[If you are using Internet Explorer 10 (or later), you might find some of the links I have used below won't work properly unless you switch to 'Compatibility View' (in the Tools Menu); for IE11 select 'Compatibility View Settings' and then add my site: anti-dialecitics.co.uk.]
Here is a summary of some of the key points from Essay Five at my site (most of the links have been removed, and the exact references can be found by following the link added at the end, in the Bibliography):
Motion Isn't Contradictory
The following represents Engels's surprisingly brief, but no less superficial, 'analysis' of motion (in support of which he offered his readers absolutely no supporting evidence, and none has been offered since):
This is, of course, an idea Engels lifted from Hegel, who in turn borrowed it from a paradox invented by Zeno, an ancient Idealist and Mystic who concluded that motion was in fact impossible."[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.]
There are several serious problems with the above passage, difficulties that need addressing even before its fatal weaknesses are exposed.
1) The first of these is connected with Engels's claim that the alleged 'contradiction' here has something to do with its "assertion" and "solution". This isn't easy to square with his other stated belief that matter is independent of mind. Who, for example, "asserted" this alleged contradiction before humanity evolved? And who did the "solving"?
Or, are we to assume that things only began to move when human beings capable of making assertions appeared on the scene?
2) The next difficulty centres around the question whether this alleged 'contradiction' can in fact explain motion (and thus if it is merely ornamental). No one imagines (it is to be hoped!) that this 'contradiction' works like some sort of internal 'metaphysical motor', powering objects along. But, as we will see in Essay Eight Part One, at my site, this is precisely what dialecticians like Lenin appeared to think:
Independently of this, it isn't easy to see how an object being in one place and not in it, as well as being in two places at once can explain how or why it actually moves. At best, this alleged 'contradiction' seems derivative -- that is, it is reasonably clear that it is motion that explains (or which initiates) the 'contradiction', not the other way round. But, if that is so, what explains motion?"The identity of opposites…is the recognition…of the contradictory, mutually exclusive, opposite tendencies in all phenomena and processes of nature…. The condition for the knowledge of all processes of the world in their 'self-movement', in their spontaneous development, in their real life, is the knowledge of them as a unity of opposites. Development is the 'struggle' of opposites. The two basic (or two possible? or two historically observable?) conceptions of development (evolution) are: development as decrease and increase, as repetition, and development as a unity of opposites (the division of a unity into mutually exclusive opposites and their reciprocal relation).
"In the first conception of motion, self-movement, its driving force, its source, its motive, remains in the shade (or this source is made external -- God, subject, etc.). In the second conception the chief attention is directed precisely to knowledge of the source of 'self-movement'.
"The first conception is lifeless, pale and dry. The second is living. The second alone furnishes the key to the 'self-movement' of everything existing; it alone furnishes the key to the 'leaps,' to the 'break in continuity,' to the 'transformation into the opposite,' to the destruction of the old and the emergence of the new.
"The unity (coincidence, identity, equal action) of opposites is conditional, temporary, transitory, relative. The struggle of mutually exclusive opposites is absolute, just as development and motion are absolute." [Lenin (1961), pp.357-58. Italic emphases in the original. Bold emphases added.]
Plainly, if dialecticians want to cling on to this 'theory', they will find they can't actually explain why objects move, which is rather odd since they spare no opportunity regaling us with the claim that they are the only ones who can!
[DM = Dialectical Materialism.]
It could be objected that DM-theorists in fact appeal to contradictory forces to account for motion, but we will see in Essay Eight Part Two that there is no interpretation that can be placed on the word "force", or on the word "contradiction", that will sustain such an ancient and animistic view of change and movement.
["Ancient" in the sense that it was an early Greek idea that moving objects needed something to sustain their motion. In contrast, modern Physics merely deals with change in motion/momentum, and in order to do that most theorists have dropped all reference to forces. Details can be found in Essay Eight Part Two, here. "Animistic" since this idea also depends on another ancient doctrine that conflict and motion can be explained in terms of the 'will' of some 'god' or other, or, alternatively, as the result of an 'animating spirit' of some description.]
But, even if forces were 'contradictory', and reference to a continual cause of motion was both available and rational, that would hardly explain how an object being in one place and not in it, and being in two places at once, could actually explain why it moves. Plainly, this alleged 'contradiction' does no work, and, as suggested above, appears merely to be ornamental.
Moreover, even in DM-terms, this fable makes little sense. Are we really supposed to believe that an object that is 'here' is made to move by its being 'not here' --, its 'dialectical' opposite, its 'other' (as Hegel and Lenin called them)? Or, that the two 'places' mentioned are locked in some sort of 'struggle', as the DM-classicists claim is the case with all such 'dialectical' opposites?
3) Engels's 'analysis' is itself based on a very brief and sketchy thought experiment (in fact, Hegel's and Zeno's were based on little other than word juggling), an 'analysis' that was in turn motivated by a superficial consideration of a limited range of terms associated with this phenomenon.
Despite this, Engels was quite happy to derive a set of universal truths about motion -- applicable everywhere in the entire universe, for all of time -- from the supposed meaning of a few words. Clearly, the concepts Engels used cannot have been derived by 'abstraction' from his (or from anyone else's) experience of moving bodies, since no conceivable experience could confirm that a moving body is in two places at once, only that it moves between at least two locations in a finite interval of time.
To be sure, that is why Engels not only had to indulge in flights-of-fancy to make his case, it is also why he had to impose his views on reality. This was despite his promise that it was something he would never do:
In which case, the following characterisation of Idealism clearly applies to Engels's 'analysis' of motion (as George Novack inadvertently pointed out):"Finally, for me there could be no question of superimposing the laws of dialectics on nature...." [Engels (1976), p.13. Bold emphasis added.]
But, this is precisely what Zeno and Hegel did, just as it accurately describes Engels's approach; all three "proceed[ed] from principles which are validated by appeal to abstract reason, intuition, self-evidence or some other subjective or purely theoretical source.""A consistent materialism can't proceed from principles which are validated by appeal to abstract reason, intuition, self-evidence or some other subjective or purely theoretical source. Idealisms may do this. But the materialist philosophy has to be based upon evidence taken from objective material sources and verified by demonstration in practice...." [Novack The Origin of Materialsm, p.17. Bold emphasis added.]
4) Putting this to one side, even if Engels's claims were impeccable, they couldn't account for movement (and hence they can't explain change), anyway. Clearly, Engels failed to notice (just as subsequent dialecticians have also failed to notice) that the way he depicts motion doesn't distinguish moving from stationary bodies. Stationary bodies can also be in two places at once, and they can be in one place and not in it at the same time. For example, a car can be in a garage and not in it at the same moment (having been left parked half-in, half-out); and it can be in two places at once (in the garage and in the yard), and stationary with respect to some inertial frame, all the while.
Exception could be taken to the above in that it implicitly uses, or it implies the use of, phrases like "not wholly in one place" (i.e., the car in question was "half-in, half-out" of the garage). It could be argued that Engels was quite clear about what he meant: motion involves a body being in one place and in another at the same time, being in and not in it at one and the same moment. There is no mention of "not wholly in" in what Engels asserted.
Or, so it could be maintained.
Clearly, this objection depends for its force on what Engels actually intended by the following words:
Here, the problem centres on the word "in". Again, it could be objected that "in" has been illegitimately replaced by "(not) totally or wholly in", or its equivalent. Even so, it is worth noting that Engels's actual words imply that this is a legitimate, possible interpretation of what he said (paraphrased below):"[E]ven simple mechanical change of place can only come about through a body at one and the same moment of time being both in one place and in another place, being in one and the same place and also not in it."
M1: Motion involves a body being in one and the same place and not in it.
If a body is "in...and not in" a certain place it can't in fact be totally in that place. So, Engels's own words allow for his "in" to mean "not wholly in", or something like it.
A mundane example of this might be where, say, a 15 cm long pencil is sitting in a pocket that is only 10 cm deep, while the jacket itself is in a wardrobe. In that case, it would be perfectly natural to say that this pencil is in, but not entirely in, the pocket -- that is, it would be both "in and not in" the pocket at the same time, and in two places at once (in the pocket and in the wardrobe -- thus fulfilling Engels's definition) --, but still at rest with respect to some inertial frame. M1 certainly allows for such a situation, and Engels's use of the word "in" and the rest of what he said plainly carry this interpretation.
Hence, it seems that Engels's words are compatible with a body being motionless relative to some inertial frame.
The only way this and other counter-examples can be neutralised by DM-fans is to re-define the relevant terms in a way that would in the end make Engels's 'analysis' inapplicable to material bodies. It would do so by applying his 'analysis' solely to immaterial, mathematical points -- plainly because only a stationary mathematical point can be in precisely one location at a certain time. Unfortunately, in that case, Engels's thought experiment would no longer concern what is supposed to be unique to moving material objects.
Either way, unless augmented in some way, Engels's words cannot be used to distinguish moving from stationary bodies. In which case, it is now quite apparent that this apparent 'contradiction' has arisen simply because of the ambiguities inherent in the language Engels used -- since his 'analysis' can't actually distinguish moving from stationary bodies. When these ambiguities have been removed (as they have been in Essay Five (link at the end)), the 'contradiction' simply disappears; no one supposes cars and/or pencils are contradictory for just remaining stationary. The same is the case with moving bodies.
Of course, mathematical points themselves cannot move -- that is, if they could move they would have to occupy still other similar points. But, points aren't containers (they have no shape, circumference or volume, otherwise they wouldn't be points -- they have no physical dimensions or rigidity, so they cannot even 'push' each other out of the way as they 'move'); so nothing can occupy them. In that case, mathematical points cannot move.
Alternatively, anyone who claimed that mathematical points could move would have a hard time explaining where they moved to, where they were before they moved, and how they could be contradictory while they did this -- indeed, if these points were only the same size as any point they allegedly 'occupied', it would mean they couldn't be in two such places at once, or they would expand. Moreover, such an 'explanation' would have to be given without an appeal to yet another set of mathematical points for them to 'occupy' or move into, shifting this problem to the next stage.
5) Furthermore, there are serious problems connected with what Engels did say: that a moving object is "in one and the same place and also not in it". But, if moving object, B, isn't located at, say, X (i.e., if it is "not in X"), then it can't also be located at X, contrary to what Engels asserted. If it isn't there then isn't there. On the other hand, if B is located at X, then it can't also not be at X. Otherwise, Engels's can't mean by "not" what the rest of us mean by that word.
But, what did he mean?
Unfortunately, he neglected to say, and no DM-fan since has been any clearer. Other than holding up their hands and declaring it a 'contradiction', there is nothing more they could say. Once more, this can only mean that they, too, mean something different by "not" -- for example, for them "is not" seems to mean "is and is not"! If so, they certainly can't respond by saying "This is not what we mean", since this use of "not" implies they really mean "This is and is not what we mean" (as each "is not" is replaced by its 'dialectical equivalent', "is and is not"), and so on.
As we can see, anyone who falls for Zeno, Hegel or Engels's linguistic conjuring trick can't actually tell us what they do mean!
Nor can it be replied that Engels's words only apply to movement and change, hence if or when dialecticians use "is not" -- as in, for example, "This is not what we mean" -- they don't also mean "This is and is not what we mean". That is because, if everything is constantly changing into what it is not (as DM-theorists maintain) then so are the words they use. Hence, "This is what we mean" must have changed into "This is and is not what we mean".
6) Engels's claim that motion is 'contradictory' only follows if a body cannot logically be in two places at once, or if it cannot be in one place and not in it at the same time. [If objects can be in two places at once, then, plainly, there would be no contradiction in supposing they could be in two places at once, would there?] Engels simply assumed the truth of this hidden premiss; he nowhere tried to justify it (and no one since seems to have bothered to do so, either).
However, because an ordinary stationary material body can be in two places at once, and in one place and not in it at the same time (as we have just seen), Engels's key premiss is not even empirically true! In that case, it certainly can't be a logical/conceptual truth restricted only to moving bodies. If it is true that stationary objects can also do what Engels says of moving bodies, then it cannot be a contradiction when moving bodies do it, too. In that case, this cannot be something that accounts for, or describes motion --, or even distinguishes it from rest.
Of course, it could be argued that the 'contradictions' Engels was interested in are 'dialectical contradictions', not logical contradictions. However, his wording doesn't support such an interpretation:
It certainly seems from this that Engels was talking about logical contradictions as much as about 'dialectical 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.]
And, believe it or not, that would prove to be good news for DM-fans, for we have at least got some sort of handle on the phrase "logical contradiction". The other sort (i.e., 'dialectical contradiction') has resisted all attempts at explanation for the last 200 years (not that anyone has tried all that hard).
7) More specifically, in relation to moving bodies, it is pertinent to ask the following question: How far apart are the two proposed "places" that a moving object is supposed to occupy while at the same time not occupying one of them? Is there a minimum distance involved? The answer can't be "It doesn't matter; any distance will do." That is because, as we will see, if a moving object is in two places at once, then it can't truly be said to be in the first of these before it is in the second (since it is in both at the same time). So, unless great care is taken specifying how far apart these "two places" are, this view of motion would imply that, say, an aeroplane must land at the same time as it took off! If any distance will do, then the distance between the two airports involved is as good as any. [I will return to this topic below.]
So, indifference here would have you arriving at your destination at the same time as you left home!
Hence, if object B is in one place and then in another (which is, I suspect, central to any notion of movement that Engels would have accepted), it must be in the first place before it is in the second. If so, then time must have elapsed between its occupancy of those two locations, otherwise we wouldn't be able to say it was in the first place before it was in the second. But, if we can't say this (that is, if we can't say that it was in the first place before it was in the second), then that would undermine the assertion that B was in fact moving, and that it had travelled from the first location to the second.
Hence, if B is in both locations at once, it can't have moved from the first to the second. On the other hand, if B has moved from the first to the second, so that it was in the first before it reached the second, it can't have been in both at the same time.
If DM-theorists don't mean this, then they must either (1) refrain from using "before" and "after" in relation to moving objects, or (2) explain what they do mean by any of the words they use. Option (1) would prevent them from explaining (or even talking about!) motion.
We are still waiting for them to respond to (or even acknowledge) option (2).
Anyway, whatever the answer to these annoying conundrums happens to be -- as is well known -- between any two locations there is a potentially infinite number of intermediary points (that is, unless we are prepared to impose an a priori limitation on nature by denying this).
Does a moving body, therefore, (a) occupy all of these intermediate points at once? Or, (b) does it occupy each of them successively?
If (a) is the case, does this imply that a moving object can be in an infinite number of places at the same time, and not just in two, as Engels asserted?
On the other hand, if Engels is correct, and a moving body only occupies (at most) two places at once, wouldn't that suggest that motion is discontinuous? That is because, such an account seems to picture motion as a peculiar stop-go sort of affair, since a moving body would have to skip past (but not occupy, somehow?) the potentially infinite number of intermediary locations between any two arbitrary points (the second of which it then occupies). This must be so if it is restricted to being in at most two of them at any one time, and is therefore stationary at the second of these two points. [That is what the "at most" qualifier here implies.]
But, that itself appears to run contrary to the hypothesis that motion is continuous and therefore 'contradictory' --, or, it runs counter to that hypothesis in any straight-forward sense, at the very least. It is surely the continuous nature of motion that poses problems for a logic (i.e., Formal Logic [FL]) which is allegedly built on a static, discontinuous view of reality, this being the picture that traditional logic is supposed to have painted --, or, so we have been told by dialecticians.
It could be argued that no matter how much we 'magnify' the path of a moving body, it will still occupy two points at once, being in one of them and not in it at the same time. And yet, that doesn't solve the problem, for if there is indeed a potentially infinite number of intermediary points between any two locations, a moving body must occupy more than two of them at once, contrary to what Engels seems to be saying:
Hence, between any two points, P and Q -- located at, say, (X(P), Y(P), Z(P)) and (X(Q), Y(Q), Z(Q)), respectively -- that a moving object, B, occupies (at the same "moment in time", T(1)), there are, for example, the following intermediary points: (X(1), Y(1), Z(1)), (X(2), Y(2), Z(2)), (X(3), Y(3), Z(3)),..., (X(i), Y(i), Z(i)),..., (X(n), Y(n), Z(n)) -- where n itself can be arbitrarily large. Moreover, the same applies to (X(1), Y(1), Z(1)) and (X(2), Y(2), Z(2)): there is a potentially infinite number of intermediate points between these two, and so on."[A]s soon as we consider things in their motion, their change, their life, their reciprocal influence…[t]hen we immediately become involved in contradictions. Motion itself is a contradiction; even simple mechanical change of place can only come about through a body being both in one place and in another place at one and the same moment of time, being in one and the same place and also not in it. And the continual assertion and simultaneous solution of this contradiction is precisely what motion is." [Ibid. Bold emphasis added.]
So, if Engels is right, B must occupy not just P and Q at the same instant, it must occupy all these intermediary points, as well -- again, all at T(1). That can only mean that B is located in a potentially infinite number of places, all at the same "moment". It must therefore not only be in and not in P at T(1), it must be in and not in each of (X(1), Y(1), Z(1)), (X(2), Y(2), Z(2)), (X(3), Y(3), Z(3)),..., (X(i), Y(i), Z(i)),..., (X(n), Y(n), Z(n)) at T(1), just as it must also be in all the intermediary points between (X(1), Y(1), Z(1)) and (X(2), Y(2), Z(2)), if it is also to be in Q at the same "moment".
And, what is worse: B must move through (or be in) all these intermediate points without time having advanced one instant!
That is, B will have achieved all this in zero seconds!
B must therefore be moving with an infinite velocity between P and Q!
Of course, we could always claim that by "same moment" Engels meant "same temporal interval", but this scuppers his 'theory' even faster. That is because if by "same moment" Engels meant "same temporal interval", then there is no reason why "same point" can't also mean "same spatial interval", at which point the alleged 'contradiction' simply vanishes.
[Indeed, we will also see that this alternative (i.e., that a moving body occupies all the intermediate points between any two points, all at the same time) poses even more serious problems for Engels's 'theory' --, that is, over and above implying that 'dialectical' objects move with infinite velocities.]
Moreover, if B moves from P to Q in temporal interval, T, comprised of sub-intervals, T(1), T(2), T(3), ..., T(n), each of which is also comprised of its own sub-intervals, then B will be located at P at T(1) and then at Q at T(n), which will, of course, mean that B won't be in these two places at the same time, although it will be located at these two points in the same temporal interval. Once again, the 'contradiction' Engels claims to see here would in that case have vanished. Few theorists, if any, think it is the least bit contradictory to suppose that B is in P at one moment and then in Q a moment later.
Consider a car travelling north across, say, Texas during a three-hour time slot. Let us suppose it is in the centre of Lubbock at 08:00am and in the centre of Amarillo (approximately 124 miles away) at 11:00am. In that case, it will have been in two locations during the same temporal interval, but not in two places in the same moment in time. Plainly, in this case, the alleged contradiction has disappeared. If so, only a very short-sighted DM-fan will want to take advantage of this escape route (no pun intended) -- i.e., referring to temporal intervals as opposed to 'moments in time'. This is probably why Engels didn't refer to temporal intervals, and, as far as can be ascertained, no DM-theorist has done so since.
8) On a different tack: Do these 'contradictions' increase in number, or stay the same, if an object speeds up? [This is a problem that exercised Leibniz -- see below.] Or, are the two locations depicted by Engels (i.e., the "here" and the "not here") just further apart? That is, are the two points that moving body, B, occupies at the same moment, if it accelerates, just further apart? But, if it occupies them at the same time, it can't have accelerated. That is because it hasn't moved from the first to the second, since it is in both at once. Speeding up, of course, involves covering the same distance in less time, but that isn't allowed here, nor is it even possible. In which case, it isn't easy to see how, in a DM-universe, moving bodies can accelerate if they are in these two locations at once.
[I am of course using "accelerate" here as it is employed in everyday speech, not as it is used in Physics or Applied Mathematics. Leibniz argued that if motion were continuous, it would be impossible to explain faster or slower speeds. If speed is the number of points a body traverses along its trajectory in a given unit of time, an increase in speed would involve that body traversing more points in the same time interval. But, the number of points in a body's trajectory is infinite; if so, it can't traverse more points in the same time interval, since, as was supposed in Leibniz's day, all such infinities are equal (i.e., in modern parlance, they have the same cardinality). The only way to account for different speeds, on this view of trajectories and infinities, is to argue that at a lower speed, a body rests at each point a bit longer -- and vice versa for those that move faster. (Leibniz coupled these observations with the conclusion that motion is in fact illusory!)]
Accelerated motion (in the above sense of this word) involves a body being in (or passing through) more places in a given time interval than had been the case before it accelerated. But, if B is in these two places at the same time, how can it pick up speed?
More to follow...