Contradictions And Motion
Readers need to make note of the fact that this Essay does not represent my final view on any of the issues raised. It is merely 'work in progress'.
If you are viewing this with Mozilla Firefox, you might not be able to read all the symbols I have used.
This Essay is over 45,000 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:
(1) Initial Problems
(d) More Dogmatism
(2) Do Contradictions Explain Motion Or Merely Re-describe It?
(b) Are Contradictions Causes?
(c) 'Internal Contradictions' And Motion
(3) Is Engels's Account Comprehensible?
(b) First Attempt At Disambiguation
(c) Second Attempt At Disambiguation
(d) Fatal Ambiguity
(4) The Classical Response To Zeno
(a) Space To Let
(6) Further Problems
(7) No Word Is An Island -- Philosophers Ignore Ordinary Language
(b) Ordinary Language And Paradox
(d) Ordinary Objects Regularly Do The Impossible
(8) Do Dialectical Objects Move -- Or Just Expand?
(a) Coordinates To The Rescue?
(10) Inferences From Language To The World
(11) Dialectical Contradictions
(12) Notes
(13) 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
[TAR = The Algebra of Revolution, i.e., Rees (1998); DM = Dialectical Materialism; FL = Formal Logic.]
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, 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; 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 were the case, what exactly 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 related to the description of motion? In that case then, his conclusions were restricted to language about motion, not motion itself.4
(2) "Solved" By Whom?
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 are that many, 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, 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, as noted above, 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.]
Now, this admission might help explain the passage referring to the "continual assertion" of contradictions, since it is 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 this itself could be a result of their own partial understanding of the 'absolute truth' about motion. On the other hand, it could be the fault of logic and/or language, 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, that in turn suggests that when reality is fully understood, all such contradictions should disappear. If so, this appears to imply that motion will one day cease, all contradictions having been 'solved'. 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, and simply carry on as normal? Or even: does this mean that nature will sort of slow down as it is understood better, and what we know about it becomes less and less contradictory?
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 to processes in the 'objective world'. But, it is still unclear how this helps answer the above questions. If the mind "solves" the contradictions involved in motion, wouldn't this mean that things actually stopped moving? Or, wouldn't it suggest that motion wasn't really contradictory to begin with? And would this not indicate, too, that movement only seemed to be contradictory because of the partial nature of knowledge? Indeed, wouldn't this imply that subjective contradictions ought to disappear as knowledge grows, and that (in the limit) reality is not 'contradictory-in-itself', since it is only their one-sided knowledge of nature that 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. More alarmingly, it might mean that the objects in question were not really moving in the first place, as Zeno originally contended.
Why then does Engels go on to 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 representation of it that is. But then again, why does Engels say that this picture reveals "precisely" what motion is, as opposed to arguing that this approach merely depicts what we subjectively think it is?
Moreover, an appeal to "objective dialectics" cannot help us comprehend what Engels meant 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, such non-existent assertions and solutions could not 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 world) for the minds of scientists and/or dialecticians to reflect.
And if that is so, what exactly has assertion and solution got to do with motion, anyway? And why did Engels think these terms were at all relevant?
(3) More Vagaries
More specifically, in relation to the motion of bodies, 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? But, 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 limits 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, does that 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, a moving body would have to skip past (but not occupy, somehow) the potentially infinite number of intermediary locations between any two arbitrary places, 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 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.
And 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?
[FL = Formal Logic; LIE = Linguistic Idealism.]
(4) Yet More A Priori Dogmatics?
Quite apart from all this, Engels's endeavour to provide an overtly linguistic solution to the problem of motion suggests that there is more than just 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 apparent 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). Because of this, 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 -- based on thought alone. 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: that of being able to say precisely what the fundamental features of reality are for all of space and time based on the alleged meanings of a few words. Indeed, Engels's claims about motion are all the more impressive when it is recalled that he made them in abeyance of any supportive evidence -- let alone a significant body of evidence. As it turns out (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 is briefly 'reflect' on the supposed meaning of a few words, and substantive truths about fundamental aspects of nature, for all of space and time, spring instantly to mind. Or, more honestly, all he/she has to do is copy such thoughts from Hegel. As we will also see, this is a key 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.]
Surprisingly then, the only 'evidence' that supports Engels's interpretation of motion is this highly compressed argument, which is itself based on a consideration of what a few innocent-looking words 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 rejoinder would immediately give 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 this will emerge in Essay Twelve Part One.]
As noted above, an appeal to evidence would be irrelevant, anyway. This is because the examination of countless moving objects would fail to confirm Engels's assertion that they occupy two places at once -- no matter what instruments or devices were 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 in Engels's day there was no scientific evidence whatsoever that supported his belief in the contradictory nature of motion, and thus why he listed none. This picture has not altered in the intervening years (indeed, no book or article on DM ever quotes any) --, 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.
However, the problem with this is that no matter how fast the shutter speed, a camera can't record an instant in time, merely an 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. Since instants (i.e., in the sense required) are mathematical fictions, it is not possible to record them.
Moreover, not even a mathematical limiting process could capture such ghostly 'entities' in the physical world, whatever else it might do in theory. But even if one could be found that did this, 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.
And that explains why he and those who accept these ideas have to force this view of motion onto nature.
Of course, part of the problem here is what the word "instant" means. 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.]
Unfortunately for Engels, if motion were to take place in one of these 'instants', that would mean that it could not exist -– that is, not unless we are prepared to reject Trotsky's own a priori conclusions, 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, and appeal to the abstract nature of some of the above points cannot rescue Engels. His analysis of motion could not have been derived by abstraction from all (or any) of the forms of motion hitherto experienced either by himself or by humanity -- or even from a finite sub-set of the same observed by scientists and/or philosophers down the ages and up until his (or even our) day. This is because his thesis clearly appeals to things that, according to Trotsky, do not exist -- such as "instants in time". And, even if the latter did exist, we could not experience or observe them, and hence we couldn't use them to confirm what Engels said -- nor could we abstract from them in order to agree with him.6
Whichever way we turn, we hit a linguistic/material wall made of very hard logical bricks.
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 universe the more fully they reflect its contradictory nature, and that substantive claims about the world 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 in fact prove inimical to DM since it would mean that this explanation of motion would contain contradictions, and, clearly, that would imply that DM is a contradictory theory.7 [The disastrous implications this has for DM are outlined in Essay Seven, and Essay Eleven Part One.]
Despite this, the above response does not neutralise the regressive consequences mentioned earlier. This is because Engels's philosophical thesis, which was the result of an extrapolation from the meaning of words to the nature of the world, is openly Idealist (on this see Essay Twelve Part One). Worse still, and for reasons given above, not only can this 'theory' not be confirmed, its subject matter (i.e., the claim that a moving body occupies and does not occupy the same place in the same instant, being in two places at once) cannot even be observed, nor can it be verified in any materially-based way.
Substantive philosophical 'truths' like this (about motion) are ambitiously universal in intent, but are thoroughly parochial in origin. Indeed, their promulgators' epistemologically imperialist intentions are plainly not matched by any obvious capacity to satisfy such voracious philosophical ambitions with adequate material support.
So, throughout history, overly 'imaginative' theorists (such as Engels -- but more particularly, Hegel) have constantly assumed that all of nature must be as their specially-engineered words supposedly depict it. However, if this were so, as we have noted several times, it would mean that the world possesses certain features merely because of the idiosyncrasies of Indo-European grammar -- the language group in which most of this overblown talk has been carried out.
(5) Explanation Or Re-Description?
Perhaps even worse: It is not easy to see how the 'contradictory' nature of motion could explain it, or even how it could form part of a wider scientific account of anything at all. At best, this way of talking simply re-describes movement, change and natural development.
More specifically, it is 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 "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." [Ibid., p.152.]
In that case, it looks like relevant questions concerning the proximate cause of motion (with the implied temporal concomitants such questions often require) cannot be answered by this way of depicting movement: the mere fact that a moving body is "here" does not appear capable of making it become "not here". Indeed, the alleged contradiction seems to lack any causal power, any capacity to make things happen. It is not so much that the dialectical batteries have run down, it is that there do not seem to have been any supplied with the original item Engels purchased from Hegel.
Now, 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 emerge one day, it is not easy to see how it could explain motion by recourse to these alleged contradictions; how does a moving body's being "here" and "not here" all at once explain why it moves (causally or in any other way)? What work do such contradictions do -- even if you believed in them?
It could be objected here that this radically misconstrues DM, for the counter-argument above misleadingly splits apart the supposed '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. For example, TAR's various discussions of causation were specifically aimed at countering mechanistic and reductionist accounts like this. Or so a response could go.
[TAR = The Algebra of Revolution, i.e., Rees (1998).]
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 couched -- that is, other than figuratively. [More on this in Essay Eight Parts One and Two.]
Even so, and despite the above, what sort of "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) to explain the rationale behind this view of motion and change is taken apart here.]
Moreover, it is difficult to see how contradictions could exercise any sort of effect on anything at all unless they were translated somehow into physical/material terms (as 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 -- 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 whatsoever), then they certainly can't serve in such a capacity in HM.
Nevertheless, if there are any contradictions in reality, they must surely 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 '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 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 this is 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 be able to see everywhere about us, so that the latter can 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, as we will soon see.
As was 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. This 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 clear it is 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 that to bring about its 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 did not 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 the following question: Which came first -- movement or contradiction? This could be why Engels spoke about these obscure entities 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 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 on 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.]
Hence, [2] suggests that contradictions are not a sufficient cause of motion, and [1] indicates they are not even necessary.
Moreover, and with respect to the first alternative 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, as even Engels saw things -- that is, there seems to be no way that they could make anything move. So, at best, they appear to be conceptually derivative, not causative. Hence, as things now stand, it looks as if things first of all move, and only then do contradictions emerge -- and even then this only applies to our depiction of motion.
If so, it might be correct to say that contradictions operate solely at a conceptual level -- they appear to have no part to play in the physical action, on the ground, as it were.
Thus, 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 "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 have to do this if literal contradictions (as opposed to a figurative DM-extension to that term) were operative in such cases. On this, see Note 1, and Essay Eight Parts One and Two.]
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' must be 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 still does not help. This 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 emerge below, there is no clearly specifiable set of possibilities -- or even actualities in the material world -- 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. This is not because he got the details wrong, or because he failed to capture nature accurately enough --, but 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 is 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.), it still would not amount to an explanation of the causal or "mediated" links that they require. 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 actually 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.]
Not only that, but the putative reflection of contradictions in the mind, which occurrence might be thought capable of providing the 'conceptual connection' that supposedly exists between a cause and its effects (or that between various mediated items in the Totality), cannot create a genuine connection if there are none in reality already there 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. But, if that is so, 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 nanometre.
Even assuming it could be shown that contradictions did in fact represent a material relation between objects 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. This 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., just assumed to exist) in order for the theory to work (in a sort of Kantian/Hegelian sense), then that would merely provide a conceptual link once more between the said events -- 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 a material aspect of reality.
[This outcome should surprise no one, given the Idealist origin of this use of "contradiction", and the way it is employed in DM.]
If, on the other hand, it is 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, 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 of motion (making them derivative), or (2) as the result of human reflection on the nature of motion (implying they are merely conceptual, and 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 all the above objections are 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 forward. 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 along.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) -- even if it were true that all bodies are in fact UOs. No matter how intense the 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 are 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 could be accounted for on the basis of a network of internal, systematically-opposed forces. This would then make the unit within which contradictions occur the whole, not the part (which seems to be the assumption underlying the comments made in previous 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.
However, even if systematically-opposed forces could somehow be interpreted as contradictions -- or at least viewed as constituting them -- that would still fail to show how internal contradictions could explain motion, or even how they could bring it about. 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 it. 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 to 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, 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 the latter 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.
Once more: even if the 'internalist/externalist' picture were correct, Engels's analysis of motion would still amount to nothing more than a re-description; 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 is worth re-emphasising this point: even if opposing forces could explain contradictory motion (which thesis is pulled apart in Essay Eight Part Two, anyway), the nature of the connection between the paradoxical states that moving bodies appear to display has still to be established. All that the addition of opposing forces has achieved is to account for the origin of one contradiction (motion) in terms of another (oppositional forces). The contradictory nature of motion itself is still locked in the descriptive mode -- it does no work. Whether 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, this still would provide no useful role for the observation that motion is itself contradictory. As far as DM is concerned (that is, on one interpretation of it 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.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 DL or FL), 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) is dependent on obsolete Aristotelian theory. If so, the fact that contradictions cannot supply a causal explanation of motion is perhaps all to the good --, for if the allegedly contradictory nature of motion caused and maintained movement, much of post-Aristotelian mechanics would have to be binned.11
But, then again if such 'contradictions' do not explain motion, 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 within 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 based 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 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 and here) that material contradictions cannot account for change, since they are locked in the descriptive mode (and a confused mode, at that).
However, one further possibility has not yet been examined: What if it were entirely unclear what Engels was trying to say in the passage under consideration? 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 as Engels sees 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 what anyone might be looking for. If we are given nothing comprehensible to search for, 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 causes of motion can begin, we need to be clear precisely what it is we are being asked to examine. As it turns out, it is 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. [The significance of these comments will emerge as the Essay unfolds.]
It is 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: the case 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 is clearly irrelevant.
A commonplace example of this sort of situation would be where, say, a train was 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.
[In this and subsequent instances 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 it, etc.
Of course, as noted above, Engels might have been referring to the motion of mathematical points, or point masses. But, even if he were, it would still leave unresolved the question of the allegedly contradictory nature of the motion of gross material bodies, and how the former relate to the latter; it is Engels's depiction of material bodies that is unclear. Since DM-theorists, like Engels, hold that their theory can account for motion in the real world, the former (i.e., 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.
In addition, 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 this 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".]
L2: Motion involves a body being in one and the same place and not in it.
A mundane example of this ambiguity might involve a case 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.
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 yard), even while it is at rest relative to a suitable inertial frame.
In which case, the alleged contradiction that Engels mentioned is not the result of motion; it are a consequence of the vagueness of his description. This can be seen from the fact that objects at rest relative to an inertial frame can and do display the same apparent 'contradictions' as do those that are in motion with respect to the same inertial frame. Naturally, if things at rest share the very same vague features as those that are in motion, it means that Engels's description does not pick out what is unique to moving bodies.
This is not a good start.
At best, L3 simply depicts the necessary but not 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 said about movement.
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 depiction of 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 like to ponder exactly how the word "change" could be explicated (given this theory) without an appeal to a definition that involved the word "motion" (a definition, it is worth remembering, that has yet to attempted by dialecticians). Of course, 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 resolved, the initial promise the above set of sentences seemed to offer soon evaporates when it is 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 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 the movement of the body in question could be accounted for along its entire trajectory. That would merely entail the use of "ti" in the place of "t1" in L8 and L6. That specific 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 is clear that B is no longer at (X1, Y1, Z1) at t1, since it is 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 this scenario was contradictory, he/she would need to explain to the rest of us just what this 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 held that objects turned into whatever their opposites were, that is, whatever were contradicted by. In this case, 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: