16-05 -- Summary Of Essay Five: Hegel And Engels Are Wrong, Motion Isn't Contradictory




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




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


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


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


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1) Dialectics -- A Doctrine Of Change That Cannot Even Account For Movement


a) Initial Problems


2) Fatal Defects


a) Reconstructing Engels's Argument


b) Demolishing Engels's Argument


3) Ambiguity -- The Mother Of Confusion


4) Yet More Dogmatic 'Super-Science' From Engels


Summary Of My Main Objections To Dialectical Materialism


Abbreviations Used At This Site


Return To The Main Index Page


Contact Me



Dialectics, The 'Doctrine Of Change' That Can't Even Account For Movement!


In Essay Five I have set out to demolish Engels's surprisingly brief, but no less superficial, 'analysis' of 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.]


This is, of course, an idea Engels appropriated from Hegel, who in turn derived it from a paradox invented by Zeno (490?-430?BC), an ancient Idealist and Mystic who concluded that motion was impossible (by just thinking about it!).



Initial Problems


There are several serious problems with the above passage, difficulties that need addressing even before its fatal weaknesses are highlighted.


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 sentient 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. No one imagines (it is to be hoped!) that this 'contradiction' works like a sort of 'internal metaphysical motor', powering objects along. But, as we will see in Essay Eight Part One, this is precisely what dialecticians like Lenin appeared to think:


"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.]


It could be argued that this is a little too glib. Maybe so, but that particular reaction will be tested to destruction in Essay Eight Part One.


Independently of that, 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' is 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?


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 archaic, animistic view of change and movement.


["Archaic" 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 dogma that conflict and motion can only be explained in terms of the 'will' of some 'god', or 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 acceptable to modern physics, that would hardly explain how an object being in one place and not in it, occupying in two places at once, could actually explain why it moves. Plainly, this alleged 'contradiction' does no work.


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? Or even that the one turns into the other -- i.e., that 'here' turns into 'not here', and 'not here' turns into 'here' --, as the aforementioned DM-worthies also asserted?


3) Engels's 'analysis' was itself based on a very brief and sketchy thought experiment (Hegel's and Zeno's were based on similar word juggling), one 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 alleged meaning of a few simple expressions. 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:


"Finally, for me there could be no question of superimposing the laws of dialectics on nature...." [Engels (1976), p.13. Bold emphasis added.]


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


"A consistent materialism can't proceed from principles which are validated by appeal to abstract reason, intuition, self-evidence or some other subjective or purely theoretical source. Idealisms may do this. But the materialist philosophy has to be based upon evidence taken from objective material sources and verified by demonstration in practice...." [Novack (1965), p.17. Bold emphasis added.]

But, this is precisely what Zeno and Hegel did, just as it accurately describes Engels's approach; 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."


4) Putting this to one side, even if Engels's claims were correct, 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 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. [Several obvious and less obvious objections to this argument have been neutralised in Essay Five.]


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:


"[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." [Loc cit.]


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):

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.

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 this by applying it solely to immaterial, mathematical points -- plainly because only a stationary mathematical point can be in precisely one point at any one time. Unfortunately, in that case, Engels's thought experiment would no longer apply to 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 clear that this apparent 'contradiction' has arisen simply because of the ambiguities inherent in the language Engels used -- since, once more, his 'analysis' can't actually distinguish moving from stationary bodies. When these ambiguities have been removed (as they have been in Essay Five), the 'contradiction' simply disappears; no one supposes cars and/or pencils are contradictory for simply remaining stationary. The same is the case with moving bodies.


Anyway, mathematical points themselves cannot move. If they could they would have to occupy still other 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 can't even 'push' each other out of the way as they 'try' to 'move'), so nothing can occupy them. In that case once more, such points can't move.


[Certainly, there are mathematicians who talk as if they believe points can move, but, beyond a certain way of speaking (i.e., figuratively), there is nothing to support the idea that they can move (and everything to suggest they can't -- not the least of which is that such points do not exist in space and time to be able to move anywhere). On this, see Essay Seven Part One, here. Indeed, if certain ways of speaking could make things move, far more of us would believe in magic.]


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 -- indeed, if these points were only the same size as any point they allegedly 'occupied', it would mean they could not be in two such places at once, or they would have expanded. [That is, one point would now be two points!] Moreover, such an 'explanation' would have to be given without an appeal to yet another set of mathematical points for them to 'occupy', shifting this problem to the next stage.


5) 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. Engels just assumed the truth of this premiss; he nowhere tried to justify it (and no one since seems to have bothered to do so, either).


[Some might point to Graham Priest's work in this area, but it is far from clear that his 'contradictions' are 'dialectical' to begin with, or even that his analysis makes sense. On that, see here.]


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 already 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, then it cannot be a contradiction when moving bodies do it, too -- or, at least, it can't be a contradiction true only of moving bodies. In that case, it cannot be something that accounts for 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:


"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.]


It certainly seems from this that Engels was talking about logical contradictions as much as about 'dialectical contradictions'.


And, believe it or not, that would in fact prove to be good news for DM-fans, for we have at least got some sort of handle on logical contradictions. The other sort (i.e., 'dialectical contradiction') has resisted all attempts at explanation for nigh on 200 years (not that anyone has been trying all that hard). [In fact, the best Marxist attempt to do this (to date) has been demolished here.]


6) 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 (since it is "not in X", i.e., it isn't there!) 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".


[The "relative stability defence" has been neutralised in Essay Six, here and here.]


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 (i) Refrain from using "before" and "after" in relation to moving objects, or (ii) Explain what they do mean by any of the words they use. Option (i) would prevent them from explaining (or even talking about!) motion.

We are still waiting for them to respond to (or even acknowledge) option (ii).

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:


"[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." [Loc cit. Bold emphasis added.]


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.

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 (no pun intended).


However, 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 Texas during a three-hour temporal interval. Let us suppose it is in the centre of Lubbock at 08:00am and in the centre of Amarillo (approximately 124 miles away) at 11:00am. In that case, it will have been in two locations during the same temporal interval (lasting three hours), but not in two places in the same moment in time. In this case, the alleged contradiction has disappeared. Indeed, this car won't even be in Lubbock and not in it at, say, 08:01, even while it is moving -- since it will be in Lubbock for several minutes (until it reaches the city boundary). So, in this instance, the car isn't in one place and not in it in this sub-section of the interval. If that is so, only a very short-sighted DM-fan will want to take advantage of this escape route (no pun intended) -- i.e, referring to temporal intervals as opposed to 'moments in time'. This is probably why Engels didn't refer to temporal intervals, and, as far as can be ascertained, no DM-theorist has done so since.


8) On a different tack, it is worth asking the following question: 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 in less time, 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?



And Now: The Fatal Defects


In this Introductory Essay, I have had to omit much of the material included in Essay Five (Sections (4)-(7)) that enters into these "fatal defects" in considerable (and technical) detail. I have also had to outline what I take to be Hegel's and/or Engels's reasons for asserting that motion is contradictory, since they themselves manifestly failed to tell us why they concluded this -- being merely content to assert it for a fact!



Reconstructing Engels's Argument


1) It isn't at all easy to ascertain the 'rationale' behind Engels's (and thus Hegel's) conclusion that motion is contradictory, but it seems to depend on this line-of-argument -- perhaps beginning with a rejection of the apparent contradiction in E1a, that rejection expressed in E1:


[E1a: An object can be in motion and at rest at one and the same time.]


E1: An object cannot be in motion and at rest at one and the same time.


E2: If an object is located at a point it must be at rest at that point.


E3: Hence, a moving body cannot be located at a point, otherwise it wouldn't be moving, it would be at rest.


E4: Consequently, given E1, a moving body must both occupy and not occupy a point at one and the same instant.



Demolishing Engels's Argument


But, if this is Engels's (or even Hegel's) rationale, then he/they offered their readers no reason why we should prefer one contradiction (E4) over another (E1a). And yet, E1a is a familiar truth, for it is possible for an object to be at rest with respect to one frame of reference and yet be in motion with respect to another (that is, that it can be at rest and in motion at the same time).


On this, Robert Mills had this comment to make (about Einstein's "Principle of Equivalence"):


"Another way of stating the principle of equivalence, a way that better reflects its name, is to say that all reference frames, including accelerated reference frames, are equivalent, that the laws of Physics take the same form in any reference frame…. And it is also correct to say that the Copernican view (with the sun at the centre) and the Ptolemaic view (with the earth at the centre) are equally valid and equally consistent!" [Mills (1994), pp.182-83. Spelling altered to conform to UK English. More on this here.]


[It is worth recalling that the late Professor Mills was co-inventor of Yang-Mills Theory in Gauge Quantum Mechanics, and thus no scientific novice.]


This means that in one frame the Earth would be stationary, in another it would be moving. In that case, if E1a is true, E4 cannot follow from E1, and the imputed rationale behind Engels's 'contradiction' disappears.


E1a: An object can be in motion and at rest at one and the same time.


E1: An object cannot be in motion and at rest at one and the same time.


E4: Consequently, given E1, a moving body must both occupy and not occupy a point at one and the same instant.


2) As noted earlier, Engels's conclusion clearly depends on an object moving between locations with time having advanced not one instant; that is, his conclusion implies that the supposed change of place must occur outside of time -- or, worse, that it happens independently of the passage of time --, which is incomprehensible, as even Trotsky would have admitted:


"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), pp.63-64.]


And yet, how else are we to understand Engels's claim that a moving body is actually in two places at once? If that were the case, a moving object would be in one place at one instant, and it would move to another place with no time having lapsed; such motion would thus take place outside of time. But, according to Trotsky, that sort of motion wouldn't exist, for it wouldn't have taken place in time.


Furthermore, it would mean that while we may divide location as finely as we wish -- so that no matter to what extent the spatial aspects of a body's position were partitioned, we would always be able to distinguish two contiguous points allowing us to say that a moving body was in those two places at once --, while we can do that with location, we can't do the same with respect to time.


Engels's 'argument' thus depends on the claim that while the location of a particular body is subject to infinite divisibility (an assumption which, one presumes, is necessary to support the claim that moving bodies must be in two places at the same time, no matter how microscopically close together they are -- which in turn implies that spatial locations can be given in endlessly finer-grained detail) -- the time interval during which this takes place isn't subject to similar division. Now, this is an a priori and non-symmetric restriction -- that is, it is applied to time, but not to space. This is impossible to justify on either empirical or logical grounds.


[Not one single DM-fan, as far as I am aware, has ever even so much as tried to justify this one-sided implied division. In fact, it is clear that not one single DM-fan even seems to be aware of it!]


If this one-sided constraint is rejected (as surely it must!), it would mean that no matter how close together the two locations occupied by a given (moving) object actually are, we can always specify a finite time interval during which the said movement occurs. That done, the alleged 'contradiction' vanishes. [As we saw earlier, few would regard it as in any way contradictory that a moving object can be in two locations during a finite temporal interval.]


Again, the only way to neutralise this response would be to counter-claim that a body must be motionless if it is in a certain place at a certain time (as we saw would be the case if E2 were true). That being so, it could be argued that if an object is moving, it must be in two places at the same time.


E2: If an object is located at a point it must be at rest at that point.


But, that just repeats the non-symmetrical restriction noted above (along with its suspect derivation, upon which doubt was cast earlier). If we can slice up places as finely as we please, so that it is possible to say an object is in two of them while the 'instant' during which this occurs remains the same, then we can surely do likewise with respect to time, specifying two times for each of these two places -- or, at least, specify a temporal interval in which such a change of place occurs. Again, the only way this response may be blocked would be to argue that while place is infinitely divisible, time isn't. And how might that be justified?


Once more, none of this is the least bit surprising since Engels's claims about motion and change date back to the a priori speculations of that ancient mystic Heraclitus -- a thinker who didn't even bother to base his wild ideas on anything remotely like evidence (having derived his 'profound' conclusions about all of reality for all of time from what he thought was true about the possibility of stepping into a certain river!) --, and to an Idealist conundrum invented by Zeno. [On Heraclitus's confusions, see here.]


[Of course, these observations dispose of the DM-dogma that contradictions between space and time are only to be expected since reality is 'fundamentally contradictory'. That is because this 'contradiction' obviously results from a lop-sided convention that interprets one of these (place) as continuous (and hence subject to infinite division) and the other (time) as discrete (and hence not so subject). However, if they are treated in the same way (as either both continuous or both discrete), there is no contradiction. These are, of course, very crude distinctions, but the lack of clarity here is a direct result of having to make sense of Hegel and Engels's own terminal lack of clarity on this issue.]


3) Engels also failed to notice that several other (even more) paradoxical consequences follow from his ideas. One of these is that if a moving body is anywhere, it must be everywhere, all at once.


The reason for saying this is as follows: Engels's argument depends on the idea that moving body, B, must be in two places at the same time -- i.e., in, say, P1 and P2 --, otherwise it would be stationary. This allows him to derive a 'contradiction': a moving body must be in two places at once, and it must both be in and not in at least one of these at the same moment.


But, clearly, if B is in P2 it must also be in P3 in the same instant. If this implication is denied, then the conclusion that a moving body must be in one place and not in it at the same instant, and in another place at the same time, will have to be abandoned. If B is in P2 then, unless it is also in P3 at the same time, it must be at rest at that time. This follows from E2:


E2: If an object is located at a point it must be at rest at that point.


No moving body can be located only at a point like P2, it has to be elsewhere at the same time.


So, if it is still true that at one and the same instant a moving body is in one place and not in it, and that it is in another place at the same time (otherwise it would be stationary), then B must be in P3 in the same instant that it is in P2 -- or it wouldn't be moving while at P2, but would be stationary at P2.


In that case, such a body must be in at least three places at once: P1, P2, and P3.


But, the same argument applies to P3, so B must also be in P4, at the same time, and then in P5..., and so on.


Hence, assuming that B is still moving while at P2, by the application of a sufficiently powerful induction, it can be shown that any moving body must be everywhere if it is anywhere, all at the same instant!


Now, that is even more absurd than Zeno's ridiculous conclusion!


But, that's Diabolical Logic for you!


[More on this, here, where the above argument is presented in greater detail and where several obvious objections have been rebutted.]


(4) Even odder is the following unrecognised, absurd consequence of Engels a priori 'argument' (briefly mentioned earlier):

E5: If Engels were correct (in his characterisation of motion and change), we would have no right to say that a moving body was in the first of these 'Engelsian locations' before it was in the second.


That follows from L1:

L1: 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.

As noted earlier, that is because, according to Engels, such a body is in both places at once. Now, if the above conclusion is valid (that is, if dialectical objects are anywhere in their trajectories, they are everywhere all at once), then it follows that no moving body can be said to be anywhere before it is anywhere else in its entire journey! Again, that is because such bodies are everywhere all at once. If so, they can't be anywhere first and then later somewhere else. In the dialectical universe, therefore, when it comes to motion and change, there is no before and no after!

In that case, according to this 'scientific theory', concerning the entire trajectory of a body's motion, it would be impossible to say it was at the beginning of its journey before it was at the end! In fact, it would be at the end of its journey at the very same time as it sets off!


So, while you might foolishly think, for example, that you have to board an aeroplane (in order to go on your holidays) before you disembark at your destination, this 'path-breaking', super-duper theory tells us you are sadly mistaken: you not only must get on the plane at the very same time as you get off it at the 'end', appearances to the contrary notwithstanding, you actually do!

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

If, indeed, these are genuine implications of Dialectical 'Logic', then there can be no "during" and no "while", either, since, as we have seen, this 'path-breaking' theory means that there is no such thing as 'before' and 'after' when it comes to motion. Hence, if there is no before or after, there can't be a during or a while. So, even though you might think you have to wait an hour for a bus, for instance, this 'theory' tells you that this appearance is illusory. In 'essence' you have been waiting no time at all -- the bus arrived at your stop in the exact same moment it left the depot! After all, this 'theory' also tells us that appearances 'contradict' underlying 'essence'; so, dear reader, it might have 'appeared' to you that it took several minutes to read this Summary, in 'essence', it took no time at all!

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



Ambiguity -- The Mother Of Confusion


We saw earlier that Engels's use of "contradiction" fails to distinguish moving from stationary objects. In that case, the alleged 'contradiction' he 'derived' is more a function of ambiguities in the language he used than it is a reflection of objects and processes in reality.


In Essay Five, here and here, I list numerous examples of similar ambiguities, each of which seems to imply a 'contradiction' (and all of which Zeno and Engels failed to notice) if we insist on treating language in this crude and Philistine way (that is, if we emulate Zeno, Heraclitus, Hegel and Engels, and ignore such ambiguities).


Now, these ambiguities are relatively easy to resolve; if the same tactic is applied to the language that the above Idealists employed, the same result emerges: these 'contradictions' soon vanish.


[I have omitted the details from this summary for reasons outlined in the Preface, so the reader is directed to Essay Five for more on this. Follow the two links above.]



Yet More A Priori, Dogmatic 'Super-science' From Engels


As noted earlier, Engels performed no experiments (designed to show his ideas about motion were correct) before or after he 'derived' his conclusion about motion, and, as far as we know, no dialectician since has performed any, either. In fact, it is impossible even to imagine or describe a single observation or experiment that could conceivably confirm Engels's claims. This is partly because the 'contradictions' to which he alluded can't be observed, and partly because of the modal, universal and omni-temporal character of the conclusions themselves. That is, no experiment could confirm that every moving body in the entire universe, for all of time, has to move as Hegel or Engels say they must.


This means that the only substantiation Engels could have offered, and did offer, in support of his claims was based on his use of language. Indeed, had anyone questioned these conclusions his only response would have involved him reminding sceptics what the words he used really meant. It would be no good advising non-believers to look harder at the phenomena, refine their search, or redo some experiment --, which is, of course, why one finds no experimental evidence at all in books on dialectics that confirms, or even so much as 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 ambiguous words. [Readers are, of course, invited to check any randomly-chosen book or article on DM to see if this allegation is itself correct. They will find it is!]


Thus, Engels's only 'evidence' would have been (indeed, was) based on an appeal to linguistic usage -- and, even then, it was based solely on Zeno's or Hegel's use of certain words! This predicament, which Engels shares with all other metaphysicians, invariably passes off unnoticed because (i) This approach to a priori 'knowledge' is de rigueur in Traditional Thought, (ii) It has been going on for over two millennia, and (iii) It is imagined that by examining the meaning of words the Armchair Philosopher is actually studying the world itself, and not simply inspecting the supposed meaning of a few specially-selected, and unrepresentative expressions. [We saw this in Essay Two. See also, Essay Twelve Part One.]


This is a hallmark of traditional, ruling-class thought: derive fundamental truths about 'reality', valid for all of space and time, from the supposed meaning of a handful of words, and then impose these 'truths' on nature, dogmatically.


True to form, and consistent with the traditional view of philosophy he had been socialised to accept (as a result of his education in bourgeois society): Engels restricted his comments neither (a) to examples of motion he had personally investigated nor (b) to the entire body of examples witnessed by humanity since records began. Despite this, he still felt confident that he could extrapolate from his own understanding of a few ordinary-looking words to conclusions 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.]


In fact, what Engels actually did -- and this is the extent of the 'careful' scientific research he carried out in this area -- all he did was copy the obscure 'analysis' of motion he found in Hegel's Logic, an analysis which, as we saw in Essay Five, was defective anyway.


As we shall also see (in Essays Nine Part One and Two, and Twelve (summary here)), this fact alone has revealing ideological implications.


Again, as George Novack pointed out:


"A consistent materialism cannot proceed from principles which are validated by appeal to abstract reason, intuition, self-evidence or some other subjective or purely theoretical source. Idealisms may do this. But the materialist philosophy has to be based upon evidence taken from objective material sources and verified by demonstration in practice...." [Novack (1965), p.17. Bold emphasis added.]


This brands Engels's work (in this area), Idealist -- which shouldn't surprise us given its origin in Hegelian, and Ancient Greek, Mysticism. Upside down or 'the right way up', Engels's conclusions are clearly (and solely) based on an "appeal to abstract reason, intuition, self-evidence or some other subjective or purely theoretical source...", and should be rejected as a result.


Word Count: 8,860


Latest Update: 06/04/17


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