and L29 true) -- which would mean that a body could be moving and at rest at the same time --, L17 might not look quite so compelling. At any rate, it is clear that dialecticians have to reject one 'contradiction' (expressed in L29) in order to derive their own (in L17).

 

L28: A body can't be at rest and in motion at the same time in the same inertial frame.

 

L29: A body can be at rest and in motion at the same time in the same inertial frame.

 

[It could be argued that the contradiction in L29 isn't dialectical. But, the 'contradiction' Engels and Hegel claimed to have found in motion isn't dialectical either. On that see Note 18a.]

 

Now, when L17 is conjoined with L28 we obtain the following:

 

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.

 

This seems to be the 'contradiction' that exercised Engels. If so, it is worth asking: Which of the following two 'contradictions' is it legitimate to accept or reject: L17 or L29?

 

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

 

L29: A body can be at rest and in motion at the same time in the same inertial frame.

 

Which of these 'contradictions' is the more absurd? If L29 were true, it looks like L17a couldn't be derived in any obvious way from L14-L27. This would in turn mean that Engels's conclusions are false -- always assuming, of course, that his 'argument' depends on such considerations and some sense can be made of anything he had to say on this topic.

 

Nevertheless, it is clear from the way that the above argument has been constructed that L17a itself depends on the truth of L28 (repeated here again for ease of reference):

 

L28: A body can't be at rest and in motion at the same time in the same inertial frame.

 

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.

 

That is because L14-L27 began with the assumed truth of L14 -- or, its equivalent, L28. The reverse implication doesn't appear to hold.

 

[It is impossible for me to say whether or not the reverse implication holds; all I am trying to do here is make sense of the idea that motion is contradictory, and this seems to be the only way to do that. Again, since DM-theorists refuse to be clear over such issues, it has been left to me to try to make sense of what they allege.]

 

This means that L28 doesn't seem to pre-suppose the truth of the conclusion drawn in L17a, whereas the conclusion drawn in L17a looks like it depends on L28. This in turn suggests that L28 might be the more fundamental of the two.

 

[L14: An object can't be in motion and at rest at one and the same time (in the same inertial frame).]

 

Be this as it may, as noted above, L28 is itself false if L29 is true:

 

L28: A body can't be at rest and in motion at the same time in the same inertial frame.

 

L29: A body can be at rest and in motion at the same time in the same inertial frame.

 

Unfortunately, L29 is a familiar truth! An object can be at rest with respect to one inertial frame, and yet be in motion with respect to another. The wording of L29 doesn't rule this out. In order to eliminate this latest difficulty, L29 must be modified; perhaps along the following lines:

 

L30: With respect to the same inertial frame and the same instant in time, a body can be at rest and in motion.

 

[L30 'contradicts' L30a:

 

L30a: With respect to the same inertial frame and the same instant in time, a body can't be at rest and in motion.]

 

L30 now certainly looks 'contradictory' (especially if "at rest" is taken to mean "not in motion with respect to the same inertial frame").

 

Nevertheless, it was the rejection of L30 (or its equivalent) that led to the derivation of L17a. Hence, if L30 is always false (i.e., if L30a is always true), it looks like L28 must always be true, too (given certain other assumptions, and if worded appropriately).

 

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.

 

L28: A body can't be at rest and in motion at the same time in the same inertial frame.

 

Consequently, if we deny that a body can be at rest and moving at the same time (in the manner indicated above), Engels's conclusion does appear to follow!

 

That much seems reasonably clear.

 

Unfortunately, however, the following line of argument also shows that the derivation of L17a from the rejection of L30 isn't inevitable, and hence that Engels's conclusion doesn't automatically follow:

 

L31: A body can't be at rest and in motion with respect to the same inertial frame at the same time.

 

L32: If a body is wholly located at a point it can't be wholly located at any other point in the same reference frame at the same time.

 

L33: But, a moving body must be located wholly at two points at the same time, otherwise it would be at rest.

 

L34: Since L33 is impossible (by L32), motion can't take place. Hence, by L31, and despite appearances to the contrary, all bodies are at rest.

 

Of course, L34 is somewhat analogous to the conclusion Zeno himself drew, and it flatly contradicts experience. It is therefore unacceptable -- that is, if we allow experience to be decisive in such cases. But, L31-L34 demonstrate that L17a doesn't have to follow from the rejection of L30, even if the alternative outcome proves unpalatable.

 

L30: With respect to the same inertial frame and the same instant in time, a body can be at rest and in motion.

 

It is now clear that the refusal to accept the 'contradiction' contained in L30 can lead to two distinct 'contradictory' conclusions. One of them is inconsistent with experience (the latter half of L34 -- i.e., L34b), while the other (i.e., L17a) is self-contradictory:

 

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.

 

Naturally, which one of these two outcomes proves to be the least unacceptable will depend on other priorities. If it is felt that experience is unreliable, L34b might be preferable. On the other hand, if contradictions are regarded as fundamental features of reality, and appearances are deemed deceptive, or unreliable, L17a might well be chosen. However, it is worth noting that neither option is empirically verifiable; in fact they both transcend any conceivable body of evidence and every possible experience.21

 

[Of course, it could be argued that L32 begs the question, since, with respect to moving bodies, DM-theorists claim bodies can wholly be located at two points at once. In fact, they (L32 and L32) both beg each other's question.]  

 

Nevertheless, given the fact that dialecticians also believe that appearances contradict underlying 'essences', they are the last ones who can legitimately appeal to experience to refute Zeno-esque conclusions like L34b. In fact, if the DM-thesis that underlying 'essences' 'contradict' appearances were itself true, then, since it appears to be the case that there are moving bodies, in 'essence' the opposite must be the case! Hence, if appearances 'contradict' reality it seems that, essentially, no bodies actually move, implying that Zeno was right all along!

 

Putting this annoying corollary to one side for now, it is worth emphasising that both halves of these two 'derivations' rely on the sorts of ambiguities encountered earlier with respect to L1-L13 (alongside several others considered below). Aprioristic 'arguments' like these only seem to work because they are shot-through with equivocation, ambiguity, and distortion; indeed, this is partly why both of the above conclusions finally descend into absurdity and incoherence -- as we are about to discover.

 

 

Theatre Of The Absurd

 

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.

 

[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.]

 

The ludicrous nature of L17a may nevertheless be made more explicit by means of the following argument:

 

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.

 

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

 

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!22

 

But, that is even more absurd than L34b!

 

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, this wouldn't help, for if a body is moving and in the second of those two places, it couldn't be in motion at this second location unless 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 rather odd 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. [Emphasis added.]

 

Without L15 (and hence L35), Engels's conclusions do not 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 the above absurdity: 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 line-of-argument 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 said 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, or in, which Engels argues a body performs such 'contradictory' miracles.]

 

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 would be at rest at that point unless it also occupied a third point at the same time. Given L15 (reproduced below), there seems to be no way around this.

 

On the other hand, a 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 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 above.]

 

In that case, if L15 still stands, then at the second of these two proposed DM-points -- say, (X2, Y2, Z2) --, a moving body will 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 that body 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.

 

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

 

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 would 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 that 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 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. Hence, 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 succeed. 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.

 

Or, so it could be argued, once more.

 

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 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 'DM-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 said 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, somewhat 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 such 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. 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 pair of the places it occupied in that journey!

 

It now looks like DM-theorists' only way of avoiding the above criticisms -- and of maintaining their view that motion is 'contradictory' -- is if they are prepared to impose a series of ad hoc stipulations on nature (of the sort mentioned above, none of which seem to work, anyway).

 

But, as we have seen several times already, such a response would be fatal to DM since it would undermine their belief that reality itself is contradictory (rather than it merely being what we say about it that is), all the while confirming the suspicion that it is only certain ways of representing nature that appear to be contradictory -- which "ways of representing nature", incidentally, still await clarification.

 

This option would, of course, mean that this part of DM (at least) is thoroughly conventional, and thus entirely subjective -- and still defective!

 

Once again: As we will see throughout this site, the source of these (and similar) 'problems' lies in the repeated attempt made by dialecticians (and metaphysicians alike) to state, or derive, 'necessary truths' about reality. Such theses are based solely on an extrapolation from the supposed meaning of a few specially-selected words, to fundamental truths about nature, valid for all of space and time. Clearly, with respect to Engels's 'analysis' of motion, this predicament is further compounded by an attempt to circumvent several fundamental conventions expressed by our use of ordinary language --, such as those expressed by the LOC and the LOI.

 

[I will endeavour to substantiate these claims below, and in detail in Essay Twelve Part One.]

 

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

 

It could be replied that the above criticisms beg the question, since dialecticians do not question the application of principles drawn from FL -- such as the LOC --, they merely point to their limitations when confronted with change and motion. That response was neutralised in Essays Four and Eight Parts One, Two, and Three.

 

Suffice it to say here that dialecticians themselves have yet to account for motion in anything like a comprehensible form -- or even depict it accurately! So, whether or not it is correct to say that FL can't account for motion and change, it is now quite clear that DL itself miserably fails in this regard.

 

Even more annoying: in Essay Four we saw that, contrary to what dialecticians tell us, FL copes with motion and change with ease.

 

 

Yet Another Absurd Dialectical Consequence

 

Another, perhaps less well appreciated consequence of the 'dialectical theory' of motion and change -- which is, if anything, even more absurd than the one outline above --, is the following:

 

If Engels were correct (in his characterisation of motion and change), we would have no right to say that a moving body was in the first of these 'Engelsian locations' before it was in the second.

 

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.

 

That is because such a body, according to Engels, is in both places at once, so it can't be in one of them before it was in the second.

 

Now, if the conclusions drawn in the previous section 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. Hence, they can't be anywhere first and then later somewhere else. In the dialectical universe, therefore, when it comes to motion and change, there is no before and no after!22a

 

In that case, according to this 'scientific theory', concerning the entire trajectory of a body's motion, it would be impossible to say it was at the beginning of its journey before it was at the end! In fact, it would be at the end of its journey at the same time as it set off! So, while you might foolishly think, for example, that in order to go on your holidays, you have to board an aeroplane 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', in fact you do!

 

And the same applies to the 'Big Bang'. While benighted, non-dialecticians might think that this event took place billions of years ago, they are surely mistaken if this 'super-scientific' theory were correct. That is because any two events in the entire history of the universe must have taken place at the same instant, by the above argument. Naturally, this means that while you, dear reader, are reading this, the 'Big Bang' is in fact is now taking place! I rather think 'duck and cover' is called for.22b

 

To be sure, this is absurd, but that's Diabolical Logic for you!

 

 

No Word Is An Island

 

And Therefore Never Send To Know For Whom The Bell Tolls; It Tolls For DM

 

Several of the points raised above require further elaboration -- in the course of which we will discover once again that Engels was in fact saying nothing at all intelligible.

 

As we have seen, Engels asserted the following:

 

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

 

However, in doing so he was clearly appealing to what he regarded as the established, inter-subjective meaning of terms like "motion", "change", "place", "moment", and "time". This can be seen from the fact that he didn't even think to define or explain what he meant by these words.

 

Engels did offer an aside (in the above comment) to the effect that motion is a "simple mechanical change of place", and idea he reiterated in DN:

 

"All motion is bound up with some change of place, whether it be change of place of heavenly bodies, terrestrial masses, molecules, atoms, or ether particles. The higher the form of motion, the smaller this change of place. It in no way exhausts the nature of the motion concerned, but it is inseparable from the motion. It, therefore, has to be investigated before anything else." [Engels (1954), p.70. Italic emphasis added.]

 

I will examine what Engels had to say later in this Essay.

 

Ordinarily, this lack of precision wouldn't in itself be a problem since we understand words like these perfectly well in our day-to-day affairs, and typically without recourse to definitions etc. But, in specialised areas of study (especially those that seek to revise or correct the way we see things), a sloppy approach to theory isn't just unacceptable, it is counter-productive. Indeed, this cavalier attitude to ordinary language has a tendency to backfire on anyone foolish enough to embrace it. Again, this is especially true of those who attempt to press the vernacular into service way beyond its prosaic remit.

 

The ability to manoeuvre one's way around linguistic conundrums like this with ease is supposedly what dialecticians mean by "grasping a contradiction". This seems to imply that when confronted with the many 'contradictions' that nature allegedly throws our way, dialecticians merely have to "grasp" them, and all is well. This neat trick then 'allows' these 'serial graspers' to ignore the internal contradictions this approach introduces into their own theory. [The fatal problems this introduces have been explored here and here.]

 

However, as we will see in Essay Seven (as well as here), DM-theorists are highly selective about which 'contradictions' they choose to "grasp", and which they try to blame on the defective nature of some theory or other -- or, indeed, on the flaws they perceive in competitive doctrines. Hence, when dialecticians "grasp" the 'contradictions' they claim to see in motion and change, they attribute them to nature itself, but fail to blame them on Hegel's logical incompetence, or on Engels's lack of clarity.

 

On the other hand, when contradictions are exposed in rival theories, those contradictions become a handy excuse for berating rival theorists and hence for rejecting their work. By way of contrast, they are remarkably forgiving of the contradictions implied by their own ideas, which do not, under any circumstances, suggest their theories are defective or which need revising.

 

So, for example, they tell us that by 'resolving' certain contradictions science is able to progress. However, if science advances by rejecting or 'resolving' contradictions in and between theories, then, plainly, the science of kinematics can't advance unless this 'dialectical contradiction' has also resolved (as, indeed, it will be by the end of this Essay --, except this will be done by dissolving it). However, just as soon as that has been done, dialecticians will surely have to abandon their belief in the 'contradictory' nature of motion, or, of course, risk holding up the progress of science.

 

This self-inflicted quandary I have called "The Dialecticians' Dilemma".

 

As seems obvious, 'dialectically grasping' a 'contradiction' doesn't make it disappear. Even as DM-theorists view things, motion is still 'contradictory', whether or not anyone else sees things this way. Hence, the significance of "grasping a contradiction" appears to be little more than this: Anything that might ordinarily seem puzzling or paradoxical suddenly stops bothering dialecticians -- that is, if it ever did. But, this only works if it is accepted that this is the way the world actually is. In that case, and on this basis, DM-theorists seem to think they can stop worrying about the contradictions their world-view places at the heart of their own theory. They accept the fact that even though nature is deeply perplexing, a pair of well-adjusted DM-spectacles allows the world to be viewed aright (where "viewed aright" in fact appears to mean "ignore what you can't explain and then accuse critics of not understanding dialectics").

 

Despite the DM-spin, this nevertheless implies that it is impossible to explain what it could possibly mean for something to be in two different places at once (save in the ambiguous manner described earlier in this Essay, and again below). If that is so, the dialectical 'analysis' of motion is of little use to anyone, least of all to dialecticians. That is because it is clear that not even dialecticians can explain motion, since all their theory does is re-describe it in a perplexing form. All that Engels's 'analysis' seems to have achieved, therefore, is stopping dialecticians worrying about their own defective theory, leaving motion, as they see it, still a 'paradox'.

 

We have also seen that, even if DM were a correct description of 'reality', this view of motion does no real work. How does it help us change the world to be told that motion is contradictory? How does it help scientists to be told motion is a contradiction? Can they use it to predict anything? Can technologists and engineers use it to help control nature? How many bridges can be built on the basis that motion is a contradiction? How many strikes won? Or even leaflets printed?

 

In that case, if there is a rational solution to this 'paradox' (if we but knew what that was), it is no good asking dialecticians for an answer. They gave up on that score the moment they leafed through Hegel's 'Logic', and began "grasping" 'contradictions'.

 

Left to DM-fans, the advancement this branch of Physics and Applied Mathematics would come to a grinding halt.23

 

[Irony intended.]

 

Ordinary Language And Paradox

 

However, Engels did at least make an attempt to use everyday terms in his endeavour to show that they were not all they seemed -- or, rather, that when considered 'dialectically' the vernacular reveals more about reality than might otherwise have been apparent, especially to those who are mesmerised by 'commonsense' and 'formal thinking', or, indeed, those who have been bamboozled by that 'inner fifth-columnist', the "abstract understanding" (very helpfully identified for us by Hegel without even the use of a consulting couch).

 

Nevertheless, anyone who disagreed with the 'dialectical' conclusion Engels drew would no doubt be reminded that these few words -- or, the 'concepts' they supposedly represented -- clearly and unambiguously implied the 'contradictions' that Engels and Hegel said they did. In that case, defenders of the 'dialectical view' of things could claim that Hegel and Engels had actually made explicit what were implicit 'contradictions'.

 

Intentionally or not, by arguing this way Engels succeeded in locating his paradoxical theses in an ancient metaphysical tradition stretching back to Zeno, Parmenides and Heraclitus -– a tradition which ordinary working people had no hand in building, but which is (demonstrably) based on ruling-class priorities, forms-of-thought and on a distortion of the vernacular, the only language that links humanity directly with the material world, as Marx himself pointed out:

 

"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 emphasis added.]

 

Indeed, Engels's approach began to falter the moment he attempted to squeeze some metaphysical juice out of such desiccated philosophical raisins; that is, when he tried to extract 'paradoxical' conclusions from a few rather innocent-looking words.

 

Naturally, only by those who have already accepted the view that reality is fundamentally 'contradictory' will agree with the conclusions Engels drew. Others, however, might be forgiven for remaining sceptical -- particularly those who (not unreasonably) think that Engels's 'solution' is far more puzzling than the original 'problem' had ever been. Indeed, if the nature of motion is problematic, calling it "contradictory", while making no attempt to explain how that actually accounts for anything, is worse than useless.

 

If these 'contradictions' do no work (again, as was argued above), then their presence here is, at best, unhelpful. That is because we can now see that they are the product of an over-active imagination, compounded by a naive acceptance of the Idealist gobbledygook Hegel and Zeno inflicted on their readers.

 

In that case, Engels's 'analysis' is an obstacle to understanding, which will, of course, need to be removed if science (let alone Marxism) is to advance.

 

 

Lack Of Imagination

 

In fact, Engels failed to consider other, far more likely possibilities; indeed, it looks like it never even occurred to him that his 'contradictory' conclusions might not follow if he had instead given consideration to the full range of words, or meanings, available to those who use ordinary language. To be sure, these are easily accessed by those determined to use the vernacular with far greater consistency, honesty and sensitivity than Engels, Hegel or Zeno ever managed.24

 

Engels clearly wanted to make a specific point about the paradoxical implications of a handful of seemingly innocent (if not straight-forward) ordinary words. As we will see, he did this by unwittingly altering their everyday use/meaning while imagining that the import of several other ordinary terms associated with them remained unaffected.

 

In doing this he wasn't, of course, alone. Semantic sleight-of-hand has been the sport of choice throughout the history of Traditional Philosophy; and the practice continues to this day. Even careful philosophers often fail to notice that their own work involves what can only be called "piecemeal selectivity" over the use of certain words. Indeed, they have invariably assumed it is possible to tinker around with several specially-chosen expressions while the meaning of any words normally associated with them remain unaffected. Selectivity like this is, alas, double-edged. In fact, these associated words -- whose meanings in this case Engels simply also took for granted -- prove to be equally (if not more) problematic than those he finally latched onto.

 

As we are about to see, this unexpected turn of events will not only vitiate Engels's 'analysis' of motion, it will undermine every single classical account, too.

 

If, according to Hegel and Engels, an ordinary word like "motion" possess 'contradictory' implications, then perhaps other terms they failed to consider might have analogously paradoxical connotations, especially given this perverse way of viewing language. What about the word "place", for instance? What if it turns out to be just as 'problematic'? In such circumstances, could we continue to accept the validity of Engels's conclusions about "motion" if the interplay between these two intimately connected words is more complex than he imagined, and an alteration to one simply altered the other?

 

More pointedly: What if certain connotations of the word "place" neutralise Engels's interpretation of the word "move"?

 

Clearly, Engels's argument relies on the meaning of "place" remaining fixed while he tinkered around with "move". But, if "place" itself has no single meaning, then any conclusions based on the supposition that it has will automatically come under suspicion. Worse still, any argument based on one aspect of the ordinary meaning of "place", which undercuts the 'philosophical' sense of "motion", will be thrown to even greater doubt. That is because, if connotations of the latter are compromised by the slippery nature of the former (or vice versa), the meaning of neither will emerge unscathed in view of their intimate connection.

 

In fact, as we are about to see, this in-built linguistic complexity has the salutary effect of deflating the philosophically grandiose conclusions Engels and others thought they could derive from a handful of mundane words, when they used a non-standard application of "motion" with what they took to be a standard use of "place", and vice versa.

 

 

Ordinary Objects Regularly Do The Impossible

 

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 or 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 (implicitly or explicitly) assumed they have a single unique (or 'essential') meaning, problems invariably arise, as Wittgenstein noted:

 

"I think that essentially we have only one language, and that is our everyday language.... [O]ur everyday language is the language, provided we rid it of the obscurities that lie hidden in it.

 

"Our language is completely in order, as long as we are clear about what it symbolizes." [Waismann (1979), pp.45-46.]

 

"You ask why grammatical problems are so tough and seemingly ineradicable. -- Because they are connected with the oldest thought habits, i.e., with the oldest images that are engraved into our language itself (Lichtenberg)....

 

"Language has the same traps ready for everyone; the immense network of easily trodden false paths. And thus we see one person after another walking down the same paths....

 

"One keeps hearing the remark that philosophy really doesn't make any progress, that the same philosophical problems that occupied the Greeks keep occupying us. But those who say that don't understand the reason this must be so. The reason is that our language has remained constant and keeps seducing us into asking the same questions. So long as there is a verb 'be' that seems to function like 'eat' and 'drink', so long as there are the adjectives 'identical', 'true', 'false', 'possible', so long as there is talk about a flow of time and an expanse of space, etc., etc. humans will continue to bump up against the same mysterious difficulties, and stare at something that no explanation seems able to remove....

 

"I read '...philosophers are no nearer to the meaning of 'Reality' than Plato got...'. What a strange state of affairs. How strange in that case that Plato could get that far in the first place! Or that after him we were not able to get further. Was it because Plato was so clever?" [Wittgenstein (2013), pp.311-12e. Italic emphases in the original; quotation marks altered to conform with the conventions adopted at this site.]

 

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 or contexts they generally fail to consider, or, rather, which they 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' don't normally bother us -- well, not until some bright spark tries to do a little 'philosophising' with them.24a

 

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 would 'understand' his use of it. {That was the point of the preamble in the previous sub-sections.]

 

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 (again, 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. [L42 contraposed.]

 

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 L43).

 

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

 

L48: But, some workers remain 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 was in L44), one connotation of "move" is automatically affected (in L45 and L46), 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 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...?

 

 

Dialectical Objects Do The Oddest Things

 

Moving While Remaining Still

 

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:

 

P1: A 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 or 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 using "motion" the way Engels and Hegel thought they could.

 

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

 

Of the countless problematic options there are before us the following seem to be most relevant to the points at issue:

 

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

 

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

 

(4) However, if an object 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 -- for example, a factory.

 

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, the problem revolves around preventing Option (3) from undermining what we might ordinarily want to call motion -- the successive occupancy of certain regions of space; i.e., the first half of (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 (if we relax the space concerned and make it larger, of example) the above difficulties soon re-appear; for it is quite clear that such objects will still move while staying in the same place -- i.e., 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 we are 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 specific 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. [And 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 can't move about in such points -- but that 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 would 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 or 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 'problems' from another set of paradoxes -- especially when those paradoxes gain purchase from the same linguistic ambiguities and vagaries about "space" that bedevilled "motion". We seem to be going round in circles.

 

[No irony or pun intended.]

 

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 can be defined by the application 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 likewise -- except they would now have a more precise "place" or 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 this must be the case with Engels's moving objects, if we depict "place" this way.

 

This is just Option (3), again!

 

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

 

Naturally, the only way to avoid this latest difficulty would be to argue that:

 

P2:  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; 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!

 

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

 

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 can move, but how it is also possible for volume intervals to move so that they can faithfully shadow the objects they contained!

 

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 in order 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 version of Option (1)!]

 

It could be countered that even though objects occupy spaces equal to their own volumes, as they move (locomote) 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 or defined precisely. On this revised scenario, moving objects would leave their old locations (their old containers) behind as they barrelled along.

 

Perhaps this is the direction we need to take.

 

[No pun intended.]

 

Do They Move Or Simply Expand?

 

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.

 

Consider, then, Option (4a): Even if (4a) were a correct interpretation of what Engels meant, and it also proved to be 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 section --, 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 (again, 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", in this case.]

 

Now, the only way to avoid the conclusion that D moves while occupying the same place, or 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 successive, 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 locomotes (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. [This is Option (1) and/or Option (3).] Hence, it must occupy at least two of these at the same time (if, that is, we accept the 'dialectical' view of motion).

 

That being 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 or volume interval bigger than either one 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.

 

Now, if that were so, and D wasn't stationary while it occupies δV2, as we saw above in an analogous context, it must also occupy δV3 at the same time, otherwise it will be stationary while in δV2, 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, (ii) expanding alarmingly like some sort of metaphysical Puffer Fish.24b

 

 

Figure One: At Last! An Organism That 'Understands' Dialectics

 

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 -- compounded by their cavalier use of language.

 

[DL = Dialectical Logic.]

 

 

Or Do They Concertina?

 

Problems don't stop there; it seems that 'Dialectical objects' must also concertina as they move.

 

Consider a simple body, B, made of 3 connected parts: P1, P2 and P3, all arranged in the same line, so that there are no gaps between them. Let B move such that at t1, the centre of the leading edge of P1 is at (X1, Y1, Z1), the centre of the leading edge of P2 is at (X2, Y2, Z2), and centre of the leading edge of P3 is at (X3, Y3, Z3). Let us also assume that the centre of the leading edge of P3 now moves to (X4, Y4, Z4). Finally, let us assume that the distances between each of (X1, Y1, Z1), (X2, Y2, Z2), (X3, Y3, Z3) and (X4, Y4, Z4) are all the same.

 

Now, if all moving objects occupy two places at once, and if B moves in a line parallel to the line joining the centre of the leading edge of P1 to the centre of the leading edge of P3, then the centre of the leading edge of P1 must occupy (X1, Y1, Z1) and (X2, Y2, Z2), the centre of the leading edge of P2 must occupy (X2, Y2, Z2) and (X3, Y3, Z3), and the centre of the leading edge of P3 must occupy (X3, Y3, Z3) and (X4, Y4, Z4), at the same time. In effect, B would concertina as it moved, with the front end of, say, P1 crushing or penetrating the back end of P2, and overlapping it right up to its own leading edge -- in effect, wiping P2 out!

 

[Again, this result depends on the answer to an earlier question: How far apart are the two places a moving body occupies that Engels envisaged? If this is left indeterminate, then any length will do. Even then, if a specific length is decided upon, we could make the distance between the above parts equal to that length, and the same result would still follow. (That has been done below, anyway.)]

 

It can't be the case that the trailing edge of P2 will leave (X2, Y2, Z2) just before the leading edge of P1 reaches it, since, as we have already seen, there is no before and now after here, since all such motion must take place at the same time for it to constitute a 'dialectical contradiction'.

 

Now, it could be objected that P1 and P2, for example, will occupy the space between (X1, Y1, Z1) and (X2, Y2, Z2) and (X2, Y2, Z2) and (X3, Y3, Z3), respectively, as B moves -- but this isn't possible. That is because there are no gaps between any of the three parts of this object for any of those parts to move into. So, if B were, say, a single carriage train, then P1 would comprise the rear section of that carriage, P2 the middle third, and P3 the front end. This view of motion would therefore have those parts of this single carriage crushing the one in front.

 

[I have considered the option that there is such a gap, again, below.]

 

It might be argued that the structural properties of B (i.e., intermolecular forces, etc.) will prevent this from happening. That is undeniable, but this response also has the unfortunate consequence that while B may be in two places at once as it moves, none of its parts could be! And that in turn would imply that while B was racing along, none of its parts would be racing with it -- since they are not allowed by these 'structural properties' to be in two places at once!

 

Similar, if not worse problems afflict any 'dialectical objects' undergoing circular or more complex forms of movement, such as helical or spiral motion.

 

So, consider a rotating disc, D, of negligible thickness divided by a diameter line, T, into two equal semi-circular sectors, S1 and S2. If we define the centre of this disc as the origin, then we can set the leading edge of S1 so that it lies along T. In addition, let there be a point, p1, on T, r units from the centre, with co-ordinates (r, θ1). Let the leading edge of S2 also lie along T, and let there be a point, p2, r units from the centre, with co-ordinates (r, θ2). Plainly, this means that p1 and p2 lie on the same trajectory, a circular path r units from D. [I have used polar co-ordinates in two-dimensions here to simplify this example.]

 

Now, if all moving objects occupy two places at once, and if B rotates clockwise, then the leading edge of S1 must pass through both p1 and p2, and the leading edge of S2 must pass through both p2 and p1, at the same time. But this is even worse than the 'dialectically linear movement' considered above, since, in this case, either (i) D will totally disappear -- as both of its sectors occupy the same semi-circle that the other one occupied -- or, (ii) Both of these sectors must stretch to cover the entire disc, ramming into the back of one another as they did so, compressing each into a region with zero area!

 

Now it might be possible to defend this picture of dialectal objects as they smash into one another by arguing that the above scenarios are heavily biased. For example, in the linear case above, while the centre of the leading edge of P3 might move to (X4, Y4, Z4), the distance between (X3, Y3, Z3) and (X4, Y4, Z4) need not be equal to that between (X1, Y1, Z1) and (X2, Y2, Z2), or that between (X2, Y2, Z2) and (X3, Y3, Z3). Let us say, therefore, that the distance between (X3, Y3, Z3) and (X4, Y4, Z4) is δL. In this case, therefore, B will move forward δL units, as will each of its parts.

 

This would have the effect on S1 such that it would no longer move to (X2, Y2, Z2), but to some intermediate point (X1+δx, Y1+δy, Z1+δz), with the same sort of thing happening to the other leading edges. The same would also happen to the trailing edge of S2, which, let us say was at (Xi, Yi, Zi), at t1. Now, the trailing edge of S2 and the leading edge of S1 can't occupy the same space, as should seem obvious; so let us say that the distance between (X1, Y1, Z1) and (Xi, Yi, Zi) can be made as small as we like -- let us stipulate that this is δP (where it is left open whether or not δP > δL). In that case, there would be a gap, δP, between at least two of the parts.

 

Hence, the trailing edge of S2 would move to (Xi+δx, Yi+δy, Zi+δz) while the leading edge of S1 moves to (X1+δx, Y1+δy, Z1+δz). Plainly, these are not the same points. [Anyone who disagrees should read the subscripts more carefully!] If so, S1 won't smash into the back of S2 as imagined above. The same sort of conclusion can be drawn in connection with the rotating disc.

 

Unfortunately, this reply fails, too. That is because the centre of the leading edge of S1 has to occupy two places at once, if Engels and Hegel are to be believed. So, the centre of the leading edge of S1 has to occupy (X1, Y1, Z1) and (X1+δx, Y1+δy, Z1+δz), and the centre of the trailing edge of S2 has to occupy (Xi, Yi, Zi) and (Xi+δx, Yi+δy, Zi+δz), at the same time. Now, if δP is zero, then (X1+δx, Y1+δy, Z1+δz) will lie beyond (Xi, Yi, Zi), which means that the leading edge of S1 will smash into the back of S2. The same will happen if δP < δL. On the other hand, if δP > δL, a gap will open up between S1 and S2, which will widen all the more as B continues to move. So, B will either (a) Begin to fragment, or (b) Concertina, as it moves. The same will happen to the disc.24b1

 

So, this 'theory' is still mired in Dialectical Mud.

 

 

Coordinates To The Rescue?

 

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 R3.24c

 

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 this SC must be written precisely, with xi, yi, and zi 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 capable of using 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 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 is 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 to now, have shown that they aren't even aware of such problems, and are likely to ignore them once they have been apprised of them!) 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).24d This trick is accomplished either by (i) The simple expedient of ignoring examples of discrete forms of motion (several of which are given below), and/or (ii) Failing to consider instances where both time and place are continuous -- all the while imagining that the relevant words drawn from ordinary language used to depict both have been employed in their usual senses, and haven't been altered by these novel contexts.25

 

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, stretch, concertina, or vanish, as noted above.

 

 

Everyday Miracles?

 

Ordinary Objects Behave 'Miraculously'

 

If the points made above are valid (no pun intended), it means that in a perfectly ordinary sense, bodies can both move and stay in the same place while doing so. Indeed, they are quite capable of remaining stationary even if they undergo a change of place, moving and not moving all at once!

 

The first of these possibilities was depicted above with respect to those stationary/mobile workers; the second (where something can both move and not move all at once -- and, in this case, this would involve a discrete sense of "move", into the bargain), is illustrated by the next example:

 

L55: NN was second in line when MM, who had been first in the queue, suddenly dropped out. Hence, NN moved to the front of the queue even though he remained rooted to the spot.26

 

In L55, we have a perfectly ordinary example where a fellow human being manages to do the 'metaphysically impossible' (without even breaking into a dialectical sweat), moving while staying still (relative to some inertial frame). Clearly, it is possible to move to the front of a queue (in one sense) even without moving at all (in another sense), relative to some inertial frame.

 

Indeed, it is also possible to think of cases of discontinuous (i.e., discrete) motion whereby, even though something once moved, nothing need now be moving -- and yet in one sense something still moves. This would also involve whatever it was that managed to do this 'moving and not moving at the same time', doing so in a different sense from that which was illustrated in L55. In fact, it is possible to show that some things can move (again in a discrete sense) while they occupy none of the intervening places between successive locations. All of these (at first sight, rather odd) possibilities are illustrated below:

 

L56: The footprints moved across the snow-covered yard, indicating where the scabs were hiding.

 

L57: Easter moves to a new date each year.

 

L58: "See, the page numbers at the top of the page in this book you sold me move about erratically. It has been printed and bound all wrong!"

 

L59: The ground staff moved the cricket pitch to the other side of the square.

 

L60: The organisers of the rally moved the meeting to seven o'clock.

 

L61: The strobe light moved across the floor picking out each dancer, one at a time.

 

In L56, we have stationary 'objects' (i.e., the footprints created by individuals who had earlier walked across the said yard), which still move (across the yard) even while each item (each footprint) is stationary.

 

In L57, nothing actually moves even while it still does! In L58, nothing moves, once again, but yet something actually moves (namely the faulty numbering), and it does so discretely while not occupying any of the intervening spaces, which spaces don't exist either for anything to move into! [Of course, in such circumstances, we would probably use "jump" instead of "move"; but to jump is also to move.]

 

A similar picture emerges in L59, where a discrete object moves a reasonable distance, but which object doesn't exist while it moves, nor does it occupy any of the intervening spaces on its 'journey', but which intervening spaces do exist! Similar situations were illustrated by L60 and L61.

 

Not only that, but continuous, and yet stationary, objects can move while remaining still:

 

L62: As I look down on the scene, the immobile line of pickets moves out of sight, curling right round the block; each striker holding her ground, rooted to the spot.

 

L63: The wire moves in a spiral around this tree. It has been in the same spot so long that the tree has partially grown around it.27

 

Finally, some things can move -- but to nowhere in particular -- and they can stay quite still while they are doing it:

 

L64: This road is going nowhere.28

 

Such mundane examples (there are countless others), using perfectly ordinary words in situations we all readily recognise and comprehend, demonstrate that the seemingly 'obvious' metaphysical principles that thinkers like Engels dreamt-up actually depend on non-standard applications (i.e., distortions) of the vernacular (indeed, just as Marx pointed out).

 

So, what at first sight might seem distinctly odd now turns out to be a rather prosaic set of examples with which we are all familiar, and which hardly raise an eyebrow in everyday life.

 

Of course, it could be objected that these examples of 'motion' are not at all what Engels meant by "motion"; indeed, he was quite careful to emphasise that he was only interested in one sort of motion: continuous change of place with respect to time:

 

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

 

"All motion is bound up with some change of place, whether it be change of place of heavenly bodies, terrestrial masses, molecules, atoms, or ether particles. The higher the form of motion, the smaller this change of place. It in no way exhausts the nature of the motion concerned, but it is inseparable from the motion. It, therefore, has to be investigated before anything else." [Engels (1954), p.70. Italic emphasis added.]

 

"Among natural scientists motion is always as a matter of course taken to mean mechanical motion, change of place. This has been handed down from the pre-chemical eighteenth century and makes a clear conception of the processes much more difficult. Motion, as applied to matter, is change in general." [Ibid., p.247. Italic emphasis in the original.]

 

In the above, Engels is perfectly clear that he meant "simple mechanical change of place", which is radically different from the non-standard senses of the word illustrated above.

 

Or, so it could be argued.

 

[Of course, this doesn't mean that Engels didn't recognise other, more complex forms of motion; quite the opposite, in fact!]

 

Unfortunately, however, as we have seen, it isn't easy to ascertain what (if anything) Engels actually had in mind by "simple mechanical change of place". Indeed, much of what he said is compatible with no movement having occurred, so that the supposedly 'contradictory' aspects of an object's trajectory have nothing to do with whether that object was moving or not. Moreover, as we have also seen, Engels's use of language implies that 'dialectical' objects threaten to expand alarmingly, concertina destructively, or spread out and occupy an entire region, whenever they try to move.

 

Furthermore, dialecticians can't appeal to what we 'all know' about the meaning of the word "motion", nor should they suppose we 'all know perfectly well' what Engels meant when he referred to it. As the above examples indicate, there is no one thing we all mean by this word (and its associated terms), even though most (if not all) speakers know what they mean when they are used in ordinary contexts (like those depicted above). Indeed, we have just seen that objects can move even while they don't undergo a "change of place", contradicting Engels.

 

And, as far as Engels's own use is concerned, we may only agree with the claim that DM-theorists know what Engels meant by "motion" when they succeed in explaining to the rest of us precisely what that is!

 

Unfortunately, to date, there have been no significant moves in that direction (irony intended).

 

In addition, the above examples were deliberately drawn from everyday situations -- those that are readily understood. It is Engels's (Hegelian) use of the word "move" that turns out to be non-standard and incomprehensible.

 

Finally, it might be felt that the above emphasis on the ordinary sense of words is inappropriate in a scientific or philosophical analysis of motion and change. This objection is considered in detail elsewhere at this site. Anyway, Engels himself used what look like ordinary words to make his point -- which was that every example of motion in reality involves a contradiction, including those parts that can be depicted by our use of the vernacular.29

 

 

Inferences From Language To The World

 

Thought Experiment In Place Of Scientific Investigation

 

Again, it could be argued that any account of motion has to involve contradictions because of what must be the case if objects in reality -- independent of thought -- actually move, which they clearly do. Hence, despite what we might say, the real world exhibit countless examples of motion and change, each of which is contradictory.

 

However, this use of modal terms is quite revealing for it confirms something that has been implicit all along (and hinted at earlier): this traditional 'family of arguments' depends on inferences from the alleged meaning of a few specially-selected words -– albeit given an idiosyncratic re-interpretation, often in isolation from other associated terms, and divorced from their ordinary contexts of use -- to 'necessary truths' about fundamental features of the world. 'Deductions' like these invariably precede even a perfunctory empirical 'investigation' -- if, that is, the latter is so much as attempted by dialecticians. The results these inferences appear to warrant are then regarded as absolute certainties, which their inventors find impossible to question. That is, of course, because these Super-truths are based on language alone, not on evidence. [On this in general, see Essay Twelve Part One.]

 

As pointed out earlier, Engels performed no controlled experiments (or any at all) or detailed observations, before or after he drew his hyper-bold conclusions about motion. In fact, it is impossible even to describe a single observation or experiment -- other than a thought experiment, which would, anyway, depend on the sorts of ambiguities highlighted above -- that could conceivably confirm Engels's claims about motion. This is partly because 'contradictions' themselves can't be observed (although an inscription of a proposition and its contradictory can, of course, be observed -- on that, see here), and partly because of the modal, universal and omni-temporal character of the conclusions themselves.30

 

This means that the only substantiation Engels could have offered to support his claims would have been language-based; he would have had to have referred anyone sceptical of his conclusions to what certain words really meant. It would be no good advising non-believers to look harder at the phenomena, refine their search or redo their experiments --, which is, of course, why one finds no evidence at all in books on dialectics aimed confirming or even so much as vaguely supporting the theory that motion is contradictory. What we find in its place is a set of dogmatic assertions, which are themselves (often) linked to a very brief thought experiment -- both of which are based on a brief consideration of a handful of the words or concepts involved.

 

[Readers are invited to check! E-mail me if they know of, or have found any such evidence, or they manage to locate a DM-supporter who references any.]

 

Furthermore, this is a doctrine that can't even be confirmed in practice! One would have thought that that fact alone would have rung alarm bells in a few dialectical heads!

 

Thus, Engels's only 'evidence' was based on a philosophical use of language -- in fact, on Hegel and Zeno's use of it --, but not on how such words feature in everyday life. This predicament (which he shares with all other metaphysicians) invariably passes unnoticed because (i) This is almost universal in Traditional Philosophy, (ii) It has been going on now for well over two thousand years ('East' and 'West'), and (iii) It is thought that by looking at certain words (or their 'real' meanings) the Armchair Philosopher is actually examining the world itself, and not simply the supposed meaning of a few specially-selected, jargonised expressions, which, because of this, have been divorced from reality.

 

The Idealist implications of the traditional approach to 'knowledge' were once again well summarised by George Novack:

 

"A consistent materialism cannot 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.]

 

[The reason for this age-old confusion of talk about talk with talk about things is examined in detail in Essay Twelve Part One (as well as throughout the rest of Essay Twelve -- summary here).]

 

Nevertheless, the denotation of the specialised jargon concocted by Traditional Theorists is simply taken for granted; indeed, the question whether such words actually have a denotation is seldom even raised.

 

The unremittingly negative view of philosophical word-magic presented at this site gains support from the additional fact that 'philosophical problems' like this can't be solved by an appeal to evidence. That is why they depend solely on a distorted use of language, and it is also why this is all Engels ever offered his readers (in this area), and why it is all he could ever have offered his readers.

 

Nevertheless, Engels restricted his comments neither to examples of motion he had personally investigated, nor to the entire set of examples experienced by humanity up until his day. Despite this, he still felt confident that he could extrapolate from his own understanding of a few ordinary-looking words to conclusions that were applicable to every conceivable instance of motion anywhere in the universe, for all of time:

 

"Never anywhere has there been matter without motion, nor can there be…. Matter without motion is just as inconceivable as motion without matter. Motion is therefore as uncreatable and indestructible as matter itself…." [Engels (1976), p.74. Bold emphases added.]

 

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

 

In fact, what Engels actually did -- and this was the extent of the 'careful' scientific research he carried out in this area -- was to reproduce the analysis of motion he found in Hegel's Logic!

 

And, truth be told, Hegel hasn't gone down in history as a great experimental scientist, either.

 

As we shall see (in Essays Nine Part One and Two, and Twelve (summary here)), these all too easily overlooked facts possess several revealing ideological implications of their own.

 

 

Metaphysical Con-Trick

 

Engels's feeling of confidence in the conclusions he so effortlessly drew no doubt arose from his consideration of one particular interpretation of "motion" (but no others). Hence, we find him claiming that:

 

"[E]ven 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." [Engels (1976), p.152.]

 

But, how could Engels possibly have known this? How could he have been so sure that every single instance of motion throughout the entire universe, for all of time, could only proceed in the way he alleged? If we rule out the absurd idea that Engels was a deity of some sort, there are in fact only two possible answers to that question:

 

(1) His certitude was based on his grasp of the 'concept' of motion itself. But, as seems obvious from his comments, Engels actually based his conclusions on his own understanding of a strictly limited set of words about motion -- on the ideas he lifted from Hegel -- but not on the 'concept' of motion itself (if there is such a thing). Neither he nor anyone else has access to such a concept independently of the words which supposedly allude to, or which express, it.

 

And yet, divorced from the wide variety of ways we ordinarily talk about motion (illustrated by the many examples given in this Essay), who is to say what is the correct way to understand such words in novel contexts like this? Or, whether the meaning of any technical terms that have been co-opted and pressed into service are the same as the meaning of the ordinary words they supposedly replaced or superseded? Or, that there is only one way to interpret them? Or, that Engels and Lenin hit upon the correct way to comprehend them (and then only after reading Hegel -- as opposed to sifting through the relevant scientific or observational data)? Or even, whether the language they finally employed means anything at all?

 

However, and more to the point: precisely who decided that such off-the-cuff conclusions (about substantive features of the world, true for all of space and time) can be read off from the alleged meaning of a few words?

 

Did the rest of us miss a meeting?

 

(2) The second possible answer revolves around a likely response that might have occurred to several readers: Surely a rejection of Engels's understanding of motion would be paradoxical, if not contradictory. That is because it would represent a repudiation of what the concept of motion itself actually implies. Consequently, on this view, anyone who fails to interpret motion along these lines (involving a body being in two places at once (etc., etc.)) only succeeds in revealing that they have misunderstood what motion is in-itself. Indeed, it would flatly contradict what we all ordinarily understand motion to be.

 

Or, so it could be claimed.

 

However, Engels's analysis of motion is paradoxical, if not openly contradictory, too; so even by its own lights there appear to be equally good reasons to reject his interpretation of motion as there are for accepting it, based on paradox alone. If it is paradoxical to reject his version, it is equally paradoxical to accept it.

 

Moreover, an appeal to experience to decide between these two alternatives is of little help, and for that is so for at least four reasons:

 

(i) As has already been pointed out, Engels drew his conclusions about motion without referring to any evidence at all. His views were clearly not based on experience; in fact, they were aimed at interpreting reality beyond any and all conceivable evidence and experience.

 

(ii) Our experience of motion is as ambiguous as the words we use to depict it. The examples given above (and in the Notes below) indicate that our ordinary ways of speaking about motion are far more complex than Engels, Zeno, Hegel, or even Lenin imagined. [Of course, in their everyday speech they will have shown that they already knew this; it was only when they began to 'philosophise' that they allowed themselves to be led astray.] Anyway, not even an indefinitely large finite number of observations of cats moving on and then off assorted mats (and the like), could confirm whether motion is or isn't (a) continuous, (b) discontinuous, or if it (c) is composed of countless discrete, concatenated 'sub-movements' -- or, indeed, whether (d) it is something else for which we have as yet no words. Even with advanced technological assistance, we still wouldn't be able to tell if motion is the one or the other.

 

[Indeed, as we have seen, there is no one thing that is motion. Our use of this word, and its associated terms, is far too complex to be constrained in this way. (See the next two points.)]

 

(iii) Ordinary language, and thus everyday experience -- as a matter of fact -- allows for both sorts of motion: discrete and continuous. This was demonstrated in the above examples. It is only a metaphysical prejudice (itself based on other priorities that will be exposed in Essay Twelve (summary here)) that (a) Consigns certain depictions of motion to the realm of "appearance", or "commonsense", while others are supposed to refer to "reality itself"; or that (b) Regards one type of motion as primary, the rest secondary.

 

(iv) The notion that there are such entities as "things-in-themselves" (or that there is something called "motion-in-itself", or "motion itself") is hopelessly confused, and that isn't just because this idea expresses a thinly disguised form of "absolute" motion -- as will be argued elsewhere at this site (until then, see Note 10). As we will see, reference to "motion-in-itself" is unintelligible; small wonder then that it has yet to be explained by anyone.31

 

Nevertheless, and once more, a repeated use of the word "must" in response to the above  -- as, for example, in a retort that might well have occurred to some readers: "That's all very well, but motion must involve a body being in two places at once…(etc., etc.)" -- could itself only have been based on a conceptual or linguistic analysis of a limited range of words associated with movement, and their varied uses. Again, that would amply confirm the view maintained in these Essays that dialecticians are happy to draw universally true inferences from a handful of specially-selected words, and then foist the results on reality -- the use of "must" revealing yet again this propensity to impose favoured a priori theses on nature.

 

When pressed to provide evidence to substantiate their claim to be in possession of Super-scientific knowledge of motion -- applicable to every region of space and time -- all that DM-theorists would be able to offer in support is the supposed meaning of a few words!

 

Once again, apart from an absurd alternative explanation for their possession of superior knowledge (i.e., that those making such claims are deities of some sort who have access to a profound, semi-mystical fountainhead of knowledge (concerning the nature of "reality-in-itself")), 'conceptual or linguistic analysis' is the only conceivable source of hyper-bold 'dialectical' claims like these.

 

And that explains why Engels omitted the data supporting his 'theory' -- and no one since has bothered to supply any.32

 

 

Exclusively Linguistic?

 

It might be felt that the above discussion completely misses the point: DM deals with real material contradictions in the actual world, verified by careful empirical investigation and tested in practice. Not only that, it is based on the thesis that reality is contradictory (and that is itself founded on the scientifically confirmed belief in universal change). It goes way beyond the idea that this is only true of the language we use to depict nature. If contradictions in nature are difficult to capture in ordinary language that is because ordinary language is inadequate to the task (as, indeed, TAR itself maintains; cf., Rees (1998), pp.45-52). It certainly doesn't show that reality is free from contradictions.

 

Or, so it could be argued, once more.33

 

However, this response won't do. Admittedly, the world is the way it is independent of language and human knowledge, but unless we are capable of expressing ideas about the world in a clear and determinate manner we are surely in no position to make any definite claims about it. This is all the more so with respect to DM where every attempt to render it perspicuous has failed -- as we have just seen in relation to Engels's account of motion (and as we will see with respect to other core DM-theses in other Essays posted at this site). This is quite apart from the fact that it is impossible to verify Engels's claims about motion "by careful empirical investigation and tested in practice", just as it ignores the fact that practice is an unreliable guide when it comes to testing the truth of a theory.

 

Moreover, Engels certainly thought he could derive what he took to be a contradiction from a consideration of ordinary words depicting movement and change. But, if his 'derivation' (and, indeed, Hegel's) is shot-through with vagueness and ambiguity, the motivation to claim that reality is contradictory is fatally compromised; and it fades further into oblivion when it is recalled that this idea itself is based on a series of egregious logical blunders that Hegel committed. What is more, it will remain in that state unless and until DM-theorists produce the evidence that motion everywhere in existence (past, present and future) is as they say it is -- or until they succeed in demonstrating that they have an alternative way of 'intuiting' the 'deeper aspects of reality' that are mysteriously unavailable to the rest of us.

 

Objects and events in nature do not confront humanity already sorted, labelled and categorised. We do not literally see contradictions in reality; they require considerable argumentative stage-setting even before dialecticians can themselves assert that they exist. Hence, the question whether there are 'objective' contradictions in nature -- based as it is (in this case at least) on a quirky misuse of language (almost on a par with the bogus question whether the King in chess really did marry the Queen -- or, indeed, whether they received planning permission to build those two Castles in the corner) -- is itself irredeemably confused. And, of course, to such non-questions there are no answers.34

 

Plainly, it is the non-standard interpretation that dialecticians put on ordinary words that conjures into existence the paradoxes they then label "contradictions" -- that is, even when they manage to get that word right.

 

In which case, far from reality being 'contradictory', it is the DM-use of language that is incoherent and paradoxical.

 

 

Conclusion

 

In this Essay, we have seen that Engels's account of motion is not only shot-through with ambiguity and equivocation, it is irredeemably obscure. Even if we knew what he was banging on about, his 'analysis' depends on an asymmetric convention that places no limit on the divisibility of space while it places a limit on the divisibility of time.

 

Even if the above asymmetric division is waved to one side, his 'theory' would imply that moving objects, if they are anywhere, they are everywhere all at once, and that they do not so much move as expand (or contract) alarmingly.

 

Finally, we have also seen that his conclusions (even if we knew what they were) only seem to follow if we ignore the many changes in meaning that words like "place" and "move" undergo in different contexts. In fact, as things turned out, no sense at all could be made of what Engels was trying to tell his readers.

 

But, what of the so-called 'Law of Identity'? Doesn't it imply that change and movement are impossible?

 

It is to this latest pseudo-problem that I now turn.

 

 

Notes

 

1. Dialectical 'Contradictions'

 

[This forms part of Note 1.]

 

It isn't easy to form a clear idea of the DM-thesis that reality is fundamentally contradictory:

 

"Instead of speaking by the maxim of Excluded Middle (which is the maxim of abstract understanding) we should rather say: Everything is opposite. Neither in heaven nor in Earth, neither in the world of mind nor of nature, is there anywhere such an abstract 'either-or' as the understanding maintains. Whatever exists is concrete, with difference and opposition in itself. The finitude of things will then lie in the want of correspondence between their immediate being, and what they essentially are.

 

"Contradiction is the very moving principle of the world: and it is ridiculous to say that contradiction is unthinkable. The only thing correct in that statement is that contradiction is not the end of the matter, but cancels itself. But contradiction, when cancelled, does not leave abstract identity; for that is itself only one side of the contrariety. The proximate result of opposition (when realised as contradiction) is the Ground, which contains identity as well as difference superseded and deposited to elements in the completer notion." [Hegel (1975), p.174; Essence as Ground of Existence, §119. Bold emphases added.]

 

"[B]ut contradiction is the root of all movement and vitality; it is only in so far as something has a contradiction within it that it moves, has an urge and activity." [Hegel (1999), p.439, § 956. Bold emphasis added.]

 

"Dialectics…prevails throughout nature…. [T]he motion through opposites which asserts itself everywhere in nature, and which by the continual conflict of the opposites…determines the life of nature." [Engels (1954), p.211.]

 

"[Among the elements of dialectics are the following:] [I]nternally contradictory tendencies…in [a thing]…as the sum and unity of opposites…. [E]ach thing (phenomenon, process, etc.)…is connected with every other…. [This involves] not only the unity of opposites, but the transitions of every determination, quality, feature, side, property into every other….

 

"In brief, dialectics can be defined as the doctrine of the unity of opposites. This embodies the essence of dialectics….

 

"The splitting of the whole and the cognition of its contradictory parts…is the essence (one of the 'essentials', one of the principal, if not the principal, characteristic features) of dialectics….

 

"The identity of opposites…is the recognition…of the contradictory, mutually exclusive, opposite tendencies in all phenomena and processes of nature…. The condition for the knowledge of all processes of the world in their 'self-movement', in their spontaneous development, in their real life, is the knowledge of them as a unity of opposites. Development is the 'struggle' of opposites…. [This] alone furnishes the key to the self-movement of everything existing….

 

"The unity…of opposites is conditional, temporary, transitory, relative. The struggle of mutually exclusive opposites is absolute, just as development and motion are absolute…." [Lenin (1961), pp.221-22, 357-58. Italic emphases in the original; bold emphases added.]

 

"Motion is a contradiction, a unity of contradictions." [Ibid., p.256.]

 

[See also Note 2, below.]

 

With respect to DM, at least, this is largely because the whole topic has been discussed (by dialecticians) with the utmost lack of clarity -– the work of Graham Priest excepted, of course.

 

In Essays Four, Six, Eight Parts One, Two, Three, and Eleven Part One, as well as below, I hope to demonstrate that while DM-theorists frequently use the term "contradiction" in their attempt to expose the alleged limitations of FL, the vast majority of them display little or no comprehension of either. Nevertheless, this hasn't prevented them from claiming that their understanding of "contradiction" is superior to that of Formal Logicians -- reminiscent of the way Donald Trump says he knows more than the Generals.

 

According to dialecticians, the wider application of this term (in DM) allows them to account for motion and change, while those who confine themselves to the use of FL are unable to do this adequately (or at all!). However, as we will see in this Essay, that allegation is grossly inaccurate -- at least with respect to motion. Indeed, the other Essays published at this site will also show that not only can DL not account for change itself, dialecticians struggle to account for something as mundane as a bag of sugar!

 

[DL = Dialectical Logic; LOC = Law of Non-Contradiction; FL = Formal Logic.]

 

Clearly, the term "contradiction" is employed in FL in a technical sense, and one that is widely misunderstood by DL-fans. [More on this in Essay Four, Eight Parts One, Two and Three, and Essay Eleven Part One.]

 

As far as ordinary language is concerned, one of the ways in which we can speak about change involves employing a linguistic rule -- which many misconstrue as a logical truth (i.e., the LOC) -- that enables us to draw certain inferences (should we choose to do so) from what might appear to be contradictory propositions. If two putatively contradictory sentences are held true at different times, then (given certain other constraints) speakers of that language would normally conclude that the subject of those sentences (if there is one) had changed. For instance, consider the following:

 

C1: NN isn't a member of Respect, at t1.

 

C2: NN is a member of Respect, at t2 (t2 > t1).

 

A change like this would usually be recorded more directly, either by the use of a tensed verb or by the employment of some form of paraphrase, as in: "NN has joined Respect", or "NN wasn't in Respect last year, but now she is", etc. This means that such apparently contradictory sentences -- coupled (i) a wider use of the negative particle (in all its forms) and the rich vocabulary we have at our fingertips (composed on verbs, adjectives and adverbs) -- are integral to our ordinary notion of change. This alone shows that the claim dialecticians make that ordinary language and FL can't cope with change is the opposite of the truth (irony intended).

 

Of course, all this is rather obvious -- but, it seems that it is so patently obvious that DM-fans regularly misconstrue it, or worse, totally ignore it.

 

[Naturally, the above was written before Respect self-destructed back in 2007! It is now called the Respect Coalition. It is also worth pointing out that the above isn't the only way we can speak about change in ordinary language! On that, see here.]

 

In which case, the idea that ordinary language and FL can't account for change is -- to speak frankly -- bizarre. In fact, without the resources available to us in the vernacular, human beings wouldn't be able to conceptualise change at all.

 

[And that comment applies equally well to scientists and dialecticians. Again, as demonstrated at the above link (at the end of the last but one paragraph), ordinary language is capable of handling change far better than the obscure and wooden terminology invented by metaphysicians. (That observation is especially true of the impenetrable jargon Hegel concocted.)]

 

In that case, if, by their use of language, dialecticians actually end up undermining the vernacular, their theory can't fail to be problematic, if not incomprehensible --, which is indeed what this Essay will demonstrate (at least with respect to the DM-'analysis' of motion).

 

Now, as far as FL is concerned, two propositions are contradictory just in case they can't both be true and can't both be false at once. [The latter condition is almost invariably ignored by DM-critics of FL i.e, that two contradictory propositions can't both be false). Some deny there is a genuine distinction here (happily confusing inconsistencies with contradictions), even after it has been pointed out to them! In fact, they tend to call such fine distinctions and careful attention to detail "pedantry", or they declare them "merely semantic". The profound dialectical confusion that results if such distinctions are ignored can be seen in all its glory, here. Its importance will emerge as this Essay unfolds.]

 

Naturally, when two contradictory propositions are conjoined -- as in ¬(p & ¬p) --, this represents the simplest form of contradiction in FL (and, in many cases, ordinary language).

 

[The difference between "contradictory" and "contradiction", also ignored by DM-fans, is explained here.]

 

Examples of more complex FL-contradictions would include either or both of the following:

 

C1: ¬[(p q) v (p r) (p (q v r))].

 

C2: ¬[¬(Ex)(Fx & ¬Gx) (x)(Fx Gx)].

 

[In the above, "(E...)" is the existential quantifier; "" is a biconditional sign (and stands for "if and only if"); "(x)" is the universal quantifier; "&" stands for "and"; "v" is the inclusive "or"; "¬" stands for the negation operator; "" is the conditional sign ("if...then"); "p", "q", and "r" are propositional variables; "F" and "G" are one-place, first-level predicate letters; and "x" is a second-level predicate-binding variable. (More details here, and here.)]

 

C1 reads: "It isn't the case that [(if p then q or if p then r) if and only if (if p then q or r)]."

 

C2 reads: "It isn't the case that [(there isn't something which is F and not G) if and only if (everything which, if it is F, is also G)]."

 

Some might wonder when sentences like these would ever be used. However, Mathematical Logic and the Foundations of Mathematics are choc full of propositions like this, and many others that are far more complex. (This links to a PDF.)

 

These are, of course, just two of the potentially infinite number of logical contradictions which can be generated in MFL. DM-theorists would be hard-pressed to find space -- even in their quirky universe -- for contradictions like these (once they have been interpreted).

 

[MFL = Modern Formal Logic; LEM = Law of Excluded Middle; PB = Principle of Bivalence.]

 

Moreover, dialecticians often conflate the LEM, the PB, propositional bi-polarity, and the LOC -- and all of them with opposites, inconsistencies, absurdities, contraries, paradoxes, puzzles, quandaries, oddities, irrationalities, oppositional processes, antagonism, forces, events that go contrary to expectations, alongside a host of other idiosyncrasies. In fact, they are so eager to see contradictions everywhere, they find they have to alter the meaning of "contradiction" so that (for them) it becomes synonymous with "struggle", "conflict" or "opposition".

 

[More details on these and other dialectical confusions and convolutions are given in Essays Four, Six, Eight Parts One, Two and Three, and Eleven Part One.]

 

A typical example of this DM-genre surfaced in a letter sent to Socialist Worker at the end of August 2011:

 

"China's elite is contradictory

 

"I'm writing regarding Charlie Hore's article on economic growth during the reform period in China (Socialist Worker, 20 August). It doesn't mention the powerful contradictions that emerged within the ruling bureaucracy as a result of the reforms. Not all sectors of the bureaucracy have benefited from the reforms. There has been a shift from ideological campaigns towards a performance-based notion of state legitimacy. This has meant that many officials have experienced anxiety about their relevance in Chinese politics and have been dragged into protest movements. A socialist analysis has to make sense of these contradictions." [Bold emphasis added. Paragraphs merged to save space.]

 

So, tensions within the communist hierarchy are 'contradictions', are they? But, no one ever explains why such things should be called "contradictions" when they are obviously far better described as "tensions" or "conflicts". [For example, do they imply one another? No. Can one exist without the other? Yes. This is quite unlike the alleged 'contradiction' between the bourgeoisie and the proletariat, where one supposedly implies the other and where both can't exist without one another.]

 

Some might conclude that this is just another example of Ms Lichtenstein's pedantry, but that isn't so. [On 'pedantry', see here.] There are important political reasons for rejecting the use of "contradiction" in the way it has been employed by Dialectical Marxists. [On that, see Essay Nine Part Two.]

 

Specifically:

 

(1) Its use 'allows' dialecticians to argue for anything they like and its opposite (often this is done by the very same dialectician, on the same page or in the same speech!), no matter how anti-Marxist or counter-revolutionary this "anything" might prove to be. These are then often 'justified' on the basis that since everything is 'contradictory', and a 'unity of opposites', Marxist theory and practice should be contradictory, too!

 

(2) It is used to rationalise a whole raft of substitutionist tactics, strategies and manoeuvres on the grounds that although Marx, for example, insisted on the self-emancipation of the working class, we can substitute for the proletariat one or more of the following: (i) The Party, (ii) The Red Army, (iii) 'Third World' guerrillas, (iv) 'Progressive' nationalists, (v) Students, (vi) Sympathetic, left-leaning politicians, or (vii) An assortment of other social forces and groups, no matter how contradictory this might seem. And of those who object..., well they just don't 'understand' dialectics, or, indeed, the 'contradictory' nature of Marxism, the class war, the former USSR..., etc., etc.

 

(3) The use of this word 'allows' DM-fans to look at the protracted failure of Dialectical Marxism and fail to see it for what it is: a long-term and profound refutation of their core theory, 'Materialist Dialectics'. In fact, it also 'allows' them to see this abysmal record as the opposite of what it is -- on the grounds that appearances 'contradict' underlying 'essence'. So, if Dialectical Marxism looks hopelessly unsuccessful and a catastrophic failure, the opposite is in fact the case. This then encourages dialecticians to stick their heads in the sand, while our movement slowly runs into those very same sands.

 

(4) Because of (3), the use of this word provides DM-acolytes with a source of consolation for the long-term ineffectiveness of their entire movement, its serial divisiveness and its ever present internecine warfare ("Well, what else can one expect in a contradictory universe?").

 

So, this isn't 'pedantry', nor is it merely 'academic' point-scoring; the use of this word has had, and still possesses, disastrous political implications.

 

[I present many more examples of the odd things DM-fans say about their 'contradictions' in Essay Eight Part Two -- here and here, for instance.]

 

Be this as it may,  DM-theorists themselves would be the first to point out that their interest lies not so much with contradictory propositions as it does with real material forces, which express, or even constitute, conflicts in nature and society (but only if they have been confirmed in practice). Furthermore, since the vast majority of classical DM-theorists believe that reality itself is fundamentally contradictory, then, according to them, propositions which accurately describe the world ought to be contradictory, too -- i.e., they should reflect the contradictions that exist in nature and society.

 

But, because (contradictory) propositions are, manifestly, linguistic expressions they plainly aren't material forces, as such. This must mean that they aren't oppositional per se -- even though they supposedly reflect, or can be used to reflect (at some level) the dynamic nature of certain processes in reality -- again, according to dialecticians.

 

On the other hand, even if contradictory propositions were oppositional, they would be so only in a derivative sense. In any case, the idea appears to be that while objects and processes in nature are contradictory (or their inter-relationships are) and subject to change, any use of language aimed at depicting reality must reflect this adequately if it is to be both accurate and objective.

 

Or, so a (very brief) case for the defence might proceed.

 

However, the principles that underlie FL merely commit us to the view that two contradictory propositions can't both be true and can't both be false at the same time. Hence, on this basis, any claim that two supposedly contradictory propositions can be, or are both true at once (or can be, or are both false at once -- as noted above, dialecticians appear to be unaware of the latter caveat) would automatically be regarded as mistaken or confused in some way.

 

Indeed, that fact alone could provide sufficient grounds for questioning whether one or both of a pair of allegedly true 'contradictory' propositions on offer were in fact propositions to begin with. If it is unclear what is being proposed (in the sense of "putting something determinate up for consideration"), then anyone attempting to do this can't be proposing anything determinate -- that is, this side of their words being disambiguated. [Examples of that strategy are given below, and later in the main body of this Essay. See also here.]

 

That is, no more than we would accept, say, that someone had presented us with a gift if they then promptly took it back again.

 

Be this as it may, several factors might contribute to this quandary: (i) The said 'propositions' could contain typographically similar words that have different denotations; (ii) They could harbour ambiguous, vague, or figurative expressions; (iii) They might be drawn from different areas of discourse; or (iv) The might have been taken out of context -- and so on.

 

Based on one or more of the above, the presumption would always be that both 'halves' of an alleged contradiction could only be held true by someone in the grip of some form of linguistic or interpretative confusion. 'Contradictions' that have been generated in this way wouldn't normally be regarded as capable of revealing fundamental truths about reality; they would perhaps convey more about the linguistic naivety of anyone so easily bamboozled.

 

In that case, the disambiguation, or clarification, of these alleged 'contradictions' should be expected to eliminate the 'problem'. Only an exceedingly naive person (or worse, a Mad Dog Idealist, like Hegel) would conclude that just because certain words, or sentences, appear to be contradictory, nature and society must be contradictory, too.

 

Indeed, the above austere approach to what appear to be contradictions should recommend itself to materialists; not only was the alternative view (that there are 'contradictions' in reality) invented by card-carrying mystics, it 'implies' that the natural world possesses properties that are only rightly attributable to human beings -- i.e., the ability to converse, argue, and disagree (i.e., they can contradict one another).

 

In addition, and to its credit, this austere approach undermines the traditional doctrine that fundamental aspects of reality may be inferred solely from the logical properties of language -- or, rather, in this particular case, that they can be derived from a series of sophomoric errors concerning the nature of contradictions (outlined a few paragraphs back, but in much more detail, here).

 

Naturally, DM-apologists will view claims like these with some suspicion; indeed, they might even appear (to them) to be dogmatic and aprioristic. Furthermore, it could be argued that this obsession with the fine detail of linguistic usage itself collapses into LIE, since it presumes to offer a linguistic solution to what is in fact a philosophical, scientific or practical problem.

 

[LIE = Linguistic Idealism. Follow the link for an explanation.]

 

However, the opposite of this is in fact the case; the approach adopted here seeks to undermine the traditional, metaphysical dogma (which dialecticians themselves have appropriated) that fundamental truths about reality may be inferred solely from language, 'thought' and/or 'concepts'. But, it is the world (or our appeal to the facts) that makes what we say true or false; it isn't what we say, or how we say it, that determines the nature of reality. It is that approach, the traditional view of philosophical 'knowledge', that is associated with Idealism:

 

"A consistent materialism cannot 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 emphases added.]

 

[As Essay Seven shows, DM-contradictions can't be confirmed by experience, nor can they be verified in any other way. (The allegation that this view of confirmation, coupled with the emphasis placed on it in these Essays, smacks of 'positivism', or even 'empiricism', has been batted out of the park, here.) In Essay Twelve, the ideological motivation underlying the contrary view will be exposed for what it is: a form of LIE (summary here).]

 

Nevertheless, it is important to be able to recognise when the descriptive, representational, and expressive capacities of language begin to break down. This is relevant with respect to DM-theses -- since they break down alarmingly quickly; indeed, when examined closely, they invariably turn out to be either hopelessly vague, terminally confused, non-sensical or incoherent -- as several Essays posted at this site have demonstrated.

 

Moreover, it is equally important to be able to distinguish spurious pictures (or, indeed, non-pictures) of reality from the genuine article. DM-theorists themselves attempt to do this when they highlight the confused or self-contradictory nature of rival theories, and advocate their rejection on that basis. [This allegation is substantiated in Essay Eleven Part One.]

 

On the other hand, DM-theorists believe that their analysis begins with reality (albeit 'mediated' by the conceptual or practical resources available to human beings at any given time); they then require that our linguistic resources are adapted, even upgraded, accordingly. On this view, if nature is contradictory and ordinary language and FL can't accommodate that fact, then that must be because they are limited, or defective, in some way -- hence, should be supplemented with concepts drawn from 'Materialist Dialectics', or even from Hegel, himself.

 

It isn't easy for a response to this to appear un-dogmatic. Language has been moulded throughout history by an evolving set of social norms and conventions, which were themselves refined by factors at work across several Modes of Production. Because of this, it might seem possible to argue that, when faced with situations that appear to be 'contradictory', human beings not only could, they actually did, develop and then adopt dialectical categories or concepts.

 

[However, the 'factual basis' underlying that supposition will be seriously undermined in Essay Fourteen Part One (summary here), and briefly below.]

 

Even so, given other conventions that were in fact adopted -- that is, in practice; no one supposes that overt decisions were taken here --, the above scenario is extremely unlikely.

 

As the word itself suggests, to contradict someone is to gain-say or deny that what they have uttered is true (or false, as the case may be). So, if NN says it is raining, and MM says it isn't, then (all things being equal) they would be contradicting one another, and this isn't affected in the slightest by either one of the following being the case (in the vicinity of these interlocutors): (a) It is pouring down with rain, or (b) It is dry as a bone.

 

Whether or not "It is raining" is actually true in no way affects the fact that these two sentences are contradictory. All that is required is that if one of them is true, the other is false, and vice versa. We wouldn't be able to understand anyone who claimed that both NN and MM were mistaken. Fanciful circumstances to one side (which was partially the point of the "all things being equal" clause being added, above), how is it possible for it to be false that it is raining and false that it isn't raining at the same time and in the same location?

 

Some might point to the vagueness of sentences like "It is raining". This would seem to mean that both of the above could in fact be false, since it might be indeterminate whether it is raining or not (i.e., when the weather is clearing up, so that anyone who said it was raining would be wrong, just as anyone who said it wasn't would be, too). To be sure, sentences like these are vague, but just as soon as it had been decided that it is actually raining, then just one of the following sentences would be false and the other true: (a) "It is raining", (b) "No, it isn't raining". The same is the case in reverse -- i.e., if it had been decided that it isn't in fact raining: one of (a) or (b) would be false, but no both. In circumstances like these, we wouldn't be able to make sense of anyone who said both were false, or both were true.

 

But, what if we can't decide if it is or it isn't raining? In that case, these sentences would be neither true nor false until a decision had been made either way. In such circumstances, they would fail to be propositions until this had been resolved. If we can't decide when it is raining or when it isn't then nothing determinate will have been proposed (i.e., put forward for consideration) by saying it is, or by saying it isn't. I am of course speaking about a radical failure to decide, here, that is, where no one could decide, even in theory, whether or not it is raining (in the vicinity of those attempting to decide). If it were in principle impossible to decide in such cases, then there would be no point to uttering such sentences, and they wouldn't have entered the language. It is raining" would lack a sense.

 

However, in what might be described as non-radical circumstances, where it still can't be decided whether or not it is training for contingent reasons -- maybe the interlocutors in question are trapped underground, are locked away in a dungeon, can't see outside, or can't receive any information from the outside for some other reason -- then these two sentences would still be contradictory, since if one of them were true (whether or not this is known) the other would automatically become false.

 

However, in everyday life (i.e., outwith the use of aesthetic, ethical, political and religious vocabulary (etc.), where the meaning of words is often "essentially contestable"), these sorts of problems do not normally arise. When in doubt, we say things like "It is trying to rain...", "It is spitting, I think...", or "I reckon it is clearing up...". Only a hardcore contrarian would come out with statements like "It is and it isn't raining" -- perhaps on the basis that there are gaps between the raindrops, or because it is raining in the vicinity, but not, say 100 metres down the road, or in the next county. If someone were consistently to adopt this approach to all such sentences, they would have very few friends or they would enjoy a severely limited social life -- either that, or they would be diagnosed with a Personality Disorder of some sort. And, if we all adopted such an attitude, inter-communication would grind to a halt. [On that, see also here.]

 

Moreover, contradicting someone could be aimed at challenging a truth, and not always confronting falsehood, as many seem to think.

 

It could be objected that it was earlier claimed that:

 

...if NN says it is raining, and MM says it isn't, then (all things being equal) they would be contradicting one another, and this isn't affected in the slightest by either one of the following being the case (in the vicinity of these interlocutors): (a) It is pouring down with rain, or (b) It is dry as a bone.

 

Whether or not "It is raining" is actually true in no way affects the fact that these two sentences are contradictory.

 

When it was asserted a few paragraphs later:

 

But, what if we can't decide if it is or it isn't raining? In that case, these sentences would be neither true nor false until a decision had been made either way. In such circumstances, they would fail to be propositions until this had been resolved. If we can't decide when it is raining or when it isn't then nothing determinate will have been proposed (i.e., put forward for consideration) by saying it is, or by saying it isn't. I am of course speaking about a radical failure to decide, here, that is, where no one could decide, even in theory, whether or not it is raining (in the vicinity of those attempting to decide). If it were in principle impossible to decide in such cases, then there would be no point to uttering such sentences, and they wouldn't have entered the language. It is raining" would lack a sense.

 

Which is it to be? If we can't say whether sentences like these are true or whether they are false, then how can they be contradictory?

 

The objector forgot to quote this caveat:

 

All that is required is that if one of them is true, the other is false, and vice versa.

 

And we can arrive at that conclusion well in advance of knowing whether one of them is in fact true, or whether one of them is in fact false. As noted below, this capacity is based on rules we have for the use of the negative particle, and, as with any rule, we can decide how that rule can or can't be applied in advance of actually applying it. For instance, we can decide what would, and what would not count as offside in football (soccer) even if there is no game actually being played when we so decide, and even if no more games are ever played --, and even if, during a game, we lose sight both of the pitch and the alleged offence itself (if the pitch is fog bound, for example). Plainly, that is because rules aren't capable of being true or false themselves; they are practical or impractical, applied or mis-applied, useful or useless, etc. Hence, this particular rule is independent of any alleged truth or falsehood, as such.
 

This topic is, of course, connected with the so-called 'Law of Excluded Middle' [LEM], as it is supposed to feature in ordinary discourse. In that case, some might be tempted to agree with Hegel when he asserted the following:

 

"Instead of speaking by the maxim of Excluded Middle (which is the maxim of abstract understanding) we should rather say: Everything is opposite. Neither in heaven nor in Earth, neither in the world of mind nor of nature, is there anywhere such an abstract 'either-or' as the understanding maintains. Whatever exists is concrete, with difference and opposition in itself. The finitude of things will then lie in the want of correspondence between their immediate being, and what they essentially are." [Hegel (1975), p.174; Essence as Ground of Existence, §119. Bold emphasis added.]

 

To which Engels added this oft quoted gloss:

 

"To the metaphysician, things and their mental reflexes, ideas, are isolated, are to be considered one after the other and apart from each other, are objects of investigation fixed, rigid, given once for all. He thinks in absolutely irreconcilable antitheses. 'His communication is "yea, yea; nay, nay"; for whatsoever is more than these cometh of evil.' [Matthew 5:37. -- Ed.] For him a thing either exists or does not exist; a thing cannot at the same time be itself and something else. Positive and negative absolutely exclude one another, cause and effect stand in a rigid antithesis one to the other.

 

"At first sight this mode of thinking seems to us very luminous, because it is that of so-called sound common sense. Only sound common sense, respectable fellow that he is, in the homely realm of his own four walls, has very wonderful adventures directly he ventures out into the wide world of research. And the metaphysical mode of thought, justifiable and even necessary as it is in a number of domains whose extent varies according to the nature of the particular object of investigation, sooner or later reaches a limit, beyond which it becomes one-sided, restricted, abstract, lost in insoluble contradictions. In the contemplation of individual things it forgets the connection between them; in the contemplation of their existence, it forgets the beginning and end of that existence; of their repose, it forgets their motion. It cannot see the wood for the trees.

 

"For everyday purposes we know and can say, e.g., whether an animal is alive or not. But, upon closer inquiry, we find that this is, in many cases, a very complex question, as the jurists know very well. They have cudgelled their brains in vain to discover a rational limit beyond which the killing of the child in its mother's womb is murder. It is just as impossible to determine absolutely the moment of death, for physiology proves that death is not an instantaneous momentary phenomenon, but a very protracted process.

 

"In like manner, every organic being is every moment the same and not the same, every moment it assimilates matter supplied from without, and gets rid of other matter; every moment some cells of its body die and others build themselves anew; in a longer or shorter time the matter of its body is completely renewed, and is replaced by other atoms of matter, so that every organic being is always itself, and yet something other than itself." [Engels (1976), pp.26-27. Bold emphases added; quotation marks altered to conform with the conventions adopted at this site.]

 

However, as I have argued in Essay Nine Part One:

 

Nevertheless, it is difficult to see what Hegel was trying to say here. That is because any attempt to interpret him requires the use of the very terms he claims are misleading. The construal of his work requires decisions be taken about whether he meant either this or that by what he actually wrote. If an author always means both (or maybe even neither) then interpretation is rendered impossible and any attempt to unravel their meaning becomes self-defeating (as we are about to see).

 

So, if Hegel were right, if absolutely "everything is opposite", and there is no "either-or" anywhere in the universe, it would be impossible to disentangle what he meant from what he didn't, since we would be unable to decide whether he believed of, say, any two sentences "P" and "Q" one or more of the following:

 

H1: (i) Both P and Q; (ii) either P or Q; (iii) neither P nor Q; or (iv) either P or Q, but not both.

 

But, if, say, P and Q were inconsistent (that is, if, for instance, Q implies not P, or vice versa -- I give an example, below), and we interpreted his words one way (perhaps that he believed both P and Q, since to do otherwise would involve the use of the dread 'either-or'), then we would have to conclude that he accepted both as part of the "unfolding of truth" (as he might have put it), which would mean by his own lights, of course, that we would be unfolding error instead!

 

So, in order to reject one or other of these two options, we would be forced to appeal to the "either-or" -- that is, we would have to conclude that Hegel accepted P or he accepted Q, but not both.

 

However, if we were to remain true to Hegel's dictum -- that "neither in heaven nor in Earth, neither in the world of mind nor of nature, is there anywhere such an abstract 'either-or' as the understanding maintains" --, then we would have to conclude he accepted both.

 

So, any attempt made now to specify exactly what Hegel meant would undermine what he actually said about the use of the "either-or of understanding", for we would have to accept that Hegel asserted one thing (P), or he asserted something else (Q), but not both. Without this assumption it would become impossible either to comprehend or defend him. If Hegel genuinely cast doubt on the "either-or of understanding" (and he wasn't being deliberately enigmatic, disingenuous, mendacious, or merely playful) -- and assuming he was correct to do so  --, then any attempt to interpret him as asserting P or asserting Q would have to conclude that he asserted both. [Again, I give a clear example of this, below.]

 

In that case, any determinate interpretation of Hegel would have to ignore his own advice, and reluctantly accept the deliverances of the "either-or" of ordinary language (or 'commonsense', along with its corollaries), and acknowledge that, concerning either P or Q, he believed only one, not both.

 

Here, truth would advance -- with yet another dialectical inversion -- by forcing us to disregard Hegel!

 

In order to make this more concrete, let us suppose that:

 

"P" is: "Neither in heaven nor in Earth, neither in the world of mind nor of nature, is there anywhere such an abstract 'either-or' as the understanding maintains",

 

and,

 

"Q" is: "There is in fact an abstract 'either-or' somewhere in the world of mind or of nature (etc.)."

 

Now, either Hegel accepted P or he accepted Q -- which would, of course, imply that there is at least one 'either-or' "in heaven or in earth (etc.)" -- i.e., here, right in front of us, right here, right now!

 

On the other hand, if he (or we!) took his advice and accepted both P and Q, rejecting this annoying "either-or", then not much sense could be made of what he was trying to say.

 

Incidentally, the above criticism isn't affected by Hegel's own interpretation of these controversial words (nor any technical meaning his epigones might want to attribute to them, since they, too, would have to conclude that he meant this or he meant that, not both), but solely concerns how we are to understand him now, in this world, by our perusal of those very material words (in print, or on a screen), quoted earlier.

 

Hence, it is beside the point whether the rationale for his own (dialectical, then speculative criticism) of the use of such words by the "abstract understanding" is legitimate or not (irony intended). Since Hegel's writings appear before us now as phenomenal objects, given also that they aren't self-interpreting (when we recall that Hegel is no longer with us to explain himself -- but, even then we would have to accept he meant either P or Q, not both), they face the ordinary cannons we employ elsewhere to understand anyone's words. In order to read and perhaps interpret Hegel as believing this or that, but not both, we are forced to ignore his advice and employ the dread "either-or".

 

Naturally, this is just one more reason why ordinary language can't be by-passed, or undermined, no matter which 'genius' cons some of us into thinking otherwise.

 

Once again, it is little use complaining that this is not how Hegel wanted his use of the "either-or" of "understanding" to be interpreted (i.e., ironically, that is, that we view it this way but not that), since he himself holed that complaint well below the water line when he asserted:

 

"Instead of speaking by the maxim of Excluded Middle (which is the maxim of abstract understanding) we should rather say: Everything is opposite. Neither in heaven nor in Earth, neither in the world of mind nor of nature, is there anywhere such an abstract 'either-or' as the understanding maintains. Whatever exists is concrete, with difference and opposition in itself. The finitude of things will then lie in the want of correspondence between their immediate being, and what they essentially are. Thus, in inorganic nature, the acid is implicitly at the same time the base: in other words, its only being consists in its relation to its other. Hence also the acid is not something that persists quietly in the contrast: it is always in effort to realise what it potentially is." [Hegel (1975), p.174, §119.]

 

Hence, if "everything is opposite", and Hegel's works were written somewhere on this planet, and copies of them still take on physical form in this universe(!), then anything he committed to paper must be its own opposite, too --  or, he was wrong.

 

[Irony intended again.]

 

In either case, it would be foolish to believe Hegel was serious (or, and what is far more likely, that he had thought things through with due care) when he wrote the above words, while also accepting what he said about the LEM -- the dread "either-or".

 

So, and following Hegel's own advice, the above passage should in fact be re-written along the following 'Hegelian' lines:

 

"Instead of both speaking and not speaking by the maxim both of Excluded Middle and not Excluded Middle and (which is and is not the maxim of abstract understanding) we should and we shouldn't rather say: Everything is, and some things are not, opposite. Neither in heaven nor in Earth, and both in heaven and in earth, neither in the world of mind nor of nature, and both in the world of mind and of nature, is there anywhere such an abstract 'either-or' as the understanding maintains, but there is, and it is everywhere, too, while it is nowhere as well. Whatever exists is concrete, and it isn't, with difference and opposition, and also without difference or opposition, in itself, and in other things, too. The finitude of things will and will not then lie in the want of correspondence, but also with actual correspondence, between their immediate being, and what they essentially are, or are not, and, indeed, both. Thus, in inorganic nature, and outside of it, the acid is and is not implicitly at the same time, and at other times, the base, but it isn't the base, either: in other words, but also in the same words, its only being, and its many other beings, consist, and do not consist, in its relation, and absence of any relation, to its other, and whatever isn't its other. Hence also the acid is not something, and it is something, that persists quietly, and noisily, in the contrast, or the accord: it is always, and is it is never, in effort to realise what it potentially is, and what it actually is not."

 

Everyday, boring old non-abstract understanding will, I think, readily see what arrant nonsense results from Hegel's 'genius' when we apply his ideas to his own words -- providing we remain in this universe.

 

Any who object to the above re-write can, of course, neutralise its implications by demonstrating that Hegel's work wasn't actually written in this universe, or on real paper, but was written on Ideal paper, neither in heaven nor on earth -- and that they themselves don't exist anywhere, either (or both, or neither), in order to do that (or not).

 

[On the 'acid and base' fiasco, even should we take Hegel seriously, see here.]

 

In a recent book [Stewart (1996)], a number of misinterpretations and misrepresentations of Hegel's work were corrected by a handful of Hegel scholars. However, there would seem to be little point to this exercise if Hegel's ideas about "either-or" are to be believed. If he were right -- that in the entire universe there is no "either-or" -- there would be some truth even in the wildest allegations about him or his work.

 

For instance, these: that (i) Hegel fully accepted without question the unlimited applicability of the LOI in every conceivable circumstance without any qualifications whatsoever (and this includes its use in dialectical and speculative thought as well as in relation to change, conceptual or material), and he did not; that (ii) he flatly denied that reality or thought is contradictory in any sense at all, and he did not; that (iii) he doubted the truth of every single one of his own ideas all the time, and he did not; that (iv) he wrote nothing at all in German in his entire life, and he did not; that (v) everything he wrote was actually written by Schelling -- in fact it was published only yesterday, and it wasn't --; that (vi) he was a Shape-shifting Martian, and he was not...

 

[Anyone attempting to reject one or more of the above alternatives on the grounds that Hegel must have accepted one of them, but not both -- or, indeed, that they must do likewise -- will, alas, have to employ the dread LEM in order to do so, vitiating Hegel's challenge, as well as their own.]

 

It could be objected that this completely misunderstands the nature of DL as Hegel himself conceived it. Unfortunately, even that response is framed in ordinary language -- and, it was foolishly written in this universe! --, so, since a decision has to be taken over whether or not it is valid, a quick reference to DL will indicate it is both.

 

This means that until DL-fans commit themselves to one or other view (but not both), it is impossible even to begin to evaluate anything they say -- and neither can they!

 

Unfortunately, just as soon as DL-fans actually manage to specify what they mean (i.e., that they genuinely intend this but not that), we must cease to take them seriously -- since they would then have employed the dread LEM (in this universe), undermining their own criticisms of it!

 

Either way, such defenders of Hegel may be ignored even before they decide whether they agree with the above criticisms, or not (or both).

 

It could be objected that the above conclusions are ridiculous and do not follow from a consistent application of the dialectical method; hence Hegel can't be saddled with any of them.

 

Once more, these 'ridiculous conclusions' either do or they do not follow from what Hegel wrote. If the above rebuttal is right, and they don't follow, then there is at least one either-or at work here, namely this one (since both options wouldn't be correct in that case -- only one option would be, namely that they don't follow). And, if that is so, then these 'ridiculous conclusions' do indeed follow, after all, since Hegel would in that case be wrong to assert there is no either-or anywhere in existence when one such has just been used to reject one option in favour of the other.

 

Hence, taking each 'ridiculous conclusion', one at a time, if we maintain it doesn't follow, then we will have applied the LEM once more -- in that we would thereby have denied that that particular 'ridiculous conclusion' both does and does not follow, and thus that one of these either-or options must obtain --, and we arrive at the same result.

 

On the other hand, if they do follow, then they do anyway.

 

Either way, they follow.

 

QED

 

The problem with sweeping claims like these (which litter Traditional Philosophy, and not just Hegel's ill-considered work) -- in this case, concerning the supposed limitations of certain principles of FL (and especially those that express patterns of inference mirrored in our use of ordinary language, such as the LOI, the LOC and the LEM) -- is that they invariably collapse into incoherence, as we have just seen.

 

Which is why, once again, we can say with complete confidence that no one (not even Hegel) could possibly understand Hegel!

 

It is of course possible to 'adapt' Engels's comments in like manner to take account of his own advice (but to save the reader's sanity, this has only been inflicted on half of his words):

 

"At first sight and not at first sight, this mode of thinking and of not thinking seems, and it does not seem to us, and not to us, very luminous and not at all luminous, because it is and it isn't that of so-called sound common sense and not so-called common sense. Only sound common sense, and anything other than common sense, respectable fellow that he is and isn't, in the homely realm of his own four walls and outside them too, has very wonderful adventures and slightly non-wonderful adventures directly he ventures out into the wide world of research, or whether he doesn't...."

 

So, not even Engels could have taken his own advice and hope to have made sense.

 

[Incidentally, his argument concerning the status of living organisms is destructively analysed here and here.]

 

Any who still have doubts, try them out on sentences like the following (i) "The Nile is longer than the Thames" and "Nile isn't longer than the Thames"; (ii) "Hitler was a Nazi", and "Hitler wasn't a Nazi". Now, can both of (i) and both of (ii) be true at once, or false at once?

 

So, the facility we have in language (which apparently goes back as far as records last, or as far back as human beings have been able to argue -- indeed, without it, we wouldn't be able to comprehend indicative sentences before we knew whether they were true or whether they were false (why that is so is explained in detail in Essay Twelve Part One)) -- this facility means that our ancestors clearly failed to take the DM-route. And it isn't difficult to see why. In fact, given the linguistic practices we now have (and the social relations from which they have arisen), it is impossible to make sense of the claim that a contradiction could be true (or, rather, that two contradictory propositions could both be true or could both be false -- that is, without (retrospectively) altering the meaning of the word "contradiction" itself). Indeed, we would fail to comprehend anyone who claimed that in a dispute (where someone gain-said what someone else had asserted) both sides could be speaking the literal truth -- ambiguous examples excepted, of course.

 

[In order to prevent the account presented here sliding into some form of Linguistic Psychologism, it should be read in conjunction with the careful distinctions set out in Shanker (1998), particularly Chapter Three, and especially pp.97-120. Of course, there is nothing wrong with employing the word "contradiction" in novel ways, but that having been done, these new uses can't affect its current, ordinary employment, nor can it be related to it, let alone to its role in FL.]

 

In cases where disputants might appear to be doing this (i.e., where both parties to an argument are gain-saying one another, but where both also seem to be speaking the literal truth), the most likely response would be to try to disambiguate their words in order to resolve the serious problems that 'true contradictions' would create in everyday life.

 

And this can be asserted with some confidence because, as noted above, the conventions we now have prevent us from understanding how a contradiction could be true (or, rather, how two contradictory propositions could both be true or both be false). Not only that, but, these conventions prevent us from understanding anyone who might think otherwise. Even worse still, they also prevent us from now understanding how humanity could ever have developed alternative conventions, or how we could make sense of anyone who supposed that they might have.

 

This is one intellectual river we can't now step back into, even once -- to paraphrase Cratylus.

 

In fact, these observations are connected with: (i) The way that negation works in language, and (ii) The capacity language has of allowing us to understand an empirical proposition (i.e., a fact-stating sentence) before we know whether it is true or whether it is false. [More on that in Essay Twelve Part One.]

 

[Incidentally, I have added the following codicil: "Or, rather, how two contradictory propositions could both be true or both be false", since most logicians (particularly mathematical logicians) regard contradictions as false, whereas if the LOC is a rule of language (or, even better, the LOC is an indirect expression of the rules we have for the use of the negative particle), and not a logical truth, a contradiction in language can't be true or false. If a contradiction could be false, then it could be true (for reasons explained in Essay Twelve Part One), which would create problems for how we use the negative particle. It is far better therefore to regard contradictions as senseless. (The word "sense", as it is used in most of these Essays, is explained here.) Of course, this view creates problems for the Truth Tables, but this can be overcome by a stipulation to the effect that in FL, a contradiction is always given the value "F". (This ad hoc stipulation shouldn't worry logicians since they have a similar stipulation that the identity relation is given the value "True", but for no good reason.)]

 

The above assertions might seem as dogmatic as they are controversial (that is, to DM-fans), so I shall defend each in turn.

 

Take the first of these -- which was that we should fail to understand anyone who believed a contradiction could be true (or, rather, how two contradictory propositions could both be true or both be false), and that we would seek to disambiguate it (or them) in order to make sense of what it or (they) said. Consider the following example:

 

B1: John Rees wrote and did not write The Algebra of Revolution.

 

B1a: John Rees wrote The Algebra of Revolution.

 

B1b: John Rees did not write The Algebra of Revolution.

 

Let us suppose someone asserted that both B1a and B1b were true. Faced with this, we would find it difficult to take this person, or what they said either literally or seriously; that is because both halves of B1 (i.e., B1a and B1b) couldn't be true, nor could they both be false.

 

[Some might think that these are not the type of contradictions that are of interest to dialecticians; that objection will be dealt with later on in this Note.]

 

However, if both B1a and B1b were still held true, then, trivial cases aside (such as the names "John Rees" and "The Algebra of Revolution" refer to two separate individuals or books) we could only make sense of the contradiction they seem to express by noting the ambiguous use of the word "write". In one sense of that term it could imply that John Rees was the author of the said work; in another quite ordinary sense it might suggest that the book wasn't hand-written, but was perhaps word-processed. [Or, even that Rees had used an amanuensis.] In that case, B1 would be expressing the fact that although John Rees authored the said book he did not hand-write it (or did not hand-write it himself). It would then be clear that B1 only appeared to be contradictory because of this elementary equivocation. We wouldn't automatically think that there were real material forces at work behind the struggle to produce this book, no matter how well-confirmed each half of B1 happened to be.

 

[This shows that an empirical check in such cases isn't relevant to what is in fact a logical or conceptual issue.]

 

Again, someone might object, arguing that the above argument reveals the LIE implicit in the logical caveats this Essay has expressed, for it seems to restrict the options available to reality by appealing to controversial logical or linguistic pre-conditions.

 

But, that would be to mistake the approach adopted here for its opposite. The strategy employed at this site seeks to undermine the idea that substantive truths about reality can be derived from logical, conceptual or contingent features of language. It does this by basing itself on what we would now try to do (prior to, and independently of, a pet theory) to interpret or understand what appear to be contradictions as and when they might arise. In that case, these Essays appeal to rules (i.e., normative social practices) we already use (or with which we comply), not to a series of truths that can be inferred from a misconception of their nature.

 

Hence, no 'philosophical truths' are being inferred (by me) from the above observations, merely a denial that any truths can be derived from a misconstrual of set of puzzling words.

 

Indeed, it is the opposite (dialectical) view that collapses into LIE, for it confuses such linguistic or logical rules with empirical -- or, what are in effect Super-empirical -- truths. In DM, this occurs when, for example, dialecticians treat the LOC as a truth, which they think could be (and often is) false -- or which is at least only true 'within certain limits'. Their criticism of the LOC leads them to argue that contradictions themselves can be true (or, that they can and do exist). But, if, as noted earlier, the LOC is in fact a rule (or if it expresses a rule we ordinarily use in relation to specific uses of the negative particle), it can't be either true or false -- any more than orders or questions can be true or false.

 

[Further ruminations on this theme will be resumed in Essay Twelve Part One, where it will be demonstrated in detail why the aforementioned confusion of rules with substantive truths about the world is a characteristic feature of Traditional Thought. That is because that age-old approach to philosophical 'knowledge' is predicated on the idea that there is a hidden world -- anterior to experience --, accessible to thought alone. It is from such ideologically-inspired confusion that Metaphysics (and now dialectics) originally arose.]

 

Admittedly, B1 is glaringly trite, but it was deliberately chosen so that the strategy of disambiguation would be clear to all.

 

B1: John Rees wrote and did not write The Algebra of Revolution.

 

Nevertheless, and against this, it could be objected that DM-theorists are more concerned with the study of real material forces operating inside Capitalism in order to assist in its demise. In that case, simplistic examples like B1 are not even remotely relevant. Nor are they dialectical contradictions, in the first place.

 

Or, so it could be argued.

 

In order to counter this response, the sort of contradictions DM-theorists are interested in will be analysed elsewhere at this site (and in unprecedented detail -- for example, here, here and here). There, it will be shown that "real material contradictions" turn out not to be contradictions to begin with (in any sense of that word -- on that, see here and here) -- and they can't be turned into "real material contradictions" howsoever they are interpreted, or, indeed, 'surgically enhanced'.

 

With respect to the other assertion made above -- that we would fail to understand alternative conventions, given those we already have --, the key point is that as social beings we may only succeed in understanding something when, plainly, it is presented to us in a language and a form with which we are familiar; typically, but not exclusively, this takes place in ordinary language. And that, too, can be asserted with some confidence since the word "understand" is (patently) in ordinary language already. [The significance of that point will emerge in Essay Thirteen Part Three.] But, discourse isn't a free-floating phenomenon; its invention and its evolution are a function of our social and material development. In addition, our use of language is subject to constraints inherited from previous generations, which we clearly had no hand in shaping. Indeed, all of us had to be socialised (by parents, siblings, carers, teachers and peers) into using language within, and in compliance with, these constraints. As individuals, we manifestly didn't socialise ourselves.

 

Moreover, we demonstrate our mastery of this complex socio-linguistic tool when we begin to communicate and interact with others. While we can form thoughts as we please, we can't do so under logico-linguistic or social conditions of our own choosing (to paraphrase Marx).

 

Now, it is tempting to think that these 'limitations' present some sort of a physical barrier -- or, at least, that they represent merely contingent constraints on our use of language --, but that would be a serious mistake. There are physical and contingent constraints on language (for example, no one could utter or understand a trillion word sentence), but these aren't the limitations intended.

 

[A clue to the nature of these limitations can ascertained by anyone who reads the Essays posted at this site, especially where it has been demonstrated time and again how quickly DM-theses fall apart, and how they can't be repaired no matter what is done with them. That sort of limitation isn't physical; it is conceptual. Another example can be found here.]

 

B1: John Rees wrote and did not write The Algebra of Revolution.

 

Fortunately, however, the negative criticisms of DM at this site do not depend on the validity of this latest batch of seemingly dogmatic assertions. Doubters need only think about how they themselves would interpret B1 (or indeed B2, below), and these points should become a little clearer.

 

[Incidentally, the aforementioned "limitations" aren't those that words exercise upon us; it expresses to how we collectively -- through our socialisation -- understand and thus use the words we already have. To suppose otherwise would be to fetishise language.]

 

In relation to understanding others who speak different languages, or individuals from the past, we can translate what they have to say (ancient or modern) into our own language, but we may do so only if we act within the constraints currently operating on us -- unless we want to restrict ourselves merely to simple transliteration. This means that because we can't make sense of contradictory speech now, we should find it equally difficult to comprehend how contradictions could ever have been held true by anyone in the past, either.

 

Of course, there have been mystics who professed all manner of odd and contradictory ideas. Other than Hegel, this includes, for instance, Buddhist logicians and 'teachers', but it is a moot point whether anyone has ever understood the strange things they say. Indeed, mystics themselves tell us they don't understand the conundrums they come out with. [More on this in Essay Fourteen Part One (summary here).]

 

Even so, we are equally incapable of translating (note: not transliterating) any language, ancient or modern, into our own in comprehensible terms while attempting to depict its users employing contradictory speech, all the while holding these contradictions true, or, indeed, imagining that those who engaged in such speech held them true, too. This doesn't imply that we have to reject the idea (as false) that such individuals actually believed these contradictions were true, but we certainly can't hold them true. We may acknowledge the fact that some individuals (in the past (or whenever)) speak, spoke, or have spoken in paradoxical ways, but given what we now mean by the words we use, it is now impossible to make sense of the supposed possibilities these ancient or mystical sayings could have presented to those who produced them -- nor, indeed, determine whether or not they presented anything determinate at all. Moreover, since these odd individuals invariably fail to explain themselves, it is quite clear they couldn't make sense of their own words either.

 

[DM-fans certainly can't explain their 'contradictions', and complain regularly that critics just don't "understand" dialectics.]

 

In which case, if it is now impossible to make sense of the possibility that individuals in the past held certain contradictions true then we manifestly can't comprehend the supposition that contradictions could ever have been held true by such individuals.

 

Once again, the various 'true contradictions' to which DM-theorists appeal will be examined elsewhere at this site (for example, follow the links posted above). Graham Priest's much more detailed (and logically informed) attempt to defend the idea that there can be, and are, 'true contradictions' in nature and society will be examined in a later Essay. [In the meantime, readers should consult Berto (2007), Goldstein (1992, 2004), Field (2008),  and Slater (2002, 2007a), as well as this review.] I have, however, added to Note 18a a few comments about Priest's sophisticated attempt to show that motion and change are contradictory; or as he puts it:

 

"I [have argued in support of] the idea that contradictions not only occur in certain sorts of change but actually are the states of change themselves." [Priest (2006), p.172.]

 

Some might take exception to the above assertions, claiming that they can imagine speakers holding certain contradictions true (and which contradictions do indeed represent real material forces), namely themselves! Dialecticians, it seems, are living disproof of the sweeping assertions made in this Essay.

 

Or, so it could be argued.

 

However, this Essay aims to show that Hegel and Engels's claims (that motion is 'contradictory') are far too vague and confused for them to be assessed for their truth or their falsehood (and hence that the 'contradiction' they claim to see in moving bodies isn't one to begin with). Again, other examples of dialectical 'contradictions' will similarly be dealt with in Essay Eight Parts One, Two and Three, as well as Essay Eleven Part One. In addition, the DM-thesis that reality is suffused with UOs will be destructively criticised in Essay Seven Parts One and Three.

 

[UOs = Unity of Opposites.]

 

Hence, because it isn't possible to make sense of any of the examples of 'dialectical contradictions' offered by DM-theorists, the above "sweeping assertions" have everything going for them. Since dialecticians have shown that they themselves are incapable of explaining these mysterious 'contradictions' to anyone, that can serve as further confirmation. [On this, see here.] Indeed, on Internet discussion boards, when academic Marxists and revolutionary activists alike are asked (often repeatedly) to explain what 'dialectical contradictions' are, to a clone, they fail to do so. [Links to many of these discussions can be found here.]

 

To be sure, as noted earlier, there have been, and still are, religious believers who assent to all manner of apparently contradictory ideas, but this doesn't refute the above allegations. Their talk is often non-propositional -- but is wall-to-wall, incoherent non-sense, as will be demonstrated in a later Essay. The same comment applies to such ideas expressed by Buddhists (this links to a PDF) -- or, more pointedly, to Zen Buddhists --, who seem to glory in paradox.

 

However, in relation to the claim that we wouldn't be able to make sense of the possibility that there might have been past generations who believed, or who could have believed, there were true contradictions, consider this example:

 

B2: This four thousand year old inscription says that its author wrote and did not write it.

 

Now, despite the fact that dialecticians assure us that reality is contradictory, not even they would attempt to understand B2 literally. This isn't because it would be especially difficult for them to do so, but because any claim to the contrary would undermine the meaning of the word "literally", at the very least.

 

But, even supposing a few Mad Dog Dialecticians [MDD] could be found who do attempt to do this, they would find it impossible to explain to anyone else in literal terms what sense they made of B2 (other than by disambiguating it).

 

As noted earlier, trite examples like B2 have been deliberately chosen to illustrate a point that is all too easily missed: when faced with the paradoxical things people sometimes say, we automatically try to disambiguate their words or their actions; we adopt what Donald Davidson once called the "principle of charity" when attempting to grasp their meaning and their intentions. [Davidson (2001).]

 

[Of course, in doing so, we have to distinguish between speakers' meaning (i.e., what an individual hopes to convey or achieve by their words) and word meaning (i.e., what those words mean in the language). The failure to do so leads us into the sort of confusion that undermined, for example, Voloshinov's work, as well as that of his epigones. (I have discussed this in considerable detail in Essay Thirteen Part Three.)]

 

Hence, when confronted with someone who asserted an apparent contradiction we would normally employ this policy (trivial examples excepted, of course). This doesn't mean that this will necessarily distort what an individual had said, or had written; rather, it is that we wouldn't be able to understand such individuals if we didn't do this.

 

In any case, if there still are any MDDs out there (that is, DM-supporters who reject some or all of the above points), they would be hard-pressed to explain to anyone else what they themselves took the sense of a true contradiction to be (that is, without playing yet another Nixon card), as the rest of this site aims to show.

 

[And that comment also applies to any 'dialectically-motivated' responses elicited from those who might think to question the above assertions.]

 

Clearly, this doesn't mean that we shouldn't exercise some degree of sensitivity toward other belief systems (past or present), but we may only do so in terms of current linguistic protocols. When confronted with what appears to be weird or paradoxical beliefs, we wouldn't be able to translate or interpret them literally and claim we understood them. On the other hand, if anyone claimed that they could do this, it would automatically throw into doubt the validity of their translation (unless the meaning of the word "translate" itself has changed) -- always supposing, of course, that they hadn't merely transliterated the relevant inscriptions or writings instead.

 

However, if what had been 'translated' were held to be literally true, and it still remained paradoxical, then whatever else we could make of it, we would have to abandon all talk of its literal truth. Either that, or, once again, we would have to understand the words "literal" and "truth" non-literally!

 

[This topic is still under intense debate; on his see Creary and Read (2000), especially Cerbone (2000). See also Conant (1991), and Forster (1998).]

 

So, until and unless DM-theorists explain themselves, we are forced to conclude that 'dialectical contradictions' fail to depict or express anything in any meaningful sense.

 

The above isn't being asserted because I personally think that reality contains no contradictions, or because I have concluded that the world either is or is not as these allegedly 'true contradictions' picture it -- or even because contradictions are always false (which is the classical view). To argue along those lines would be to fall into the same trap that ensnares DM-theorists, since it would amount to the derivation of the opposite a priori thesis about reality to that adopted by DM-theorists, based on an alternative linguistic convention, which I might in this case have found more acceptable.

 

On the contrary, contradictions fail to picture the world not because they are false, but because they aren't pictures to begin with. They represent the disintegration of the depictive capacity of language, since they violate materially-grounded linguistic rules we already have for the use of the negative particle. [On this, see Essay Twelve Part One.]

 

Finally, it could be argued that the above comments are misguided since dialecticians do not question the general application of principles drawn from FL, such as the LOC; they merely point to their limitations when it comes to accounting for change. Hence, contradictions like those illustrated in B1 and B2 above, are completely irrelevant.

 

B1: John Rees wrote and did not write The Algebra of Revolution.

 

B2: This four thousand year old inscription says that its author wrote and did not write it.

 

Since thee above do not depict change, their use is beside the point.

 

Or, so it could be argued.

 

That particular response will be put under considerable pressure throughout this and other Essays at this site, where it will be shown that it is dialecticians who can't actually account for motion and change.

 

Added 12/02/10: A story on the BBC website ("Do speedy elephants walk or run?") illustrates how an "either-or" question is answered by scientists without having to agree with, or even consult, Hegel:

 

"Instead of speaking by the maxim of Excluded Middle (which is the maxim of abstract understanding) we should rather say: Everything is opposite. Neither in heaven nor in Earth, neither in the world of mind nor of nature, is there anywhere such an abstract 'either-or' as the understanding maintains. Whatever exists is concrete, with difference and opposition in itself. The finitude of things will then lie in the want of correspondence between their immediate being, and what they essentially are. Thus, in inorganic nature, the acid is implicitly at the same time the base: in other words, its only being consists in its relation to its other. Hence also the acid is not something that persists quietly in the contrast: it is always in effort to realise what it potentially is." [Hegel (1975, p.174; Essence as Ground of Existence, §119. Bold emphasis added.]

 

The answer scientists give in this case is that elephants do both, they run and walk. Is this a contradiction? Does this refute the claims made above? Can this anomaly be 'resolved', DM-style by means of (i) a series of a priori, dogmatic assertions about all of reality for all of time? Or, by (ii) disambiguation? Which tactic is going to work?

 

Well, here is the article's explanation how this conundrum was in fact resolved:

 

"With their awkward, lumbering gait, elephants moving at high speed are not the most graceful of animals -- but are they walking or running? Now scientists believe they have an answer: new research confirms that they do both -- at the same time.

 

"By observing elephants moving across a hi-tech track, the team found the hefty creatures run with their front legs but walk with their back legs. The research is published in the Journal of Experimental Biology. Earlier research had suggested that elephants perform a strange, part-walk/part-run while travelling at speed. But a team from Belgium, Italy and Thailand was able to investigate this further by using a specially built track that was able to precisely measure (sic) the forces exerted with each weighty elephant step.

 

"Professor Norman Heglund, an author of the paper from the Catholic University of Louvain, Belgium, told BBC News: 'We had to build the plates -- you just can't go down to your local hardware shop and pick up an elephant-sized force plate.' Armed with these, the researchers headed to the Thai Elephant Conservation Centre to study the big beasts, which ranged from an 870kg baby to a four tonne adult. The Asian elephants were encouraged to move across the track, at speed, by their keepers....

 

"They were...filmed using high-speed cameras. By comparing the measurements from the sensitive force-measuring platform with each frame of the footage, the scientists were able to look at every tiny movement that the elephants were making.

 

"This enabled them to calculate the amounts of potential energy (stored energy) and kinetic energy (the energy that is associated movement), that the creatures were using. Measuring the relationship between potential and kinetic energy is the key to defining whether something is walking or running.

 

"For example, when walking, as an animal raises its foot from the ground and moves it forwards, it is converting the stored energy in its muscles and tendons -- the potential energy -- into kinetic energy. As its foot lands, the kinetic energy converts back into potential energy, and then back into kinetic energy as the foot is once again raised, and so on. All the time the creature is walking, the energy is transferred back and forth between potential and kinetic energy.

 

"But while running, the exchange between potential energy and kinetic energy is continuous -- rather than one form of energy being recycled into the other, back and forth, the energy exchange is happening all the time.

 

"Professor Heglund explains: 'The running gait, in most animals, is a bouncing mechanism. In this case, the potential and kinetic energy are in phase, they both hit a maximum at the same time and a minimum at the same time, so they cannot be transferred back and forth.'

 

"However, the researchers found that fast-moving elephants seem to both run and walk at the same time. Professor Heglund said: 'When an elephant goes at higher and higher speeds, the kinetic and potential energy shift and start to become more in phase. But when we looked in detail, we see that the animal appears to be running -- bouncing -- with the front legs, and walking with the back legs. It is as if he is getting up to a transition speed where he wants to transition from a walk to a run, but he can't quite do it. It's like he can't quite get up into second gear.'...

 

"The scientists now plan to look at other large animals, such as hippos and rhinos, to find out if they run or walk. This latest study confirms the findings of other research, published in the journal Nature and the Journal of Experimental Biology, that have previously shown that elephants perform a run-walk hybrid. However, there are some differences -- while this latest paper suggests the front legs run and the back legs walk, the other studies suggested the opposite." [Quoted from here. Bold emphasis alone added. Several paragraphs merged to save space. Minor typo corrected.]

 

So, this apparent contradiction was resolved by detailed observations (coupled with clear definitions and a modicum of common sense), which led to a new discovery: that elephants run with their front legs, but walk with their back legs (or the other way round!). Had these researchers been dialecticians, it is unlikely that this advance would have been made; we would merely have been told to "grasp" this 'contradiction' and move on (no pun intended).

 

[More on that in Essay Seven Part One. Compare this with the Mickey Mouse Science one finds in books on DM. General logical issues are discussed in Essay Four, and other related topics -- such as the "interpenetration of opposites" and change through "internal contradiction" -- are reviewed in Essays Seven Parts One and Three, as well as Essay Eight Parts One, Two and Three. Those who feel that the above comments do not in fact address 'dialectical contradictions' should read this, this, this, and this, and then perhaps think again.]

 

2. Engels was, of course, openly borrowing from Hegel:

 

"If, now, the first determinations of reflection, namely, identity, difference and opposition, have been put in the form of a law, still more should the determination into which they pass as their truth, namely, contradiction, be grasped and enunciated as a law: everything is inherently contradictory, and in the sense that this law in contrast to the others expresses rather the truth and the essential nature of things. The contradiction which makes its appearance in opposition, is only the developed nothing that is contained in identity and that appears in the expression that the law of identity says nothing. This negation further determines itself into difference and opposition, which now is the posited contradiction.

 

"But it is one of the fundamental prejudices of logic as hitherto understood and of ordinary thinking that contradiction is not so characteristically essential and immanent a determination as identity; but in fact, if it were a question of grading the two determinations and they had to be kept separate, then contradiction would have to be taken as the profounder determination and more characteristic of essence. For as against contradiction, identity is merely the determination of the simple immediate, of dead being; but contradiction is the root of all movement and vitality; it is only in so far as something has a contradiction within it that it moves, has an urge and activity.

 

"In the first place, contradiction is usually kept aloof from things, from the sphere of being and of truth generally; it is asserted that there is nothing that is contradictory. Secondly, it is shifted into subjective reflection by which it is first posited in the process of relating and comparing. But even in this reflection, it does not really exist, for it is said that the contradictory cannot be imagined or thought. Whether it occurs in actual things or in reflective thinking, it ranks in general as a contingency, a kind of abnormality and a passing paroxysm or sickness....

 

"Now as regards the assertion that there is no contradiction, that it does not exist, this statement need not cause us any concern; an absolute determination of essence must be present in every experience, in everything actual, as in every notion. We made the same remark above in connection with the infinite, which is the contradiction as displayed in the sphere of being. But common experience itself enunciates it when it says that at least there is a host of contradictory things, contradictory arrangements, whose contradiction exists not merely in an external reflection but in themselves. Further, it is not to be taken merely as an abnormality which occurs only here and there, but is rather the negative as determined in the sphere of essence, the principle of all self-movement, which consists solely in an exhibition of it. External, sensuous movement itself is contradiction's immediate existence. Something moves, not because at one moment it is here and at another there, but because at one and the same moment it is here and not here, because in this 'here', it at once is and is not. The ancient dialecticians must be granted the contradictions that they pointed out in motion; but it does not follow that therefore there is no motion, but on the contrary, that motion is existent contradiction itself.

 

"Similarly, internal self-movement proper, instinctive urge in general, (the appetite or nisus of the monad, the entelechy of absolutely simple essence), is nothing else but the fact that something is, in one and the same respect, self-contained and deficient, the negative of itself. Abstract self-identity has no vitality, but the positive, being in its own self a negativity, goes outside itself and undergoes alteration. Something is therefore alive only in so far as it contains contradiction within it, and moreover is this power to hold and endure the contradiction within it. But if an existent in its positive determination is at the same time incapable of reaching beyond its negative determination and holding the one firmly in the other, is incapable of containing contradiction within it, then it is not the living unity itself, not ground, but in the contradiction falls to the ground. Speculative thinking consists solely in the fact that thought holds fast contradiction, and in it, its own self, but does not allow itself to be dominated by it as in ordinary thinking, where its determinations are resolved by contradiction only into other determinations or into nothing

 

"If the contradiction in motion, instinctive urge, and the like, is masked for ordinary thinking, in the simplicity of these determinations, contradiction is, on the other hand, immediately represented in the determinations of relationship. The most trivial examples of above and below, right and left, father and son, and so on ad infinitum, all contain opposition in each term. That is above, which is not below; 'above' is specifically just this, not to be 'below', and only is, in so far as there is a 'below'; and conversely, each determination implies its opposite. Father is the other of son, and the son the other of father, and each only is as this other of the other; and at the same time, the one determination only is, in relation to the other; their being is a single subsistence. The father also has an existence of his own apart from the son-relationship; but then he is not father but simply man; just as above and below, right and left, are each also a reflection-into-self and are something apart from their relationship, but then only places in general. Opposites, therefore, contain contradiction in so far as they are, in the same respect, negatively related to one another or sublate each other and are indifferent to one another. Ordinary thinking when it passes over to the moment of the indifference of the determinations, forgets their negative unity and so retains them merely as 'differents' in general, in which determination right is no longer right, nor left left, etc. But since it has, in fact, right and left before it, these determinations are before it as self-negating, the one being in the other, and each in this unity being not self-negating but indifferently for itself.

 

"Opposites, therefore, contain contradiction in so far as they are, in the same respect, negatively related to one another. Ordinary thinking when it passes over to the moment of the indifference of the determinations, forgets their negative unity and so retains them merely as 'differents' in general, in which determination right is no longer right, nor left left, etc. But since it has in fact right and left before it, these determinations are before it as self-negating, the one being in the other, and each in this unity being not self-negating but indifferently for itself." [Hegel (1999), pp.439-41, §955-§960. Bold emphases alone added.]

 

Detailed comments on the above passage (as it has been interpreted by a particular DM-theorist, James Lawler) can be accessed here; several more will be posted in Essay Twelve Part Five at a later date.

 

3. An alternative translation -- which appears in Volume 25 of Marx and Engels Collected Works (MECW) -- renders the last sentence as follows:

 

"And the continuous origination and simultaneous solution of this contradiction is precisely what motion is." [MECW, Volume 25, p.111. This can be accessed here.]

 

The above version manages to neutralise some of the criticisms outlined in the main body of this Essay, but not all. Who, for instance, "solves" these contradictions, and how exactly do they do it? More pointedly, how do they manage to do this quite so quickly (i.e., simultaneously with the "origination" of each new contradiction)? And so many times (there must be billions of these 'solutions' dotted all along the trajectory of even the shortest journey)? When this contradiction is "solved" does this mean that a moving object is no longer in two places at once, in one of these and not in it at the same time? If not, what does it mean?

 

Perhaps even more significant: has a single DM-fan ever asked these questions, let alone tried to answer them? Or have they become so theoretically supine that their critical faculties have failed them?

 

Furthermore, this passage introduces several difficulties of its own, for it leaves it entirely mysterious from where these contradictions originated. Indeed, it appears to promote contradictions above motion; they seem to cause it, not it them.

 

Naturally, in a system that has descended with modification from AIDS -- where reality is just the development of Mind -- the ability of 'contradictions' to cause change, or make things move, seems to make some sort of crazy sense. Apart from that, it doesn't.

 

[AIDS = Absolute Idealism.]

 

4. On this, see Note 3, above.

 

However, as we discovered in other Essays posted at this site, dialecticians regularly make this mistake, imagining that they are talking about the world when in fact they are indirectly drawing attention to their own idiosyncratic use of language and the implications thereof. That is, of course, part of the reason why DM is classified here as a form of LIE. [For more on this, see Essays Three Part One and Twelve Part One.]

 

[LIE = Linguistic Idealism.]

 

The fact that DM falls apart so easily when its many linguistic confusions have been exposed readily confirms the accuracy of that observation.

 

4a. I have just read Thomas Weston's 'answer' to some of these questions -- Weston (2012). I will add a few comments about this in the next few days.

 

5. To be sure, the picture is far more complicated than this opening salvo might suggest. Later in this Essay, examples will be given where both stationary and moving objects occupy two places at once. Nevertheless, it is reasonably clear that Engels didn't have these in mind when he spoke quite so boldly and peremptorily about the alleged contradictory nature of motion, conclusions supposedly true for all space and time. On the other hand, if he had taken them into account, his whole 'analysis' would have been completely undermined from the get-go.

 

Quantum phenomena that supposedly violate this caveat (i.e., the claim there is no evidence that moving objects occupy two places at once, etc.) don't affect this negative conclusion. No one supposes that in experiments which suggest an electron, for example, can be in two places at once, that this particle moves from one of these places to the other -- and, indeed, in no time at all. What is supposed to happen is that when one electron is aimed at a double slit and focused on a screen, it appears to have taken two separate paths at the same time. So, it hasn't moved between the latter two locations at the same time; it has, it seems, merely followed two trajectories. Why DM-supporters view this a confirmation of their theory, is, therefore, something of a mystery.

 

It could be argued that the fact one object can take two paths at once is obviously a contradiction, which shows that nature is fundamentally contradictory. But, do these two paths 'struggle' with and then turn into one another (which they should do if the DM-classics are to be believed)? Do they imply one another so that one can't exist without the other? If not, then whatever else this phenomenon illustrates, it can't be a 'dialectical contradiction' -- if, that is, we are ever told what one of these mysterious relations or processes actually is.

 

Furthermore, there are, of course, those who question the standard interpretation of such experiments.

 

[This topic is obviously connected with wave-particle duality. More about that, here.]

 

5a. However, and independently of the comments made in the main body of this Essay, if instants have no duration then -- according to Trotsky -- they don't, or can't, exist, since they are merely 'abstractions'. But, what they have been 'abstracted' from, or what they are predicated upon, Trotsky forgot to say. How does one abstract an instant? Indeed, insubstantial spectres such as these can't be what all temporal intervals have in common: non-existent duration-less 'points'? Is this what duration is composed of, something that not only has no duration, but doesn't actually exist? [On this, see Note 6.]

 

6. 'Abstraction' is critically dissected in Essay Three Parts One and Two.

 

Instants in time share nothing with our experience of time, and so they can't be derived from it by a 'process of abstraction'. Moreover, attributing such durationless points to "moments in time" would be to assign them properties they don't have -- namely, non-existence! Ordinarily, we associate a "moment in time" with a few seconds (depending on context). If someone were to say "Wait a moment!", and such a moment were durationless, that would be tantamount to saying "Don't wait at all"! The phrase "a couple of moments" would be the equivalent of "no moments whatsoever".

 

Of course, it could be argued that scientists and philosophers extrapolate from finite moments in time (i.e., from finite time intervals) to such instants all the time (no pun intended). Hence, as such, these instants are Ideal constructs, capable of being mapped onto, or by, the Real Numbers. That argument/analogy has been neutralised here (and, in general, in the two Essays linked to above).

 

7. This idea might proceed as follows: If knowledge results from the reflection in the mind of the complexities found in reality (mediated by practical activity) -- which knowledge is "relative" and hence correct only "within certain limits" -- then, even a provisionally correct theory must faithfully represent the contradictory nature of the world. In this limited sense, human, or social, categories would be relatively adequate to the world (again, if they are correct, and have been tested in practice), but they won't have been projected, or imposed, onto it. This interpretation might then allow DM-theorists to draw substantive conclusions about the world from a consideration, or application of the concepts and categories found in thought (howsoever they got there). Even so, such theories would still only approach absolute truth asymptotically. [Indeed, some might want to call concepts and categories like this, "presuppositions".]

 

[If, on the other hand, the Kantian or Hegelian route is taken by dialecticians, whereby the concepts and categories of thought are what they are because of the nature of cognition, or of 'dialectical reason' itself, then they should be honest, and admit that they have indeed imposed their ideas on nature, contrary to what they swear they never do. To date, only certain HCDs seem prepared to take this 'Kantian/Hegelian' detour.]

 

Of course, this flies in the face of what Novack said:

 

"A consistent materialism cannot 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 emphases added.]

 

Be this as it may, such claims are examined in greater detail here and here.

 

In addition to the above, it is worth highlighting several serious problems this approach to knowledge brings in its train:

 

(1) Elsewhere, it will be argued that this way of looking at language forms part of what I have called the RRT. This is a theory that in fact projects 'knowledge' onto nature under the pretence that language/'cognition' merely reflects what is already there.

 

[RRT = Reverse Reflection Theory; this will be explained in more detail Essay Twelve Part Four.]

 

Because of their implicit acceptance of the RRT dialecticians assume that they are in a position to state in advance of experience what the world must be like before anyone knows what it is like. This involves them in specifying what it is that certain 'concepts'/words correspond with in reality solely on the basis of the supposed logico-linguistic features of the mode of expression in which they have been expressed (i.e., the 'concepts' and the language used to that end).

 

[They certainly wouldn't want to characterise the above ideas this way, nor would they even recognise that this is what they actually do. However, scores of examples were given in Essay Two that show that all dialecticians appear to have what can only be described as a neurotic tendency to assert dogmatic and a priori theses about fundamental aspects of reality -- true for all of space and time -- based on the supposed meaning of a handful of expressions, or 'concepts', practically all of which have been imported from Hegel and Traditional Thought. (A detailed analysis of the class-compromised origin of core DM-theses can be accessed here and here.)]

 

Of course, this DM-thesis (i.e., that language reflects the world) can't itself have been derived from the world. [Or, if it can, we have yet to see the proof.] In that case, this theory -- which claims that knowledge is a complex 'reflection of reality' -- must itself have been imposed on nature (once more, contrary to the claim that this is never done).

 

Nevertheless, an additional motivating idea operating behind the scenes here seems to be that reference to experience, observation or practice is necessary if we are to weed out certain items that aren't actually found in nature, or which do not reflect 'objective' reality. [Otherwise, of course, an appeal to empirical checks and practice to test which linguistic expressions are genuinely represented in nature by real material processes or relations would be an empty gesture.] In fact, because it is impossible to specify ahead of time which parts of this (now supposedly legitimate) a priori picture of the world might never be eliminated after testing in this manner, all knowledge is deemed provisional.

 

Or, so it could be, and has been, argued.

 

Despite this, DM-theorists still aim to tell their readers what the fundamental aspects of reality are, valid for all of space and time. They inform us that everything in reality is contradictory and constantly changing, that all objects and processes are powered by, and change because of, the interplay between 'interpenetrated, internal opposites', and that the world is a single interconnected 'Totality' composed of 'mediated' parts/wholes, governed by the laws of dialectics, and which is susceptible to 'rational' explanation. In addition, we are informed that each part is dependent on every other part, and that the nature of the whole is determined by the complex interconnections between the parts, etc., etc.

 

But, the only 'evidence' 'substantiating' universal theses like this is, it seems, a series of inappropriate extrapolations from a few heavily doctored linguistic expressions -- indeed, as we will see as this Essay proceeds --, which are then 'justified' by an appeal to a series of highly dubious, but nonetheless seriously garbled examples, that utilise what can only be called, Sub-Aristotelian Logic, supported by a handful of highly clichéd, specially-selected, constantly recycled, contentious examples. [I call this Dialectical Dog's Dinner, Mickey Mouse Science, in Essay Seven Part One.]

 

Unfortunately, this means that if we were looking for a theory that was capable of explaining, or helping us understand, nature, DM would fail to make the bottom of the reserve list of viable candidates.

 

Be this as it may, if nature were reflected in thought, so that aspects of reality were embodied in language, and if it were then claimed that this justified inferences from language to the world, it would be impossible to account for falsehood. If thought is indeed a reflection of the world, then it could never be incorrect -- in the same way that a mirror image or reflection is never wrong.

 

Of course, it could be argued that a sophisticated application of the RTK (not to be confused with the RRT), with its emphasis on the 'partial' or 'relative' status of truth, on practice and the "one-sided" nature of abstractions (etc., etc.), is able to neutralise these difficulties. After all, mirrors can and do distort reality (at least with respect to left-right symmetry, or an object's morphology (in, say, a hall of mirrors), etc.), but few are taken in by this. Moreover, it could be maintained that when other criteria are incorporated into the mix (such as increased consistency and greater explanatory power), defective theories could be weeded out as part of the search for an ever more accurate account of the world --, and, of course, how to change it.

 

[RTK = Reflection Theory of Knowledge.]

 

Maybe so, but mirrors can't reflect what isn't there. Hence, if language and thought were mirrors (or even lenses, to vary the metaphor) -- distorting or otherwise -- we would have to conclude that everything expressible in language must exist in reality. Even though they might distort things, mirrors can't conjure into existence objects and processes that aren't there. But -- followers of Meinong excepted --, who in their left mind is prepared to admit that whatever language contains must exist/subsist somewhere in nature? Who wants to allow for the existence of, say, Harpies and Gorgons -- even in a distorted form -- simply because we have words for them? On the other hand, if it were possible to include such 'entities' so easily into 'Being' (by the expedient of simply naming them), why bother looking for evidence in support? In fact, if this approach to knowledge were viable, any search that went beyond leafing through every Dictionary, Thesaurus, Encyclopaedia of Mythology, and Textbook of Grammar on the planet would be superfluous. In that case, Science would become a sub-branch of Lexicography, or, indeed, of Hermeneutics.

 

It could be argued that even mythical beasts and fictional characters are composed of 'images' that have been derived from experience. This is where human judgment can go wrong: it knits together some of these elements in incorrect or fanciful ways. For example, a Harpy is formed from a combination of human and animal 'images', but experience tells us that these beasts don't exist. Hence, we can imagine all sorts of 'possible beasts'/'objects', only some of which actually exist (as far as we know).

 

This particular response will be tackled in Essay Three Part Five, and Essay Thirteen Part One (here). Suffice it to say that (a) The idea under review here is that it is words, not 'images', that reflect reality. In that case, this metaphor is committed to the view that if we have words for something, it must exist, and (b) If we are to rely on 'images' then we would be stuck in a solipsistic world. ['Images' are examined in detail in Essay Thirteen Part One.]

 

Of course, anyone committed to such a theory (i.e., that which was alluded to in (a) above) would have problems pointing out the ontological equivalent of prepositions, conjunctions, adverbs, definite or indefinite articles, and the like -- that is, precisely what it is in the world they 'reflect.

 

It might be wondered why anyone committed to the above view of images (i.e., the allegation presented in (b) above) would in effect be trapping themselves in a "solipsistic world". The answer is quite simple: they would have no way of checking the 'veracity' of their images except by checking them against yet more images. Practice would be no use here, since all that such an individual would have access to would be images of practice. Nor would it do to appeal to 'commonsense', or to the "naive beliefs of ordinary people" (as Lenin attempted to do), and that is because all that such an individual would have are images of 'commonsense', and images of ordinary folk and their beliefs. That is why it was asserted above: "they would have no way of checking the 'veracity' of their images except by checking them against yet more images." In short, they would be trapped in a world composed of their own 'subjective' images -- a solipsistic world. [This is a greatly shortened version of a much longer and more detailed argument set-out in Essay Thirteen Part One.]

 

Putting even this worry to one side, it might be difficult, too, for anyone who accepts this view of language (i.e., that which was alluded to in (a) above, again) to explain how words for non-existent beings (such as Harpies and Gorgons), even if these are based on 'images' stored in each individual dialectical head, can be harmonised with a social interpretation of language.

 

However, the specific point under consideration here was in fact the following counter-response:

 

[That the aforementioned] interpretation might then allow DM-theorists to draw substantive conclusions about the world from a consideration, or application of the concepts and categories found in thought (howsoever they got there). Even so, these theories would still only approach absolute truth asymptotically.

 

Now, we have already established that DM-theorists go way beyond seemingly modest disavowals like this, claiming to know what the fundamental features of reality are -- valid for all of space and time --, but, derived solely from the alleged meanings of certain words.

 

Some might think to bring in ideology here, but that can't affect the above comments. Ideology supposedly 'inverts' things. Even if this were an apt metaphor, ideology can't create (merely by inversion or reflection) what isn't there. [Of course, this metaphor mightn't be apt. I will say more about this in Essay Three Parts Four and Five. Until then, see here.]

 

Moreover, an earlier reference to the hermeneutic gyrations required to make this theory work was deliberate. The latter word in italics is in fact derived from the Greek 'deity', Hermes, the interpreter of the 'Gods'. That term was chosen because of the many accusations advanced at this site that DM is just a latter-day version of Hermeticism.

 

This allegation is also linked to another ancient idea: that Philosophy and Theology were invented by Hermes (or, in Egypt, by 'his' equivalent, Thoth -- on this see Boylan (1999), Faivre (1995), and Fowden (1993)). Of course, Philosophy as a discipline was invented by ruling-class theorists, but it was also an important part of an ideological package aimed at tracing the supposed source of ruling-class ideology back to the thoughts of the 'gods' themselves. [Why this is so will be explored in Essay Twelve Parts Two and Three (summary here), where the phrase "ruling-class theorist" will be explained more fully. Until then, see here, here, here and here.]

 

Furthermore, this isn't as wild an accusation as it might at first sight seem. In fact, it was derived from Marx himself:

 

"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.]

 

[Indeed, it is arguable that this is part of the reason why Marx had abandoned Philosophy by the mid-, to late-1840s; on that, see here.]

 

This ancient approach to knowledge -- which has, in one form or another, dominated much of 'Western' (and 'Eastern') thought ever since -- sought to connect obscure philosophical jargon with the divine, 'rational', a priori, structure of reality (i.e., with 'Being Itself').

 

It is this observation that partially motivates the claim advanced in these Essays that Traditional Thought represents, or is an 'image' of, not the material world, but an ancient ruling-class view of an Ideal World; a world that supposedly 'exists' anterior to experience, which is more real that the universe we see around us. Boss-class theorists further inform us that this hidden world -- accessible to thought alone -- underlies 'appearances', and lends to reality its 'essence'. That world is therefore thoroughly immaterial.

 

Given the traditional approach to knowledge, it is the language used by its theorists that tells them what this hidden world must be like -- for they have no other access to it. In that case, this hidden world is a reflection of specific forms-of-thought/language --, not the other way round. [As noted earlier, I call this the RRT. More about that in Essay Twelve Part Four when it is published.]

 

In each Mode of Production, different versions of the same general belief (in the divine, or a priori, structure of reality) have been put to use by Traditional Thinkers to rationalise the wealth and power of contemporaneous elites, and thus the different relations of production that dominated human beings in each such mode. It is precisely here -- where dialecticians have accepted, appropriated and imported into Dialectical Marxism significant segments of this ancient world-view -- that ruling ideas have succeeded in ruling militant minds.

 

Some might object that philosophical ideas can't have remained the same for thousands of years, across different Modes of Production; that idea runs counter to core ideas in Historical Materialism.

 

But, we don't argue the same for religious belief. Marx put no time stamp on the following, for example:

 

"The foundation of irreligious criticism is: Man makes religion, religion does not make man. Religion is, indeed, the self-consciousness and self-esteem of man who has either not yet won through to himself, or has already lost himself again. But man is no abstract being squatting outside the world. Man is the world of man -- state, society. This state and this society produce religion, which is an inverted consciousness of the world, because they are an inverted world. Religion is the general theory of this world, its encyclopaedic compendium, its logic in popular form, its spiritual point d'honneur, its enthusiasm, its moral sanction, its solemn complement, and its universal basis of consolation and justification. It is the fantastic realization of the human essence since the human essence has not acquired any true reality. The struggle against religion is, therefore, indirectly the struggle against that world whose spiritual aroma is religion.

 

"Religious suffering is, at one and the same time, the expression of real suffering and a protest against real suffering. Religion is the sigh of the oppressed creature, the heart of a heartless world, and the soul of soulless conditions. It is the opium of the people.

 

"The abolition of religion as the illusory happiness of the people is the demand for their real happiness. To call on them to give up their illusions about their condition is to call on them to give up a condition that requires illusions. The criticism of religion is, therefore, in embryo, the criticism of that vale of tears of which religion is the halo." [Marx (1975c), p.244. Italic emphases in the original.]

 

The above remarks applied back in Babylon and the Egypt of the Pharaohs, just as they did in Ancient China and the rest of Asia, The Americas, Greece, Rome and throughout Europe, Africa, Australasia, as they have done right across the planet ever since.

The same is true of the core thought-forms of Traditional Philosophy -- that there is indeed this 'invisible world', accessible to thought alone --, especially since Marx, as we have seen, also argued 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.]

 

This helps explain why Marx thought this entire discipline was based on distorted language and contained little other than empty abstractions and alienated thought-forms -- and, indeed, why he turned his back on it from the late 1840s onward.

 

[This topic is spelt out in more detail in Essay Fourteen Part One (summary here); the pernicious effect it has had on Dialectical Marxism is exposed here.]

 

Naturally, the (postulated!) DM-account of the origin of mythical beings is more sophisticated than previous paragraphs might suggest. But, a distorted view of reality, howsoever it is produced -- whether or not this is a result of alienation, or based on a "one-sided" theory, or ideology, or, indeed, is a spin-off from the process of abstraction itself -- even if it results in an upside down image, a blurred one, or even one wearing a pink tutu -- it matters not; it is still a view of reality (given the applicability of the reflection metaphor, sophisticated version or otherwise), and in that case it is an Ideal view. A mirror can't invent. Hence, this metaphor implies that things like dragons, fairies, ghosts and hobgoblins -- not to mention Atlantis, heaven, hell and Nowhere -- must exist somewhere, in some form, just because we have the words for them!

 

On the other hand, if these 'entities' don't exist, then the mirror metaphor is defective and should be abandoned.

 

[DL = Dialectical Logic.]

 

Of course, it could be objected that raising superficial objections like those above, based on contingent features of mirrors, or even the world, entirely misses the point: dialecticians are interested in the essential nature of reality, and these are reflected in (or by) DL.

 

Nevertheless, more-or-less the same objections can also be ranged against the principles supposedly encapsulated by DL. But worse: as we have seen (here, here, here, here and here), DL is far too confused to have 'captured' anything in thought, distorted or otherwise.

 

Or, to put the same point in reverse: if the essential nature of reality is reflected in (or by) DL, then reality would be a madhouse.

 

 

Figure Two: What The World Might Look Like

If DL Were An Accurate Reflection

 

Furthermore, since these general/'essential' features of reality are often highly abstract (or they are expressed in suitably abstract language), the contention advanced here (that these are the product of misconstrued rules of grammar, and aren't truths in any shape or form) has more than just a little prima facie plausibility going for it.

 

[Incidentally, the above comments can also count as an answer the objection that the a priori concepts and categories of DL capture the form but not the content of reality. Again, since this topic is examined in more detail in Essay Three Part One and Essay Twelve, no more will be said about it here.]

 

(2) The phrases "relative adequacy" and "relative truth" are themselves hopelessly unclear. Expressions like these are obviously linked to the DM-thesis that human knowledge "asymptotically" approaches 'absolute truth', over time. However, when examined more closely, these ideas are in fact inimical to DM. This is because they imply that humanity is and always will be infinitely ignorant of everything, no matter how "relatively" complete our knowledge of anything might seem to be at any given point in history. On that basis, far from being "relatively adequate", or even "relatively true", knowledge will always remain infinitely far from the truth, and hence possess an infinitely high probability of being false. That in turn is because the difference between a finite and an infinite body of knowledge is itself infinite.

 

A relevant passage from Engels comes to mind again (which was commented on in Essay Two):

 

"The identity of thinking and being, to use Hegelian language, everywhere coincides with your example of the circle and the polygon. Or the two of them, the concept of a thing and its reality, run side by side like two asymptotes, always approaching each other but never meeting. This difference between the two is the very difference which prevents the concept from being directly and immediately reality and reality from being immediately its own concept. Because a concept has the essential nature of the concept and does not therefore prima facie directly coincide with reality, from which it had to be abstracted in the first place, it is nevertheless more than a fiction, unless you declare that all the results of thought are fictions because reality corresponds to them only very circuitously, and even then approaching it only asymptotically…. In other words, the unity of concept and phenomenon manifests itself as an essentially infinite process, and that is what it is, in this case as in all others." [Engels to Schmidt (12/03/1895), in Marx and Engels (1975), pp.457-58.]

 

First of all Engels failed to say how he knew it was true that knowledge is convergent. Of course, if what Engels actually said were true, it would be infinitely wrong, or, as noted above, it would possess an infinitely high probability of being false. That is because, when asserted that claim must itself be infinitely far from the 'truth', if we are to believe what Engels says in the above passage. And, manifestly, the fact that knowledge is an infinitary process can't be confirmed in practice (or, indeed, in any other way).

 

Secondly, the idea of an asymptotic approach in mathematics is connected with the concept of a limit -- if the limit concerned can be shown to exist. Alas, Engels failed to prove that there is such a limit for knowledge to approach in the required manner (in fact, he didn't even so much as attempt such a proof; and, as far as can be ascertained, no dialectician since has bothered to do fill in the details, either). In that case, Engels's 'mathematical metaphor' is doubly inappropriate: if there is no limit, human knowledge must be divergent. And, if that is so, then at any point in human history, our knowledge must be infinitely far from 'Epistemological Valhalla' -- which, it is worth recalling, still hasn't been shown to exist. On this view, given Engels's inapt metaphor, humanity will always be infinitely ignorant of anything and everything!

 

Kant's Noumenon by any other name?

 

[On convergence, see here.]

 

Of course, it could be argued that just because certain iterative functions in mathematics yield infinite sequences that doesn't mean that the distance between any intermediate value given by a partial sum of that function and the point toward which it is converging is itself infinite. For example, the sequence: 1 + 1/2 + 1/4 + 1/8 +...+ 1/2n converges on 2 (as n +∞), but none of the rational numbers (formed from the partial sums of this series) is infinitely far from 2.

 

This isn't strictly true (since the (mathematical) distance between any two rational numbers is itself infinite), but even if it were, the above would have been an effective response had Engels bothered to prove that the limit he claims exists (implied by the asymptote metaphor) actually does exist. But since he didn't, it isn't.

 

The only way the above sceptical conclusions can be neutralised would involve a denial that 'absolute knowledge' is in any way infinitary. Clearly, that would place a condition on the object of knowledge before we knew what it was! Of course, it would also mean that several passages from the DM-classics (quoted elsewhere at this site) would need to be revised -- or ignored --, along with the above 'asymptote' metaphor, since they manifestly do imply such an infinitary task. Indeed, they go further -- they say it is infinite, and even call this a "demand".

 

7a. That is to say, our everyday -- or even our scientific -- thoughts about motion aren't contradictory, whereas those concocted by Idealist Philosophers might be (that is, if any sense can be made of what they actually said about it!).

 

8. As noted above, in Hegel's system, the existence of 'real contradictions' made some sort of crazy sense. Hence, if reality is just "thought" writ large, then linguistic categories may be projected ("foisted") onto reality quite 'legitimately', since nature is 'self-developing Mind' anyway --, or, at least, it is an aspect of it. But, as we will see in Essay Twelve, this doctrine is itself a throwback to Ancient Greek (and earlier) religious ideas, where conflicts in nature and society were depicted in mythical, anthropomorphic, and theological terms (i.e., where it was thought that the universe was the playground of evil or benevolent agents/'gods') -- but later translated into in ethical, political, conceptual and purely abstract linguistic forms, after philosophical speculation had kicked in.

 

[The reason why this ancient view of the world was conducive to wider ruling-class interests will also be outlined in Essay Twelve (summary here) -- but it was hinted at in Note 7. (Also see: here and here.)]

 

8a. Of course, it could be argued that since everything in the universe is in motion, the question, "Which came first, motion or contradictions?" doesn't arise. However, as we will see, things aren't quite this straight-forward. Quite the reverse, in fact. [No pun intended.]

 

9. Quotations from Lenin (and others) concerning 'internal contradictions' and self-development (etc.) were posted in Essay Two. Cf., Rees (1998), p.7. This topic is examined in much more detail in Essay Eight Parts One and Two.

 

9a. Although Woods and Grant came very close to asserting this (i.e., that there is an 'internal motor' in moving objects that makes keeps them moving):

 

"So fundamental is this idea to dialectics that Marx and Engels considered motion to be the most basic characteristic of matter.... [Referring to a quote from Aristotle:] [T]his is not the mechanical conception of motion as something imparted to an inert mass by an external 'force' but an entirely different notion of matter as self-moving....

"The essential point of dialectical thought is not that it is based on the idea of change and motion but that it views motion and change as phenomena based on contradiction.... Contradiction is an essential feature of all being. It lies at the heart of matter itself. It is the source of all motion, change, life and development. The dialectical law which expresses this idea is the unity and interpenetration of opposites....

"The universal phenomena of the unity of opposites is, in reality, the motor-force of all motion and development in nature. It is the reason why it is not necessary to introduce the concept of external impulse to explain movement and change -- the fundamental weakness of all mechanistic theories. Movement, which itself involves a contradiction, is only possible as a result of the conflicting tendencies and inner tensions which lie at the heart of all forms of matter....

"...Matter is self-moving and self-organising." [Woods and Grant (1995), pp.43-45, 47, 68, 72. Bold emphases added.]

 

The long quotation from Hegel, given above, shows where these two 'discovered' these odd ideas -- they certainly didn't obtain them from any scientists living on this planet. [On this, see Essay Eight Part One.]

 

10. In fact, Engels himself torpedoed the idea that forces can be viewed as contradictions when he claimed that:

 

"All motion is bound up with some change of place…. The whole of nature accessible to us forms a system, an interconnected totality of bodies…. [These] react one on another, and it is precisely this mutual reaction that constitutes motion…. When two bodies act on each other…they either attract each other or they repel each other…in short, the old polar opposites of attraction and repulsion…. It is expressly to be noted that attraction and repulsion are not regarded here as so-called 'forces', but as simple forms of motion." [Engels (1954), pp.70-71. Bold emphasis added.]

 

As will be argued in detail in Essay Eight Part Two, this observation pulls the rug from under anyone who (i) wants to maintain that forces can be used to model contradictions, and (ii) regards Engels as some sort of authority in such matters.

 

Anyway, and despite the above, this DM-account of motion does no real work; the explanation of movement isn't advanced one nanometre by re-describing it as "contradictory". The supposed 'contradiction' in motion (where a body both is and is not, etc., -- not the 'contradiction' that relates to the status of opposing forces) neither initiates nor sustains movement.

 

Furthermore, if Absolute Space is left out of the picture, the precise nature of motion clearly depends on the inertial frame chosen. It doesn't depend on the simultaneous non-occupancy and occupancy of point locations. This can be seen from the fact that given a particular frame of reference, a body could be at rest relative to that frame, but with respect to another frame it could be in motion. Hence, motion is inertial-frame-sensitive, not 'vaguely-located-point-occupancy-and-non-occupancy'-dependent.

 

It would seem, therefore, that unless DM-theorists believe in Absolute Space, their insistence that motion is contradictory (because of their quirky view of two-point occupancy) is unsustainable. Relative notions of space imply that the 'contradictory' behaviour of moving bodies (if such it be) is a consequence of a change of reference frame: in that case, bodies are in motion -- or they are stationary -- depending on which inertial frame was selected. But they wouldn't be either motionless or moving because of the alleged contradictions inherent in motion itself. In which case, the 'contradictory' nature of motion can't be an 'objective' feature of reality if it promptly disappears as soon as a different inertial frame was selected.

 

It could be argued that just because motion apparently stops and starts according to the choice of reference frame no more means its contradictory nature isn't objective than it would we mean, say, the boiling point of water wasn't really 100ºC if it were measured in degrees Fahrenheit or in degrees Kelvin.

 

Unfortunately, if that constitutes an effective reply to the points made above, it would at the same time prove fatal to the DM-view of motion. That is because it openly concedes that scientific knowledge is conventional.

 

Again, exception could be taken to that response. It could be argued that the fact that the temperature of a body can be read on two or more different conventionalised scales doesn't imply that temperature itself (or whatever it supervenes upon) isn't an objective feature of reality. The same goes for the depiction of motion in different reference frames.

 

However, these two cases aren't analogous; no matter what system we use, a body has some temperature or other (with the latter defined perhaps in terms of its energetics). This isn't the case with motion and the choice of inertial frame (unless, of course, we count a zero velocity as a velocity by default -- but, even then, the alleged 'contradiction' would still vanish).

 

In one particular frame, a body could be in motion and (assuming DM is correct) appear to be 'objectively' contradictory. In another frame, and at the same time, that body could be stationary and objectively non-'contradictory' (in Engels's sense), too. Hence, at the same time, a body could be moving and not moving, 'contradictory' and 'not contradictory'. Which of these options is finally settled upon will be a consequence, not of the nature 'motion itself' (whatever that is), but of the choice of reference frame. Since reference frames aren't 'objective' features of the world (they are human inventions!), and since the 'contradictory' nature of motion is sensitive to choice of frame, the conclusion seems inescapable: the 'contradictory' nature of motion (if such it be) isn't an 'objective' feature of reality, either.

 

Alert dialecticians at this point might want to argue that this sentence is eminently contradictory:

 

"Hence, at the same time, a body could be moving and not moving, 'contradictory' and 'not contradictory'."

 

But, this is just another ambiguous sentence, and its allegedly contradictory nature will disappear upon disambiguation, as we saw, for example, here.

 

It could be argued that the above would mean that motion itself isn't an objective feature of reality if it disappears in the above fashion when a different reference frame is chosen. But, that isn't so, for if an object is moving with reference to one frame, but is stationary with respect to a second frame, then other objects will thereby be moving in a different way with respect to that frame. So, while the alleged contradiction would disappear, motion in the wider system wouldn't. For example, if the first reference frame is a volume interval containing only, say, the Moon, and that frame is stationary, the Earth will be in motion relative to that frame even while the Moon isn't. Swap the reference frame to a volume interval that contains only the Earth, mutatis mutandis, and the Moon will now be moving relative to a stationary Earth.

 

[Sure, the Earth will still be rotating, but all we have to do is make the reference frame a finite region on the Earth's surface, and the Earth would stop rotating relative to this new frame. For example, from where you are now sat, or stood, the earth appears not to be rotating, which used to be one of the strongest arguments that the earth is stationary. (On whether or not the earth is 'objectively' in motion, see here.)]

 

This means that relative motion (at least as it is viewed in modern Physics) is a conventionalised bi-product of the choice of inertial frame. Therefore, if DM-theorists are to rescue the 'objectivity' of their theory from the trashcan of 'subjectivity', it looks like they will have to postulate the existence of Absolute Space. Otherwise, they will have to concede that the 'contradictions' they attribute to motion are in fact artefacts of the choice of reference frame, and not something inherent in moving bodies.

 

It isn't easy to see a way out of this DM-cul-de-sac, or at least one that makes no further concessions to conventionalism -- or, indeed, one that makes unwelcome concessions to Space/Time Absolutism.

 

This partly explains why (a few generations ago), in Stalinist Russia, philosophers and scientists found it difficult to square Einstein's theory with DM, and hence why some rejected the TOR. If revolutionaries are still unaware of these problems, STDs certainly weren't. [Cf., Graham (1971), pp.111-38; see also Joravsky (1961), Krementsov (1997), Vucinich (1980, 2001), and Wetter (1958).]

 

[STD = Stalinist Dialectician; TOR = Theory of Relativity.]

 

Once more, it could be objected that even if the above were correct, once moving (in a suitable inertial frame), an object will be doing something contradictory.

 

My reply to that objection will occupy the rest of this Essay.

 

11. This isn't meant to single Engels out here for special attention; it is equally impossible to determine what, if anything, Zeno, Hegel or Lenin were trying to tell us about motion.

 

However, if it is maintained that systems of supposedly contradictory forces are responsible for the contradictory nature of motion, then it would be difficult to account for un-accelerated motion. Clearly, this sort of (constant) change takes place where no net forces are operating. That being so, the exact source of the alleged contradictions here would be even more obscure.

 

Of course, one consequence of DM seems to be that there might be no un-accelerated motion in nature (in that (i) The opposite supposition would involve a body possessing identically the same velocity from moment to moment -- which would, of course, amount to a fatal concession to the LOI -- or that (ii) It wouldn't be moving in a gravitational field, which, in this universe, is impossible). Nevertheless, DM-induced conundrums like this will not, I take it, worry genuine scientists too much, or for very long.

 

[LOI = Law of Identity.]

 

And all this is, of course, quite apart from the fact that such a DM-view of velocity (if such it may be called) will have to be imposed on nature.

 

As far as (ii) is concerned, given the additional fact that gravitational forces have been edited out of the picture in Relativity Theory (on that, see here), even if this were so, an appeal to such forces to account for acceleration would be to no avail, since there are none!  

 

Moreover, in relation to (i), if a suitable frame of reference is chosen, any body can be said to have zero velocity and be undergoing acceleration for about as long as it takes hard-core DM-fans to abandon their criticisms of the LOI.

 

Hence, for any body b moving at v kmph relative to the centre of mass of the Galaxy, say, let a reference frame for it also move at v kmph with respect to that centre of mass. In that case, b will have zero velocity with respect to that frame. The only response a DM-acolyte could make to this would, it seems, have to involve a reference to 'abstractions' (i.e., in that this involves the use of "abstract identity"). This last ditch, desperate DM-defence will also be examined, and demolished, in Essay Six.

 

11a. Hegel's 'analysis' of Identity was partially covered here, and again indirectly throughout Essay Six; it will be examined more fully in Essay Twelve (summary here).

 

11b. That is because, if it is unclear what is being proposed -- as is the case with L9, given the convention introduced in L7 -- then nothing has yet been proposed.

 

L9: B is at (X1, Y1, Z1), at t1 and not at (X1, Y1, Z1), at t1, and B is at (X2, Y2, Z2), at t1.

 

L7: (X1, Y1, Z1) is not the same place as (X2, Y2, Z2).

 

Of course, if L9 depicts one of the ambiguous cases mentioned already (that is, if B is in fact stationary -- like the car which was half in, half out of that garage), then it will be clear what is being proposed. But, in that case, L9 won't provide us with the required necessary and sufficient conditions for movement, and we would be back to square one again.

 

Anyway, in order to see if some sense can be made of what Engels was trying to tell us, I have ignored this serious difficulty for the present. However, I will return to it later since it will soon become apparent that his theory can only be made to work if we ignore the ordinary use of language and substitute for it distorted 'philosophical' jargon --, as both Marx and Engels pointed out:

 

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

 

Engels clearly forgot about his earlier warning when he began to import Hegelian gobbledygook into Marxism!

 

This isn't either a minor or a trifling point; it is in fact central to understanding why Traditional Philosophers and dialecticians find they have to impose their theories on the world, and why their ideas invariably collapse into LIE. [On this, see Essay Twelve Part One and Essay Two.]

 

12.  A detailed discussion of these aspects of Zeno's analysis of motion can be found in Angel (2002). Also, see Note 19a and Note 24, below.

 

[Incidentally, this way of looking at the Reals is outlined in Newton-Smith (1980). On whether time is composed of 'instants', see Read (2007), pp.79-115.]

 

12a. But Trotsky wasn't, of course, the only one to ignore this distinction. Engels also failed to consider the possibility that an object could be in two times for the same place -- i.e., in and not in one instant, at that place. But, if time advances while bodies move (or indeed stay still), and everything is contradictory, then this must surely be possible. And if that is so, what is to stop us saying that a moving body occupies the first place in one of these 'odd instants', and the next place in the second overlapping instant -- locating the alleged contradiction in time, and not in space or motion (or, perhaps, even eliminating both)?

 

Of course, it could be pointed out that if a body is in two times for the same place then it must be stationary.

 

In order to neutralise that objection it might be wise to examine the subtle differences that exist between these two sentences (always assuming there are any):

 

B1: Body b is in two different times for the same place.

 

B2: Body b is in the same place at two different times.

 

I don't propose to do that here, but it is worth noting that neither of these imply that the said object is stationary, since that object could still be moving and could return to the original location at a later time --, hence, a moving object could be in the same place at two different times.

 

13. This is taken to be an important DM-assumption since it is the only way that Engels's claims about the contradictory nature of motion can be defended, as argued at length in the main body of this Essay.

 

14. It is worth pointing out that L13 doesn't say that b is both at p1 and not at p1 at t. What it does say is this:

 

L13: For some b, for just one instant t, for three places p1, p2 and p3, b is at p1 at t, but not at p2 at t, and b is at p3 at t, where p2 and p3 are proper parts of p1.

 

Hence, a finer-grained analysis of position allows for the fact that, while at the macro-level an object might be locatable in one place (say, p1) at one 'instant', at the micro-level it could still be in that same place (i.e., still in p1) while also being in one or more other sub-spaces of p1 (for example, p3) at the same time. In other words, b could be in p1, and while not in all of p1 (i.e., not in, say, p2, which is a proper part of p1), it would still be in p1 (in this case, in, say, p3, which is also a proper part of p1).

 

Hence, b could be in p1 at t, but not in every part of p1 at t -- and either be in motion or stationary, at that time --, meaning that b would be in two places at once: p1 and p3. So, if the location of bodies can be given in finer-grained detail -- even if this manoeuvre is inconsistently disallowed of time -- a body could still be in one place and not in it, and be in two places at once, while being stationary, with no contradiction implied.

 

[This is the simplest of these cases; the reader is left to determine more complicated examples for herself. The complex nature of ordinary and/or technical language allows for the depiction of motion and location in ways undreamt of by Zeno, Heraclitus, and Hegel -- or even Engels -- that is, in their 'philosophical' deliberations. On this, see below and in the main body of this Essay.]

 

Some might think this ignores what Engels actually says:

 

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

 

However, as we saw earlier, it is far from clear what Engels meant by this:

 

"...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." [Ibid.]

 

Here, Engels says that a moving object is "in one and the same place and not in it." He is clearly using "in" in a rather odd way, and it isn't too clear whether he (or any other dialectician) is capable of explaining how this could be literally true -- save they just label it a 'contradiction', take their bat and ball home, and then retreat into a dialectical sulk. But, this just highlights the problem, it doesn't make it any easier to determine what Engels is proposing, or if he is proposing anything determinate at all.

 

In that case, it is worth pointing out that in L13:

 

L13: For some b, for just one instant t, for three places p1, p2 and p3, b is at p1 at t, but not at p2 at t, and b is at p3 at t, where p2 and p3 are proper parts of p1,

 

Again, in this case: b is in p1 and not in it in the following sense: it is in p1 but not in all of p1 at the same time. This is just as legitimate an interpretation of Engels's words as the traditional (but hopelessly unclear) version is.

 

This analysis might be contested on the grounds that it removes the contradiction from Engels's analysis.

 

But, and despite what he himself says, it isn't too clear that Engels's words were contradictory to begin with, since little sense can be made of them as they stand. If we can form no clear idea what Engels is trying to say, then it can't justifiably be said to be "contradictory".

 

"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." [Ibid. Bold emphasis added.]

 

We have already seen that extended bodies can be in two places at the same time --even while they are stationary -- with no contradiction implied, so the allegedly contradictory aspect of motion must arise from the following clause:

 

"...being in one and the same place and also not in it [at the same moment in time -- RL]."

 

Well, is this the contradiction we have been led to all along to accept?

 

If so, imagine the following scenarios:

 

[1] NN is queuing for tickets, and finds herself at the front of the queue at 11:55am (before the Ticket Office opened at noon), but she needs to leave the queue to get something to eat. So, she asks MM to act as her proxy in the queue while she goes off to buy some sandwiches, which she does at 11.57am. Here, NN is both in and not in the queue at 11:57. She is still in the queue since MM is guarding her place, but she isn't in the queue since she has left to get food. Here we have a moving body, NN, who is both in the queue and not in it at the same time, with no contradiction implied. This only appears contradictory because of the equivocal meaning of "in", in this case.

 

[2] NM is selected by his coach to play for the first team squad. The team leaves for a match at 15:00 hours, but NM misses the plane. So, NM is in the team (the coach hasn't dropped him), but not in the team (he isn't accompanying them), all at the same time, and this could be true whether or not NM is moving. [Some might want to point out that a team is not a place, but quite apart from the fact that Engels was unclear what he meant by "place", we often speak about a player securing or gaining their place in the team.] Here, once again, the equivocation centres on "in" and "place".

 

[3] Consider the Klein Bottle:

 

 

 

Figures Three And Four: The Non-Dialectical Klein Bottle

 

Let an object slide down the central tube that runs through this bottle. Now, because the inside of this bottle is the same as the outside, that object will be inside and not inside this bottle at the same moment; it would be in and not in the same place at once. And, this would be so whether or not the said object was moving. [Here, the equivocation centres on "same place", i.e., whether "inside" can be the same as "outside" in certain circumstances. A similar ambiguity also features in example [5], below.]

 

[An analogous 'contradiction' can be manufactured for a stationary object on the surface of a Möbius Strip, or even worse, on a set of Möbius Gears:

 

 

Figure Five: A Möbius Strip -- Concocted By The CIA?

 

 

Figure Six: Möbius Gears -- A CIA Invention?

 

 

Video One: Möbius Gears

 

[See also here. A stationary object on these gears would be on top and not on top of one surface all at once. Here we can see that equivocations like this aren't confined to the preposition "in".]

 

[4] MN has had her amputated hand replaced by a prosthetic. At 02.20pm she inserts this artificial hand into a glove. Hence, her hand is both in and not in that glove. Her hand is in the glove in the sense that this is her hand now. But, it isn't in the glove in the sense that it isn't a real hand, or the hand she was born with. [Here the equivocation is over "same object".]

 

[5] NN is in the corridor of a hotel outside her room at 17:30 hours (on a Friday), but at the same time she is inside the hotel. So, she is outside and inside (or outside and not outside), all at once. There are countless examples of this use of prepositions and adjectives. For example, a book on a shelf may be above the floor but below the roof. So, it is at one and the same time above and not above. A box might be stored near a wall but far from the door; so, at one and the same time, it is both near and not near. [Ancient Greek Philosophers made much of these equivocations.]

 

It might be objected that not only are these examples artificial and forced, they are not at all what Engels had in mind.

 

But, as we have seen, it isn't at all clear what Engels meant. Anyway, only [3] was arguably artificial.

 

That isn't the case with the following:

 

Here is a sports story from the BBC (concerning the 3000 metre steeplechase final at the 2014 European Games):

 

"France's Mahiedine Mekhissi-Benabbad has been stripped of his 3,000m steeplechase gold medal at the European Championships for taking his shirt off on the home straight. Mekhissi-Benabbad put his top in his mouth after pulling clear of the field. Initially he appeared to be shown a yellow card by an official but was subsequently disqualified. Frenchman Yoann Kowal now wins gold, Poland's Krystian Zalewski gets silver and Spain's Angel Mullera wins bronze." [Quoted from here. Accessed 15/08/2014. Paragraphs merged to save space.]

 

As a result, Yoann Kowal was moved from second to first, Krystian Zalewski from third to second, and Angel Mullera from fourth to third, even while none of them were in two places at once, in one and not in it at the same time. So, the Olympic officials moved and did not move Yoann Kowal; he is and isn't the winner of the Gold Medal at these Games; he is both in and not in first place. Is anyone taken in, or even puzzled by, these 'contradictions'?

 

Moreover, the examples given in [5] aren't artificial, either; indeed, there are countless instances of this sort of equivocation right across the planet (nay, right across the universe) every day of the week: Pluto is both near the Earth (compared to its shortest distance from Proxima Centauri), and far from the Earth (compared to its shortest distance from Neptune) -- hence, Pluto is both near and not near the Earth. Does anyone in their left mind think this is a contradiction?

 

And, as we will discover, in the abstract, while Engels's 'theory' might seem (to some) to be eminently sound, when we look at concrete examples (like those above, or even those below), it can be seen for what it is: artificial and forced itself.

 

For more examples like this, and worse, see Note 15, Note 16, as well as the main body of this Essay.

 

14a. It could be objected that (X1, Y1, Z1) in this example is a mathematical point. If so, it can't have other points located inside of it -- so it can't be the case that: "(X3, Y3, Z3) and (X2, Y2, Z2) are both located inside (X1, Y1, Z1)."

 

That is easily rectified:

 

L13c: A stationary body b, observed over the course of an instant, is located in a finite region, , and at (X3, Y3, Z3), but not at (X2, Y2, Z2), where (X3, Y3, Z3) and (X2, Y2, Z2) are both located inside .

 

L13d: A moving body b, observed over the course of an instant, is located in a finite region, , and at (X3, Y3, Z3), but not at (X2, Y2, Z2), where (X3, Y3, Z3) and (X2, Y2, Z2) are both located inside .

 

15. The following is an example of this type of motion partially expressed in vector algebra:

 

V1: Let B be a body moving in 3 (or some Vector Space) with respect to a given reference frame.

 

V2: Let B be at both (X1, Y1, Z1) and (X2, Y2, Z2) at t1.

 

V3: Let B be a complex composed of n segments, b1 to bn, arranged in an ordered n-tuple <b1,..., bn>.

 

V4: Let the position vectors of the centre of mass of b1 and bn be u and v, respectively.

 

V5: Let vu = w.

 

V6: Let the distance between (X1, Y1, Z1) and (X2, Y2, Z2) be mod d, (where d is the vector joining (X1, Y1, Z1) to (X2, Y2, Z2)).

 

V7: Let mod w > mod d.

 

V8: Let the direction vector parallel to d be λw (where λ is a Real Number).

 

V9: Let B be moving at time t1 with velocity vector s, such that s = μw (where μ is a Real Number).

 

V10: In that case, part of B is at (X1, Y1, Z1), and another part of B is at (X2, Y2, Z2), but other parts of B are at neither of these two points, all at t1.

 

V11: So, B is moving parallel (in either sense) to the line joining these two points, also at t1.

 

V12: Or, alternatively, B is stationary (with respect to some inertial frame); i.e., if s = 0 (or even if μ = 0), and all the above considerations would still apply.

 

Here, we have a slightly more technical version of the ambiguous case mentioned in the main body of this Essay (concerning a boat entering port, etc.). Translated, the above could apply to the following scenario:

 

Ports are generally bigger than boats, and are composed of countless parts (land, water, buildings, shorelines, etc.). A boat can, therefore, be in port and be located at several points within that port, and yet not be located at every point in that port (with no implication that it is both in and not in the entire port, even though it is both in and not in several parts of it -- for example, it could be in the dry dock but not in the harbourmaster's office), all at the same time. And these would all be true independently of whether or not that boat is moving with respect to a suitable inertial frame (that is, if we set s at zero).

 

16. This observation would remain true even when such 'spatial location sentences' employ co-ordinates (expressed as real number triples). As we shall see, technical specifications aren't free from ambiguities of their own.

 

An example of just such an equivocation would be the following: in <x1, y1, z1> and <x1, y1, z1> (no misprint!), each variable letter is in the "same place" (i.e., each is situated in its respective ordered triple, first, second, or third) while also being in a different place on the page or screen at the same time.

 

Indeed, not only are the letters in the same place, they are also in different places while they are in the same place (i.e., they are on your screen and mine -- and, clearly, they are all in the solar system), all at the same time!

 

Consider, too, this variation on the same theme: <x1, y1, z1> and <y1, z1, x1>; here, each letter is in the same place (they are on the same page or screen -- or even geographical location -- as each other), and yet each letter is in a different place from the other elements (in the ordered set). So, each letter is and is not in the same place.

 

Did you see any of them moving?

 

Now, try saying any of that in Hegel-speak!

 

And these are very simple examples! I won't do so here, but it would be possible, if not all that easy, to construct examples that are genuinely difficult to follow -- since they would involve much more detail, involving increasingly complex equivocations --, but with sufficient concentration, it would be possible to ascertain their content, all of which would make the same point -- that is, that it is laughably easy to manufacture 'contradictions' when using equivocal language -- whether these are ordinary or technical.

 

[Of course, with technical languages, the equivocations emerge only when they are translated into ordinary language (unless the definitions are defective to begin with). Despite this, no one working with ordered n-tuples, for example, would regard them as 'inherently contradictory'. (I have in fact posted examples that are analogous with the above, but expressed in words associated with identity and difference, in Essay Six, here.)]

 

To paraphrase Wittgenstein: the conventions of ordinary language are exceedingly complex. Dialecticians ignore them at their non-dialectical peril.

 

17. Some might conclude that this is because ordinary language is defective (at least, in certain respects); cf., TAR pp.45-50.

 

It is important to note that the view that ordinary language is defective isn't shared by the present author; the opposite is in fact the case. This topic will be addressed in detail in Essay Twelve Part Seven. [However, on this, see the lengthy discussion posted here.]

 

18. Although, at this point, because we have reached linguistic bedrock -- i.e., in order to proceed further we should have to question, revise. or reject fundamental linguistic conventions, in this case, for instance, promulgating non-symmetrical stipulations in relation to one or other of space and time --, this latest "must" is in effect the argumentative equivalent of thumping the table, and nothing more.

 

18a. This 'assumption' sometimes masquerades as part of the claim that motion is an 'inherent' property of motion –- that certainly appears to be Graham Priest's interpretation of Hegel's views in this regard. [Priest (2006), pp.175ff.] The most obvious problem with this view is that a body can be moving in one reference frame while stationary in another. Hence, the idea that there is something 'inherent' (or 'intrinsic') to moving bodies seems to rely on space being Absolute!

 

Priest, however, denies he is committed to an absolutist interpretation of space and time (ibid. p.172), but it is difficult to see how his approach can avoid absolutism in this regard; I can find nowhere in his work where he tackles this problem.

 

It is worth pointing out first of all that much of what Priest has argued is susceptible to many of the comments found in this Essay -- that is, about the ambiguities surrounding words that have traditionally been used by theorists working in this area -- such as "move" (and its cognates), "place", "time", and "instant", etc. Priest, true to form, helps himself to such words and rarely if ever discusses such ambiguities, so it is hardly surprising that, like Hegel, Engels and the rest, he finds 'contradictions' popping up at every turn.

 

Secondly, one of the problems Priest's work presents logical novices is that, like many other mathematical logicians, he uses non-standard logical symbols; for example, instead of expressing a contradiction as follows: "p & ¬p", he uses expressions like this: "α & ¬α". He compounds this by peppering his books and articles with other Greek symbols. For instance, instead of labelling four possible alternatives related to what he calls "the instant of change", "A", "B", "C", and "D", he labels them "A", "B", "Γ" and "Δ" (where the first two letters are capital versions of α and β!). It isn't too clear why he does this, except it might make his work look more technically sound than it might otherwise seem (if he used the usual symbols).

 

[Priest in fact uses the logical symbol "Λ" in place of "&", used in this Essay. I have employed the latter symbol throughout since it is easer to access on my computer.]

 

Far worse, however, is this -- there is a fatal infinite regress implied by his analysis of motion:

 

"We have seen that a certain kind of change from α holding to β holding produces a nexus where α & β holds. We may, however, go a step further. We may take the nexus state produced to be the state of change itself. The state described by α & ¬α just is the state described by α changing into the state described by ¬α. Thus, there is such a thing as the state of change, and it does take time, if only an instant.... Not only is there a state of change that takes time, but it commences while the prior state obtains and terminates only after the posterior state has begun." [Priest (2006), p.170.]

 

However, if these states are X, Y, and then Z, and if, X is state α, Y is state α & ¬α, and Z is state ¬α, and if all change follows this pattern, then the change from X to Y must also exhibit this pattern, otherwise this analysis is fundamentally defective. That is we must have these three stages:

 

P1: (i) X, (ii) X & ¬X, and (iii) ¬X (where ¬X is Y).

 

So, in that case, we would have these three states as X changes into X and ¬X itself -- that is as α changes into ¬(α & ¬α):

 

P2: (i) α, (ii) α & ¬(α & ¬α), and (iii) ¬(α & ¬α).

 

So, as α changes into ¬(α & ¬α), it could only do so through intermediary state (ii), α & ¬(α & ¬α), if this model of change is universally applicable.

 

But, if there is change here, too, we must also have the following as α itself changes into α & ¬(α & ¬α); that is, it, too, must go through intermediary state, α & ¬(α & ¬(α & ¬α)):

 

P3: (i) α, (ii) α & ¬(α & ¬(α & ¬α)), and (iii) ¬(α & ¬(α & ¬α)).

 

And so on as intermediary stages emerge, ad infinitem.

 

Priest attempts to block this fatal regress (with a comment he relegated to a footnote):

 

"If we suppose there to be states of change, does this not start an infinite regress? For what if the change between, e.g. the prior state described by α, and the sate of change, described by α & ¬α? There is no infinite regress. The nexus state between these two states is described by α & ¬(α & ¬α), i.e. ¬(α & ¬α), which is the original nexus state. Thus to be changing into a state of change is already to be in that state of change, as one might expect." [Priest (2006), pp.170-71, ftn.17.]

 

But, if all change is to be modelled on this pattern, then it won't do to ignore the change from one state to another, howsoever it is described or labelled. It certainly won't do to try and block this with this bluff response: "Thus to be changing into a state of change is already to be in that state of change", since if that change is itself a state of change, then it must be governed by these 'contradictions', if it is to develop from a state that isn't a state of change into one that is.

 

In fact, if this were the case: "to be changing into a state of change is already to be in that state of change", there can be no change, unless we are told how this setup itself changes from a state that isn't changing to one that is. If, Priest wants to exempt such a change from his own model of change then he can hardly complain if others exempt every instance of change from this model. If this model fails at each moment of change, then it fails everywhere. On the other hand, if the change from no change to a scenario where there is change is itself abrupt, and does not pass through an intermediary contradictory state of affairs, then all change must be like this.

 

In other words, Priest can't in the end explain change, and his work in this area is simply wasted effort -- as one might have expected of anyone who unwisely takes logical and philosophical advice from a Christian Mystic.

 

[This is, of course, on top of the other logical confusions that have been highlighted by Priest's critics.]

 

More importantly for Marxists: Are any of these changes 'dialectical'? If they aren't then there seems to be no point to any this. So, do these states of affairs struggle with one another? Do they change into each other, as we are told they must? Does ¬(α & ¬α) change into α after these two have slugged it out? If so, every such change will go backwards!

 

Furthermore, does one change imply the other, such that one can't exist without the other? They would have to do so if they were 'dialectical opposites'. As far as I can tell Priest is silent about this. Indeed, it isn't easy to see how this could be the case if we turn to Priest's account of motion. Furthermore, and once again, there doesn't seem to be any point to all of this, since these 'contradictions' play no causal role in motion. [I have dealt with this 'problem' in much more extensively here; readers are directed there for more details.]

 

Further comments about relevant parts of Priest's analysis will be added in the next re-write of this Essay, as will several in relation to Marquit (1978, 1982), alongside the views of several other dialecticians.

 

18b. L15 is taken to mean:

 

L15a: If an object is wholly located at a point it must be at rest at that point.

 

It is also assumed that for such an object to be stationary it must be located at this point (and nowhere else) over a finite time period.

 

18b1. Lenin had the following to say about this option:

 

"Movement is the presence of a body in a definite place at a given moment and in another place at another, subsequent moment -- such is the objection which Chernov repeats (see his Philosophical Studies) in the wake of all the 'metaphysical' opponents of Hegel. This objection is incorrect: (1) it describes the result of motion, but not motion itself; (2) it does not show, it does not contain in itself the possibility of motion; (3) it depicts motion as a sum, as a concatenation of states of rest, that is to say, the (dialectical) contradiction is not removed by it, but only concealed, shifted, screened, covered over." [Lenin (1961), p.257. Italic emphases in the original; bold added. Quotation marks altered to conform with the conventions adopted at this site.]

 

Lenin here speaks about "motion itself". How he knew what "motion itself" amounted to he unfortunately kept to himself. As we will see, there are plenty of examples of motion that actually do what this character, Chernov, said of them. [On that, see Note 18c.]

 

Anyway, the point is that Lenin rejected this possibility, so we can see that this assumption (i.e., the truth of L16) underpins at least his understanding of 'dialectical motion':

 

L16: Hence, a moving body can't be located at a point, otherwise it wouldn't be moving, but would be at rest.

 

In fact, Lenin quotes Hegel approvingly on this topic (I have reproduced the whole passage; Lenin quoted only part of it):

 

"If we wish to make motion clear to ourselves, we say that the body is in one place and then it goes to another; because it moves, it is no longer in the first, but yet not in the second; were it in either it would be at rest. Where then is it? If we say that it is between both, this is to convey nothing at all, for were it between both, it would be in a place, and this presents the same difficulty. But movement means to be in this place and not to be in it, and thus to be in both alike; this is the continuity of space and time which first makes motion possible. Zeno, in the deduction made by him, brought both these points into forcible opposition. The discretion of space and time we also uphold, but there must also be granted to them the over-stepping of limits, i.e. the exhibition of limits as not being, or as being divided periods of time, which are also not divided. In our ordinary ideas we find the same determinations as those on which the dialectic of Zeno rests; we arrive at saying, though unwillingly, that in one period two distances of space are traversed, but we do not say that the quicker comprehends two moments of time in one; for that we fix a definite space. But in order that the slower may lose its precedence, it must be said that it loses its advantage of a moment of time, and indirectly the moment of space." [Hegel (1995), pp.273-74; partially quoted in Lenin (1961), p.257. (The editors of Lenin's text have clearly used a slightly different translation of Hegel.)]

 

I have attempted to clarify certain aspects of Hegel's argument in L18-L27, in the main body of this Essay. Lenin had plenty more to say about Zeno and the dialectical nature of motion in the surrounding pages.

 

I will consider these comments, and those advanced by Hegel, in a later re-write of this Essay.

 

Here, though, is John Somerville, making heavy weather of the idea that motion is a contradiction:

 

"Implicit in Engels' reasoning is the conception that a moment of time, even the tiniest instant, is a duration, an interval during which something happens. Time is obviously a flow, in which things happen. If we could not say that much, then we would not be able to say that the world (or the self) had a history. In that case there probably would be no problem. The problem arises after we have perceived that there are events, happening in sequence. If this is real, what follows? It seems quite clear that if time were made up of moments or instants during which or at which nothing happens, then nothing would happen or move, as Zeno saw long ago. However, if things do happen and move, it must be that even the smallest instant or interval of time is a flow. What Engels is saying, then, is that motion of anything is a process during which the moving thing is both at a given point and beyond that given point (in the sense of 'being in one and the same place and also not in it,' not simply in the sense of one part being in and another part not) during the smallest possible instant of time; and that if this were not possible, then there would be no motion.

 

"Now this assertion, that moving body X is simultaneously (during the same instant of time) at point Y and not at point Y, is recognized by all concerned to be a contradiction, as formal logic construes contradiction. But if body X could not manage that, then it could never move, since the only other alternative would keep it at point Y, or some other point, at every nonflowing instant. If all instants were instants at which a given thing is stationary, it is obvious there could never be a time at which anything could move, as time is by definition made of instants. The alternative is that time is made up of instants during which a change takes place, which means the possibility of a simultaneous A and non-A, the possibility of the same part of X simultaneously being at Y and not being at Y. Strictly speaking there are no instants at which, only instants during which. (But among these are instants during which the changes taking place in A make no difference to a certain problem, instants during which the motion of X makes no difference in relation to a certain point of view and a certain scale of measurement.)" [Somerville (1968), pp.66-67 -- these are in fact the page references to the 1974 reprint. Quotation marks altered to conform with the conventions adopted at this site. Italic emphases in the original.]

 

I think Max Black manages to cut through the confusion manifested by Somerville and Engels:

 

"It would be startling indeed if examination of experience could show that the traditional principles of logic were sometimes false. Somerville's argument to this effect does not inspire confidence. He cites, with approval, the hackneyed and muddled text from Engels in which it is alleged that 'motion is a contradiction' and that a moving body is constantly 'asserting' and simultaneously 'solving' this contradiction. That an inanimate body should assert anything at all does not strike Somerville as being odd. At any rate, he himself is prepared to assert that the moving body 'is simultaneously (during the same instant of time) at point Y and not at point Y.' Well, what does Somerville mean by an 'instant'? If he really means an instantaneous moment, then he really is contradicting himself, in the most elementary fashion.... But, if by 'instant' he means a small interval of time, then, of course, there is no logical contradiction in saying that during such an interval a moving body will at one instant be