Essay Five: Motion Is Not Contradictory
This essay should be read in conjunction with Essays Four and Eight Parts One and Two.
Readers should make note of the fact that this Essay does not represent my final views on any of the issues raised. It is merely 'work in progress'.
If you are viewing this with Mozilla Firefox, you might not be able to read all the symbols I have used.
This Essay is just under over 61,500 words long; a short summary of its main ideas can be found here.
Quick Links
Anyone using these links must remember that they will be skipping past supporting argument and evidence set out in earlier sections. [If your Firewall has a pop-up blocker, you will need to press the "Ctrl" key at the same time or these and the other links here won't work!]
(1) Introduction
(2) Initial Problems
(b) "Solved" In What Way, And By Whom?
(d) More Dogmatism
(3) Do Contradictions Explain Motion Or Merely Re-describe It?
(b) Are Contradictions Causes?
(c) 'Internal Contradictions' And Motion
(4) Is Engels's Account Comprehensible?
(b) First Attempt At Disambiguation
(c) Second Attempt At Disambiguation
(d) Fatal Ambiguity
(5) The Classical Response To Zeno
(a) Space To Let
(7) Further Problems
(c) Samuel Beckett Eat Your Heart Out
(8) No Word Is An Island -- Philosophers Ignore Ordinary Language
(b) Ordinary Language And Paradox
(d) Ordinary Objects Regularly Do The Impossible
(9) Dialectical Objects Do The Oddest Things
(a) Do They Move -- Or Just Expand?
(b) Or Do They In Fact Concertina?
(c) Coordinates To The Rescue?
(10) Everyday Miracles?
(11) Inferences From Language To The World
(12) Dialectical Contradictions
(13) Conclusion
(14) Notes
(15) References
Abbreviations Used At This Site
In this Essay, I aim to examine the role that 'contradictions' are supposed to play in explaining motion and change.1
Several prominent DM-theorists have attempted to illustrate the allegedly contradictory nature of reality by appealing to a variety 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
"[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.]3
In common with other dialecticians (indeed, as is well-known, he lifted these ideas from Hegel), Engels here connects change with motion, and both with "contradictions" in material reality.
However, before this passage is examined in detail, there are a number of serious problems it faces which need addressing first since they influence the overall interpretation of Engels's conclusions; left unresolved they threaten to undermine its content completely.
There are in fact five general difficulties with the above passage:
(1) "Asserted" By Whom?
Engels's closing sentence is rather odd:
"[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.]
Exactly who is supposed to do the "asserting", and who the "solving", here? It could be that these words were meant to be taken metaphorically. But, if that is so, what is the force of Engels's use of the term "precisely"?
Even more to the point: if Engels was speaking figuratively what has "assertion and simultaneous solution" got to do with motion? This is not even a good metaphor! Perhaps Engels intended to say that these merely pertain to the description of motion? In that case then, 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 such when they have been resolved. Is this the same with these contradictions? If it is, do new ones immediately take their place? Is each "solved" contradiction then replaced by the 'same' contradiction, or by an entirely new one? How might we decide? 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, how are they all connected with any given body in motion? Does each arise and fall as that body moves? Or is there a single, extended contradiction smeared or spread out, as it were, right across its entire trajectory? Is the latter contradiction then 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' would be required in the first place, but which now mysteriously helps propel the moving object further along (if it does)? On the other hand, if a 'solution' is required, how was this achieved 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 emphases added.]
This might help explain why the passage refers to the "continual assertion" of contradictions, since it's evident that only human beings can assert things. If so, it looks like Engels thought that human observers cannot avoid "asserting" such contradictions whenever they attempt to describe motion, and that could be a result of their partial understanding of the 'absolute truth' about motion. On the other hand, this could be a fault of logic or 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 again.
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 meant to assume that nature is Mind, or 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 should disappear. If so, this implies that motion will one day cease, all contradictions having been 'solved'. Moreover, if contradictions actually 'cause' motion, then their total resolution should, it seems, freeze nature in its entirety. Or, is it that motion will just stop being (or appearing to be) contradictory one day, but otherwise carry on as normal? Or even: does this mean that nature will just slow down as it is understood better, and what we know about motion and change becomes less and less contradictory? Who can say? Certainly, in the 140 years since Engels wrote these words, DM-fans have been more content merely to repeat these words than they have been intent on posing these 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 relating to processes in the 'objective world'. But, it's still unclear how this helps answer the above questions. If the mind "solves" the contradictions involved in motion, wouldn't this mean that things had actually stopped moving? And wouldn't this indicate, too, that movement only seemed to be contradictory because of the partial nature of knowledge, implying that motion wasn't really contradictory to begin with? That is because these subjective contradictions ought to disappear as knowledge grows, meaning that (in the limit) reality was not 'contradictory', after all. Only 'one-sided knowledge' of nature fools human observers into concluding otherwise.
Well, perhaps then this just means that we do not really understand such 'contradictions' to begin with? But, yet 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 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. Emphasis added.]
This seems to confirm the view that motion is not really 'contradictory-in-itself', and that it is simply our one-sided perspective on it that misleads us. After all, Engels tells us that the "continual assertion" and "solution" of this contradiction which is "precisely what motion is". And yet, why 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" cannot help us comprehend what Engels meant here either, since neither assertions nor solutions occur in nature (apart, that is, from the intelligent beings who make/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. If assertions and solutions do not themselves exist in the world independent of the minds involved, there would be nothing there (in the material world) for the minds of scientists and/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?
(3) More Vagaries
More specifically, in relation to the motion of 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 cannot be said to be in the first of these before it is in the second. So, unless great care is taken specifying how far apart these two places are, this view of motion would have, say, an aeroplane landing at the same time it took off! If any distance will do, then the distance between these two airports is as good as any.
Anyway, whatever the answer to that question turns out to be -- as is well known -- between any two locations there is a potentially infinite number of intermediary places (that is, unless we are prepared to impose a priori limitations on nature and deny this).
Does a moving body, therefore, occupy all of these at once? Or does it occupy each successively? If the former is the case, does it imply that a moving object can be in an infinite number of places at the same time, and not just in two, as Engels said? On the other hand, if Engels is correct, and a moving body only occupies (at most) two places at once, would that not suggest that motion is discontinuous ? This is because, on such an account, this seems to picture motion as peculiar a 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 places (the second of which it then occupies), if it is restricted to being in at most two of them at any one time. But, that itself appears to run contrary to the hypothesis that motion is continuous and therefore contradictory --, or, it does so at least in any straight-forward sense. It is surely the continuous nature of motion that poses such problems for a logic (i.e., FL) which is allegedly built on static, discontinuous points in space and time, this being the picture that traditional logic is supposed to paint, according to dialecticians.
It could be argued that no matter how much we 'magnify' the trajectory of a moving body, it will occupy two locations at once, being in one of these and not in it at the same time. But, that does not solve the problem, for if there is a potentially infinite number of intermediary places between any two locations, a moving body musty occupy more than two 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 -- that a moving object M occupies (at the same "moment in time", T1), there are the following intermediary points: (X1, Y1, Z1), (X2, Y2, Z2), (X3, Y3, Z3),..., (Xi, Yi, Zi),..., (X
n, Yn, Zn). And the same applies to (X1, Y1, Z1), and (X2, Y2, Z2), 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 too -- 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, if it is also to be in Q at the same "moment". And M must move through all these points without time having advanced one instant!
It will have done 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's no longer distance divided by time.
But, then, what 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.]
However, as we will see later, this alternative (i.e., that a moving body occupies all the intermediate points between any two points, all at the same time) poses other serious problems for Engels's theory, over and above it countenancing infinite velocities.
On a different tack, do these contradictions increase in number, or stay the same, if an object speeds up? Or, are the points depicted by Engels (i.e., the "here" and the "not here") just further apart, in that case?
So many questions. So few answers...
(4) Yet More A Priori Dogmatics?
Quite apart from all this, Engels's endeavour to provide an overtly linguistic/'conceptual' solution to the 'problem of motion' suggests that there is more than a hint of LIE in his account. And no wonder: he borrowed this approach from Hegel, an Idealist of the worst possible kind.
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 apply in this area, expressed though in ordinary-looking words -- the meaning of which Engels simply took for granted (more on this later). Based on thought alone, Engels imagined he was able to conclude what must be true of every moving body in the entire universe, for all of time, without exception. But, how could he possibly have known all this with so little evidence to rely on?
"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.]
Clearly, Engels possessed a truly remarkable skill: the ability to determine fundamental features of reality, valid for all of space and time, based on the alleged meanings of a few words/'concepts'. Indeed, Engels's claims about motion are all the more impressive when it's recalled that he made them in abeyance of any supportive evidence -- let alone a significant body of evidence. As it turns out (and this will be demonstrated below), 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/'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 he/she has to do is read Hegel's 'Logic'. As we will also see, this is a core feature of ruling-class forms-of-thought, 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 argument/'thought experiment', which is itself based on a consideration of what a few innocent-looking words/'concepts' must mean. Pressed for a justification of this line of reasoning, all that Engels could possibly have offered by way of substantiation would have been a rather weak claim that this is what the word "motion" really means. Clearly, such a (imagined, but plausible) rejoinder gives the game away since it would reveal that substantive truths about motion had indeed been derived from the meanings of 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's because the examination of countless moving objects would fail to confirm Engels's assertion that they occupy two places at once. This is so no matter what instruments or devices are used to carry out these hypothetical observations, and regardless of the extent of the magnification used to that end, or 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), and in one of these and not in it at the same time. This, of course, explains why Engels offered no scientific evidence whatsoever that supported his belief in the contradictory nature of motion. And this picture has not altered in the intervening years -- indeed, no book or article on DM even so much as thinks to quote such evidence in support of this thesis --, and this situation is not likely ever 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 to support 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. 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's not possible to record them.
It could be countered that as we increase the shutter speed of a camera, any photographs taken will always show some blurring. This supports the contention, then, that moving objects are never located in one place at one time. Maybe so, but 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 is not reasonable to conclude this. Not even a mathematical limiting process could capture such ghostly 'entities' in the physical world, whatever else it might do in theory. But even it could, no camera (or radar device, or piece of equipment) could record it. Hence, even if an appeal to mathematical limiting processes was both viable and/or available, it would be of no assistance. No experiment could conceivably substantiate any of the conclusions Engels reached about moving bodies.
And that explains why he (and those who accept these ideas) have to force this view of motion onto nature.
Hence, this view has not emerged from 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.]
Of course, as noted above, part of the problem here is what the word "instant" means. [I am taking this to mean the same as "moment in time" used by Engels.] So, it might be thought that this 'problem' could be solved by means of a suitable definition. However, even if this were possible, such an 'adjustment' would merely represent the adoption of a new convention, and would have no bearing at all on the nature of reality.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 could not exist -– that is, not unless we are prepared to reject the a priori conclusion Trotsky expressed in the above passage.
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 the latter do not exist (according to Trotsky)? 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, an appeal to the abstract nature of some of the points made above cannot rescue Engels, either. His analysis of motion is no less abstract itself! And, it can't have been derived itself by abstraction from all (or any) of the forms of motion hitherto experienced by either himself or humanity -- or even from a finite sub-set observed by scientists and/or philosophers down the ages. This is because his thesis clearly appeals to things that, according to Trotsky, do not 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. Worse still, we couldn't abstract from such instants in order to agree with him, either.6
Whichever way we turn we hit yet another non-dialectical brick wall.
To be sure, Engels promptly changed direction 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 objected that Engels was actually arguing that our thoughts about motion are contradictory because motion itself is. That is, our theories more truly depict the world more fully when they reflect its contradictory nature, and that substantive claims about the universe are justified if and when our ideas capture reality more precisely (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-theory itself contains contradictions, which would imply it's a contradictory theory.7
[The disastrous implications that particular conclusion has for DM are outlined in Essay Seven, and Essay Eleven Part One.]
However, 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 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.
The problem with this fall-back position is that (as will be apparent by the end of this Essay): our thoughts about motion aren't the least bit contradictory, either.
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 the meaning of a handful of words/'concepts' to fundamental aspects of reality, is openly Idealist (on this see Essay Two and Twelve Part One). 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 emphasis added.]
Compare these 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 instant, being in two places at once) resists all attempts to make sense of it, as we will see.
Substantive philosophical 'truths' like this (about motion) are ambitiously universal in intent, but are thoroughly parochial in origin. Indeed, their promulgators' epistemologically imperialist intentions (which stretch across all regions of space and time) remain manifestly unmatched by any obvious capacity to satisfy excessive philosophical ambitions like these with adequate material support.
So, throughout history, traditional theorists (like Engels -- but 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 specially-engineered words and theses seem to them to depict it. However, if this were so, it would mean that the universe possessed these features simply because of the idiosyncrasies of Indo-European Grammar -- the language group in which most of this overblown talk has been expressed.
(5) Explanation Or Re-Description?
Perhaps even worse still: It is not 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's difficult to see how one 'part' of a '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 that "not here") could make anything move. [A more general objection to this way of seeing change can be found here.]
[UO = Unity of Opposites.]
As Engels depicts things, both 'parts' of this UO seem to appear 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 questions concerning the proximate cause of motion (with the implied temporal concomitants such questions often motivate) cannot be answered by anyone adopting this way of depicting movement, The mere fact that a moving body is "here" does not appear to be capable of making it become "not here". Indeed, this alleged contradiction seems to lack any causal powers whatsoever, any capacity to make things happen. It is not so much that the dialectical batteries have run down as it's that there do not seem to have been any supplied with the original item.
This probably explains why Engels does not 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 filled in the gaps). But, even if a DM/causal account were to be provided one day, it's not easy to see how these alleged contradictions could explain motion; how does a being "here" and "not here" (all at once) explain why anything moves (causally or in any other way)? What work do such contradictions do -- even if you believe in them?
It could be objected here that this radically misconstrues DM, for the counter-argument above misleadingly splits apart the assumed 'sections' of a contradiction 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 does not 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 TAR -- 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 figuratively. [More on this in Essay Eight Parts One and Two.] And this is quite apart from the fact that this alleged contradiction (in motion) does not appear to be relational at all. What precisely is being related to what? What "relation" is this particular one meant to be? Is a body related to itself as it moves? But, how would that make it move?
[The best attempt that I have so far seen from a Marxist dialectician to explain the rationale behind this view of motion and change is taken apart here.]
Moreover, it's not easy to see how contradictions could exercise any sort of effect on anything at all unless they were translated or expressed somehow into physical/material terms (which 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"), drawn from AIDS, does not seem to have the required physical presence -- the oomph, as it were -- to carry out menial tasks of this sort.8
[AIDS = Absolute Idealism; HM = Historical Materialism.]
Furthermore, if the volunteered DM-response above were correct (but see below), contradictions would not appear to 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, would not, therefore, make anything actually happen. What would therefore power social development would be totally obscure, given this (assumed) rejection of any causal role for such contradictions to play. Hence, 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 would not be able to explain why anything actually happened in nature or society. [Of course, that might be the real reason why they can't do this --, but they certainly do not 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, contradictions could be dispensed with at no loss to HM, since (given the above response) contradictions would do no work in HM either, playing no causal role. 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 managed to stifle Marxist theory.
If so, it means that dialecticians need to specify -- as a matter of some urgency -- 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 do not appear to be part of the action; at best, they seem to be 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 will soon see.
As hinted at 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 not 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'/'moment'. The problem is: How does this actually explain motion causally -- or 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's worth pondering once again the answer to this question: Do contradictions cause motion (i.e., do they make it happen), or 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. But, as we will soon see, this would mean that one or both of the following hypotheticals would have to be true:
(1) If contradictions didn't exist, motion could still take place.
(2) If motion ceased, contradictions would still remain.
(1) The relevance of the first of these is underlined by the fact that unless motion was already underway, a contradiction could not be inferred.
At the very least, this option prompts a further question: Which came first -- movement or contradiction? The answer to this might be why Engels spoke about contradictions being "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 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 this is the case here, too?8a
(2) The second option above follows from the simple observation that a stationary body can occupy two places at once, and it can be in one place and not in it at the same time. [Examples of both are given below.]
In that case, (2) suggests that contradictions aren't a sufficient cause of motion, whereas (1) indicates they aren't even necessary.
Moreover, and with respect to (1), once more, 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, as far as Engels saw things -- that is, there seems to be no way that they could make anything move. At best, 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 things first of all move, and only then do contradictions emerge -- and even then this just applies to our depiction of motion.
If so, it might be correct to say that contradictions operate solely at a 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 do not to do so because they become embroiled in literal contradictions.
[So, for example, moving bodies do not 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 things.
However, this way of depicting motion is clearly unacceptable to DM-theorists; they insist that we must begin with material reality not with a description of it. From there, according to them, we must postulate only those contradictions that really exist in nature or society -- based perhaps on their reflection in human thought, confirmed in practice. Clearly, human beings study motion and its attendant contradictions using the conceptual resources they have to hand, which 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 latter three quarters of this Essay. Also, see here.]
In relation to Engels's account of motion, as will soon emerge, there is no clearly specifiable set of possibilities -- or even actualities -- 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's not 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's because his words fail to be a description in the first place. Hence, Engels's 'description' of motion is not just empty, it's not even a description!
Again, it could be objected that the above analysis is misguided since it compartmentalises reality, distorting the account of nature given in DM.
In response to this it's worth pointing out that we do not 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 would not amount to an explanation of the causal or "mediated" links that are required. A widening of the domain (to the entire Totality if need be) cannot suddenly provide an explanation of how the simultaneous presence and absence of an object in one and the same place 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 cannot account for movement and change in DM-terms. [That cryptic comment will also be explained in Essay Eight Parts One and Two.]
Furthermore, but 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 in the Totality), cannot create a genuine connection if there are none already there in reality for it to reflect. Contradictions must have some sort of material basis if they are to be reflected in thought; they cannot just be conceptual. And yet, what material form do they take?
Unless 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 some sort of grist for the DM-causal/mediational mill to grind away at, a DM-style reflection would advance the explanation of motion not one inch.
Even assuming it could be shown that contradictions do in fact represent a material relation between objects and/or processes -- 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 such a causal (mediational) link between events must to be postulated (i.e., 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 were filled in. Without the latter, the contradictory nature of motion would remain at best a conceptual, but not yet a material aspect of reality.
[That outcome should surprise no one given the Idealist origin of DM-use of "contradiction".]
If, on the other hand, it's claimed that the mere presence of the said conceptual connection indicates that such causal links must exist in reality -- that is, if the complex reflection theory of knowledge is assumed to be true (wherein the human mind acquires knowledge actively, in practice etc.) --, then that would still not explain how contradictions could actually cause motion. How do contradictions succeed in moving things about the place? Here, the dialectical spade is not 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 not helped by an account that depicts them (1) As the product, not the cause of motion (making them derivative), or (2) As the result of human reflection on the nature of motion (implying 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 actually explains why anything 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 do not 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 do not 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, but worse) --, and this would be so 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:
"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 (1961), p.110. Bold emphasis added. This entire topic is examined in great detail in Essay Eight Parts One and Two.]
Furthermore, there do not appear to be any identifiable contradictions situated at the leading edge of a moving body 'dragging' it along, 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.
In that case, with regard to individual bodies, motion cannot be an example of change through "internal contradictions".
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 would then 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 previous few 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. On 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 each object in that system.
However, 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, a change in motion), or even how they could initiate it. Nor would it account for 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/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.
Hence, whether it is true or not that movement is caused/mediated by a disequilibrium within a system of incipient forces ('internal' or otherwise), this still does not affect the alleged fact that once moving, a body appears to do contradictory things. Even given the truth of such an 'internalist'/'externalist' account of contradictions and forces, 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) does not also cause motion in addition to the forces at work in the system. Indeed, while forces might cause motion (or, rather, 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'/'externalist' picture were correct, Engels's analysis of motion would still amount to nothing more than a re-description of it; it would still be the case that motion makes bodies do allegedly contradictory things, not the other way round. Hence, the contradictions Engels highlights are still derivative, and not at all explanatory.
It's 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 paradoxical states that moving bodies appear to display and forces has still to be established. All that the addition of opposing forces here 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 motion (or even changes in motion) is not 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, motion (or, indeed, 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 this, 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 one particular interpretation that appears to be inconsistent with what Engels himself said about forces -- again, see Note 10), what seems to be important 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 (and/or contradictory totalities) is no less misguided. There, it will be demonstrated in extensive 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 forces, either.]
[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 it is contradictory or not) depends on an obsolete Aristotelian theory. If so, the fact that contradictions cannot 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 (Newtonian) mechanics would have to be binned.11
But, then again, if such 'contradictions' do not explain motion (i.e., they do not change or initiate it), why make such a fuss about them?
Well, despite the above, it could be objected that this whole discussion seriously misunderstands the nature and role of contradictions in dialectics. As John Rees points 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 criticisms is that they substitute an abstract analysis for one that should be 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 to illustrate their theory -- as well as the spurious claim that dialecticians do not use their theory as a "master key" to unlock reality, when they clearly do. [On that, see Essay Two.]
The claim will also be revived here and here (but, more specifically here, here and here) that material contradictions cannot account for change, since they are locked in the descriptive mode (and a confused mode, to boot).
However, one further possibility has not yet been examined: What if it's 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 saw 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 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, for example, for your keys if you do not 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 Account Comprehensible?
Before an empirical investigation into the real material cause of motion can begin, we need to be clear precisely what it is we are being asked to examine. As things turns out, it's not possible to determine what Engels was trying to claim 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 these allegations, several further ambiguities in Engels's account will need to be addressed first.
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 do not immediately look equivalent:
L1: Motion involves a body being in one place and in another place at the same time.
L2: Motion involves a body being in one and the same place and not in it.
L1 asserts that a moving body must be in two places at once, whereas L2 says that it must both be in one place and not in it, while leaving it unresolved whether it is in a second place at the same or some later time -- or even whether it could be in more than two places at once. To be sure, it could be argued that it's implicit in what Engels said that this occurs in the "same moment of time"; however, I am trying to cover every conceivable possibility, and it is certainly possible that he did not. [The significance of these comments will emerge as the Essay unfolds.]
It's important to be clear what Engels means 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 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). But since all real bodies are extended in this way, the mathematical point option seems irrelevant, here. [Anyway, it will be considered below.]
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.]
[In this and subsequent paragraphs I will endeavour to illustrate the alleged ambiguities in Engels's account by an appeal to everyday situations (for obvious materialist reasons). However, these can all be translated into a more rigorous form using vector algebra and/or set theory. In the last case considered below, just such a translation will be given to substantiate that particular claim.]
Unfortunately, even this ambiguous case could involve a further equivocation regarding the meaning of the word "place" -- the import of which Engels clearly took for granted. As seems plain, "place" could either mean the general location of a body (roughly identical with that body's own topological shape, equal in volume to that body --, or, on some views 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 relates to the latter. Because it's Engels's depiction of motion that's unclear, I will concentrate on ordinary material bodies. Anyway, since DM-theorists hold that their theory can account for motion in the real world, the the motion of mathematical points -- even where literal sense can be made of them and of the idea that they can move; if such points do not exist in physical space, they can hardly be said to move -- will not in general be entered into here.
L2 itself 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". However, it could be objected that "in" has been replaced by with "totally inside". But, it's worth pointing out that Engels Engels actual words imply this is a legitimate 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. So, a mundane example of this ambiguity is where, say, a 15 cm long pencil is sitting in a pocket that is only 10 cm deep. In that case, the pencil would be in, but not entirely in, the pocket -- that is, it would be both in and not in the pocket at the same time, but still at rest with respect to some inertial frame. L2 certainly allows for such a situation. Engels's use of the word "in" and the rest of what he said implies this ambiguity.
Hence, it seems that Engels's words are compatible with a body being motionless relative to some inertial frame. And this would still be the case even if L1 and L2 were combined, as Engels intended they should:
L3: Motion involves a body being in one place and in another place at the same time, and being in one and the same place and not in it.
An example of L3-type -- but apparently contradictory -- 'lack of motion' would involve a situation where, say, a car is parked half in, half out of a garage. Here the car is in one and the same place and not in it (in and not in the garage), and it is in two places at once (in the garage and in the grounds of the house), even while it is at rest relative to a suitable inertial frame.
In which case, the alleged contradiction Engels is interested in can't be the result of motion; it is in fact a consequence of the vagueness or the ambiguity of his description. This can be seen from the further fact that objects at rest relative to some inertial frame can and do display the same apparent 'contradictions' as those that are in motion with respect to the same inertial frame. Naturally, if things at rest share the very same vague or ambiguous features (when they are expressed in language) as those in motion, Engels's description clearly fails to pick out what is unique to moving bodies.
This is not a good start.
At best, L3 simply depicts the necessary but not the sufficient conditions for motion. In that case, the alleged contradictory nature of L3 has nothing to do with movement actually occurring, since the same description could be true of bodies at rest, which share the same necessary conditions. As already noted, alleged paradoxes like this arise from the ambiguities implicit in the language Engels himself used -- and, as it turns out, misused. [This will be discussed in greater detail below.]
Nevertheless, in the next few sections several attempts will be made to remove and/or resolve these equivocations in order to ascertain what, if anything, Engels might have meant by the things he tried to say about moving bodies.
First Attempt At Disambiguation
As will also be demonstrated in Essay Six -- in relation to Trotsky's (and indirectly Hegel's) attempt to analyse the LOI --, Engels's account of motion is in fact far too vague 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 body B in motion involves 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) is not the same place as (X2, Y2, Z2).
[Where, (Xi, Yi, Zi) etc., are coordinate triples, and tk is a temporal variable.]
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 does succeed 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; I will leave that for others to decide.
[Still others, of course, might wonder exactly how the word "change" could be explicated (given this theory) 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 would not alter the truth of L5, but it would make it eminently circular.]
However, even if this 'niggle' is resolvable, the initial promise the above set of sentences seemed to offer soon evaporates when it's remembered that L5-L7 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 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 motion of this object will only attract the same criticisms -- that is, if L5-L7 were merely replaced with propositions that just change the temporal variable to t2, while no other adjustments are 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 failed to do this originally.
L6-L8 below attempt to fix this glitch.
The problem, it seems, lies with L5, since it does not connect the motion it mentions to the same instant recorded in L6 and L7. Hence, the following emendations need to be made, it would seem:
L8: A body B in motion involves 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) is not 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 "ti" in the place of "t1" in L8 and L6. This complication will be ignored here, since it does not seem to affect the points at issue.
Unfortunately, however, L6-L8 do not appear to imply a contradiction --, that is, not unless it's clear that B is no longer at (X1, Y1, Z1) at t1, since it's possible for a 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, 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 that scenario was contradictory, he/she 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 against what it was 'struggling'! As we will see in Essay Seven, the dialectical classicists hold that objects turn into whatever their opposites are, that is, whatever they turn into whatever they are contradicted by. In this example, that would seem to involve such cakes turning into the buildings that housed them! Since no one in their left mind could reasonably be expected to believe this, cakes in supermarkets cannot be regarded as in anyway contradictory of the bricks and mortar around them. Anyone who still thinks this is encouraged to seek professional help.
So, in order to rectify this, we need to replace L6 with L9, as follows:
L8: A body B in motion involves 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) is not the same place as (X2, Y2, Z2).
Now, this set (henceforth called L) certainly looks inconsistent. The question, though, is: Can all 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 L.
[At this point it's 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 formed from elements of S are contradictory just in case (1) those elements are inconsistent and (2) they cannot also be false. In short, they cannot both be true and they cannot both be false. This salient fact is invariably overlooked by DM-theorists, which, naturally, leads them into confusing contradictions with inconsistencies and/or contraries -- and, in many cases, with a host of other unrelated things, too. (Any who object to the alleged 'pedantry' here should read this first and then think again.)]
The question is, therefore: Can all of the elements of L be false at once? If they can, then it won't be possible to construct a contradiction from all and only elements of L. I propose to resolve this question by considering each of L'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.
[In fact L9 is an inconsistent sentence anyway, and hence it is false (either that, or it is not a proposition to begin with (which is what I would maintain, anyway)11b --, depending on which branch of the Philosophy of Logic one attends to). But since DL is based on the claim that inconsistent sentences can be true, I have ignored this alleged fact here since 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.
(3) L7 could be false if (X1, Y1, Z1) was the same place as (X2, Y2, Z2). This would make L9 false, as well.
In which case, it looks like we can imagine situations in which, while not all of L's elements could be true at once, all could be false at once. This means that it's not possible to construct a contradiction from all and only elements of L.
Knowledgeable readers will have noticed the illegitimate way in which the schematic sentences of L (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 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 must be allowed to stand if L11 is to work, 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 is so is explained in Essay Twelve Part One). Since protracted examples of motion take place over very long time periods, we cannot appeal to the relative stability of language to fix the reference of these variables (or that of their ordinary language counterparts), if the LOI is not applicable in all cases.
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 L) depended on ignoring some or all of these conventions; as a result those objections were entirely illegitimate. Of course, that ploy itself was aimed at highlighting this very point: the use of variables in FL is based on conventions that DM-theorists must themselves observe (in ordinary discourse, and/or in logic) if Engels's analysis of motion is to be rendered comprehensible, but which conventions vitiate their own criticisms of the LOI! Naturally, it's a moot point which horn of this dilemma they will want to "grasp": either accept the Hegelian criticisms of the LOI and sink Engels's analysis of motion, or accept Engels's account and abandon Hegel's criticism of the LOI.
It could be objected that the above comments represent a caricature of the criticisms that dialecticians make of the LOI. The relative stability of both material bodies and linguistic expressions permits them to talk about such things as the "same body", the "same word", the "same variable", and so on. Moreover, dialecticians do not flatly deny 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 detail in Essay Six (the relative stability argument, for example, is neutralised here); 'dialectical contradictions' themselves are analysed in Note 1 and here.
[MFL = Modern Formal Logic; LOI = Law of Identity.]
Of course, hard-nosed dialecticians might choose to ignore MFL altogether. That is, of course, their right. But they would then find it rather difficult to say what Engels actually meant in the quoted passage above. [Anyway, that bolt hole will be blocked later on in this Essay.]
Unfortunately however, even as it stands, and despite the foregoing (that is, if the contentious claims made above about the LOI and MFL are indeed misconceived, and are thus withdrawn), L11 would still not 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 ones considered so far.
This latest 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's always possible to argue that L11 really amounts to the following:
L12: For some b, during interval T, and for two 'instants' t1 and t2 [where both t1 and t2 belong to T, such that t2 > t1], and for two places p and q, b is at p at t1, but not at p at t2, and b is at q at t2.
[In the above, t1 and t2 are themselves taken to be sets of nested sub-intervals, which can be put into an isomorphism with suitably chosen intervals of real numbers; hence the 'scare' quotes around the word "instant" in L12.]
Clearly, the implication here is that the unanalysed variable "t" in L11 actually picks out a time interval T (as opposed to a temporal instant) -- brought out in L12 -- during which the supposed movement takes place. This would licence a finer-grained discrimination among T's sub-intervals (i.e., t1 and t2) during which this occurs.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…
Indeed, this is how motion is normally conceived: as change of place in time -- i.e., with time having advanced while it occurs. If this were not so (i.e., if L12 is rejected), then L11 would imply that the supposed change of place must have occurred outside of time -- or, worse, that it happened independently of the passage of time --, which is either incomprehensible (as even Trotsky would have admitted), or it would imply that, for parts of their trajectory, moving objects (no matter of how low their speed) moved with an infinite velocity! This was in fact pointed out earlier.
And yet, how else are we to understand Engels's claim that a moving body is actually in two places at once? On that basis, a moving body would move from one place to the next outside of time -- that is, with time having advanced not one instant. In that case, a moving body would be in one place at one instant, and it would move to another place with no lapse of time; such motion would thus take place outside of time. But, according to Trotsky, that sort of motion would not exist, for it would not have taken place in time.
Indeed, we would now have no right to say that such a body was in the first of these Engelsian locations before it was in the second. [That is because "before" implies an earlier time, which has just been ruled out.] By a suitable induction clause, along the entire trajectory of a body's motion it would not, therefore, be possible to say that a moving body was at the beginning of a journey before it was at the end! [The reasons for saying this will be detailed below, but the latter conclusion depends on the argument presented here, which should be read first.]
[Trotsky's worries about instants are examined below, and in Essay Six. The contrary idea that if a body is located at a point at an instant, it must be stationary, is also examined below.]
Despite this it would seem that this latest difficulty can only be neutralised by means of the adoption of an implausible stipulation to the effect that whereas time is not composed of an infinite series of embedded sub-intervals -- characterised by suitably defined nested sets of real numbers --, location is. [Naturally, 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 position a body occupies as it moves along as finely as we wish -- so that no matter to what extent we slice a body's location, we would always be able to distinguish two contiguous points allowing us to say that a moving body was in both of these places at the same time --, while we can do that with respect to location, we cannot do the same with respect to time.
Clearly, this is an inconsistent approach to the divisibility of time and space -- wherein we are allowed to divide one of these (space) as much as we like while this is disallowed of the other (time). [It could even be argued that this is where the alleged 'contradiction' originally arose -- it was introduced into this 'problem' right at the start by this inconsistent (implicit) assumption, so no wonder it emerged at a later point -- no puns intended.]
This protocol might at first sight seem to neutralise an earlier objection (i.e., that even though a moving body might be in two places, we could always set up a one-one relation between the latter and two separate instants in time, because time and space can be represented as equally fine-grained), but, plainly, it only achieves this by stipulating (without any justification) that the successful mapping of places onto (nested intervals of) real numbers (to give them the required density and continuity) is denied of temporal intervals.
So, there seem to be three distinct possibilities with these two distinct variables (concerning location and time):
(1) Both time and place are infinitely divisible.
(2) Infinite divisibility is true of location only.
(3) Infinite divisibility is true of either but not both (i.e., it is true of time but not place, or it is true of place but not time).
Naturally, these are not the only alternatives, but they seem to be the only three that are relevant to matters in hand.
Of course, one particular classical response to this dilemma ran along the lines that the infinite divisibility of time and place implies that an allegedly moving body is in fact at rest at some point; so, if we could specify a time at which an object was located at some point, and only that point at that time, it must be at rest at that point at that time. [This seems to be how Zeno at least argued.]
Nevertheless, it seemed equally clear to others that moving bodies cannot be depicted in this way, and that motion must be an 'intrinsic' (or even an 'inherent' property) of moving bodies (that is, we cannot depict moving bodies in a way that would imply they are stationary), so that at all times a moving body must be in motion, allowing it to be in and not in any given location at one and the same time. [This seems to be Hegel's view of the matter -- but good luck to anyone trying to find anything that clear in anything he wrote about this!]
If so, one or more of the above options must be rejected. To that end, it seems that for the latter set of individuals 1) and 3) must be dropped, leaving only 2):
(2) Infinite divisibility is true of location only.
However, it's worth pointing out that the paradoxical conclusions classically associated with these three alternatives only arise if other, less well appreciated assumptions are either left out of the picture or are totally ignored -- i.e., in addition to those alluded to above concerning the continuity of space and the (assumed) discrete nature of time. As it turns out, the precise form taken by several of these suppressed and unacknowledged premisses depends on what view is taken of the allegedly 'real' meaning of the words like "motion" and "place".
In Essay Three Part One and Essay Twelve Part One, it was argued that philosophical 'problems' of this sort only arise when ordinary words are twisted beyond recognition (which view, incidentally, was endorsed by Marx), and the new conventions for the use of such terms that emerge as a result are then misinterpreted as super-empirical truths, not conventions at all.
In short, the 'classical' approach only gets off the ground if linguistic conventions/stipulations, and/or rules, are mistakenly viewed as Super-Scientific, mega-empirical propositions, or matters of fact.
That is, this approach mistakes an implicit decision to use certain words in novel ways as a fundamental truth about reality itself.
Indeed, this is precisely how theorists (in ancient Greece) began to misread the products of social relations (conventions/rules) as if they were the real relations between things, or even as those things themselves (thus fetishising language). Because of this they imagined they could 'derive' Super-theses like these from idiosyncratic jargon they had invented.
Because of this 'wrong turn' (although there were clear ideological motives for taking it -- on this, see below and here), traditional Philosophers reasoned that the word "motion", for example, implied there was some sort of 'problem' (or 'contradiction', or 'paradox'), which needed to be resolved. Few, if any, questioned the original distortion/fetishisation that had been inflicted on ordinary words (for motion, place and change), which had artificially created such 'difficulties'.
This is because, of course, such thinkers came from sections of society that had been divorced from the world of collective labour and communal life, and whose theories reflected the ideal view of reality this privileged life-style encouraged. For the same reasons it also arose from an ideologically-motivated denigration of the vernacular. [These allegations will be fully-documented in Essay Twelve (summary here).] So, in their view, if the world was ultimately Ideal, it would of course be quite 'safe' to infer Super-Scientific truths about realty from language alone, as we saw George Novack point out earlier.
The fact that the classical 'paradox' of motion was 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) cannot be (and has never been) based on evidence of any sort. Severally or collectively, each of these alternatives is founded on a linguistic convention overtly or covertly accepted by all parties to this metaphysical con-trick, one that 'uncovers'/uses 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").
Moreover, the choice of one or more of options (1) to (3) (as a way motivating a favoured 'solution' to this artificially-induced 'problem') also depends on the idea that even if the specification of the location of a body was in no way problematic (in that we can always declare that a moving body is in two places at once), the specification of time is.
Thus while the identification of point instants in time was seen to be a problem, the specification of points in space hardly raised a eyebrow. With respect to DM, this can be seen by the way that Trotsky, for example, failed to draw the same conclusions about locations in space that he drew about points in time.12a
(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, these appear to be among the fundamental issues that have exercised 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 perhaps the word "indefinite" replacing "infinite" here in some cases.]
As has already been noted, this choice was motivated by a surreptitious exclusion: the indefinite division of time was ruled out, while that of position wasn't.13
Finally, but most importantly, the traditional metaphysical 'solutions' on offer were also 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 every day 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.
However, as we shall soon see (and again in several other Essays posted at this site), the protocols of ordinary language and common understanding are not so easily ignored, dismissed, or depreciated.
However, there are (and can be) no (a priori) empirical constraints on the length of time intervals. In fact, as was also noted above, Engels's account of motion was not (and could not have been) derived from observation, mediated via the naïve or the sophisticated version of the RTK. Nor could his idea of 'motion in general' -- nor, indeed, of 'abstract motion' -- have been materially-grounded, either.
[RTK = Reflection Theory of Knowledge.]
This 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 enough 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'.
And it's little use objecting that this or that 'must' be true of 'motion itself', for that would be to concede the fact that a 'musts' like this had been derived from the meanings of a few words, which, as we will soon see, are far less straight-forward than traditional theorists would have us believe.
It could be objected 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 is based on one of these, via Hegel. So, what's the problem?
Once more, the problem is that the deducibility or otherwise of these conclusions depends on the use of several artificially modified words (such as "place", "move", "time", "moment", etc.), which have either been idiosyncratically, or narrowly (re-)defined, or which have had their meanings altered in other ways. In that case, nothing reliable can follow from them (as I hope to show later). This was the point Marx was trying to make.
Even worse, not only does nothing follow from such distorted language (and/or abstract 'concepts'), it's impossible to give a clear sense (or any sense) to the classical account (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; they not only do not say anything comprehensible about the world, they can't.
In that case, if humanity does in fact possess an 'abstract' idea of motion (and this will be contested below, and in other Essays posted at this site), it cannot have been derived from 'reflection', nor could it have been based on anything found in the material world. And those observations become all the more apposite if this allegedly 'abstract' idea of motion itself originated from (a) The inequitable constraint mentioned above -- i.e., that which was arbitrarily imposed on the allowable length of 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 was not based on reflection (howsoever this 'process' is understood), on evidence, or on abstraction, but only on 'concepts' that are themselves the product of traditional/classical stipulations (or covert conventions) -- which were then imposed on reality inequitably!
Returning now to consider several earlier options:
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 (while this condition is asymmetrically allowed of space) -- i.e., if option (2) above is imposed on the phenomena) --, then there seems 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 is not contradictory at all, since a body can be in two places at once whether it moves or not (as we have seen), with no implication that it both is and is not 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).
An everyday example of L13 might involve a case where a ship, say, enters port: here the ship could both be in the water and in the port at the same time (and hence simultaneously extended across several locations, and thus be in at least two places at once), and be moving, but with no implication that it is entirely in any one of these 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 would not be in, say, the dry dock (which is also part of that port), nor in the staff canteen, nor in a host of other places in that port, at that time.
Moreover, if the ship were stationary with respect to some inertial frame, the same possibilities would still apply. Here, this ship could be in one place and not in it (fully), and in two or more places at once, and stationary (or moving), and yet imply no contradiction. 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.
[I have given a more technical version of this scenario in Note 15.]15
As pointed out above, L12 and/or L13 can only be rejected successfully 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 do not 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's not one based on any genuine features of reality.16
At worst, it's merely a product of a confused use of philosophical jargon.
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 cannot be in motion and at rest at one and the same time (in the same inertial frame).18a
L15: If an object is located at a point it must be at rest at that point.18b
L16: Hence, a moving body can't be located at a point, otherwise it would not be moving, it 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 were not 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 movement is depicted in, say, film. Here, motion 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 would not be enough to make this picture of motion false, no more than quantum discontinuities now invalidate QM -- that is, given the way that motion is depicted in traditional Philosophy.19
[QM = Quantum Mechanics.]
Options (a) and (b) are absurd and will not be considered in this Essay.
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):
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, motion is no more than successive point occupancy. This means that locomotion must be composed of either: (a) Successive states of instantaneous rest, or (b) 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 moment of location/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.
[This 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 Leibniz held a version of this theory.]
L21: L20(a) involves a body in discontinuous motion separated by periods of instantaneous rest. L20(b) involves a body, or series of bodies, in discontinuous existence at contiguous locations.
L22: L20(b) must be rejected as absurd.
L23: If L20(b) is rejected then L20(a) implies that in between each successive point occupancy a body must pass through an indefinite (possibly infinite) number of intervening locations. [Of course, this depends on there being an infinite, or a potentially infinite, number of points between any two points.]
L24: Hence, even on the assumption that motion is discontinuous, there must 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 cannot be at rest at any of those intermediate points.
L25: Consequently, if motion takes place -- and 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 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 cannot be wholly discontinuous.
[It is possible to strengthen L27 into L27a, but that option will not be pursued here:
L27a: Therefore, either motion is impossible or illusory (which is absurd), or motion cannot be discontinuous.]19a
However, it's worth noting that the above argument begins with the rejection of an apparent contradiction -- that which is expressed in L14 (restated here for ease of reference, but re-numbered L28, and hence very slightly altered) alongside its alleged contradictory, L29:
L28: A body cannot 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, this depends on whether these are genuine contradictories; I will ignore that minor complication here. On the other hand, if they are not even propositions, then they cannot 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
Hence, if these 'niggles' are ignored, L29 is true if L28 is false, and vice versa.
As is well-known, an analogous series of assumptions motivated Zeno to try to 'prove' that motion was either impossible or illusory. DM-theorists obviously reject Zeno's conclusion, but it seems they can only do that by accepting L28 (or its equivalent), and 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's clear that dialecticians have to reject one 'contradiction' (expressed in L29) in order to derive their own (in L17).
Now, when L17 is conjoined with L28 we obtain the following:
L17a: Since a body cannot 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's worth asking: Which one of the following '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 is true, it looks like L17a cannot be derived in any obvious way from the sorts of considerations advanced in L14-L27. This would mean that Engels's analysis is defective -- always assuming, of course, that his 'argument' depends on such considerations and that some sense can be made of anything he said in this area.
Nevertheless, it's 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 cannot be at rest and in motion at the same time in the same inertial frame.
L17a: Since a body cannot 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 is because L14-L27 began with the assumed truth of L14 -- or, its equivalent in L28. The reverse implication does not appear to hold. This means that L28 does not 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.
Be that as it may, L28 is itself false if L29 is true:
L28: A body cannot 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 does not rule this out. In order to eliminate this new difficulty, therefore, L29 must be modified; perhaps in the following manner:
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 cannot 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).
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! This much seems reasonably clear.
Unfortunately, however, the following line of argument also shows that the derivation of L17a from the rejection of L30 is not inevitable, and that Engels's conclusion does not automatically follow:
L31: A body cannot 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 cannot be located wholly 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 cannot 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 decide. But, L31-L34 demonstrate that L17a does not have to follow from the rejection of L30, even if the alternative outcome proves unpalatable.
It's now clear that the refusal to accept the 'contradiction' contained in L30 can lead to two distinct 'contradictory' conclusions. One is inconsistent with experience (i.e., the latter half of L34, i.e., L34b), while the other is self-contradictory (i.e., L17a):
L17a: Since a body cannot 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 held to be deceptive, or unreliable, L17a might well be chosen. It's also worth noting, however, that neither option is empirically verifiable; in fact they both transcend any conceivable body of evidence and all possible experience.21
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 is 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 move!
Putting this annoying corollary to one side for now, it's worth emphasising that both halves of these two derivations rely on the sorts of ambiguities encountered earlier in L1-L13 (alongside several others analysed below). Aprioristic 'arguments' like these only seem to work because they are shot-through with equivocation and distortion; indeed, this is partly why these two conclusions both finally descend into absurdity -- as we are about to find out.
The absurdity in L34b is quite plain for all to see and need not detain us any longer. However, the ludicrous nature of L17a is not perhaps quite so obvious. It 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's even more absurd than L34b!
L34b: Despite appearances to the contrary, all bodies are at rest.
The only way to avoid such an outlandish conclusion would be to maintain that L35 implies that a moving body is in no more than two places at once. But even this would not help, for if a body is moving and in the second of those two places, it would not now 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 way of viewing things. The proposed dialectical derivation outlined above required that very assumption, repeated here:
L15: If an object is located at a point it must be at rest at that point.
L35: Motion implies that a body is in one place and not in it at the same time; that it is in one place and in another at the same instant.
Without L15 (and hence L35), Engels's conclusions would 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 just what creates this latest problem.
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, this latest objection is misconceived.
Or, so it might be maintained.
The latter 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 could not do:
L17c: A moving object must occupy at most two places at once.
This is because, between any two points there is a third point, and if the body is in (X1, Y1, Z1) and (X2, Y2, Z2) at t1 then it must also be in any point between (X1, Y1, Z1) and (X2, Y2, Z2) at t1 --, say (Xk, Yk, Zk). Once that is admitted, there seems to be no way to forestall the conclusion drawn above that if a moving body is anywhere it is everywhere, at the same time.
[And that is why the question was posed earlier about the precise distance between the points at/in which Engels says a body performs such 'contradictory' marvels.]
On the other hand, the combination here of an "at least two places at once" with and an "at most two places at once" would be equivalent 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.
But, any attempt by DM-theorists to restrict a moving body to the occupancy of exactly two places at once would work only 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 all falls foul of the intermediate points objection, 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 must still be moving, and hence in and not in that second point at the same instant, too.
It's worth underling this conclusion: if a body is located at a second point (say, (X2, Y2, Z2)) at t1, it will be at rest there at t1, contrary to the assumption that it is moving. Conversely, if it is still in motion at t1, it must be elsewhere also at t1, and so on. Otherwise, the condition that a moving body must be both in a place and not in it at the very same instant will have to be abandoned. So, DM-theorists cannot afford to accept L17d.
Consequently, the unacceptable outcome --, which holds that as a result of the 'contradictory' nature of motion, a moving body must be everywhere along its trajectory, if it is anywhere, at the same instant -- still follows.
Again, it could be objected that when body A is in the second place at the same instant, a new instant in time could begin. So, while A is in (X2, Y2, Z2) at t1, a new instant, say t2, would start.
To be sure, this amendment avoids the disastrous implications recorded above. However, it only succeeds in doing so by introducing several new difficulties of its own, for this would mean that A would be in (X2, Y2, Z2) at t1 and at t2, which would plainly entail that A was located in the same place at two different times, which would in turn mean that it was stationary at that point!
It could be objected, once more, that A-like objects occupy two places at once, namely (X1, Y1, Z1) and (X2, Y2, Z2), so the above argument is defective. Indeed, this is why the above 'derivation' cannot work. We can perhaps clarify this objection by means of the following
L38: L35 also implies that A is at (X2, Y2, Z2) and at another place at t1, hence it is also at (X3, Y3, Z3) at t1.
[L35: Motion implies that a body is in one place and not in it at the same time; that it is in one place and in another at the same instant.]
The idea here is that if we select, pair-wise, any two points that a body occupies in any order (either (X1, Y1, Z1) and (X2, Y2, Z2), or (X1, Y1, Z1) and (X3, Y3, Z3), or (X1, Y1, Z1) and (Xn, Yn, Zn), and so on), then L17c will be satisfied:
L17c: A moving object must occupy at most two places at once.
Unfortunately, this escape route turns into yet another cul-de-sac.
Engels just needs a body to be in two places at once; the third place above -- (X3, Y3, Z3) -- is not implied by his description of the 'contradiction' involved here. L38 only works by ignoring the fact that the other place that A is in is precisely (X1, Y1, Z1); so, it cannot be in (X3, Y3, Z3) at that time --, or it does not have to be, which is all that is needed. So, when A is both in (X1, Y1, Z1) and (X2, Y2, Z2), and (X1, Y1, Z1) and (X3, Y3, Z3), and so on, it cannot be in at most two places at once, since it is in more than two. Here, the use of "and" scuppers this line of defence.
It could be objected that this latest response only works because an "and" has been substituted for an "or". The original response in fact argued as follows:
R1: If we select pair-wise any two points a body occupies in any order (either (X1, Y1, Z1) and (X2, Y2, Z2), or (X1, Y1, Z1) and (X3, Y3, Z3), or (X1, Y1, Z1) and (Xn, Yn, Zn), or..., and so on), then L17c will be satisfied.
But not:
R2: If we select pair-wise any two points a body occupies in any order (i.e., (X1, Y1, Z1) and (X2, Y2, Z2), and (X1, Y1, Z1) and (X3, Y3, Z3), and (X1, Y1, Z1) and (Xn, Yn, Zn), and..., and so on), then L17c will be satisfied.
Unfortunately, once more, this just catapults us back to an earlier untenable position, criticised above, as follows:
"This is because, between any two points there is a third point, and if the body is in (X1, Y1, Z1) and (X2, Y2, Z2) at t1 then it must also be in any point between (X1, Y1, Z1) and (X2, Y2, Z2) at t1 --, say (Xk, Yk, Zk). Once that is admitted there seems to be no way to forestall 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. 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. In that case, R2 is still a valid depiction.
In order to see this, a few of the subscripts in R2 have been altered, as follows:
R3: If we select pair-wise any two points a body occupies in any order (i.e., (X1, Y1, Z1) and (X2, Y2, Z2), and (X1, Y1, Z1) and (Xk, Yk, Zk), and (X1, Y1, Z1) and (Xi, Yi, Zi), and so on), then L17c will not be satisfied.
And it is surely philosophically irrelevant whether we label such points with iterative letters (i.e., "k" or "i") or with the numerals "1", "2" or "3". [Recall, the points 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.
Moreover, it's also worth asking of L38: Is A at (X2, Y2, Z2) at t1? If it is, then it must be elsewhere at the same time, or it will be stationary, once more. So much is agreed upon. In that case, the only way to stop the absurd induction (i.e., that which derived the conclusion that if a moving body is anywhere it must be everywhere) 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.]
However, this 'straw' has unfortunate consequences that desperate dialecticians might want to think about before they clutch at it too eagerly:
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 in these two places at two different times.
Hence, dialecticians can only escape from the absurd consequence that their theory implies that moving objects are everywhere at the same time by abandoning their belief in the contradictory nature of motion at an indefinite number of locations intermediate in its transit (for example, right after it leaves the first two places it occupied in its journey)!
It now looks like DM-theorists can only short-circuit the above criticisms, and maintain their view that motion is 'contradictory', if they are prepared to impose several more 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 (and not just the things we say about it that are), all the while confirming the suspicion that it's only certain ways of representing nature that are seemingly 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!
As we will see throughout the Essays posted at this site, the source of these (and similar) 'problems' lies in the repeated attempt made by dialecticians (and metaphysicians alike) to state 'necessary truths' (i.e., a priori 'theses') about reality. Such theses are based solely on an extrapolation from the supposed meaning of a few words to fundamental truths about reality, valid for all of space and time. Clearly, with respect to Engels's analysis of motion, this predicament is further compounded by his attempt to circumvent several other fundamental conventions of ordinary language --, such as those expressed in the LOC and the LOI. [I 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.]
Finally, it could be argued that the above criticisms beg the question, since dialecticians do not doubt the application of principles drawn from FL -- such as the LOC --, they merely point to their limitations when confronted with change. That particular claim is neutralised in Essay Four and Essay Eight Parts One and Three.
Suffice it to say here that dialecticians themselves have yet to account for motion in anything like a comprehensible form. So, whether or not it is correct to say that FL can account for change, it's now clear that DL cannot.
Even more annoying: in Essay Four we saw that, contrary to what dialecticians try to tell us, FL can cope with change.
Yet Another Absurd Dialectical Consequence
Another, perhaps less well appreciated consequence of this view of motion and change -- which, if anything, is 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.
This is because such a body, according to Engels, is in both places at once. Now, if the conclusions in the previous section are valid (that is, if dialectical objects are anywhere in their trajectories, they are everywhere in them all at once), then it follows that no moving body can be said to be anywhere before it is anywhere else in its entire journey! That is because such bodies are everywhere all at once. If so they can't be anywhere first and then later somewhere else.
In the dialectical universe, therefore, there is no before and no after!22a
In that case, along the entire trajectory of a body's motion it would be impossible to say that that object was at the beginning of its journey before it was at the end! So, while you might foolishly think, for example, that you have to board an aeroplane (in order to go on your holidays) before you disembark at your destination, this 'path-breaking' theory tells us you are mistaken, and that you must get on the plane at the very same time as you get off it at the 'end' of your journey!
And the same applies to the 'Big Bang'. While we might think that this event took place billions of years ago, we are surely mistaken if this 'super-scientific' theory is 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 are reading this, the 'Big Bang' is in fact taking place!22b
To be sure, this is absurd, but that's Diabolical Logic for you!
And Therefore Never Send To Know For Whom The Bell Tolls; It Tolls For DM
Several of the points raised above require further elaboration, since we will soon discover that Engels was in fact saying nothing at all intelligible.
When Engels wrote 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.]
he was clearly appealing to what he regarded as the acceptable and well-established, inter-subjective meaning of terms like "motion", "change", "place", "moment", and "time". This can be seen from the fact that he did not even think to define or explain what he meant by these words. Ordinarily, that in itself would not be a problem, since we understand phrases like these perfectly well in our day-to-day affairs without recourse to unnecessary pedantry. But, in specialised areas, a sloppy approach to theory like this is unacceptable. Indeed, such a cavalier attitude to ordinary language has a tendency to backfire on those foolish enough to adopt one. This is especially true of those who then attempt to press the vernacular into service way beyond its materialist remit.
The ability to think one's way around such linguistic conundrums 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 individuals to ignore the internal contradictions this approach has introduced into their own theory. [More on that here and here.]
However, as we will see in Essay Seven (and here), DM-theorists are highly selective over which 'contradictions' they choose to "grasp", and which they blame on defective or competitive theories. Hence, when dialecticians "grasp" the 'contradictions' they claim to see in motion and change, they attribute these to nature itself, and fail to blame them on Hegel's logical incompetence, or on Engels's lack of clarity, or both.
On the other hand, when contradictions appear in rival theories, these become a handy excuse for rejecting them. In this way, they tell us that by rejecting or 'resolving' such contradictions science can advance. But if science advances by rejecting or 'resolving' contradictions in and between theories, then, plainly, the science of kinematics cannot advance unless this 'contradiction' too is resolved (as, indeed, it will be by the end of this Essay, except this will be achieved 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 risk holding up the progress of science.
This self-inflicted quandary I have called "The Dialecticians' Dilemma".
As seems obvious, 'dialectically' clutching at a 'contradiction' does not make it disappear. Even as DM-theorists view reality, motion is still 'contradictory', whether or not anyone else sees things this way. Hence, the significance of "grasping a contradiction" appears to be this: anything that might ordinarily seem puzzling or paradoxical suddenly stops bothering a dialectician (if it ever did). But, this move only works if it is accepted as a fact that this is the way the world actually is. If so, and on this basis, DM-theorists seem to think they can cease worrying about the contradictions this approach introduces right to 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 in the right way (where "viewed" in fact means "Ignore what you can't explain", and then "Accuse critics of not understanding dialectics").
Despite the spin, this nevertheless implies that it is not possible 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 below). And if that is so, the dialectical 'analysis' of motion is of little use to anyone, least of all to dialecticians, now that it's plain that not even they can explain motion, merely re-describe it in perplexing ways. All that Engels's 'analysis' seems to have achieved, therefore, is stop dialecticians worrying about their defective theory, leaving motion, as they see it, still locked in 'paradox'.
In that case, if there is a rational solution to this paradox (if we but knew what it was), it's no good asking dialecticians to search for it. They gave up on that endeavour the moment they leafed through Hegel's 'Logic', and began "grasping" 'contradictions'.
Left to them, this branch of Physics would simply grind to a halt.23
However, Engels did at least make an attempt to use everyday terms in his endeavour to show that they were not all they seemed to be. Or, rather, that when considered 'dialectically', the vernacular reveals more about reality than might otherwise be apparent -- especially to those who are mesmerised by 'commonsense', or perhaps those duped by that inner fifth-columnist, the "abstract understanding".
Nevertheless, anyone who disagreed with the 'dialectical' conclusion Engels drew would no doubt be reminded that these few words -- or the 'concepts' they supposedly represent -- clearly and unambiguously implied the 'contradictions' that Engels and Hegel said they did. In that case, defenders of this view of things could claim that these two had simply made several implicit 'contradictions' explicit.
Intentionally or not, by arguing this way Engels succeeded in situating his paradoxical theses in an ancient metaphysical tradition stretching back as far as Zeno, Parmenides and Heraclitus -– a tradition which ordinary working people had no hand in building, but which is (demonstrably) based on ruling-class 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 as soon as he attempted to squeeze some metaphysical juice out of such desiccated raisins; that is, when he tried to extract 'paradoxical' conclusions from a few innocent looking words.
Naturally, the conclusions Engels reached will be agreed only by those who have already capitulated to the view that reality is fundamentally 'contradictory'. Others, however, might be forgiven for remaining sceptical --, particularly those who (not unreasonably) think that Engels's 'solution' is in fact far more puzzling than motion ever was! Indeed, if the nature of motion is problematic, calling it "contradictory", while making no attempt to explain how this actually accounts for anything, is surely far worse.
If these alleged 'contradictions' do no work (as was argued above), then their presence here is, at best, unhelpful. This is because we can now see that these 'contradictions' are the direct product of an over-active imagination, compounded by a naive acceptance of the Idealist gobbledygook Hegel inflicted on humanity.
In that case, Engels's 'analysis' is an obstacle to understanding, which impediment, of course, will need to be removed if science is to advance.
In fact, Engels failed to consider other, far more likely, possibilities; indeed, it looks like it never occurred to him that his 'contradictory' conclusions might not follow if he had instead given consideration to the full range of words/meanings available to us in 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 ordinary words. As we will see, he did this by unwittingly altering their usual senses while imagining that the meanings of several other everyday terms, with which these are normally associated, remained unaffected.
In doing this he was, of course, not alone; this semantic sleight-of-hand has been practiced time and again throughout the history of traditional Philosophy. And linguistic tricks like this are still being played. Even careful philosophers often fail to notice that their own work involves what can only be called "piecemeal selectivity" concerning the use of certain words. Indeed, they have invariably assumed it's possible to tinker around with a few specially chosen expressions while the meaning of words associated with them remain unaltered. Selectivity like this is, alas, two-edged. In fact, these associated words -- whose meanings Engels 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 fatally undermine every single classic account, too.
If, for example, an ordinary word like "motion" possess 'contradictory' implications -- according to Hegel and Engels --, then perhaps other terms they failed to consider might have analogously paradoxical connotations, given this perverse way of using and 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 changed the other?
More pointedly: What if certain senses 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 "motion". But, if "place" itself has no set 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", must be subject to even greater doubt. That is because, if the sense of the latter is compromised by the slippery nature of the former (or vice versa), the meaning of neither can emerge unscathed, in view of their intimate connection.
In fact, as we are about to see, this in-built complexity has the salutary effect of deflating the philosophically grandiose conclusions Engels (and others) thought he (they) could derive from a handful of mundane-looking words when he (they) used a non-standard application of "motion" with what he (they) took to be a standard use of "place", and vice versa.
Ordinary Objects Regularly Do The Impossible
Many of the ambiguities noted above (in relation to Engels's analysis of "motion") actually depend on systematic vagueness in the meaning of the word "place" and its cognates. Even when translated into the precise language of coordinate algebra/geometry, the meaning of this particular word does not become much clearer.
[Of course, this is not to criticise the vernacular; imprecision is one of its strengths. Nor is it to malign mathematics! But, when such terms are transposed into Philosophy, where it is assumed they have a single unique ('essential') meaning, problems automatically and invariably arise.]
In fact, as it turns out, there is no such thing as the meaning of the word "place".
This lack of clarity carries over into our use of technical terms associated with this 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 be explained in more detail presently.]
Nevertheless, it is quite easy to 'demonstrate' (by means of the sort of selective linguistic 'adjustment' beloved of metaphysicians, but applied in contexts they generally fail to consider) that ordinary objects and people are quite capable of doing the metaphysically impossible. The flexibility built into everyday terms actually 'enables' the mundane to do the magical, and on an alarmingly regular basis. Such everyday 'prodigies' do not normally bother us -- well, not until some bright spark tries to do a little 'philosophising'.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, it could be objected here 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 did not tell us what he meant by this term; he simply assumed we'd understand his use of it. If, however, it is now claimed that he did not mean by his use of the word "place" a sort of vague "general location" (like the factory used in this example), then that would confirm the point being made in this part of the Essay: Engels did not say what he meant by "place" since there was nothing he could have said that wouldn't have ruined his entire argument. Tinker around with the word "place" and the meaning of "motion" cannot fail to be compromised (as noted above). This can be seen by considering the following highly informal 'argument':
L42: Nothing that moves can stay in the same place.
L43: If anything stays in the same place, it cannot move.
L44: A factory is one place in which workers work.
L45: Workers move about in factories.
L46: Any worker who moves cannot stay in the same place (by L42, contraposed).
L47: Hence, if workers move they cannot do so in factories (by L44 and L45).
L48: But, some workers stay in factories while they work; hence, while there they cannot move (by L43).
L49: Therefore, workers work and do not work in factories, or they move and they do not move.
As soon as one meaning of "place" is altered (as it is in L44), one sense of "move" is automatically affected (as in L45), and vice versa (in both L47 and L48). In one sense of "place", things cannot move (in another sense of "move") while staying in one place (in yet another sense of "place"). But, in another sense of both they can, and what is more, they can typically do both. Failure to notice this produces 'contradictions' to order, everywhere (as in L49). Even so, who believes that workers work and do not work in factories? Or that they move and do not move while staying in the same place?
Perhaps only those who "understand" dialectics...?
Do Dialectical Objects Move -- Or Just Expand?
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 just what his 'theory' cannot do, as we shall see.
It could now be objected here that if "place" is defined precisely (without altering the meaning of "move") it would be possible to understand what Engels and Hegel were trying to say. 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 think.
Of course, the problem here is that in the example above (concerning those contradictory mobile/stationary workers), if we try to refine the meaning of the word "place" a little more precisely, it will come to mean something like "finite (but imprecise) three-dimensional region of space large enough to contain the required object". Well, plainly, in that sense things can and do move about while they remain in the same region (i.e., "place") -- since, by default, any object occupies such a region as it moves (that is, it must always occupy a three-dimensional region of space large enough to contain it as it moves; it certainly doesn't occupy a larger or a smaller space (unless it expands/contracts)!), and objects occupy finite regions as they move in relation to each other (or they would not be able to move). Hence, if defined this way, moving objects always occupy the same space, and hence they do not move! [Revising this caveat so that objects successively occupy spaces equal to their own volumes as they move will not help either, as will see presently.]
In that case, if the 'regions' mentioned above are constrained too much, nothing would be able to move. Put each worker in a tightly-fitting steel box that exactly fits him or her and watch all locomotion grind to a halt.
The difficulty here is clearly now one of relaxing the required region each occupies sufficiently enough to allow things to move from one place to another without stopping them moving altogether, all the while providing an account that accommodates the movement of medium-sized objects in the material world. But, once this has been done the above difficulties soon re-appear, for it is quite clear that objects still move while staying in the same place -- if the place allowed them is big enough for them to do just that!
Indeed, this fact probably accounts for most (if not all) of the locomotion in the entire universe. Clearly, and in the limit, if anything moves in nature it must remain in the same place, i.e., in the universe!
Nevertheless, at first sight the above objection (concerning a tight enough definition of "place") seems reasonable enough; Engels clearly meant something a little more precise that a vague or general sort of location. But what?
It might seem that his argument could be revived if tighter protocols for "place" are legislated --, 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 be about mathematical point locations (or about the movement of mathematical points themselves -- and we saw that this was a non-starter earlier).
Clearly, things cannot move about in such points -- but this has nothing to do with the supposed nature of reality. These 'entities' do not (and could not) exist in nature for them to contain anything. This is because such points located by SCs are not containers. They have no volume and are made of nothing.
As noted above, if Engels meant something like this as part of his use of "place", his account would fail to explain/accommodate the movement of gross material bodies in nature, for the latter do not occupy mathematical points.
And it's no use appealing to larger numbers of such points located by SCs; no material body can occupy an arbitrary number of points, since points are not containers.
Hence, it is far more likely that Engels's use of the word "place" implied a covert reference to a finite three-dimensional volume interval (whose limits could be defined by the use of well-understood rules of Real and Complex Analysis, 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 the latter can move about in locations big enough to hold them, and remain in the same place while doing so, Engels's moving objects can do so, too -- except they would now have a more precise "place" in which to do it.
But, this sense of "place" is no use at all, for when such workers move, they will, by definition, stay in the same place!
Naturally, the only way to avoid this latest difficulty would be to argue that the location of any object must be a region of space (i.e., volume interval) equal to an object's own volume. This is in effect one classical definition (among several). In that case, as the said object moves, its own exact volume interval would move with it, too; the latter would follow each moving object around more faithfully than its own shadow, and more doggedly than a world-champion bloodhound. But, plainly, if that were the case, that would mean that objects would still move while staying in the same place -- since, plainly, any object always occupies that space equal to its own volume, which would, on this view, travel everywhere with it, like a sort of metaphysical glove.
As seems plain: if this is so, we now have two problems where once there was just one, for we should have to explain not only how bodies move, but how volume intervals also move so that they can faithfully shadow the objects they contain!
However, and far worse: in that case, 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 region of space could we appeal to, to allow regions of space to move into them?
And 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 mittens', as it were, to the original 'ontological gloves'. Metaphorically speaking, this theory, if it took such a turn, would be moving backwards, since an infinite regress would soon confront it, as spatial mittens inside containing gloves, inside holding-case gauntlets, piled up alarmingly to account for each successive spatial container and how it could 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', with a potentially infinite number of 'skins'!
It could be countered that even though objects occupy spaces equal to their own volumes, as they move along they then go on 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 precisely. On this scenario, moving objects will leave their old locations behind as they barrel along.
But, even if this were correct (and sense could be made of these new, and accommodating locations without re-duplicating the very same problem), no DM-theorist could afford to appeal to such successive volume intervals. 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!
To see this more clearly, it would be useful to examine the above 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 different. Thus, if the COM of D is in two such spaces (i.e., (Xk, Yk, Zk) and (Xk+1, Yk+1, Zk+1)) at once, D would be in S, and would occupy δV1. But, once again, that would mean that D would move while remaining in the same space -- i.e., it would remain inside S, or in δV1 (whichever is preferred), as its COM moved from (Xk, Yk, Zk) to (Xk+1, Yk+1, Zk+1), in the same instant.
Now, the only way to avoid the conclusion that D moves while occupying the same space S and/or δV1 --, and hence that it appears to stay still while it moved, just like the 'mobile/stationary' workers we encountered earlier -- would be to argue that such spaces remain where they were while D moves into successively new locations.
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 also contain (Xk+1, Yk+1, Zk+1) and (Xk+2, Yk+2, Zk+2) -- otherwise it would not be a new containing volume interval that satisfied the requirement that moving bodies occupy at least two such "places" at the same time, being in one of them and not in it.
Plainly, all objects have to occupy some volume interval or other at all times (or they would 'disappear'). However, in D's case it has to do this while also occupying new volume intervals at the same time as it moves along (otherwise, as we saw, it would move while being in the same place). So, if D occupied only one S or only one δV at once, it would be at rest in either. In that case, it must occupy at least two of these (if, that is, we accept the 'dialectical' view of motion) at the same time.
Hence, 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 are partially 'overlapping', perhaps not), at once. Unfortunately, this would now mean that D-like objects would have to occupy a volume/volume interval bigger than either of S or δV at once, and thus 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) -- that is, δV1 would contain (Xk, Yk, Zk) and δV2 would contains (Xk+1, Yk+1, Zk+1) --, so the above is incorrect. 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), otherwise such objects couldn't occupy two spaces (two δVs) at the same time.
But, if that is so, and D is not stationary while it occupies δV2, it must also occupy δV3 at the same time, and so on. This means that, as we saw above in an analogous context, 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 moving while staying still, or, from 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" cannot remain the same, and 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/logical resources DL supplies its unfortunate victims.
[DL = Dialectical Logic; SC = Spatial Coordinate.]
On the other hand, it seems that 'Dialectical objects' 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 these parts. 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 equal.
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!
[This result, of course, depends on the answer to an earlier question: How far apart are the two places that Engels referred to? If this is left indeterminate, then any length will do. Even then, if a specific length is decided upon, then we could make the distance between these parts equal to that length, and the above result will still follow. This is done below, anyway.]
It cannot 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 after here, since all this 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 is not 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 these parts of this single carriage crushing the one in front. [However, I have considered the option that there is such a gap, below.]
[At a later date, I will add diagrams to make this and the other examples considered here clearer to the reader.]
Again, it might be argued that the structural properties of B (intermolecular forces, etc.) will prevent this from happening. That is undeniable, but this also has the unfortunate consequence that while B may be in two places at once as it moves, none of its parts would be! And that in turn would imply that while B was racing along, none of its parts would be moving (since they are not allowed 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 set the centre of this disc as the origin, then we can set the leading edge of S1 so that it lies along T (which passes through the centre of D), In addition, let there be a point p1 on that line, r units from the centre, with co-ordinates (r, θ1). Let the leading edge of S2 also lie along T (which passes through the centre of D), and let there be a point p2, r units from the centre, with co-ordinates (r, θ2). [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 (1) D will totally disappear -- as both of its sectors occupy the same semi-circle that the other one occupied -- or, (2) 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 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) and (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 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 cannot 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 δS (where it is left open whether or not δS > δL). In that case, there is a gap, δS, 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. If so, S1 will not smash into the back of S2 as imagined above. And, the same sort of conclusion can be drawn in connection with the rotating disc, too.
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 δS 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 δS < δL. On the other hand, if δS > δL then a larger and larger gap will open up between S1 and S2, which will widen all the more as B continues to move. So, in this case, B will either (1) Begin to fragment, or it will (2) Concertina, as it moves. The same will happen to the disc.
So, this 'theory' is still stuck in a Dialectical Ditch.
Despite this, it could be argued that if the ordinary word "place" is so vague then it should be replaced with 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 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 such an SC must be written precisely this way, with xi, yi and zi (etc.) all in their correct places.
L53: But, the situating of such elements cannot 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) cannot be defined (without circularity) by means of SCs.
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 aright.
Therefore, the ordinary word "place" cannot 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 like these.
Of course, this is not to malign coordinate geometry, but it reminds 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. Everyday facts like these are soon forgotten (in the course of one's education), since, as Wittgenstein pointed out, we are taught to squash such simple questions very early on. As a result we inherit the mythological structures that previous generations have built on top of unexamined foundations like this.
If, on the other hand, a typographically identical word (viz.: "place") were to be defined in this way, and then used in mathematics or physics, it would not 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 it was no longer confused with the less precise phrase "general location".
Since this has yet to be done (even by DM-advocates, who, up until now, have in fact revealed that they aren't even aware of this problem!) it remains to be seen whether this promissory note is redeemable. However, even if it were, it would still be of little help. As we have seen, and will see again, the word "place" (even as it is used in mathematics) is itself ambiguous, and necessarily so. [There is more on this in Note 25.]
Moreover, Engels's account requires motion to be depicted by a continuous variable, while one or both of time or place is/are held to be discrete, otherwise a contradiction would not emerge (which is, of course, something even Hegel recognised).24d This trick is accomplished either by (1) the simple expedient of ignoring examples of discrete forms of motion (several of which are given below), and/or by (2) failing to consider instances where both time and place are continuous -- all the while imagining that the relevant ordinary words use to depict both have been employed with their usual senses, and have not been altered by these new contexts.25
Even assuming a stricter sense of "place" could be cobbled-together somehow, that would still be of little help. This 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 would not so much move as expand or stretch, as noted earlier.
This means that in a perfectly ordinary sense, things can both move and stay in the same place while they do so. Indeed, they are quite capable of remaining stationary while they undergo a change of place, moving and not moving all at once!
The first of these was depicted above with respect to those stationary/mobile workers; the second (where something can both move and not move all at once -- and here involving a discrete sense of "move" into the bargain), is illustrated in 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's 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 did all this 'moving and not moving at the same time' doing so in a different sense from that which is illustrated in L55. In fact, it's 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 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 in this book you sold me move about erratically. The book 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.
In L56, we have stationary 'objects' (i.e., the footprints created by individuals who had earlier moved 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 do not exist either for anything to move into! [Of course, in such circumstances, we'd 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 does not exist while it moves, nor does it occupy any of the intervening spaces on its 'journey', but which intervening spaces do exist! Similar situations are illustrated in L60 and L61.
Not only that, but continuous and yet stationary things 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's 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 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 (as Marx pointed out).
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. Italicised emphases added.]
In this passage, Engels is perfectly clear that he meant "simple mechanical change of place", which is different from the non-standard senses of the word paraded above. Or, so it could be argued.
Unfortunately, however, as we have seen, it's not easy to ascertain what (if anything) Engels actually did have 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 is 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 to 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 or its associated terms, even though we all do know what we mean by each of them individually when they feature in ordinary, material contexts (like those depicted above).
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's Engels's 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/philosophical analysis of motion and change. This objection is considered in detail elsewhere at this site. Anyway, Engels himself used 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
It could be maintained at this point that any account of motion would have 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 contains countless examples of motion and change, each of which is contradictory.
Now, the use of modal terms here is quite revealing for it confirms something that has been implicit all along (hinted at earlier): this type of argument depends on inferences being made from the alleged meaning of a few specially selected words -– which have been given an idiosyncratic re-interpretation in isolation from other associated terms, divorced from their ordinary contexts of use -- to necessary truths about the world. 'Deductions' like these invariably precede a perfunctory empirical 'investigation' -- if, that is, the latter is even so much as attempted by dialecticians. The results that these inferences appear to warrant are then regarded as absolute certainties, which their inventors find it impossible to question. This is, of course, because such Super-truths are based on language alone, and not on evidence. [On this in general, see Essay Twelve Part One.]
As noted earlier, Engels performed no controlled experiments before or after he drew the above conclusions about motion. In fact, it is impossible even to describe a single observation or experiment -- other than a thought experiment, which would itself depend on the sorts of ambiguities highlighted above -- that could conceivably confirm Engels's claims about motion. This is partly because 'contradictions' themselves cannot be observed, 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 to refer 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 in books on dialectics that either confirm or even vaguely support a belief in the contradictory nature of motion. All we find in its place are dogmatic assertions based on a brief consideration of a few words/concepts. [Readers are invited to check!]
Thus, Engels's only 'evidence' was an appeal to the philosophical use of language -- and to Hegel and Zeno's use, too --, not how such words feature in everyday life. This predicament (which he shares with all other metaphysicians) invariably passes unnoticed because (1) In traditional thought it is so widespread, (2) It has been going on now for well over two thousand years ('East' and 'West'), and (3) It's imagined that by looking at certain words (or their 'real' meanings) the Armchair Philosopher is actually examining the world itself, and not simply a few specially-selected, jargonised expressions.
The idealist implications of this traditional tactic were highlighted by 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 the traditional confusion of talk about talk with talk about things is examined in Essay Twelve Part One (and in other Parts of that Essay -- summary here).]
Nevertheless, the denotation of this specialised vocabulary is simply taken for granted; indeed, the question whether such words actually have a denotation is seldom ever raised.
This critical view of traditional philosophical word-magic gains support from the fact that 'philosophical problems' like this cannot be solved by an appeal to evidence. That is why they depend solely on a quirky use of language, and it's also why this is all Engels ever offered his readers, and why it's all he could have offered his readers in this respect.
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. Still, he felt quite confident that he could extrapolate from his own understanding of a few ordinary-looking words to conclusions that were applicable to every conceivable example 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.]
If fact, what Engels actually did -- and this was the extent of the 'careful' scientific research he carried out in this area -- was to copy the analysis of motion he found in Hegel's Logic!
And Hegel has not gone down in history as a great experimental scientist.
As we shall see (in Essays Nine Part One and Two, and Twelve (summary here)), these (easily missed) facts possess revealing ideological implications of their own.
Engels's feeling of confidence in the results he obtained so effortlessly 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." [Ibid., p.152.]
But, how could Engels possibly have known this? How could he have been so sure that every single example of motion throughout the entire universe, for all of time, could only occur in the way he alleged? If we rule out the absurd reply that Engels was some sort of deity, there are in fact only two possible answers to that question:
(1) Engels's certainty 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 handful of words about motion, and 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 that supposedly allude to 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 the correct way to understand such words in novel contexts like these is? Or, whether the meanings of any technical terms used are the same as those of the ordinary words they allegedly replace? Or, that there is only one way to interpret them? Or, that Engels and/or Lenin hit upon the correct way of comprehending them (and then only after reading Hegel -- as opposed to sifting through the relevant scientific data)? Or even whether the language they used 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 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, namely: Surely a rejection of Engels's understanding of motion would be paradoxical, if not contradictory itself. That's because this would represent a repudiation of what the concept of motion 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.)) reveal they had 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 itself paradoxical and (openly) contradictory; so even by his own lights, there appear to be equally good reasons for rejecting his interpretation of motion as there are for accepting it. If it's 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 this is so for four reasons:
(A) 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; they were aimed at interpreting reality beyond any and all conceivable experience.
(B) Our experience of motion is as ambiguous as the words we use to depict it are. 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 Lenin ever imagined. Anyway, not even an indefinitely large finite number of observations of cats moving about, on or off assorted mats (and the like), could confirm whether motion is or is not continuous, discontinuous, or whether it is composed of countless discrete, concatenated 'sub-movements' -- or, indeed, whether it's something else we have as yet no words to describe. Even with advanced technological assistance, we would not be able to tell if motion was the one or the other.
(C) 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's only a metaphysical prejudice (itself based on other priorities that will be exposed in Essay Twelve (summary here)) that (i) Consigns certain depictions of motion to the realm of "appearance", or "commonsense", while others are said to refer to "reality itself"; (ii) Regards one type of motion as primary, the rest secondary.
(D) 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 this is not just because it represents a thinly disguised form of "absolute" motion -- as will be argued elsewhere at this site. 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 uses of words associated with locomotion. Again, that would amply confirm the view maintained here that dialecticians are happy to draw inferences from a handful of specially-selected words, and then foist the results on reality -- the use of "must" here would reveal 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 like this -- applicable to every region of space and time -- all that DM-theorists would be able to offer in support would be 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/linguistic analysis' is the only conceivable source of hyper-bold 'dialectical' claims like this.
And that explains why Engels omitted the data supporting his 'theory' -- and no one since has bothered to supply any.32
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's 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 does not show that reality is free from contradictions.
Or so it could be argued.33
However, this response will not 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).
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 Hegel's) is shot-through with error and ambiguity, the motivation to claim that reality is contradictory weakens considerably (and it fades even more when it's recalled that this idea itself was based on a series of egregious logical blunders that Hegel himself committed). And in that state it will remain 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 alternative ways of 'intuiting' 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 (somewhat akin to the bogus question whether the King in chess ever 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's the non-standard interpretation that dialecticians put on ordinary words that finally conjures-up the paradoxes they label "contradictions" -- that is, even where they manage to get the latter word right.
In that case, far from reality being 'contradictory', it is the DM-use of language that's incoherent and paradoxical.
In this Essay, we have seen that Engels's account of motion is not only shot-through with ambiguity and equivocation, it's irredeemably unclear. Even if we knew what he was on about, his 'analysis' depends on an asymmetric convention that places no limit on the divisibility of location while it places just such a limit on that of time.
Even if this is waved to one side, his 'theory' would imply that dialectical objects, when they move, 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 surroundings. In fact, as it turned out, no sense at all could be made of what Engels was trying to tell us.
But, what of the so-called 'Law of Identity'? Doesn't this mean that change and movement are impossible? It is to this non-problem that I now turn.
[This part of Note 1.]
It's not easy to form a clear idea of the 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.]
[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, and Three and Eleven Part One, I hope to demonstrate that while DM-theorists frequently use the term "contradiction" in their attempt to expose the alleged limitations of FL, the majority display little or no comprehension of either or both. Nevertheless, this has not prevented them from claiming that their understanding of "contradiction" is superior to that of Formal Logicians.
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 FL are unable do this. However, as we will see in the present Essay, this allegation is inaccurate, at least with respect to motion. Indeed, the rest of this site will show that not only can DL not account for change itself, dialectical logicians even 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, one that is widely misunderstood by DL-aficionados. [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 rule (that many also misconstrue as a logical truth (i.e., the LOC)), which enables us to draw 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 had changed. For instance, consider the following:
C1: NN is not a member of Respect.
C2: NN is a member of Respect.
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 with wider uses of negation -- are integral to our ordinary notion of change. This alone shows that the claim dialecticians make that ordinary language and FL cannot cope with change is misguided.
[Of course, the above was written before Respect self-destructed back in 2007! It's now called the Respect Coalition.]
That being so, the idea that ordinary language and FL cannot account for change is, quite frankly, bizarre. In fact, without the resources found in the vernacular, human beings would not have been able to conceptualise change at all.
[And that caveat applies equally well to scientists and dialecticians. Again, as demonstrated here, ordinary language can handle change far better than the obscure and wooden terminology invented by metaphysicians. That observation is especially true of the impenetrable jargon found in Hegel.]
In that case, if, by their use of language, dialecticians actually end up undermining the vernacular, their theory cannot fail to become problematic, if not incomprehensible --, which is indeed what this Essay will demonstrate (at least with respect to Engels's 'analysis' of motion).
Now, as far as FL is concerned, two propositions are contradictory just in case they cannot both be true and cannot both be false at once. [The latter condition is almost invariably ignored by DM-critics of FL. Many deny there is a distinction here, even after it has been pointed out to them! They call such fine distinctions "pedantic". However, its importance will emerge later.] Naturally, this characterisation represents the simplest form of FL-contradiction.
Examples of more complex contradictions would include one or both of the following:
C1: ~[(P→Q)v(P→R)↔(P→(QvR))].
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 negation; "→" 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's not 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's not the case that [(there isn't something which is F and not G) if and only if (everything which, if it is F, it is also G)]."
Some might wonder when sentences like these would ever be used. However, Mathematical Logic and the Foundations of Mathematics are full of propositions like this, and far worse. (This links to a PDF.)]
These, of course, are 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 confuse the LEM, the PB -- and particularly the LOC -- with one another, and all of them with opposites, inconsistencies, absurdities, contraries, paradoxes, puzzles, quandaries, oddities, irrationalities, oppositional processes, forces, events that go contrary to expectations, and a host of other idiosyncrasies. In fact, they are so ready and eager to see contradictions everywhere, they find they have to alter the meaning of that word so that (for them) it becomes synonymous with "struggle", "conflict" and "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 genre appeared in a letter sent to Socialist Worker at the end of August 2011:
"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."
So, tensions within the communist hierarchy are 'contradictions', now, are they? But, no one ever explains why such things should be called "contradictions" when they are far better described as "tensions", or "conflicts".
Some might conclude that this is just another example of Ms Lichtenstein's pedantry, but that is not so. [On 'pedantry', see here.] There are important political reasons for rejecting the use of "contradiction" in the way it's employed by Dialectical Marxists. [On that, see Essay Nine Part Two.]
Specifically, (1) It allows them to argue for anything they like and it's opposite (often by the same individual, and in the same breath!), no matter how anti-Marxist this is or how counter-revolutionary it might prove to be ('justified' on the grounds that everything is 'contradictory', and a 'unity of opposites', so Marxist theory and practice should be contradictory, too!); (2) It's used to rationalise a whole range of substitutionist tactics and strategies (on the grounds that, although Marx insisted on the self-emancipation of the working class, we can substitute for them (a) The Party, (b) The Red Army, (c) 'Third World' guerrillas, (d) 'Progressive' nationalists, (e) Students, or any number of other social forces/groups), since those who object to this do not 'understand' dialectics or the 'contradictory' nature of Marxism/the former USSR; (3) It 'allows' them to survey the long-term decline of Dialectical Marxism and fail to see it for what it is (a protracted and profound refutation of their core theory, 'Materialist Dialectics'), on the grounds that appearances 'contradict' underlying reality. So, if DIM looks hopelessly unsuccessful, the opposite is in fact the case. This then 'allows' dialecticians to stick their heads in the sand, while their movement runs into the very same sands. And, (4) Because of (3), it provides them with a source of consolation for the ineffectiveness of their entire movement, it's perennial divisiveness and its ever present internecine warfare ("Well what else can one expect in a contradictory universe?").
So, this is not pedantic point-scoring; it has very real and disastrous political consequences.
[DIM = Dialectical Marxism/Marxist, depending on context.]
[I give many more examples of the odd things DM-fans say about 'contradictions' in Essay Eight Part Two -- here and here, for instance.]
Be this as it may, DM-theorists themselves would be quick 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, and which must be confirmed in practice before they are deemed "objective". Furthermore, since most DM-theorists believe that reality itself is fundamentally contradictory, propositions accurately describing 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 linguistic expressions they are plainly not material forces as such. This must mean that they are not themselves oppositional per se -- even though they supposedly reflect at some level the dynamic nature of objects and processes in reality, according to dialecticians. On the other hand, even if such propositions were oppositional, they would only be so in a derivative sort of sense, one supposes. In any case, the idea appears to be that while objects and processes in nature are contradictory and subject to change, any use of language aimed at depicting reality must reflect them adequately if it is to be objective. Or, so the case for the defence might go.
However, the principles that underlie FL merely commit us to the view that two contradictory propositions cannot both be true and cannot both be false at the same time. Hence, on this basis, any claim that two allegedly contradictory propositions are both true at once (or are both false at once -- as noted above, dialecticians do not appear to be aware of this particular 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 the allegedly true contradictory propositions on offer were in fact propositions to begin with. If it's unclear what's being proposed (in the sense of "putting something determinate up for consideration"), then anyone attempting to do this cannot be proposing anything determinate -- that is, this side of their words being disambiguated. [Examples of this are given below, and later in the main body of this Essay. See also here.]
Several factors might contribute to this state of affairs: (1) The said 'propositions' could contain typographically similar words that have different denotations; (2) They could harbour ambiguous, vague, or figurative expressions; (3) They might be drawn from different areas of discourse, and so on. From such a perspective, the presumption would always be that both 'halves' of an alleged contradiction could only be held true by someone in the grip of some sort of linguistic or interpretative confusion. 'Contradictions' that have been generated in this way would not normally be regarded as capable of revealing fundamental truths about reality; they would perhaps convey more about the linguistic naivety of anyone so easily taken in.
In that case, the disambiguation or clarification of these alleged 'contradictions' should eliminate this 'problem'. Only an exceedingly naive person (or worse, a Mad Dog Idealist -- like Hegel) would conclude that just because certain words and/or sentences appeared to be contradictory, nature and society must be contradictory, too.
Indeed, this austere approach 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 and to disagree (i.e., to contradict).
In addition, and to its credit, the austere approach helps undermine the influence of the traditional doctrine that fundamental aspects of reality may be inferred solely from the logical properties of language -- or, rather, in this particular case, they can be derived from a series of sophomoric errors concerning the nature of contradictions (outlined a few paragraphs back and in much more detail, here).
Naturally, DM-apologists will view claims like these with some suspicion; indeed, they might even appear to be dogmatic and aprioristic. It could be argued that this obsession with the fine detail of linguistic usage must itself collapse into LIE, since it presumes to offer a linguistic solution to what is in fact a philosophical, scientific or practical problem.
[LIE = Linguistic Idealism.]
However, the opposite of this is in fact the case; the approach adopted here seeks to undermine the traditional metaphysical belief (which dialecticians themselves have bought into) that fundamental truths about reality may be inferred from language/'concepts'. But, it's the world that makes what we say true or false; it's not what we say, or how we say it, that determines the nature of reality.
[As Essay Seven shows, DM-contradictions cannot be confirmed by experience, nor can they be verified in any other way. (The allegation that this smacks of 'positivism', or even 'empiricism', is batted out of court, here.) In Essay Twelve, the ideological motivation underlying the contrary view is exposed for what it is: a form of LIE (summary here).]
Nevertheless, it's important to be able to recognise when the descriptive capacities of language begin to break down. This is highly relevant with respect to DM-theses since they break down alarmingly easily; indeed, when examined closely, they invariably turn out to be confused, ambiguous or non-sensical -- as several Essays posted at this site demonstrate.
Moreover, it's equally important to be able to distinguish spurious pictures (or, indeed, non-pictures) of reality from the genuine article. DM-theorists themselves do this when they highlight the confused and/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/practical resources available to human beings at any given time); they then require that these linguistic resources are adapted accordingly. On this view, if nature is contradictory, and if ordinary language and FL cannot accommodate that fact, then both must be judged limited and/or defective in some way and in need of supplementation with concepts drawn from 'Materialist Dialectics' -- or even from Hegel.
It's not 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 have themselves been refined by countless factors at work across diverse Modes of Production. Because of this, it might seem possible to argue that when faced with situations that appeared to be 'contradictory', human beings not only could, they actually did develop dialectical categories. [However, the 'factual basis' for this supposition will be undermined in Essay Fourteen Part One (summary here).]
Even so, given other conventions that were in fact adopted -- in practice; no one supposes that overt decisions were taken, here --, this supposition is far more than highly unlikely.
As the word itself suggests, to contradict someone is to gain-say or deny what they say is true (or false, as the case may be). So, if someone says it's raining, and someone else says it isn't, they are contradicting one another, and that fact is not altered by either of these cases: (1) It is indeed raining, or (2) The weather is dry as a bone. Whether or not "it's 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 these is true, the other is false, and vice versa. We'd not be able to understand anyone who claimed both of these characters were in error. How is it possible for it to be false that it is and false that it isn't raining?
Some might point to the vagueness of sentences like "It's raining". This would mean that both 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 mistaken, too). To be sure, sentences like these are vague, but just as soon as it had been decided that it is actually raining, then one of the following sentences would be false and the other true: (a) "It's raining", (b) "No, it's not raining". The same is the case in reverse if it had been decided that it isn't in fact raining. In circumstances like these, we'd not 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. In such circumstances, these sentences would fail to be propositions until such a decision had been made. If we can't decide when it's 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 is is raining or not.
However, in everyday life (i.e., outside the use of aesthetic, ethical, political and/or religious vocabulary (etc.)), where the meaning of words is often "essentially contestable", these sorts of conundrums do not normally arise. If in doubt, we'd say things like "It's trying to", "It's spitting, I think...", or "I reckon it's clearing up...". Only a hardcore contrarian would say things 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 away, or in the next county. If someone were consistently to adopt this approach to all sentences like these, they would either have very few friends or 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, communication would grind to a halt.
Moreover, contradicting someone could be aimed at challenging a truth, and not always confronting falsehood, as many imagine.
It could be objected that it was earlier claimed that:
...if someone says it's raining, and someone else says it isn't, they are contradicting one another, and that fact is not altered by either of these cases: (1) It is indeed raining, or (2) The weather is dry as a bone. Whether or not "it's 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