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, no camera (not even this one) 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 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:
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 is, though, 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 is worth recalling that a set S of sentences is inconsistent just in case not all of its elements can be true at once. But a "contradiction" requires more than this. In the simplest case, the elements of a binary sub-set of sentences formed from elements of S are contradictory just in case (1) those elements are inconsistent and (2) both cannot also be false. In short, they cannot both be true and they cannot both be false. That salient fact is invariably overlooked by DM-theorists, which leads them to confuse contradictions with inconsistencies, or contraries -- and, indeed, with a host of other unrelated things, too.]
The question is, therefore, can all of the elements of L be false at once? 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) --, 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 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, too.
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 is 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 as a 'logical truth'). 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 held to be 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 they 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.
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 escape route will be blocked later on in this Essay.]
[MFL = Modern Formal Logic.]
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 this 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 is always possible to argue that L11 really amounts to the following:
L12: For some b, during interval T, and for two 'instants' t1 and t2 [where both t1 and t2 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. If this were not so (i.e., if L12 is rejected), then L11 would imply that the supposed change of place occurs outside of time -- or, worse, that it happened independently of the passage of time --, which is incomprehensible (as even Trotsky would have admitted).
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.
[Trotsky's worries about instants are examined below, and in Essay Six. The idea that if a body is located at a point at an instant, it must be stationary, is also examined below.]
This latest difficulty can only be neutralised, it would seem, 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 position as finely as we wish -- so that no matter to what extent the physical aspects of a body's location are partitioned, we would always be able to distinguish two contiguous points, allowing us to say that a moving body is in these two places at once --, while we can do that with respect to location, we cannot do the same with respect to time.
Now, this inconsistent view of the divisibility of time and space might seem to rule out 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 it only achieves this by stipulating that the successful mapping of places onto real numbers (to give them the required density and continuity) is denied of temporal intervals.
In that case, and so far, there seem to be three distinct possibilities:
(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).
Naturally, these are not the only three 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 a point; so, if we could specify a time at which the said object was located at that point, and only that point at that time, it must be at rest at that point at that time. Nevertheless, it seemed clear to others that moving bodies cannot be depicted in this way (and that motion was an 'intrinsic' property of bodies, so that at all times a moving body must be in motion, allowing it to be in and not be in any given location at one and the same time), and that therefore one or more of the above options must be ruled out.
However, it is worth pointing out here 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 earlier 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 word "motion".
In Essay Three Part One and Essay Twelve Part One, it was argued that philosophical 'problems' of this sort occur when ordinary words are twisted beyond recognition, and that the new conventions for the use of such terms that emerge as a result are themselves confused with empirical propositions.
In short, the 'classical' approach only gets off the ground if linguistic conventions/stipulations, and/or rules, are mistakenly viewed as superscientific, empirical propositions.
Indeed, this is how and why 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) -- and because of this they imagined they could 'derive' super-theses like these from such an idiosyncratic use of language.
As a result of this 'wrong turn' (although there were clear ideological motives for taking it -- see below), traditional Philosophers assumed that, for example, the word "motion" itself implied there was some sort of 'problem' (or 'contradiction', or 'paradox'), which needed to be resolved if Physics and Mathematics were to avoid unremitting confusion. 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 those sections of society that had been divorced (by class division) from the world of collective labour, whose theories reflected their ideal view of reality and sprang from an ideologically-motivated denigration of material language. [These allegations are fully-documented in Essay Twelve (summary here).] Hence, if the world was ultimately Ideal, it would of course be quite 'safe' to infer superscientific truths about realty from language alone.
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 moves like this is confirmed by the further fact that the acceptance or rejection of one or more of the three options listed above cannot be (and was never, and has never been) based on evidence of any sort. Severally or collectively, each of these alternatives was/is founded on a prior linguistic convention overtly or covertly accepted by all parties to this metaphysical con-trick, one that 'uncovers' 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 (like "place", "time" or "instant").
Moreover, the choice of one or other of options (1) to (3) (as a way leading to a favoured 'solution'), repeated below, was in turn dependent on the idea that even if the specification of place was in no way problematic (in that we can always declare that a moving body is in two places at once), that 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 the latter case, however, the preferred DM-solution appears to rule out the possibility of a moving object being in two contiguous places (if we could specify such) at two different times. This means, therefore, that dialecticians have implicitly opted for alternative (2):
(2) Infinite divisibility is true of location only.
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 (material) understanding of motion, which is that moving bodies occupy different places at different times. This is such a mundane connotation of our ordinary grasp of certain kinds of motion that it seldom features in classical discussions, except perhaps where it is rejected out of hand as too 'crude' to be worthy of consideration.
However, as we shall soon see (and again in several other Essays posted at this site), ordinary language is not so easily dismissed and/or ignored.
However, there are (and can be) no (a priori) empirical constraints on the length of time intervals. Furthermore, as was also noted above, Engels's own 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', or 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 is little use objecting that this or that 'must' be so, for that would be to concede the fact that these 'musts' had been derived solely from the meanings of a few words, whose meanings, as we will see, are far less straight-forward than tradition would have us believe.
It could be argued that the classical analysis of motion follows deductively from certain incontestable premises. There are only a handful of possibilities that the world could conceivably present to us; Engels's account is derived from one of these, via Hegel. So, what's the problem?
Once more, as we will soon see, the problem with this is that the deducibility or otherwise of the conclusions drawn above depends on the use of several artificially modified words (such as "place", "move", "time", "moment", etc.), which have either been idiosyncratically (or narrowly) 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).
Even worse, not only does nothing follow from these transmogrified words and 'concepts', it is impossible to give a clear sense even 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 cannot.
In that case, if humanity does in fact possess an 'abstract' idea of motion (and this will be questioned below, and in other Essays posted at this site), it cannot have been derived from 'reflection', nor have been based on anything found in material reality. And that observation becomes all the more apposite if this allegedly 'abstract' idea can itself be shown to have originated from 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.
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.
[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 is rejected as an alternative interpretation of L11 (that is, if the idea that time is continuous is flatly denied (but this condition is asymmetrically allowed of space) -- i.e., if option (2) is imposed on the phenomena) --, then there seems to be no consistent way of ruling out the following as yet another alternative 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 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 it 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 that finite region (so that it need not be in other areas of that port 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, or in a host of other places in that port, at that time.
Moreover, if the ship is 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. This 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 more.
[I have given a more technical version of this scenario in Note 15.]15
As pointed out above, L12 and/or L13 may 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 it has been shown that Engels's claims still do not work!
In which case, of course, the alleged contradictory nature of motion (but, as we have just seen, it is not even that!) is at best an artefact of convention -- and one that only works by constraining the divisibility of time but not of place --; hence it is not one based on genuine features of reality.16
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 cannot be located at a point, otherwise it would not be moving, it would be at rest.
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 might suggest that motion is either impossible or illusory --, or even that is a sort of 'stop-go' affair. In the latter case, motion would be analogous to the way it is depicted in, say, film. Here, movement only appears to be continuous when in fact it is discontinuous, being composed of rapidly sequenced 'freeze frames', as it were, which, when they are played at a certain speed, fool the human eye into 'seeing' movement. On this 'quasi-static' view, a 'moving' body 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 and 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 invalidate QM -- that is, given the way that motion is depicted in traditional Philosophy.19
[QM = Quantum Mechanics.]
In order to reject this 'quasi-static' view, 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 be rather like the way that neon lights in a complex sign, say, can be turned on and off in sequence to create the illusion of motion.]
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.
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 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 'rest', at successive instants.
L27: Therefore, either motion is impossible (which is absurd), or motion cannot be wholly discontinuous.
[It is possible to strengthen L27 into L27a, but that avenue will not be pursued any further here:
L27a: Therefore, either motion is impossible (which is absurd), or motion cannot be discontinuous.]
However, it is 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 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 all depends on whether these are genuine contradictories (but, 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 for the purposes of this argument -- their status as propositions will, however, 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 so by accepting L28 (or its equivalent) 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 is false (and L29 true) -- which would mean that a body can be moving and at rest at the same time --, L17 might not look quite so compelling. At any rate, it is clear that dialecticians have to reject one 'contradiction' (expressed in L29) in order to derive their own (in L17).
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 is 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 is clear from the way that the above argument has been constructed that L17a itself depends on the truth of L28 (repeated here again for ease of reference):
L28: A body 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 L17a, whereas L17a looks like it depends on L28. This suggests that L28 might be the more fundamental 'thesis' 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.]
Anyway, L30 itself 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 at last appear to follow! This much seems 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, 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, L31-34 demonstrate that L17a does not have to follow from the rejection of L30, even if the alternative outcome proves unpalatable.
It is 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 is worth noting, however, that neither option is empirically verifiable; in fact they both transcend any conceivable body of evidence and every possible experience.21
Nevertheless, given the fact that dialecticians also believe that appearances contradict underlying 'essences' they are the last ones who can appeal legitimately to experience to refute Zeno-esque conclusions like L34b. In fact, since it appears to be the case that there are moving bodies, in essence the opposite must be true -- that is, if appearances contradict reality. Thus, it seems that essentially no bodies move!
Putting this annoying corollary to one side for now, it is worth emphasising that both halves of these two derivations rely on the sorts of ambiguities encountered in L1-L13 (alongside several others analysed below). A prioristic 'arguments' like this only seem to work because they are shot-through with equivocation and distortion; indeed, this is partly why they both finally descend into absurdity -- as will now be demonstrated.
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 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 is even more absurd than L34b!
L34b: Despite appearances to the contrary, all bodies are at rest.
The only way to avoid such an outlandish conclusion would be to maintain that L35 implies that a moving body is in no more than two places 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 in this second place -- unless it were in a third place at the very same time (by L15). 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.
Without L15, 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 would 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.
The latter would indeed be misconceived if Engels had managed to show that a body can only be in at most two (but not that it was 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 it the 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 that it occupies as it hurries along), 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.
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.
It is worth underling this: 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.
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 -- clearly 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, this new instant, say t2, would start.
To be sure, this amendment avoids the disastrous implications recorded above. However, it only succeeds in doing this by introducing several serious 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:
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.
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 is another cul-de-sac.
Engels just needs a body to be in two places at once; the third place above 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. The use of "and" scuppers this line of defense.
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 it the body is anywhere it is everywhere at the same time."
In that case, the reply encapsulated in L38/R1 fails. Hence, 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. If so, R2 is still valid.
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 numbers. R3 thus implies that L17c is false.
L17c: A moving object must occupy at most two places at once.
Moreover, it's 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. So much is agreed upon. Now, 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 thus:
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 (X3, Y3, Z3).
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) 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 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 short-circuit the above criticisms, and maintain their view that motion is 'contradictory', only 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 the belief that reality itself is contradictory (and not just the decisions we make about it that are), all the while confirming the suspicion that it's only certain ways of representing nature that are contradictory -- which "ways of representing nature", incidentally, still await clarification.
That, of course, would mean that this part of DM (at least) is thoroughly conventional, and thus entirely subjective.
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, theses that are based solely on an extrapolation from the supposed meaning of a few words. Clearly, with respect to Engels's analysis of motion, this predicament is further compounded by his attempt to circumvent several other fundamental conventions of material 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 Two.
Suffice it to say here that dialecticians themselves have yet to account for motion in a comprehensible form. So, whether or not it is correct to say that FL can account for change, it is 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.
And Therefore Never Send To Know For Whom The Bell Tolls; It Tolls For DM
Several of the points raised above require further elaboration.
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 meanings of terms like "motion", "change", "place", "moment", and "time". This can be seen from the fact that he did not even think to define what he meant by such 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 theoretically-sloppy approach of this sort is unacceptable. Indeed, such a cavalier attitude to ordinary language has a tendency to backfire on those foolish enough to go down that route. 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 them to ignore the internal contradictions this now introduces into their own theory. [More on that 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 allege that 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 it has been here, but 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 can cease worrying about the contradictions at the heart of their own theory; they accept the fact that even though nature is deeply perplexing, a pair of well-adjusted DM-spectacles allows it to be viewed in the right way (where "viewed" in fact means "ignored").
Nevertheless, and despite the spin, this still means 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 manner described earlier in this Essay). And if that is so, the dialectical 'analysis' of motion is of little use to anyone --, least of all to dialecticians now that it is plain that not even they can explain motion. All that Engels's 'analysis' has achieved, therefore, is stop dialecticians worrying about their defective theory, leaving motion, as they see it, still 'paradoxical'.
In that case, if there is a rational solution to this paradox (if we but knew it), it would be 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 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 these 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 both on ruling-class forms-of-thought and on a distortion of the vernacular, the only language that links humanity directly with the material world.
Indeed, Engels's approach began to falter as soon as he attempted to squeeze some metaphysical juice out of such theoretically desiccated fruit; that is, when he tried to extract 'paradoxical' conclusions from a few innocent-looking words.
Naturally, the conclusions Engels reached will be agreeable only to those who have already capitulated to the view that reality is fundamentally 'contradictory'. Others might be forgiven for remaining sceptical --, but particularly those who 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 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 removing 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 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 ordinary words. As we will see, he did this by unwittingly altering their usual senses while at the same time 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 piecemeal selectivity over the use of words. Indeed, these thinkers invariably assume that they can tinker around with a few specially chosen expressions while the meaning of words associated with them remain the same. Selectivity like this is, alas, double-edged. In fact, these associated words -- whose meaning Engels also took for granted -- prove to be equally (if not more) problematic than those he latched onto. As we are about to see, this unexpected turn of events will not only vitiate Engels's 'analysis' of motion, it will put paid to every single classic account, too.
If, for example, an ordinary word like "motion" possessed '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 also alters 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. This is because, if the sense of the latter is compromised by the slippery nature of the former (or vice versa), then the meaning of neither will 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 connotation 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, the meaning of this 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 meaning, problems 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 demonstrate 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 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 also 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?
It could be objected here that if "place" is defined precisely (and without altering the meaning of "move") it would be possible to understand what Engels and Hegel were trying to say. In that case, it might 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 one might think.
Of course, the problem here is that in the example above (concerning these contradictory mobile/stationary workers), if we try to refine the meaning of the word "place" a little more precisely, it will start 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, and objects occupy finite regions as they move in relation to each other (or they would not be able to move).
Clearly, Engels's 'theory' of motion has to be able to take account of such ordinary objects if it is to apply to the real world and not just to an abstraction, or to physically meaningless mathematical 'points'. But this is just what it cannot do, as we shall see.
On the other hand, 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 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 in reality objects move while staying in the same place, that is, 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 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 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. This is because such an account would be about mathematical point locations (or about the movement of mathematical points themselves -- and we saw that that was a non-starter earlier).
Clearly, things cannot move about in such points -- but this has nothing to do with the nature of reality. These 'entities' do not (and could not) exist in nature for them to contain anything. This is because SCs are not containers. They have no volume and are made of nothing.
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, as noted earlier.
And it is no use appealing to larger numbers of 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 coordinate algebra/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, 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 that region of space (i.e., that volume interval) equal to that object's own volume. This is in effect the classical definition. 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, obviously, if that were the case, it would still mean that such an object 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 the one, for we should have to explain not only how bodies move, but how volume intervals also move so that they can shadow the objects they contain!
However, and far worse: in that case, we would not only have to explain how locations (i.e., such volume intervals) were themselves capable of moving, but 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 seeing things). And if they do that, then these new 'extra' locations for the volume intervals themselves must act now 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 loom into view, as spatial mittens inside containing gloves, inside holding-case gauntlets piled up alarmingly, to account for each successive container. 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. They thus 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. This 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 objects would plainly occupy at least two of these volume intervals at once.
In that case, 'dialectical objects' would not so much move as stretch, or expand!
Of course, if this were not the case, and no stretching occurred, then a 'dialectical' object would threaten to occupy more than its fair share of space as it moved (and, as we will soon see, alarmingly more!).
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), that moving object would have to occupy a space larger than its own volume to do 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 "δV", leaving it open for the time being whether S and δV are the same or different. Thus, if the COM of 'dialectical' object 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 δV. 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 δV (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 δV --, and hence that it appeared to stay still while it moved, just like the 'mobile/stationary' workers we encountered earlier -- would be to argue that such spaces stay where they were while D moved into successively new locations.
But, as D moves it still occupies δV, only we now have to argue that as it does so it also moves into a new δV each time, say, δV1 -- except that δV1 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 would expand or stretch, again!
Of course, as we saw above in an analogous context, successive applications of this argument would have D occupying bigger and bigger volume intervals. In the limit, D could fill the entire universe (or, at least, the entire volume interval of it own trajectory), all at the same time, if it moved --, 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, we witness yet another dialectical disaster area.
The reader should now be able to see for herself the Hermetic mayhem introduced into our reasoning by this cavalier use of 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 and logical resources DL supplies its unfortunate adepts.
[DL = Dialectical Logic; SC = Spatial Coordinate.]
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:
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).
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 every SC must be written precisely this way, with xi, yi and zi (etc.) in their correct places.
L53: But, the placing 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 in fact itself dependent on a perfectly ordinary meaning of "place", and further, that the latter 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 rather mundane facts such as these.]
Of course, this is not to malign coordinate geometry, but it reminds us that any branch of human knowledge (even one as technical 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, and as a result we inherit the mythological structures that previous generations have built on top of unexamined foundations like these.
If, on the other hand, a typographically identical word (viz.: "place") were to be so defined, 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 is used to define the movement of objects in DM, then the motion of gross bodies would still be left unaccounted for.
It could be objected here that it is surely possible to disambiguate the ordinary word "place" so that it could be employed in a DM-analysis of "motion" --, meaning that it was no longer confused with the less precise phrase "general location".
Since this has yet to be done (even by DM-advocates, who, up until now, have only revealed that they are not even aware of the 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 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 have emerged (which is, of course, something even Hegel recognised). This trick is accomplished either by (1) the simple expedient of ignoring examples of discrete forms of motion (several of which are given below), 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 surroundings.25
Even assuming a stricter sense of "place" could be cobbled-together somehow, that would still be of little use. 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, or it would not so much move as expand or stretch, as noted earlier.
All this means that in a perfectly ordinary sense, things can both move and stay in the same place as 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 -- 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 is 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 this 'moving and not moving' all at once doing so in a different sense from that illustrated in L55. In fact, it is possible to show that some things can move (again in a discrete sense) while they occupy none of the intervening places between successive locations. All of these 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 groundsman 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 (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!
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 can 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.
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 is 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 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 what that is to the rest of us. Unfortunately, to date, there have been no significant moves in that direction.
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 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 all moving aspects of reality are contradictory, including those parts of it that can be depicted by our use of the vernacular.29
It could be argued 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, 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 -– but ones which have been given an idiosyncratic re-interpretation, and this has been done in isolation from other associated terms divorced from their ordinary contexts of use -- to necessary truths about the world. 'Deductions' like these invariably precede (i.e., they are a priori to) 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, ones 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 tactic 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. 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 have referred anyone sceptical of his conclusions to what certain words really meant. It would be no good advising non-believers to look harder at the phenomena, refine their search or redo their experiments --, which is, of course, why one finds no evidence at all in books on dialectics that either confirms or even vaguely supports 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 linguistic usage -- and to Hegel and Zeno's, at that --, not how such words feature in everyday life. This predicament (which he shares with all other metaphysicians) invariably passes unnoticed because (1) it is so widespread in traditional thought, (2) it has been going on for so long, and (3) it is imagined that by looking at certain words (or their 'real' meanings) the Armchair Philosopher is actually examining the world itself, and not merely a few specially-selected bits of jargon.
[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 these specially-selected words is simply taken for granted; indeed, the question whether such words actually have a denotation is seldom even 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 (and, truth be told, typically they weren't derived from any, either). That is why they depend solely on a quirky use of language, and it is also why this is all Engels offered his readers, and it is all he could have offered his readers.
Nevertheless, Engels restricted his comments neither to examples of motion he had personally investigated, nor to the entire set of instances experienced by humanity to date. 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.]
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.
As we shall see (in Essays Nine Part One and Two, and Twelve (summary here)), that fact alone has revealing ideological implications associated with it.
Engels's feeling of confidence in the results he obtained so easily 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. Bold emphasis added.]
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 indicated? There are only two plausibly correct answers to these questions:
(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 varieties 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 is in novel contexts like these? 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 understanding them (and then only after reading Hegel -- as opposed to sifting through the relevant scientific data)? Or even that, when used philosophically, this sort of language means anything at all?
However, and even more to the point: precisely who decided that such off-the-cuff conclusions (about substantive, physical features of the world, true for all of space and time) can simply 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: surely a rejection of Engels's understanding of motion would be paradoxical, if not contradictory itself. This is because it would represent a repudiation of what the concept of motion actually implies. Consequently, on this view, for anyone to interpret motion as not involving a body being in two places at once (etc., etc.) would be tantamount to their failing to comprehend 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 own analysis of motion is paradoxical and 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 is paradoxical to reject his version, it is equally paradoxical to accept it.
Moreover, an appeal to experience to decide between these two alternatives is of little help, and for this is so for four reasons:
(A) As has already been noted, Engels drew his conclusions 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 was or was not continuous, discontinuous --, or whether it was composed of innumerably many discrete concatenated 'sub-movements' -- or, indeed, whether it was 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 is only a metaphysical prejudice (itself based on other priorities that will be exposed later) that (1) consigns certain depictions of motion to the realm of "appearance", or "commonsense", while others are said to refer to "reality itself"; or that (2) 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") 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 words, and then foist the results on reality -- the use of "must" here reveals yet again this propensity to impose favoured theses on nature. When pressed to provide evidence to substantiate their claim to be in possession of Superscientific knowledge of motion like this -- applicable to every region of space and time -- all that DM-theorists would be able to point to in support would be the meaning of a few words.
Apart from an absurd alternative explanation for their possession of superior knowledge (i.e., that those making such Super-empirical claims are deities of some sort, who have access to profound, semi-mystical sources of knowledge (of the nature of "reality-in-itself")), 'conceptual/linguistic analysis' is the only conceivable source of such hyper-bold 'dialectical' claims.
And that explains why Engels omitted the data supporting his 'theory' -- and no one has bothered to supply any since.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 is based on the thesis that reality is contradictory (and that itself is founded on the scientifically-confirmed belief in universal change). It goes way beyond the view 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 this particular 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 sort of 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 that of Hegel) is shot-through with error and ambiguity, the motivation to claim that reality is contradictory weakens alarmingly (and it weakens even more when it is recalled that this idea is based on a series of egregious logical blunders 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' the nature 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 assert 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, the non-standard interpretation that dialecticians put on ordinary words is what finally conjures-up the paradoxes they label "contradictions" -- that is, even where they get the latter word right.
In that case, far from reality being 'contradictory', it is the dialectical use of language that is incoherent and paradoxical.
It is not easy to form a clear idea of the claim that reality is fundamentally contradictory. With respect to DM, at least, this is primarily 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 and Two, and Eleven Part One, I hope to demonstrate that while DM-theorists avowedly use the term "contradiction" in their attempt to expose the alleged limitations of FL, most of them show little or no comprehension of either or both. Nevertheless, this has not prevented them from claiming that their understanding of contradictions 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 the 'laws' of FL cannot do this. However, as we will see in this Essay, this particular claim is inaccurate, at least with respect to motion. Indeed, the rest of this site aims to show that not only can DL not account for change, dialectical logicians 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 Essays Four, Eight and 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 want to do so) from what might appear to be contradictory propositions. Take one example: 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 contradictory sentences -- coupled with wider uses of negation -- are integral to our ordinary notion of change.
This being so, the idea that ordinary language and FL cannot account for change is bizarre; in fact, without the resources found in the vernacular, human beings would not have been able to conceptualise change at all. And this constraint applies equally to scientists and dialecticians. Again, as demonstrated here, ordinary language can handle change far better than the obscure and wooden terminology invented by metaphysicians; and 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. [This latter condition is almost invariably ignored by DM-critics of FL. Its importance will emerge later.] Naturally, this characterisation represents the simplest form of FL-contradiction.
Examples of more complex contradictions would include either 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; "(x)" is the universal quantifier; "&" stands for "and"; "v" is the inclusive "or"; "~" stands for negation; "→" is the conditional sign; "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.]
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 such as 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, contraries, paradoxes, oddities, irrationalities, struggles, oppositional processes, forces, events which go contrary to expectations, and a host of other things. In fact, they are so ready 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.]
Nevertheless, as DM-theorists themselves are quick to point out, their interest lies not so much with contradictory propositions as 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 many of them also believe that reality itself is fundamentally contradictory, propositions accurately describing the world ought rightly to be contradictory, too -- i.e., they should reflect the contradictions that exist in reality.
But, because propositions are linguistic expressions they are plainly not material forces as such. That must mean that they are not themselves oppositional per se -- even though they can reflect at some level the dynamic nature of objects and processes in reality, according to dialecticians. On the other hand, even if 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 this must reflect such things adequately if it is to be objective. Or so the case for the defence might go.
Now, 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 that 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 that particular caveat) would automatically be regarded as mistaken in some way.
Indeed, that fact alone could provide sufficient grounds for questioning whether one or both of the allegedly true contradictory propositions were in fact propositions to begin with. To be sure, if it is unclear what is being proposed, any sentence in which that is supposedly being attempted cannot be proposing anything -- that is, this side of its disambiguation. [Examples of the latter process are given below, and later in the main body of this Essay. See also here.]
Several factors might contribute to this state of affairs: the said 'propositions' could contain typographically similar words that have different denotations; they could harbour ambiguous, vague, or figurative expressions; they might have been taken 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 the nature of reality; they would perhaps convey more about the linguistic naivety of anyone so easily taken in.
In that case, one would expect that the disambiguation or clarification of these alleged 'contradictions' would eliminate the problem. Only an exceedingly naive person (or worse, a 'mad dog Idealist' -- like Hegel) would conclude that just because certain words/sentences appeared to be contradictory, nature must be so 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, this 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, from a series of simple 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 them to be dogmatic and aprioristic. Moreover, 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 appropriated) that truths about reality may be inferred from contingent -- or even from logical -- features of language. Manifestly, it is the world that makes what we say true or false; it is not what we say that determines the nature of reality.
[As Essay Seven argues, DM-contradictions cannot be verified by experience, nor can they be confirmed in any other way. In Essay Twelve, the ideological motivation underlying the contrary view is exposed for what it is: LIE (summary here).]
Nevertheless, it is 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, they invariably turn out to be confused, ambiguous or non-sensical when examined closely -- as several Essays posted at this site demonstrate.
Moreover, it is equally important to be able to distinguish spurious pictures of reality from the genuine article. Indeed, DM-theorists do precisely this themselves 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 human beings have to hand); they then require that our linguistic habits adapt accordingly. On this view, if nature is contradictory, and ordinary language and FL cannot accommodate that fact, then both must be judged limited and/or defective in some way, and thus in need of supplementation with concepts drawn from 'Materialist Dialectics'.
It is not easy for a response to this to appear un-dogmatic. However, 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), this 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). This facility in language (which apparently goes back as far as records last, and as far back, one supposes, as human beings have been able to argue) means that our ancestors clearly failed to take the DM-route. And it is not difficult to see why. In fact, given the concepts we now have (and the social practices from which they have arisen), we can make no sense of the claim that a contradiction could be true. Indeed, we would fail to comprehend anyone who claimed that in a dispute (where someone gain-said what someone else had asserted) both sides could be speaking the literal truth -- ambiguous examples excepted.
In cases where disputants might appear to be doing this, the most likely response (then as now) would be to try to disambiguate their words in order to resolve the serious problems that 'true contradictions' would create in everyday life.
And this can be asserted with some confidence because, as noted above, the conventions we now have prevent us from understanding how a contradiction could be true. Not only that, these conventions prevent us from understanding anyone who might think otherwise. Worse still, they also prevent us from understanding how humanity could ever have developed alternative conventions, or how we could make sense of anyone who supposed that they could have done so.
This is one intellectual river we cannot now step back into even once -- to paraphrase Cratylus.
[In fact, this is connected with (1) the way that negation works in language, and (2) the capacity language affords us of understanding empirical propositions before we know whether they are true or false. More on that in Essay Twelve Part One.]
These claims are as bold as they are controversial, so I shall defend each in turn.
Take the first -- which was that we should fail to understand anyone who believed a contradiction could be true, and that we would seek to disambiguate it (or them) in order to make sense of what it or (they) said. Consider the following example:
B1: John Rees wrote and did not write The Algebra of Revolution.
B1a: John Rees wrote The Algebra of Revolution.
B1b: John Rees did not write The Algebra of Revolution.
Let us suppose someone asserted that B1 was true -- or that both B1a and B1b were true. Faced with this, we would find it difficult to take that person or what they said either literally or seriously; this is because both halves of B1 could not be true, nor could they both be false.
[Some might think that these are not the type of contradictions that are of interest to dialecticians; that objection will be fielded later on in this Note.]
However, if B1a and B1b were still held true, then we could only make sense of the contradiction they seem to express by noting the ambiguous use of the word "write". In one sense of that term it could imply that John Rees was the author of the said work; in another quite ordinary sense it might suggest that the book was not hand-written, but was perhaps word-processed. In that case, B1 would be expressing the fact that although John Rees authored the said book he did not hand-write it. Hence, B1 would then only appear to be contradictory because of such an elementary equivocation. We would not automatically think that there were real material forces at work behind the struggle to produce Rees's book, no matter how well-confirmed each half of B1 happened to be.
[Naturally, this indicates that an empirical check in such cases is not relevant to what is in fact a logical/conceptual issue.]
Again, someone might object, arguing that the above line of attack reveals the LIE implicit in the logical caveats this Essay lays down, for it seems to restrict the options available to reality by appealing to a controversial logical/linguistic pre-condition.
But this would be to mistake the approach adopted here for its opposite. The strategy employed here seeks to undermine the idea that substantive truths about reality can be derived from logical or contingent features of language. Here, it does this by basing itself on what we would now try to do (independently of any theory) to interpret/understand contradictions as and when they might arise. In that case, this Essay appeals to rules (i.e., normed social practices) we already use, and not to truths that can be inferred from a misconception of the nature of such rules.
In that case, no truths are being inferred (by me) from the above logical observations, merely a denial that anyone can derive any truths at all from a misconstrued set of puzzling words.
Indeed, it is the opposite view to that taken here that tails-off into LIE, for it confuses linguistic/logical rules with empirical (or Superempirical) truths. In DM, this is done, for example, when dialecticians treat the LOC as a truth which they think could be (and often is) false. This leads them to argue that contradictions themselves could be true (since the 'law' debarring them, the LOC, is false when it is applied to the real world and to change, etc.). But, if the LOC is in fact a rule, or if it merely formalises a rule we ordinarily use, it cannot be either true or false.
[Further ruminations on this theme will be resumed in Essay Twelve Part One, where it will be demonstrated in detail why the aforementioned confusion of rules (i.e., normed linguistic practices, conditioned by the material and social world) with substantive truths, is a characteristic feature of ruling-class thought (since it undermines the communally-motivated aspects of ordinary language, and thus the experience of working people). It is from such ideologically-motivated confusion that Metaphysics (and now dialectics) originally sprang.]
Admittedly, the example quoted above (in B1) is glaringly trite, but it was deliberately chosen so that the strategy of disambiguation would be clear to all. Nevertheless, and against this, it could be objected that DM-theorists are more concerned with an analysis of the forces operating inside the Capitalist system, so that they can assist in its demise; in that case, simplistic examples like B1 are not even remotely relevant.
In order to counter this response, the types of contradictions to which DM-theorists regularly refer will be analysed elsewhere on this site (for example, here and here), and in unprecedented detail. There, it will be shown that many of the favourite examples used by dialecticians to illustrate "real material contradictions" turn out not to be contradictions (in any sense of the word; on that see here, here and here) -- and they cannot be turned into them howsoever they are interpreted, or 'surgically enhanced'.
With respect to the other assertion made above -- that we would fail to understand alternative conventions, given the ones we already have --, the key point is that as social beings we may only succeed in understanding something when, plainly, it is presented to us in a language and a form with which we are familiar --, and typically, but not exclusively, this takes place in ordinary language. And this, too, can be asserted with some confidence since the word "understand" is (patently) in ordinary language already. But, discourse is not a free-floating phenomenon; its invention and evolution were and are functions of our social and material development. In addition, our use of language is subject to constraints we have inherited from previous generations, ones which we clearly had no hand in shaping. Indeed, all of us had to be socialised (by parents, siblings, carers, teachers and peers) into using language within and with regard to these constraints. We manifestly did not socialise ourselves.
Moreover, we demonstrate our mastery of this complex socio-linguistic invention when we begin to communicate and interact with others. While we can form thoughts as we please, we cannot do so under logico-linguistic/social conditions of our own choosing (to paraphrase Marx).
Now, it is tempting to think that such limitations are physical -- or at least that they represent merely contingent constraints on the use of language --, but that would be a serious mistake. There are physical and contingent boundaries to language, but these are not the limitations alluded to above.
[A clue to the nature of these limitations can ascertained by anyone who reads the Essays posted here, where it has been demonstrated time and again how quickly DM-theses fall apart, and how they cannot be repaired no matter what is done to them. That sort of limitation is not physical; it is conceptual. Another example can be found here.
This topic will be discussed in more detail in an Essay to be posted in the Additional Essays section in 2008 or 2009.]
B1: John Rees wrote and did not write The Algebra of Revolution.
However, the points made in this Essay are not dependent on the validity of this latest batch of seemingly dogmatic claims. Doubters need only think about how they would interpret B1 (or indeed B2, below), and this point should become a little clearer.
Of course, we can translate other languages (ancient or modern) into our own, but we may do so only if we act within the constraints currently operating on us -- unless we want to restrict ourselves merely to simple transliteration. This means that because we cannot make sense of contradictory speech now, we cannot comprehend the supposition that contradictions could ever have been held true by anyone in the past. Indeed, we are equally incapable of translating any language (ancient or modern) into our own in comprehensible terms while attempting to depict its users using contradictory speech, holding contradictions to be true in any form we could now understand. We may be able to record the fact that certain people spoke in paradoxical ways in the past (or whenever), but given what we now mean by the words we use, we would not be able to make sense of what these ancient 'paradoxes' could have presented to their alleged 'believers', or, indeed, determine whether or not they presented anything at all.
The various 'true contradictions' to which DM-theorists appeal will be examined elsewhere at this site (for example, follow the links posted here). Graham Priest's much more sophisticated attempt to depict 'true contradictions' will be examined in a later Essay. In the meantime, readers should consult Berto (2007), Goldstein (1992) and Slater (2007a), as well as this review.
Incidentally, the aforementioned limitations are not those that words exercise upon us, but how we collectively -- through our socialisation -- understand and thus use the words we already have. To suppose otherwise would be to fetishise language.
Some may take exception to the above, claiming that they certainly can imagine speakers holding certain contradictions true (or representing real material forces), namely themselves! Dialecticians, therefore, are living disproof of the above sweeping allegations.
However, this Essay aims to show that Hegel and Engels's claim that motion is 'contradictory' is too confused for it to be assessed for its truth or falsehood (and hence that this alleged 'contradiction' isn't one to begin with). Other examples of dialectical 'contradictions' will similarly be dealt with in Essay Eight Parts One and Two, and Essay Eleven Part One. In addition, the dialectical thesis that reality is suffused with UOs will be consigned to the mystical trash can of history, where it belongs, in Essay Seven Part One.
[UO = Unity of Opposites.]
In which case, because it is not possible to make sense of any of the examples DM-theorists give of 'dialectical contradictions', the above "sweeping allegations" have everything going for them. Indeed, since dialecticians have shown they are incapable of explaining their mysterious 'contradictions' to a living soul, they themselves can serve as further confirmation. [On that, see here.]
To be sure, there have been, and still are, religious believers who assent to all manner of apparently contradictory ideas -- but this does not refute the above. Their talk is non-propositional, and wall-to-wall non-sense, as will be demonstrated in a later Essay. The same comment applies to Buddhists (or, more pointedly, Zen Buddhists), who seem to glory in paradox.
However, in relation to the claim that we would not be able to understand past generations who held contradictions true, consider this example:
B2: This four thousand year old inscription says that its author wrote and did not write it.
Now, despite the fact that dialecticians assure us that reality is contradictory, not even they would attempt to understand B2 literally. This is not because it would be especially difficult for them to do so, but that any claim to the contrary would undermine the meaning of the word "literally".
But, even supposing a few die-hard (and rather confused) dialecticians could be found who attempted to do this, they would find it impossible to explain to anyone else in literal terms what sense they made of B2 (other than by trying to disambiguate it in ways similar to those outlined above, for instance).
As noted earlier, trite examples like these have been deliberately chosen to illustrate a point that is all too easily missed: when faced with the paradoxical things people sometimes say, we automatically try to disambiguate their words and their actions; we adopt what Donald Davidson once called the "principle of charity" when attempting to grasp their meaning. [Davidson (2001).] Hence, when confronted with someone who asserted an apparent contradiction we would normally employ this policy (trivial examples excepted, of course). This does not mean that the result of this exercise would be a distortion of what was said; it is rather that we would not be able to understand them if we did not do this, and we would be unable to make sense of anyone who did not do this -- or who rejected this principle in practice.
In any case, DM-rejectionists would be hard-pressed to explain to anyone else what they themselves took the sense of a true contradiction to be (that is, not without using another Nixon card), as the rest of this site aims to show. [And that comment covers the 'dialectically-motivated' responses of any who think to question the above assertions.]
Clearly, this does not mean that we shouldn't exercise some degree of sensitivity toward other belief systems (past or present), but we may only do so in terms of current linguistic protocols. If confronted with what appeared to be weird and/or paradoxical beliefs, we would not be able to translate or interpret them literally and claim we understood them. And, if anyone claimed that they could do this, it would automatically throw into doubt the validity of their translation (unless the meaning of the word "translate" itself had changed) -- always supposing, of course, that they hadn't merely transliterated the relevant inscriptions/writings instead.
However, if what had been translated were still held to be literally true but paradoxical, then whatever else we could make of the translated passage, we would have to abandon all talk of its literal truth. Either that, or, once again, we would have to understand the word "literal" non-literally!
[This topic is still under intense debate; on his see Creary and Read (2000), especially Chapter 12: Cerbone (2000). See also Conant (1991), and Forster (1998).]
Hence, it is reasonable to conclude that contradictions do not depict reality in any meaningful sense.
Nevertheless, it is important to note that this is not being asserted because I personally think that reality contains no contradictions, or because I have concluded that the world either is or is not as these allegedly 'true contradictions' might seem to depict it -- or even because contradictions are always false (which is the classical view). To argue thus would be to fall into the same trap that ensnares DM-theorists, and would amount to the derivation of an opposite a priori thesis about reality from an alternative linguistic convention, which I might have found more acceptable.
On the contrary, contradictions fail to depict the world not because they are false, but because they are not depictions to begin with. They represent the disintegration of description, since they violate materially-grounded linguistic rules we already have for picturing reality. [On this, see Essay Twelve Part One.]
Finally, it could be argued that the above comments beg the question since dialecticians do not query the general application of principles drawn from FL, such as the LOC; they merely point to their limitations when it comes to accounting for change.
Now, that particular claim will be put under considerable pressure in this Essay (and in others), where it will be shown that it is dialecticians who cannot account for motion, and hence change.
[General logical issues are discussed in Essay Four, and other related topics (such as the "interpenetration of opposites" and change through "internal contradiction") are reviewed in Essays Seven and Eight, Parts One and Two. Those who feel that the above comments do not in fact address 'dialectical contradictions' should read this, this and this.]
2. Engels was openly borrowing from Hegel:
"If, now, the first determinations of reflection, namely, identity, difference and opposition, have been put in the form of a law, still more should the determination into which they pass as their truth, namely, contradiction, be grasped and enunciated as a law: everything is inherently contradictory, and in the sense that this law in contrast to the others expresses rather the truth and the essential nature of things. The contradiction which makes its appearance in opposition, is only the developed nothing that is contained in identity and that appears in the expression that the law of identity says nothing. This negation further determines itself into difference and opposition, which now is the posited contradiction.
"But it is one of the fundamental prejudices of logic as hitherto understood and of ordinary thinking that contradiction is not so characteristically essential and immanent a determination as identity; but in fact, if it were a question of grading the two determinations and they had to be kept separate, then contradiction would have to be taken as the profounder determination and more characteristic of essence. For as against contradiction, identity is merely the determination of the simple immediate, of dead being; but contradiction is the root of all movement and vitality; it is only in so far as something has a contradiction within it that it moves, has an urge and activity.
"In the first place, contradiction is usually kept aloof from things, from the sphere of being and of truth generally; it is asserted that there is nothing that is contradictory. Secondly, it is shifted into subjective reflection by which it is first posited in the process of relating and comparing. But even in this reflection, it does not really exist, for it is said that the contradictory cannot be imagined or thought. Whether it occurs in actual things or in reflective thinking, it ranks in general as a contingency, a kind of abnormality and a passing paroxysm or sickness....
"External, sensuous movement itself is contradiction's immediate existence. Something moves, not because at one moment it is here and at another there, but because at one and the same moment it is here and not here, because in this 'here', it at once is and is not. The ancient dialecticians must be granted the contradictions that they pointed out in motion; but it does not follow that therefore there is no motion, but on the contrary, that motion is existent contradiction itself.
"If the contradiction in motion, instinctive urge, and the like, is masked for ordinary thinking, in the simplicity of these determinations, contradiction is, on the other hand, immediately represented in the determinations of relationship. The most trivial examples of above and below, right and left, father and son, and so on ad infinitum, all contain opposition in each term. That is above, which is not below; 'above' is specifically just this, not to be 'below', and only is, in so far as there is a 'below'; and conversely, each determination implies its opposite. Father is the other of son, and the son the other of father, and each only is as this other of the other; and at the same time, the one determination only is, in relation to the other; their being is a single subsistence. The father also has an existence of his own apart from the son-relationship; but then he is not father but simply man; just as above and below, right and left, are each also a reflection-into-self and are something apart from their relationship, but then only places in general. Opposites, therefore, contain contradiction in so far as they are, in the same respect, negatively related to one another or sublate each other and are indifferent to one another. Ordinary thinking when it passes over to the moment of the indifference of the determinations, forgets their negative unity and so retains them merely as 'differents' in general, in which determination right is no longer right, nor left left, etc. But since it has, in fact, right and left before it, these determinations are before it as self-negating, the one being in the other, and each in this unity being not self-negating but indifferently for itself.
"Opposites, therefore, contain contradiction in so far as they are, in the same respect, negatively related to one another. Ordinary thinking when it passes over to the moment of the indifference of the determinations, forgets their negative unity and so retains them merely as 'differents' in general, in which determination right is no longer right, nor left left, etc. But since it has in fact right and left before it, these determinations are before it as self-negating, the one being in the other, and each in this unity being not self-negating but indifferently for itself." [Hegel (1999), pp.439-41; available here, §955-§960. Bold emphasis alone added.]
Several comments on the above (as they were interpreted by a particular DM-theorist) were made here, and a few more will be posted in Essay Twelve, a later date.
3. An alternative translation -- which appears in Volume 25 of Marx and Engels Collected Works (MECW) -- renders the last sentence as follows:
"And the continuous origination and simultaneous solution of this contradiction is precisely what motion is." [MECW, Volume 25, p.111. This can be found here.]
This version manages to defuse some of the criticisms outlined in the main body of this Essay, but not all. Who, for instance, "solves" these contradictions, and how do they do it? More pointedly, how do they manage to do this quite so quickly (i.e., simultaneously with the "origination" of each new contradiction)?
Moreover, this passage introduces several difficulties of its own, for it leaves it entirely mysterious from where contradictions originate. Indeed, it appears to promote contradictions above motion; they cause it, not it them.
Naturally, in a system derived from AIDS, where reality is just the development of Mind, the ability of contradictions to cause change, or to make things move, seems to make some sort of crazy sense. Apart from that, it doesn't.
[AIDS = Absolute Idealism; LIE = Linguistic Idealism.]
4. On this, see Note 3, above.
However, as we have seen in other Essays posted at this site, dialecticians regularly make this mistake, imagining that they are talking about the world when in fact they are indirectly drawing attention to their own idiosyncratic use of words. This is, of course, part of the reason why DM is here classified as a form of LIE. [For more on that, see Essay Twelve Part One.]
The fact that DM falls apart so easily when these linguistic confusions are exposed merely confirms the accuracy of the above observation.
5. However, as usual, the picture is far more complicated than this opening salvo might suggest. Later on in this Essay, examples will be given where both stationary and moving objects occupy two places at once. It is reasonably clear that Engels did not have these in mind when he spoke so boldly of the contradictory nature of motion. On the other hand, if he had done so, his whole 'analysis' would have been completely undermined.
5a. However, and independently of the comments in the main body of this Essay, if instants have no duration then -- according to Trotsky -- they do not exist since they are abstractions. But, what they are abstracted from Trotsky forgot to say. How does one abstract an instant? Insubstantial spectres like these cannot be what all temporal moments have in common: non-existent duration-less 'points'. On this, see Note 6.
6. Abstraction is dealt with in Essay Three Parts One and Two.
Instants in time share nothing with our experience of time, and so cannot be derived from it by a process of abstraction.
Of course, it could be argued that scientists and philosophers extrapolate from finite moments in time (i.e., from time intervals) to such instants. Hence, as such, such instants are mental/Ideal constructs, capable of being mapped onto the Real Numbers. This line of argument is neutralised here (and in general in the Essays mentioned above).
7. The idea here might run as follows: if knowledge results from the reflection of the complexities of the world in the human mind (mediated by practical activity) -- which are correct only "within certain limits" -- then even a provisionally correct theory must faithfully represent the contradictory nature of reality. In this limited sense, human/social categories would then be relatively adequate to the world (if they are correct, and have been tested in practice), but they would not have been projected onto it. This interpretation might then allow DM-theorists to draw substantive conclusions about the world from a consideration, or application of the concepts and categories found in thought (howsoever they got there) -- but only if these are continually checked against experience. Even so, such theories would still only approach absolute truth asymptotically. Indeed, some might want to call such concepts and categories "presuppositions".
[If the Kantian/Hegelian route is taken by dialecticians, whereby the concepts and categories of thought are what they are because of the nature of cognition/'dialectical reason' itself, then they ought to having imposed their ideas on nature, contrary to what they swore they would never do. To date, only HCDs seem prepared to take this line.]
Claims like this are examined in greater detail in several Essays at this site (for example here and here). However, in advance of that it is worth highlighting several serious difficulties faced by this approach to knowledge:
(1) Elsewhere, it will be shown that this way of looking at language forms part of what I call the RRT. The latter is a theory that projects 'knowledge' onto nature under the pretence that language/'cognition' is merely reflecting what is already there.
[RRT = Reverse Reflection Theory.]
Because of their acceptance of this theory, dialecticians seem to believe that they are in a position to state (in advance of experience) what the world must be like before anyone knows what it is like. This involves them in being able to specify what certain concepts/words correspond with in reality based solely on the mere presence of certain logico-linguistic features in the expression of such thoughts. [Numerous examples were given in Essay Two of the propensity all dialecticians have for asserting dogmatic and a priori theses (about fundamental aspects of reality, true for all of space and time). A detailed analysis of the origin of core DM-theses can also be found here.]
Of course, this claim itself (that language reflects the world) cannot have been derived from the world, nor from language. [Or, if it can, we have yet to see the proof.] In that case this theory, which claims that knowledge is a complex reflection of reality, must itself have been imposed on nature (once more, contrary to the claim that this is never done).
Nevertheless, an additional idea seems to be that subsequent reference to experience, observation and practice are necessary if we are to weed out items of supposed knowledge which are not actually found in nature, or which do not reflect 'objective' reality. [Otherwise, of course, the appeal to empirical checks to test which linguistic expressions are genuinely represented in nature by real material processes would be an empty gesture.] In fact, because it is impossible to specify ahead of time which parts of this (now supposedly legitimate) a priori picture of the world might never be so expunged, all knowledge is provisional. Or so it could be argued.
Despite this, DM-theorists still seek to inform us what the fundamental aspects of reality are, for all of time and space. Thus they tell us that everything in reality is contradictory and constantly changing, that all objects and processes are powered by the interplay between interpenetrated 'internal opposites', that the world is a single interconnected Totality composed of "mediated" parts/wholes, governed by the laws of dialectics and susceptible to 'rational' explanation. In addition, we are informed that each part is dependent on every other part, and that the nature of the entire ensemble is determined by the complex interconnections between such parts, and reciprocally with the whole, etc., etc.
But, the only evidence for such universal theses is a series of inappropriate extrapolations from a few highly tortured linguistic expressions -- justified by an appeal to some rather shaky but nonetheless badly garbled Stone Age Logic --, substantiated by a few highly clichéd and contentious examples.
Unfortunately for its supporters, this means that if a list were to be made of theories that were, or could be, viable candidates for explaining nature to us, DM would, at best, be right at the bottom.
However, if reality were reflected in thought, and if aspects of it appeared to be embodied in our language about it, and if this were held to justify such inferences from words to the world, it would be impossible to account for falsehood. If thought is a reflection of the world, then it would seem that it could never be incorrect -- in the same way that a mirror image is never wrong.
Of course, it could be argued that a sophisticated application of the RTK [not to be confused with the RRT], with its emphasis on the 'partial' or 'relative' status of truth, on practice and the "one-sided" nature of abstractions (etc., etc.), might be able to neutralise these difficulties. After all, it could be pointed out, mirrors can and do distort reality (at least with respect to left-right symmetry, and human morphology, etc.); but few are taken in by this. And it could be added here that when other criteria are incorporated into the mix (such as increased consistency and greater explanatory power), defective theories could be weeded out as part of our endeavour to arrive at a more accurate account of the world and how to change it.
[RTK = Reflection Theory of Knowledge.]
Maybe so, but mirrors cannot reflect what is not there. Hence, if language and thought were indeed mirrors -- distorting or not -- we would have to conclude that everything expressible in language must exist in reality. Mirrors cannot conjure into existence objects and processes that are not there. But, followers of Meinong excepted, who in their left mind is prepared to admit that whatever language contains must exist/subsist somewhere? Who wants to allow for the existence of, say, Harpies and Gorgons -- even in a distorted form -- simply because we have words for them? On the other hand, if such 'entities' are so easily admitted into being (by merely naming them), why bother looking for evidence in support? Indeed, if this were so, any search that went beyond leafing through all dictionaries, encyclopaedias of mythology and textbooks of grammar in the libraries of the world would appear to be superfluous. In that case, Science would become a sub-branch either of lexicography or of hermeneutics.
Naturally, it could be argued that even mythical beasts and fictional characters are composed of 'images' that have been derived from experience. Where human judgment goes wrong is in knitting some of these together in fanciful ways. For example, a Harpy is made out of the combination of human and animal 'images'. However, experience tells us that these beasts do not exist. Hence, we can imagine all sorts of 'possible beasts', only some of which actually inhabit this universe (as far as we know). This argument will be tackled in Essay Three Part Five, and Essay Thirteen Part One (here). Suffice it to say here that the claim under review here is that it is words, not 'images', that reflect reality. In that case, this metaphor is committed to the view that if we have words for something, it must exist.
Of course, anyone committed to such a belief would have problems pointing out the ontological equivalent of prepositions, conjunctions, adverbs, the definite article, and so on. Putting that to one side, it might be difficult, too, for anyone who accepted this view of language to explain how words for non-existent beings (such as Harpies and Gorgons), if based on individualised images in separate heads, can be harmonised with a social interpretation of language. [That topic will be addressed in an Additional Essay to be published later in 2008.]
[There is a variant of this theme, but based on 'images' once more, in MEC. Lenin's argument is demolished in Essay Thirteen Part One.]
[MEC = Materialism and Empirio-Criticism, i.e., Lenin (1972).]
However, the specific point under consideration here was in fact the following:
That the aforementioned interpretation might then allow DM-theorists to draw substantive conclusions about the world from a consideration, or application of the concepts and categories found in thought (howsoever they got there) -- but only if these are continually checked against experience.
Now, we have already established that DM-theorists go way beyond such seemingly modest aims, claiming to know what the fundamental features of reality are -- which are valid for all of space and time -- and which have been derived solely from the alleged meanings of certain words.
Some might think to bring in ideology here, but that cannot affect the above. Ideology supposedly 'inverts' things; but even if this were an apt metaphor, on this view, it cannot create (by inversion or reflection) what is not there. I will say more about this in Essay Three Parts Four and Five. Until then, see here.
The reference to the hermeneutics required here to make this theory work was deliberate, in view of the origin of this word (it having been derived from Hermes, the interpreter of the Gods), and because of the many accusations made in these Essays that DM is just a modern form of Hermeticism.
This is linked to another ancient idea: that Philosophy and Theology were invented by Hermes (or in Egypt, by 'his' equivalent, Thoth -- from whom the Greeks derived their word for God, "Theos", and we our word "theory"). Of course, Philosophy was invented by ruling-class theorists, but it was part of the ideological package to trace it back to the 'gods'. [Why this is so will be explored in Essay Twelve Parts Two and Three (summary here).]
This approach to knowledge -- which has, in one form or another, dominated much of Western thought since -- sought to connect arcane philosophical theory with the divine, or a priori, structure of reality (i.e., with 'Being' itself).
It is this observation that partially motivates my claim that traditional thought represents, not the material world, but an ancient ruling-class view of an ideal world. Hence, we are told by ruling-class theorists that this hidden world, accessible to thought alone, underlies appearances, lending reality its 'essence'. That world is thus immaterial.
On this view, it is language that tells us what this hidden world must be like (for we have no other access to it), In that case, this hidden world is a reflection of language --, not the other way round. [As noted earlier, I later call this the RRT. More about that in Essay Twelve Part Four.]
In each Mode of Production, in diverse class societies, different versions of the general belief in the divine/a priori structure of reality have been used by traditional thinkers to rationalise the power and authority of the state. It is precisely here, where dialecticians accept significant parts of this ancient Hermetic world-view, that ruling ideas succeed in ruling militant minds.
[This topic is spelt out in more detail in Essay Fourteen Part One (summary here).]
Naturally, the DM-account of the origin of mythical beings is more sophisticated than previous paragraphs might suggest. But, a distorted view of reality, howsoever it is produced (be it from alienation, "one-sided" theory formation, from ideology, or indeed from the process of abstraction itself) -- whether it results in an upside down image, a blurred one, or even one wearing a pink tutu -- it matters not; it is still a view of reality (given the applicability of this reflection metaphor, sophisticated version or otherwise), and in this case, an Ideal view. A mirror cannot invent. In that case, this metaphor implies that things like dragons, fairies, ghosts and hobgoblins -- not to mention Atlantis, heaven, hell and Nowhere -- must exist somewhere, in some form, in Reality, just because we have the words for them.
On the other hand, if these 'entities' do not actually exist, then the mirror metaphor is defective and should be abandoned.
[DL = Dialectical Logic.]
Of course, it could be objected that raising superficial objections based on such contingent features of reality entirely misses the point: dialecticians are interested in the essential nature of reality, and these are reflected in DL.
Nevertheless, more or less the same objections can be aimed at the principles supposedly encapsulated in DL. But worse: as we have seen (here, here, here and here), DL is far too confused to have 'captured' anything in thought, distorted or not.
Or, to put the same point in reverse: if the essential nature of reality is reflected in DL, then reality must be a madhouse.
Furthermore, since these general/'essential' features of reality are often highly abstract (or are expressed in suitably abstract language), the contention advanced here (that these are all misconstrued rules of grammar and are thus not truths at all) has more than just a little prima facie plausibility going for it.
[Incidentally, the above comments also answer the objection that the a priori concepts and categories of DL capture the form but not the content of reality.
Again, since this topic is examined in more detail in Essay Three Part One and Essay Twelve, no more will be said about it here.]
(2) The phrases "relative adequacy" and "relative truth" are themselves hopelessly unclear. Terms such as these are obviously linked to the DM-thesis that human knowledge "asymptotically" approaches 'absolute truth' over time. However, if these words mean anything at all, they would in fact be inimical to DM. This is because they imply that at any point in history, humanity must be infinitely ignorant of everything, no matter how "relatively" complete our knowledge of anything might seem to be at any given point in history. On this basis, far from being "relatively adequate", or even "relatively true", our ideas would be infinitely incorrect. This is because the difference between a finite and an infinite body of knowledge is itself infinite.
A relevant passage from Engels comes to mind again (which was commented upon in Essay Two):
"The identity of thinking and being, to use Hegelian language, everywhere coincides with your example of the circle and the polygon. Or the two of them, the concept of a thing and its reality, run side by side like two asymptotes, always approaching each other but never meeting. This difference between the two is the very difference which prevents the concept from being directly and immediately reality and reality from being immediately its own concept. Because a concept has the essential nature of the concept and does not therefore prima facie directly coincide with reality, from which it had to be abstracted in the first place, it is nevertheless more than a fiction, unless you declare that all the results of thought are fictions because reality corresponds to them only very circuitously, and even then approaching it only asymptotically…. In other words, the unity of concept and phenomenon manifests itself as an essentially infinite process, and that is what it is, in this case as in all others." [Engels to Schmidt (12/03/1895), in Marx and Engels (1975), pp.457-58.]
First of all Engels failed to say how he knew it was true that knowledge is convergent. Of course, if what Engels said were itself true, it would then be infinitely wrong. This is because, when asserted, that claim must be infinitely far from the 'truth' (according to its own content). And, manifestly, the fact that knowledge is an infinitary process cannot be confirmed in practice (or in any other way).
Secondly, Engels failed to prove that there was such a limit for knowledge to approach in the required manner (in fact, he did not even so much as attempt such a proof; and as far as can be ascertained no dialectician has bothered to plug this gap since). In that case, Engels's 'mathematical metaphor' is doubly inappropriate: if there is no limit, human knowledge must be divergent. And if that is so, then at any point in human history, our knowledge must be infinitely far from 'Epistemological Valhalla' -- which still hasn't been shown to exist. On this view, given Engels's inapt metaphor, humanity will always be infinitely ignorant of anything and everything.
Kant's Noumenon by any other name?
[On convergence, see here.]
Of course, it could be objected that certain iterative functions in mathematics might yield infinite sequences; and yet that does not mean that the distance between any intermediate value given by a partial sum of that function and the point toward which it is converging is itself infinite. For example, the sequence: 1 + 1/2 + 1/4 + 1/8 +...+ 1/2n-1 converges on 2, but none of the rational numbers (formed from partial sums of this series) is "infinitely far" from 2.
This is not strictly so, but even if it were the case, the above would have been an effective response had Engels bothered to prove that the limit he claims exists (implied by the asymptote metaphor) actually does exist; but since he didn't, it isn't.
The only way this sceptical conclusion can be avoided would be to deny that 'absolute knowledge' is in any way infinitary. Clearly, that would place a condition on the object of knowledge before we knew what it was! Of course, it would also mean that several passages from the DM-classics (quoted elsewhere on this site) would need to be revised -- or ignored --, along with the above 'asymptote' metaphor, since they manifestly imply such an infinitary task. Indeed, they go further -- they say it is infinite.
8. As noted above, in Hegel's system, the existence of 'real contradictions' made some sort of crazy sense. If reality is just "thought" writ large, then linguistic categories may be projected ("foisted") onto nature quite legitimately. But, as we will see in Essay Twelve, that doctrine is itself a throwback to ancient Greek ideas, where conflicts in material reality were at first pictured in theological terms (i.e., it was thought that nature is, for example, the playground of evil and/or benevolent agents/'gods'), then later in an ethical, conceptual or a purely abstract linguistic form.
[The reason why this view of the world was conducive to wider ruling-class interests will also be outlined in Essay Twelve (summary here) -- but it was hinted at in Note 7.]
8a. Of course, it could be argued that since everything in the universe is in motion, the question, "Which came first, motion or contradictions?" does not arise. However, as we will see later, things are not quite that straight-forward.
9. Quotations from Lenin (and others) concerning 'internal contradictions', and self-development (etc.) were given in Essay Two; cf., Rees (1998), p.7. This topic is examined in much more detail in Essay Eight, Parts One and Two.
9a. Although Woods and Grant came very close to asserting this:
"So fundamental is this idea to dialectics that
Marx and Engels considered motion to be the most basic characteristic of
matter.... [Referring to a quote from Aristotle:] [T]his is not the
mechanical conception of motion as something imparted to an inert mass by an
external 'force' but an entirely different notion of matter as self-moving....
"The essential point of dialectical thought is not that it is based on the idea
of change and motion but that it views motion and change as phenomena based on
contradiction.... Contradiction is an essential feature of all being. It lies at
the heart of matter itself. It is the source of all motion, change, life and
development. The dialectical law which expresses this idea is the unity and
interpenetration of opposites....
"The universal phenomena of the unity of opposites is, in reality, the
motor-force of all motion and development in nature. It is the reason why it is
not necessary to introduce the concept of external impulse to explain movement
and change -- the fundamental weakness of all mechanistic theories. Movement,
which itself involves a contradiction, is only possible as a result of the
conflicting tendencies and inner tensions which lie at the heart of all forms of
matter....
"...Matter is self-moving and self-organising." [Woods and Grant (1995),
pp.43-45, 47, 68, 72. Bold emphases added.]
The long quotation from Hegel, given above, shows where these two discovered such odd ideas -- they certainly did not obtain them from scientists. [On this, see Essay Eight Part One.]
10. In fact, Engels himself torpedoed the idea that forces can be viewed as contradictions when he claimed that:
"All motion is bound up with some change of place…. The whole of nature accessible to us forms a system, an interconnected totality of bodies…. [These] react one on another, and it is precisely this mutual reaction that constitutes motion…. When two bodies act on each other…they either attract each other or they repel each other…in short, the old polar opposites of attraction and repulsion…. It is expressly to be noted that attraction and repulsion are not regarded here as so-called 'forces', but as simple forms of motion." [Engels (1954), pp.70-71. Bold emphasis added.]
As will be argued in detail in Essay Eight Part Two, this observation pulls the rug from under anyone who wants to maintain that forces can be used to model contradictions.
Anyway, and despite the above, this entire account of motion does no real work; the explanation of movement is not advanced one nanometre by re-describing it as "contradictory". The supposed contradiction (that is, the one relating to where a body is and is not, and when -- but, not that which relates to the allegedly contradictory nature of forces) neither initiates nor sustains movement. Worse still, the appeal to 'contradictions' obscures the clear explanations we already have in Physics.
Furthermore, if Absolute Space is left out of the picture, the precise nature of motion clearly depends on the inertial frame chosen. It does not depend on the simultaneous non-occupancy and occupancy of point locations. This can be seen from the fact that given a particular frame of reference, a body could be at rest relative to that frame, but with respect to another such frame it could be in motion. Hence, motion is inertial-frame sensitive, not 'vaguely-located-point-occupancy and non-occupancy' sensitive.
It would seem, therefore, that unless DM-theorists believe in Absolute Space, their insistence that motion is contradictory (because of their quirky view of point-occupancy) is unsustainable. Relative notions of space imply that the contradictory behaviour of moving bodies (if such it be) is a consequence of change of reference frame: in that case, bodies would be in motion -- or they would be stationary -- depending on which inertial frame was selected; but they would not be either motionless or moving because of the alleged contradictions inherent in motion itself. In which case, the contradictory nature of motion could not be an 'objective' feature of reality if it promptly disappeared as soon as a different inertial frame was selected.
It could be objected here that just because motion apparently stops and starts according to the choice of reference frame does not mean that its contradictory nature is not objective. No more would we conclude that, say, the boiling point of water was not really 100ºC if it was then measured in degrees Fahrenheit or in degrees Kelvin.
To be sure; but unfortunately, if that constitutes an effective reply to the points made above, it would at the same time prove fatal to the DM-view of motion. This is because it openly concedes that scientific knowledge is conventional.
Again, exception could be taken to that response. It could be argued that the fact that the temperature of a body can be read on two or more different conventionalised scales does not imply that temperature itself (or whatever it supervenes upon) is not an objective feature of the world. The same goes for the depiction of motion in different reference frames.
However, these two cases are not at all the same: no matter what system we use, a body has some temperature or other (with the latter explicated perhaps in terms of energetics). This is not so with choice of inertial frame (unless, of course, we count a zero velocity as a velocity by default -- but even then the alleged 'contradiction' would still vanish).
In one particular frame, a body could be in motion and (assuming DM is correct) appear to be 'objectively' contradictory. In another frame, and at the same time, that body could be stationary and objectively non-'contradictory' (in Engels's sense), too. Hence, at the same time, a body could be moving and not moving, 'contradictory' and 'not contradictory'. Which of these options is finally settled upon will be a consequence, not of nature, but of choice of reference frame. Since reference frames are not 'objective' features of the world (they are human inventions!), and since the 'contradictory' nature of motion is sensitive to choice of frame, the conclusion seems inescapable: the 'contradictory' nature of motion is not an 'objective' feature of reality either.
It could be argued that the above would mean that motion is not an objective feature of reality if it disappears in the above fashion when a different reference frame is chosen. This is not so, for if an object is moving with reference to one frame, but is stationary with respect to a second frame, then other objects will be moving in a different way with respect to that frame. So, while the alleged contradiction would disappear, motion in the wider system would not. For example, if the first reference frame is a volume interval containing only the Moon, and is stationary, the Earth will be in motion relative to that frame while the Moon is stationary. Swap the reference frame to a volume interval that contains only the Earth, mutatis mutandis, and the Moon will now be moving relative to a stationary Earth.
[Sure, the Earth will still be rotating, but all we have to do is make the reference frame any finite area on the Earth's surface, and the Earth would stop rotating relative to this new frame.]
This means that motion (at least as it is viewed in modern Physics) is a conventionalised bi-product of the choice of inertial frame. Therefore, if DM-theorists are to rescue the 'objectivity' of their theory from the trashcan of 'subjectivity', it looks like they might have to postulate the existence of Absolute Space. Otherwise, they would have to concede that the 'contradictions' they attribute to motion are in fact artefacts of the choice of reference frame, and not something inherent in moving bodies.
It is not easy to see a way out of this DM-cul-de-sac, or at least one that makes no further concessions to conventionalism -- or, alternatively, one that makes unwelcome concessions to Space/Time Absolutism.
This partly explains why (a few generations ago) in Stalinist Russia, philosophers and scientists found it difficult to square Einstein's theory with DM, and why some rejected it. If revolutionaries are still unaware of these problems, STDs certainly weren't. Cf., Graham (1971), pp.111-38; see also Joravsky (1961), Krementsov (1997), Vucinich (1980, 2001), and Wetter (1958).
[STD = Stalinist Dialectician.]
[Since writing the above, I have read Mason (2007), which points out that Woods and Grant (in Woods and Grant (1995)) appear to accept the reality of Absolute Space.]
Once more, it could be objected that even if the above were correct, once moving (in a suitable inertial frame), an object must be doing something contradictory.
The reply to that overall objection occupies the rest of this Essay.
11. This is not meant to single Engels out here for special attention; it is equally impossible to determine what, if anything, Zeno, Hegel or Lenin were trying to tell us about motion.
However, if it is held that systems of supposedly contradictory forces are responsible for the contradictory nature of motion, then it would be difficult to account for un-accelerated motion. Clearly, this sort of change takes place where no net forces are operating. That being so, the exact source of the alleged contradictions here would be even more obscure.
Of course, one consequence of DM seems to be that there might be no un-accelerated motion in nature (in that the opposite supposition would involve a body possessing identically the same velocity from moment to moment), which would, of course, amount to a fatal concession to the LOI. Nevertheless, DM-induced conundrums like this will not, I take it, worry physical scientists too much, or for too long.
[LOI = Law of Identity.]
And all this is, of course, quite apart from the fact that such a DM-view of velocity would have to be imposed on nature.
Nevertheless, if a suitable frame of reference is chosen, any body can be said to have zero velocity and acceleration for about as long as it takes hard-core DM-fans to abandon their criticisms of the LOI.
Hence, for any body b moving at v kmph relative to the centre of mass of the Galaxy, say, let a reference frame for it move at v kmph with respect to that centre of mass. In that case, b will have zero velocity with respect to that frame. The only response a DM-acolyte could make to this would seem to have to involve a reference to 'abstractions' (i.e., in that the foregoing involves the use of "abstract identity"). That last ditch DM-defence is also examined, and demolished, in Essay Six.
11a. Hegel's 'analysis' of Identity is partially covered here, and indirectly in Essay Six; but will be examined more fully in Essay Twelve.
12. A detailed discussion of these aspects of Zeno's analysis of motion can be found in Angel (2002). Also, see Note 24, below. Incidentally, this way of looking at the Reals is outlined in Newton-Smith (1980).
12a. But Trotsky was, of course, not the only one to do this. Engels also failed to consider the possibility that an object could be in two times for the same place -- i.e., in and not in one instant, at that place. But if time advances while bodies move (or indeed stay still), and everything is contradictory, then this must surely be possible. And if that is so, what is to stop us saying that a moving body occupies the first place in one of these odd instants, and the next place in the second overlapping instant -- locating the alleged contradiction in time, and not in space/motion (or, perhaps, even eliminating both)?
Of course, it could be pointed out that if a body is in two times for the same place then it must be stationary.
However, in order to neutralise this objection it might be wise to examine the subtle differences that exist between these two sentences (assuming there are any):
B1: Body b is in two different times for the same place.
B2: Body b is in the same place at two different times.
I do not propose to do that here, but it is worth noting that neither of these imply that the said object is stationary, since that object could still be moving and could return to the original location at a later time --, hence it could be in the same place at two different times.
Moreover, it is worth recalling that evidence cannot distinguish between these two a priori 'possibilities'.
13. This is taken to be an important DM-assumption since it is the only way that Engels's claims about the contradictory nature of motion can be defended, as is argued in depth in the main body of this Essay.
14. It is worth pointing out that L13 does not say that b is both at p1 and not at p1 at t. What it does say is:
L13: For some b, for just one instant t, for three places p1, p2 and p3, b is at p1 at t, but not at p2 at t, and b is at p3 at t, where p2 and p3 are proper parts of p1.
Hence, a finer-grained analysis of position allows for the fact that, while at the macro-level an object might be locatable in one place (say, p1) at one 'instant', at the micro-level it could still be in the same place (i.e., in p1) while also being in one or more other sub-locations (say, p3) at the same time. In other words, b could be in p1, and while not in all of p1 (i.e., not in, say, p2, which is a proper part of p1), it would still be in p1 (in this case, in, say, p3, which is also a proper part of p1).
Hence, b could be in and not in every part of p1 at t, and either be in motion or stationary at that time, meaning that b would be in two places at once: p1 and p3. So, if the location of bodies can be given in finer-grained detail -- even if this manoeuvre is inconsistently disallowed of time -- a body could still be in one place and not in it, and in two places at once, while being stationary, with no contradiction implied.
[This is the simplest of these cases; the reader is left to determine more complicated ones for herself. The complex nature of ordinary and/or technical language allows for the depiction both of motion and location in ways undreamt of by Zeno, Heraclitus, Hegel or even Engels. On this, see below and in the main body of this Essay.]
15. The following is an example of this type of motion partially expressed in vector algebra:
V1: Let B be a body moving in ℝ3 with respect to a given reference frame.
V2: Let B be at/in both (X1, Y1, Z1) and (X2, Y2, Z2) at t1.
V3: Let B be a complex composed of n segments, b1 to bn, arranged in an ordered n-tuple <b1…bn>.
V4: Let the position vectors of the centre of mass of b1 and bn be u and v, respectively.
V5: Let v – u = w.
V6: Let the distance between (X1, Y1, Z1) and (X2, Y2, Z2) be mod d, (where d is the vector joining (X1, Y1, Z1) to (X2, Y2, Z2)).
V7: Let mod w > mod d.
V8: Let the direction vector parallel to d be lw (where l is a Real Number).
V9: Let B be moving at t1 with velocity vector s, such that s = mw (where m is a Real Number).
V10: In that case, part of B is at (X1, Y1, Z1), and another part of B is at (X2, Y2, Z2), but other parts of B are at neither of these two points, all at t1.
V11: So, B is moving parallel (in either sense) to the line joining these two points, also at t1.
V12: Or, alternatively, B is stationary (with respect to some inertial frame); i.e., if s = 0 (or even if m = 0), all the above considerations would still apply.
Here we have a more technical version of the ambiguous case mentioned in the text (concerning a boat entering port, etc.). Translated, the above could apply to this scenario:
Ports are generally bigger than boats, and are composed of countless 'parts' (land, water, buildings, shorelines, etc.). A boat can, therefore, be in port and be located at several points within that port, and yet not be located at every point in that port (with no implication that it is both in and not in all of that port, even though it is both in and not in several parts of it -- for example, it could be in the dry dock but not in the harbourmaster's office), all at the same time. And these could all be true independently of whether the boat is moving or is stationary with respect to a suitable inertial frame.
16. This observation would remain true even if such spatial location sentences employed co-ordinates (expressed as real number triplets). As we shall see, technical specifications are not without their own ambiguities.
Another example of one such is the following: in <x1, y1, z1> and <x1, y1, z1>, each variable letter is in the same place (in its respective ordered pair, namely, first, second or third) while also being in a different place (on the page/screen), and yet not only are both in the same place, they are also in different places while they are in the same place (i.e., they are on your screen -- and, clearly, they are all in the universe), all at the same time!
[Now, try saying any of that in Hegel-speak!]
To paraphrase Wittgenstein: the conventions of ordinary material language are exceedingly complex. Dialecticians ignore them at their own metaphysical peril.
17. Some might think that this is because ordinary language is defective (in certain respects); cf., TAR pp.45-50.
It is important to note that the view that ordinary language is defective is not shared by the present author; the opposite is in fact the case. However, this topic will be addressed in detail elsewhere on this site. On this, see the lengthy discussion here.
18. Although, at this point, because we have reached linguistic bedrock (i.e., in order to proceed further we should have to revise fundamental linguistic conventions by promulgating non-symmetrical stipulations about space and time), this latest "must" is in effect the argumentative equivalent of thumping the table, and nothing more.
18a. This 'assumption' sometimes masquerades as part of a claim that motion is an 'inherent' property of bodies in motion –- that certainly appears to be Graham Priest's interpretation of Hegel's views in this area. [Priest (2006), p.175ff.]
Priest's analysis will be considered here at a later date, as will that of Marquit (1978, 1982), and the views of other dialecticians.
18b. L15 is taken to mean:
L15a: If an object is wholly located at a point it must be at rest at that point.
19. In fact, the analogy with moving pictures creates its own problems for DM since even a freeze-frame (or still) picture contains some blurring of the depicted motion (no matter how fast the shutter speed). This is because such pictures actually depict intervals, not instants, in time. [However, that minor niggle can be overcome somewhat by considering flip cards and cartoons. On this, check out the moving horse here.]
If anything, this analogy is more closely in tune with a view of change pictured by certain uses of ordinary language, which is that motion takes place in time and has nothing to do with the sorts of abstract 'metaphysical instants/moments' that Engels or Trotsky (and other dialecticians) were fixated upon. In that case, what little evidence there is, is consistent with the picture adopted here.
To be sure, this 'stop-go' view of motion would present problems for certain fundamental physical laws (namely the conservation of momentum); but if this is indeed how nature behaves, they will need to be revised, anyway. Other significant advances in science have certainly been predicated on overturning what at one time seemed to be fundamental laws. One thing we cannot do is lay down a priori caveats that nature has to obey --, unless, of course, we wish to impersonate Idealists.
20. What these are will be left somewhat vague for the time being, but they have something to do with the sorts of ambiguities discussed in later sections of this Essay.
Nevertheless, in the text, the following are taken to be contradictories:
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.
Strictly speaking these should be:
L28: A body cannot be at rest and in motion at the same time in the same inertial frame.
L29a: It is not the case that a body cannot be at rest and in motion at the same time in the same inertial frame.
However the more colloquial L29 has been adopted for obvious reasons.
21. It might be thought that L34b is both testable and false. But L34b said the following:
L34b: Despite appearances to the contrary, all bodies are at rest.
But, it is not possible to test something "despite appearances to the contrary", for obvious reasons.
[This is because, plainly, any test has to depend on the appearances delivered by instruments, computers, recording devices... More on this in Essay Three Part Two.]
This is not to suggest that there are no theoretical problems bedevilling either option, but there is no way of experimentally testing them. If moving bodies occupied points in space (and were thus stationary) during intervals of the order of, say, 10-1000000 seconds (or less), we would never be able to tell.
On the other hand, if they occupy at most two such places in the same interval (in accord with Engels's analysis), we would still not be able to tell. This should not surprise us; both options are metaphysical and are not therefore based on objects or processes in the material world, having been conjured into 'existence' by a distortion of the only language that secures our knowledge of that world: the vernacular.
Of course, certain aspects of modern Physics postulate minimum times and distances (etc.):
Planck mass: 2.17645(16) 10-8 kg; Planck temperature: 1.41679(11) 1032 K; Planck length: 1.61624(12) 10-35 m; Planck time: 5.39121(40) 10-44 s
But these are conventions -- they are required by theory. Even if all but the first are never actually measured, there is no way they can be shown to be universally/eternally valid minima.
22. Naturally, a full derivation here would involve a potentially infinite number of steps, but that does not prevent the implications of the theory being clear if they are given by a rule. [And it would require small changes in direction.]
[Anyone familiar with "space filling curves" will know what I mean.]
23. This is not, of course, a quandary that afflicts only DM-theorists; traditional Philosophers (i.e., metaphysicians) still cannot explain motion, and neither can modern science -- if by "explain motion" we mean "provide a metaphysical and/or necessary account of motion". Vectors, tensors, geodesics and scalar energy gradients cannot physically move things about the place. Motion is not produced by some sort of Inverse Square Law of Abstraction.
This is no slur on science; all that is being denied here is the capacity of anyone to provide a metaphysical explanation of motion, as opposed to a scientific account.
The dilemma facing dialecticians is here called the "Dialectician's Dilemma"; the disastrous consequences this spells for DM are outlined in Essay Seven and Essay Eleven Part One.
24. For a much more illuminating analysis of these terms, cf., Black (1954). Also see Grünbaum (1967), Salmon (1970), and Note 12, above.
24a. Needless to say, the alleged fact "that ordinary objects and people are quite capable of doing the metaphysically impossible" is meant to be taken ironically! These prodigies are only possible if we insist on reading ordinary words in the crass way metaphysicians constantly do.
24b. This might look like a topological version of the infamous 'Quodlibet' argument (that is, from a contradiction, everything follows). I have not used this hackneyed objection to Hegelian 'logic' in these Essays, since, applied unrestrictedly, it is not a principle with which I agree. However, applied here, restrictedly, it seems to imply that moving 'Hegelian objects' must fill the entire universe, all at once. [That is, if we incorporate small changes in direction.]
A sample derivation of 'Ex Falso Quodlibet' can be found here.
25. Contextualism of this sort will be examined in more detail in another Essay posted at this site.
However, in addition to cases where ordinary objects seem to be able to move while remaining in the same place, there are numerous other examples that illustrate the fact that two or more objects (howsoever these are interpreted) can be in the same place at the same time. Here are a few more:
(1) Consider the following 4-tuples: <x1, x2, x3, t1> and <x4, x2, x3, t1>.
In this case, at least two variables (i.e., x1 and x4) occupy the same place at the same time, namely the first place in their respective 4-tuples (by the ordering rules).
However, we do not have to rely on 'abstract' examples like this to make the same point:
(2) Consider, say, two waves travelling across the surface of a body of water, but orthogonal to one another (or, indeed, at any angle greater than zero but less than 360 degrees). At some point, these two waves will cross, and the moment they do, they will both be in the same place at the same time. This would still be the case whether or not it is true to say that motion is contradictory, or that time is made of instants.
In fact, ordinary examples of this 'impossibility' are even easier to find:
(3) Imagine two workers in the same canteen at work at precisely 10 am on the same day. Here we have two 'objects' in the same place at the same time: these two workers in the canteen at 10 am.
(4) Part of a mother and her unborn baby occupy the same space at the same time. So do any of her/your internal organs.
(5) Ten workers complete an application form. Each puts his/her name in the same box at the top of the page. Here, there would be 10 names occupying the same place (namely, the top of each form) at the same time. Alternatively, a teacher tells a class of thirty, six-year olds to write their names in the same place, namely at the top of the page. Here, once more, there would be thirty 'objects' in the same place (namely at the top of each page, once more), even though they are also in different places (i.e., on different pages, in different parts of the classroom).
(6) This sentence ends in the same place as the next. This sentence ends in the same place as the next. This sentence ends in the same place as the next. This sentence ends in the same place as the next…
Indeed, it is possible to imagine cases where moving objects somehow manage to remain stationary while they are moving -- revealing yet another amazing 'contradiction':
(7) Consider an object located at (x1, x2, x3, t1) with respect to some inertial frame. Let that frame itself move with respect to another inertial frame. In that case, the object in question could remain stationary with respect to the first frame, while it moves with respect to the second.
Again, an ordinary example will suffice to illustrate this 'contradiction':
(8) A child is ascending a descending escalator in such a way that she remains stationary (even momentarily) with respect to an arbitrary point not on that escalator.
Of course, in all such cases, the alleged 'paradoxes' and 'contradictions' they reveal are easily resolved by removing the many equivocations and ambiguities they contain. Unfortunately, this eminently reasonable strategy is not available to DM-enthusiasts -- that is, not without it undermining what few examples of 'real contradictions' they have managed to scrape together over the last two hundred years to support their ramshackle 'theory'.
26. To compound the problem, a queue does not have to be composed of a line of people actually standing anywhere; for example, it could consist of a list of the names of patients due for an operation, or of a group of people waiting for a call-centre operator to answer their calls. Clearly, in cases like these we would have instances of movement (in one sense) even where no movement (in another sense) had taken place, if one or more in each queue drops out, and others move up the list, while not moving anywhere.
In such circumstances, 'queue jumping' could also occur when the said interloper was neither on the list nor located anywhere near any others on the list (there being no list in this case, just an electronic queue, perhaps). Here, queuers could move while remaining stationary, as indeed would queue 'jumpers'.
This illustrates how, when the circumstances surrounding the use of certain words are altered sufficiently, the sense of those words (and of those associated with them) changes accordingly (and indeed vice versa) -- something Engels and the vast majority of philosophers appear not to have noticed.
However, having said that, DM-theorists and traditional philosophers are not quite this semantically-challenged in their everyday use of language; they only become 'linguistic Philistines' when they attempt to do some a priori Superscience (i.e., Metaphysics), employing words as if they were complete novices, or were using an alien language for the first time.
Linguistic naivety is the price one has to pay, it seems, for the low grade skills involved in discovering 'philosophical truths'. In fact, this is the first hurdle adepts have to negotiate: learn to be a linguistic Philistine.
27. In this example, it is irrelevant whether the wire has actually shifted position in the intervening years, because that particular sense of "move" is not the same as the one being used in this instance. Wires can move around trees (with no change of place) just as gaps can run through crowds, and holes through Polo Mints. Here, the wire moves around the tree (i.e., it winds through the same 360 degrees of turn, perhaps several times) while not itself rotating around the tree's geometric centre (in one sense of "rotate"), whether or not the radius of each turn alters over the years. Winding around a tree is a different sort of movement from that of, say, gripping that tree more or less tightly over time -- or, indeed, of slipping down the trunk.
28. Several other examples of motion that are not easy to squeeze into this 'dialectical straightjacket' include the following:
(1) Imagine a situation where the sun is shining intermittently through the clouds, sometimes casting shadows, sometimes not. In such circumstances, someone could say:
M1: "An hour ago, the shadow of that telegraph pole was over there, now it's moved over here."
In this case, although it would be correct to say the shadow had moved, in the circumstances depicted, that shadow's episodic existence means that there would be no continuity between its successive locations. Here, we would have something that moved, which had been in two (possibly) widely separated locations, but which had not been in any of the intermediate points between them. In this case, therefore, we would have something that moved that did not move!
It could be objected here that since a shadow is not a moving object it is not a counter-example to Engels's claims about motion. Perhaps so, but according to Lenin a shadow only has to be objectively external to the mind for it to be material.
"[T]he sole 'property' of matter with whose recognition philosophical materialism is bound up is the property of being an objective reality, of existing outside our mind." [Lenin (1972), p.311. Italic emphasis in the original.]
"Thus…the concept of matter…epistemologically implies nothing but objective reality existing independently of the human mind and reflected by it." [Ibid., p.312. Italic emphasis in the original.]
If so, shadows would be moving material objects (in Lenin's sense).
Moreover, in the above example, the shadow, while moving, was not in two places at once, nor in any between. In that case, we may rescue Engels only by contradicting Lenin -- or vice versa. [Of course, if shadows are not material, but they can move, then motion can occur without matter, meaning that both Engels and Lenin were wrong -- on this see Essay Thirteen Part One.]
(2) Consider the case where, say, a woman is consulting the plans for her new house, who, upon being shown the latest drawings, exclaims:
M2: "Wait a minute, you've moved the front door. We agreed it should go here next to the window, but you've put it to over there near the sink!"
Her