Essay Five: Why Motion Isn't A Contradiction
Visitors are encouraged to read this Essay in conjunction with Essay Four Part One and Essay Eight Parts One, Two and Three.
Internet Explorer 11 will no longer play the videos I have posted to this page. As far as I can tell, they play as intended in other Browsers. However, if you have Privacy Badger [PB] installed, they won't play in Google Chrome unless you disable PB for this site. They play in IE11 if you have upgraded to Windows 10! It looks like the problem is with Windows 7 and earlier versions of that operating system.
If you are using Internet Explorer 10 (or later), you might find some of the links I have used won't work properly unless you switch to 'Compatibility View' (in the Tools Menu); for IE11 select 'Compatibility View Settings' and add this site (anti-dialectics.co.uk). Microsoft's browser, Edge, automatically renders these links compatible; Windows 10 does likewise. I don't yet know if that is the case with Windows 11.
However, if you are using Windows 10, IE11 and Edge unfortunately appear to colour these links somewhat erratically. They are meant to be mid-blue, but those two browsers render them intermittently light blue, yellow, purple and red!
Firefox and Chrome reproduce them correctly.
Several browsers also appear to underline these links erratically. Many are underscored boldly in black, others more lightly in blue! They are all meant to be the latter.
Finally, if you are viewing this with Firefox, you might not be able to read all the symbols I have used; that browser often replaces them with a "º". Chrome and Edge reproduce them correctly; I don't know if that is the case with other browsers.
As is the case with all my Essays, nothing here should be read as an attack either on Historical Materialism [HM] -- a scientific theory I fully accept --, or, indeed, revolutionary socialism. I remain as committed to the self-emancipation of the working class and the dictatorship of the proletariat as I was when I first became a revolutionary over thirty-five years ago.
The difference between Dialectical Materialism [DM] and HM, as I see it, is explained here.
Several readers have complained about the number of links I have added to these Essays because they say it makes them very difficult to read. Of course, DM-supporters can hardly lodge that complaint since they believe everything is interconnected, and that must surely apply even to Essays that attempt to debunk that very idea. However, to those who do find these links make these Essays difficult to read I say this: ignore them! Unless, of course, you want to access further supporting evidence and argument for a particular point, or a certain topic fires your interest.
Others wonder why I have added links to subjects or issues that are part of common knowledge (such as recent Presidents of the USA, UK Prime Ministers, the names of rivers and mountains, films, or certain words that are in common usage). I have done so for the following reason: my Essays are read all over the world by people from all 'walks of life', so I can't assume that topics which are part of common knowledge in 'the west' are equally well-known across the planet -- or, indeed, by those who haven't had the benefit of the sort of education that is generally available in the 'advanced economies', or any at all. Many of my readers also struggle with English, so any help I can give them I will continue to provide.
Lastly, on this specific topic, several of the aforementioned links connect to web-pages that regularly change their URLs, or which vanish from the Internet altogether. While I try to update these links when it becomes apparent that they have changed or have disappeared, I cannot possibly keep on top of this all the time. I would greatly appreciate it, therefore, if readers informed me of any dead links they happen to notice.
In general, links to 'Haloscan' no longer seem to work, so readers needn't tell me about them! Links to RevForum, RevLeft, Socialist Unity and The North Star also appear to have died.
It is also worth pointing out that 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 further details.
[**Exactly how this applies to DM will, of course, be explained in several other Essays published at this site (especially here, here and here). In addition to the three links in the previous paragraph, I have summarised my argument (but this time written for absolute beginners!) here.]
It is also worth pointing out that a good 25% of my case against DM has been relegated to the End Notes. Indeed, in this particular Essay, much of the supporting evidence and argument is to be found there. That has been done to allow the main body of the Essay to flow a little more smoothly. In many cases, I have added numerous qualifications, clarifications and considerably more detail to what I have to say in the main body. In addition, I have raised several objections (some obvious, many not -- and some that might well have occurred to the reader) to my own arguments, to which I have then responded. [I explained why I have adopted this tactic in Essay One.]
If readers skip this material, then my replies to any qualms or objections they might have will be missed, as will my expanded comments and clarifications.
[Since I have been debating this theory with 'dialectical comrades' for well over 25 years, I have heard all the objections there are! Many of the more recent on-line debates are listed here.]
Update 07/03/2014: I have just received a copy of Burger et al (1980), the existence of which I had been unaware until a few weeks ago. One of the contributors to this book, Hyman Cohen [Cohen (1980)] seems to have anticipated (and answered) one or two of the points I have raised in this Essay. Unfortunately, Cohen's 'answers' also fail miserably; I will attempt to explain why that is so in a future re-write of this Essay.
Update 29/11/2016: I have now added a few thoughts about Cohen's egregious logical confusions to Essay Four Part One.
Finally, anyone puzzled by the unremittingly hostile tone I have adopted toward DM/'Materialist Dialectics' [MD] in these Essays might do well to read this first.
As of September 2023, this Essay is just over 96,000 words long; a much shorter summary of some of its main ideas can be accessed here, an even shorter one, here.
The material presented below does not represent my final view of any of the issues raised; it is merely 'work in progress'.
[Latest Update: 01/09/23.]
Anyone using these links must remember that they will be skipping past supporting argument and evidence set out in earlier sections.
If your Firewall/Browser has a pop-up blocker, you will need to press the "Ctrl" key at the same time or these and the other links here won't work!
I have adjusted the font size used at this site to ensure that even those with impaired vision can read what I have to say. However, if the text is still either too big or too small for you, please adjust your browser settings!
(1) Introduction
(2) Dialectical 'Contradictions'
(b) Formal And Colloquial Contradiction Vs 'Dialectical Contradictions'
(c) 'Resolving' Contradictions
(d) Hegel Screws Up
(e) Disambiguation
(3) Initial Problems
(b) "Solved" In What Way? And By Whom?
(e) Motion 'Itself'
(4) Do Contradictions Explain Motion? Or Merely Re-Describe It?
(b) Are Contradictions Causes?
(ii) Are These Even 'Dialectical' Contradictions?
(iii) Are These Contradictions Real Or Are They Merely Fictional?
(c) 'Internal Contradictions' And Motion
(5) Is Engels's Theory At All Comprehensible?
(c) A First Attempt At Disambiguation
(d) A Second Attempt At Disambiguation
(e) Fatal Ambiguity
(6) The Classical Response To Zeno
(b) Space To Let
(8) Further Problems
(a) The Background To Engels's Argument?
(i) Interlude One -- Moving Pictures
(i) Interlude Two -- 'Appearances To The Contrary'
(i) Interlude Three -- Terminology
(d) Samuel Beckett Eat Your Heart Out
(9) No Word Is An Island -- Philosophers Ignore Ordinary Language
(b) Ordinary Language And Paradox
(d) Ordinary Objects Regularly Do The Impossible
(10) 'Dialectical Objects' Do The Oddest Things
(a) Moving While Remaining Perfectly Still
(b) Do 'Dialectical Objects' Move Or Simply Expand?
(c) Or Do 'Dialectical Objects' Concertina?
(d) Coordinates To The Rescue?
(11) Everyday Miracles?
(a) Ordinary Objects Behave 'Miraculously'
(i) Interlude Four -- Movement Where There Is No Movement
(b) Yet More 'Anti-Dialectical' Examples Hegel And Engels Simply Ignored
(12) Inferences From Language To The World
(a) Thought Experiments In Place Of Scientific Investigation
(13) Conclusion
(14) Notes
(15) Appendix A: Thomas Weston -- How To 'Resolve' A Contradiction
(16) References
Summary Of My Main Objections To Dialectical Materialism
Abbreviations Used At This Site
In this Essay the role that 'contradictions' are supposed to play in explaining motion and change will be critically examined, and at a level of detail never before attempted by a revolutionary socialist in the entire history of Marxism.1
[DM = Dialectical Materialism/Materialist, depending on the context; FL = Formal Logic.]
In general, DM-theorists illustrate what they mean by the 'contradictory nature of reality' by appealing to a handful of examples (which they have been using and re-using, over and over, for more than a century), one of which is loosely based on a paradox invented by an ancient Greek mystic called Zeno. So, in order to highlight the limitations of FL Engels directed the attention of his readers to the 'contradictory nature of motion', depicting it in the following way:2
"[S]o long as we consider things as at rest and lifeless, each one by itself, alongside and after each other, we do not run up against any contradictions in them. We find certain qualities which are partly common to, partly different from, and even contradictory to each other, but which in the last-mentioned case are distributed among different objects and therefore contain no contradiction within. Inside the limits of this sphere of observation we can get along on the basis of the usual, metaphysical mode of thought. But the position is quite different as soon as we consider things in their motion, their change, their life, their reciprocal influence on one another. Then we immediately become involved in contradictions. Motion itself is a contradiction: even simple mechanical change of position can only come about through a body being at one and the same moment of time both in one place and in another place, being in one and the same place and also not in it. And the continuous origination and simultaneous solution of this contradiction is precisely what motion is." [Engels (1976), p.152.]3
Engels openly derived the above idea from the über-mystic himself, Hegel. [Notice how these ideas originated with mystics?] In the above passage, Engels linked change with motion and then both with 'contradictions' that supposedly exist in nature and society (something else he confidently asserted elsewhere in the same book).
However, before this passage is examined in detail there are several problems it presents that will need to be addressed first since they influence the overall interpretation placed on the conclusions Engels effortlessly drew. Left unresolved they threaten to undermine completely what he had to say about motion and change --, and much else besides.
But, before Engels's enigmatic words are examined in detail, some sense needs to be made of the phrase "dialectical contradiction" and the idea that reality is 'fundamentally contradictory'.
[The following material used to form part of Note 1. I begin my actual analysis of Engels's words quoted above, here.]
As we are about to discover it is impossible to form any clear idea of the theory that reality is fundamentally contradictory. This Essay will however concentrate on one aspect of this claim: Engels's (and derivatively on Hegel's) remarks concerning the supposedly contradictory nature of motion. In addition to the passage quoted in the previous sub-section, we have the following remarks that are connected (directly or indirectly) with that specific idea:
"Instead of speaking by the maxim of Excluded Middle (which is the maxim of abstract understanding) we should rather say: Everything is opposite. Neither in heaven nor in Earth, neither in the world of mind nor of nature, is there anywhere such an abstract 'either-or' as the understanding maintains. Whatever exists is concrete, with difference and opposition in itself. The finitude of things will then lie in the want of correspondence between their immediate being, and what they essentially are.
"Contradiction is the very moving principle of the world: and it is ridiculous to say that contradiction is unthinkable. The only thing correct in that statement is that contradiction is not the end of the matter, but cancels itself. But contradiction, when cancelled, does not leave abstract identity; for that is itself only one side of the contrariety. The proximate result of opposition (when realised as contradiction) is the Ground, which contains identity as well as difference superseded and deposited to elements in the completer notion." [Hegel (1975), p.174; Essence as Ground of Existence, §119. Bold emphases added.]
"[B]ut contradiction is the root of all movement and vitality; it is only in so far as something has a contradiction within it that it moves, has an urge and activity." [Hegel (1999), p.439, § 956. Bold emphasis added.]
"Dialectics…prevails throughout nature…. [T]he motion through opposites which asserts itself everywhere in nature, and which by the continual conflict of the opposites…determines the life of nature." [Engels (1954), p.211.]
"[Among the elements of dialectics are the following:] [I]nternally contradictory tendencies…in [a thing]…as the sum and unity of opposites…. [E]ach thing (phenomenon, process, etc.)…is connected with every other…. [This involves] not only the unity of opposites, but the transitions of every determination, quality, feature, side, property into every other….
"In brief, dialectics can be defined as the doctrine of the unity of opposites. This embodies the essence of dialectics…. The splitting of the whole and the cognition of its contradictory parts…is the essence (one of the 'essentials', one of the principal, if not the principal, characteristic features) of dialectics….
"The identity of opposites…is the recognition…of the contradictory, mutually exclusive, opposite tendencies in all phenomena and processes of nature…. The condition for the knowledge of all processes of the world in their 'self-movement', in their spontaneous development, in their real life, is the knowledge of them as a unity of opposites. Development is the 'struggle' of opposites…. [This] alone furnishes the key to the self-movement of everything existing…. The unity…of opposites is conditional, temporary, transitory, relative. The struggle of mutually exclusive opposites is absolute, just as development and motion are absolute…." [Lenin (1961), pp.221-22, 357-58. Italic emphases in the original; bold emphases added. Several paragraphs merged.]
"Motion is a contradiction, a unity of contradictions." [Ibid., p.256.]
[For Hegel's more detailed (and even more obscure) remarks on this topic, see here.]
The problem is that the entire theory has been handled with the utmost lack of clarity by its proponents (the work of Graham Priest excepted, of course -- although it is arguable that the 'contradictions' on which he focuses aren't even 'dialectical' to begin with; on that, see here and here).
In Essay Four Part One, Essay Six, Essay Eight Parts One, Two, and Three and Essay Eleven Part One (as well as in the present work), I have shown that while DM-theorists frequently use the term "contradiction" (among other things, in their attempt to expose the (alleged) limitations of FL), the vast majority display little or no comprehension of the subject matter itself (i.e., FL and the word "contradiction" itself!). Nevertheless, that hasn't prevented them from claiming that their understanding is superior to that displayed by qualified logicians themselves.
[Essay Four Part One (link above) showed how far from the truth that claim is!]
According to dialecticians, one of the advantages of a wider (Hegelian) application of the term "contradiction" is that it allows them to account for motion and change. Contrast that with those who confine themselves to the straight-jacket of FL, or even the cloying banalities of 'commonsense', who employ conceptual resources totally inadequate to the task howsoever much they seem to work in everyday contexts.
Or so it might be argued...
Despite this, as we will discover in what follows, the above claims are wildly inaccurate -- at least, with respect to motion and change. Indeed, as several other Essays published at this site also show, not only is DL incapable of accounting for change itself, dialecticians struggle to account for something as mundane as a bag of sugar!
[DM = Dialectical Materialism/Materialist, depending on the context; FL= Formal Logic; DL = Dialectical Logic.]
Formal And Colloquial Contradictions Vs 'Dialectical Contradictions'
Clearly, the word "contradiction" is a technical term in FL, but, as we are about to find out, it is woefully misunderstood by DM-theorists themselves.
[LOC = Law of Non-Contradiction.]
As far as ordinary language is concerned, one of the ways in which we are able to speak about change involves the (implicit or even explicit) use of a linguistic rule that many misconstrue as a logical truth (i.e., the LOC), which nevertheless enables us to draw specific inferences from what might otherwise appear to be contradictory propositions. So, if two apparently contradictory sentences are held true at different times, then (given other considerations) speakers of that language would normally conclude that the subject of those sentences had changed. For instance, consider the following two (semi-formal) sentences:
C1: NN isn't a member of the Labour Party, at t1.
C2: NN is a member of the Labour Party, at t2. [t2 > t1]
Obviously, a change like that would usually be expressed in ordinary language more directly -- either by the use of tensed verbs or the employment of a paraphrase of some sort. For instance:
C1a: NN wasn't a member of the Labour Party last week.
C2a: NN is a member of the Labour Party today.
C2b: NN has just joined the Labour Party.
This means that apparently contradictory sentences like these -- coupled with a wider use of the negative particle (in all its forms), in tandem with the rich vocabulary available to us in the vernacular (e.g., the use of verbs, adjectives, adverbs, pronouns, etc.) -- are integral to our ordinary notion of change. This alone shows that the claim dialecticians make that ordinary language and FL can't cope with change is a gross distortion. As we can see, it is in fact the opposite of the truth.
Of course, this facility we have with language is rather obvious; indeed, it appears to be so blindingly obvious that DM-fans regularly misconstrue it, or they fail to see its significance.
[It is worth adding that the above isn't, of course, the only way we can speak about change in ordinary language! On the seemingly countless ways we are able to do that, see here.]
If so, the allegation that ordinary language and FL can't cope with, or account for, change isn't just the opposite of the truth, it is quite bizarre. In fact, without the resources available to us in the vernacular, human beings wouldn't be able to conceptualise change at all, let alone evaluate the many and varied theories of change that philosophers regularly concoct.
[And that comment applies equally well to the theories that scientists and dialecticians come out with. Again, ordinary language is capable of handling change far better than the obscure jargon invented by metaphysicians; in fact, it is demonstrably and markedly better than the wooden language concocted by Christian Mystics like Hegel. On that, see here.]
In that case, if, by their peculiar use of language, dialecticians end up undermining the vernacular, their theory can't fail to be problematic, if not incomprehensible --, which is indeed what this Essay will demonstrate (at least with respect to their 'theory of motion').
Now, as far as FL is concerned, two propositions are contradictory just in case they can't both be true and can't both be false, at once. [The second condition is almost invariably ignored by DM-critics of FL -- i.e., that two contradictory propositions can't both be false at the same time. Some even try to deny there is a genuine distinction here (so such individuals happily confuse inconsistencies with contradictions), even after it has been pointed out to them! In fact, they tend to call such fine distinctions and careful attention to detail "pedantry" (or they declare them "merely semantic"). The profound dialectical confusion that results if such distinctions are ignored can be seen in all its glory, here. Its importance will emerge as this Essay unfolds. On the confusion it would create in science, let alone anywhere else, if contradiction and inconsistency were conflated, see here.]
Naturally, when two contradictory propositions are conjoined -- as in this formal sentence: ¬(p & ¬p) -- it represents the simplest form of FL-contradiction (and, in many cases, that is also the case in ordinary language (when it has been interpreted)).
[The difference between "contradictory" and "contradiction", also ignored by DM-fans, is explained here.]
Two examples of the potentially infinite number of more complex FL-contradictions are the following:
C3: ¬[(p → q) v (p → r) ↔ (p → (q v r))].
C4: ¬[¬(Ex)(Fx & ¬Gx) ↔ (x)(Fx → Gx)].
[In the above, "(E...)" is the existential quantifier (equivalent to "at least one" or "some"); "↔" is a biconditional sign, "iff" (which stands for "if and only if"); "(x)" is the universal quantifier (equivalent to "all" or "every"); "&" stands for "and"; "v" is the inclusive "or" (i.e., "and/or"); "¬" stands for the negation operator ("It is not the case that..."); "→" is the conditional sign (i.e., "if...then"); "p", "q", and "r" are propositional variables; "F" and "G" are one-place, first-level predicate letters; and "x" is a second-level, place-holding symbol. (More details can be accessed, here and here.)]
C3 reads: "It isn't the case that ((if p then q) or if (p then r)) if and only if (if p then (q or r))."
C4 reads: "It isn't the case that [(there isn't something which is F and not G) if and only if (everything which, if it is F, is also G)]"; or even,
C4a: "It isn't the case that [(there isn't anything which is F and not G) if and only if (everything which, if it is F, is also G)]."
[C4a is perhaps a little more colloquial.]
Some might wonder when formal sentences like these would ever be used. Well, Mathematical Logic, the Foundations of Mathematics, Discrete Mathematics, and Number Theory -- to name just a few disciplines -- use propositions like these all the time, and, indeed, others far more complex. (This links to a PDF.)
These are, of course, just two of the potentially infinite number of logical contradictions which can be generated in MFL. DM-theorists would be hard-pressed to find space -- even in their quirky universe -- for contradictions like these (once they have been interpreted).
[MFL = Modern Formal Logic; LEM = Law of Excluded Middle; PB = Principle of Bivalence.]
Moreover, dialecticians often confuse the LEM, the PB, propositional bi-polarity and the LOC with one another -- and, what is more, all of them with opposites, inconsistencies, absurdities, contraries, paradoxes, puzzles, quandaries, oddities, irrationalities, oppositional processes, antagonisms, forces of attraction and repulsion, events that go contrary to expectations, alongside a host of other idiosyncratic, non-equivalent concepts. In fact, they are so eager to see contradictions everywhere, that they find they have to tinker with the meaning the word itself so that (for them) it becomes synonymous with "struggle", "conflict", or "opposition".
[Numerous examples of these and other dialectical confusions in this area were given in Essays Four, Six, Eight Parts One, Two and Three and Eleven Part One.]
A typical example of DM-profligacy in this respect (that is, in the way that DM-fans carelessly and unthinkingly throw "contradiction" at the page or screen) surfaced in a letter sent to Socialist Worker at the end of August 2011:
"I'm writing regarding Charlie Hore's article on economic growth during the reform period in China (Socialist Worker, 20 August). It doesn't mention the powerful contradictions that emerged within the ruling bureaucracy as a result of the reforms. Not all sectors of the bureaucracy have benefited from the reforms. There has been a shift from ideological campaigns towards a performance-based notion of state legitimacy. This has meant that many officials have experienced anxiety about their relevance in Chinese politics and have been dragged into protest movements. A socialist analysis has to make sense of these contradictions." [Bold emphasis added. Paragraphs merged. I have quoted several more cases of DM-profligacy over the use of this word in Essay Eight Part Two, here, here, here, here, and here -- but there countless other examples I could have used.]
So, according to the above, tensions within the communist hierarchy are 'contradictions'. But, no one ever explains why such things should be called "contradictions" to begin with, especially when they are far more accurately to be described as "tensions" or "conflicts". Nor do they even think to show that such 'contradictions' are 'dialectical'. In this case, for example, the above letter writer never once asked if the elements (the supposed 'dialectical opposites') in any of these 'contradictions' implied each other. [The answer, it seems, is 'No they don't'. If anyone thinks differently, please email me with the details.] Was it ever asked if either can exist without the other? No, that was never asked, or answered. But, that is quite unlike the alleged 'contradiction' between the bourgeoisie and the proletariat. There, these two classes supposedly imply one another so that neither can exist without that other. [I have used "alleged" and "supposedly" here for reasons set out in Essay Eight Part Two.] There is no 'internal' relation exposed in the above example from China, no 'interpenetrated opposites'. Do the tensions in the Chinese ruling elite struggle with and then turn into each other (which is what the DM-classics assure all such 'dialectical opposites' do)? Not that anyone has noticed.
So, even if it were correct to say this is a 'contradiction', it can't be a 'dialectical contradiction'. In that case, what is it doing in the above article?
This is just is standard fare in DM-circles. Anyone who harbours doubts should try the following experiment: Over the next few years, as you read the material pumped out by DM-fans, make a note of the number of times the word "contradiction" has been airily thrown at the page or screen and the number of times the individual(s) doing that bother to show that the 'contradictions' they see everywhere are indeed 'dialectical'. That is: how many times they ask the sort of questions posed in the previous paragraph and how many times they are answered. After having read such material now for nigh on forty years, I have only ever seen this done twice: (i) Concerning the alleged 'dialectical relation' between the proletariat and the capitalist class, and (ii) In connection with the 'master-slave dialectic' -- both of which cases I have destructively criticised in Essay Eight Part Two, here and here. Hence, in connection with the overwhelming number of cases encountered by those willing to rise to the above challenge, I can safely predict the above questions won't be asked (let alone answered) by the individuals carelessly using the word "contradiction", which means the 'contradictions' they speak about won't turn out to be 'dialectical'.
Some might conclude that this is all academic, and represents just another example of Ms Lichtenstein's abstract formalism and pedantry; but that isn't so. [On 'pedantry', see here.] There are important political reasons for rejecting the use of "contradiction" in the loose and cavalier way it is employed by Dialectical Marxists. [On that, see Essay Nine Part Two.]
Specifically:
(1) The use of this word 'allows' dialecticians to argue in favour of anything they find expedient and its opposite -- often this trick is often performed by the very same dialectician, on the same page, same paragraph, or even in the same speech! --, no matter how anti-Marxist or counter-revolutionary that anything might prove to be. These moves are then 'justified' on the basis that since everything is 'contradictory', and a 'unity of opposites', Marxist theory and practice should be contradictory, too! Here is a classic example (courtesy of 'The Great Teacher', Stalin):
"The flowering of cultures that are national in form and socialist in content under the dictatorship of the proletariat in one country for the purpose of merging them into one common socialist (both in form and content) culture, with one common language, when the proletariat is victorious all over the world and when socialism becomes the way of life -- it is just this that constitutes the dialectics of the Leninist presentation of the question of national culture. It may be said that such a presentation of the question is 'contradictory.' But is there not the same 'contradictoriness' in our presentation of the question of the state? We stand for the withering away of the state. At the same time we stand for the strengthening of the dictatorship of the proletariat, which is the mightiest and strongest state power that has ever existed. The highest development of state power with the object of preparing the conditions for the withering away of state power -- such is the Marxist formula. Is this 'contradictory'? Yes, it is 'contradictory.' But this contradiction us bound up with life, and it fully reflects Marx's dialectics." [Political Report of the Central Committee to the Sixteenth Congress of the CPSU(B), 27/06/1930. Bold emphases alone added; quotation marks altered to conform with the conventions adopted at this site. Paragraphs merged.]
So, less democracy was also more democracy and the suppression of national culture is the opposite of what it appears to be (for those who don't 'understand' dialectics, of course)!
[Several more examples of this bizarre, almost Zen, phenomenon were given in Essay Nine Part Two.]
(2) This linguistic dodge is also used to rationalise substitutionist strategies, tactics and moves on the basis that even though Marx insisted on the self-emancipation of the working class, we can substitute one or more of the following classes or social fractions for them: (a) The Party, (b) The Red Army, (c) 'Third World' guerrillas, (d) 'Progressive' nationalists, (e) Students, (f) Sympathetic, left-leaning politicians, or (g) An assortment of social forces, 'rainbow coalitions' and protest groups, no matter how contradictory this might otherwise seem. And concerning those who might object..., well, once again, they just don't 'understand' dialectics -- nor, indeed, do they comprehend the 'contradictory' nature of Marxism, the class war, the former USSR..., etc., etc.
(3) The use of this word 'allows' DM-fans to look at the long-term failure of Dialectical Marxism and fail to see it for what it is: a protracted and profound refutation of their core theory, 'Materialist Dialectics'. Indeed, it 'allows' them to interpret this abysmal record as the opposite of what it is -- on the grounds that appearances 'contradict' underlying 'essence'. So, if Dialectical Marxism looks like it is hopelessly unsuccessful and seems to be a long-term, abject failure, the opposite is in fact the case. This then encourages dialecticians to stick their heads in the very same sands into which our entire movement has been running for several generations.
(4) Because of Alternative (3), above, this word also provides DM-acolytes with a source of consolation for the almost total ineffectiveness of their entire movement, its divisiveness and the sectarianism of its warring parties/tendencies: "Well, what else can you expect in a contradictory universe? Marxism should look the opposite of the way it really is! Dialectics allows us to grasp this contradiction." Indeed, as Lenin pointed out:
"The splitting of a single whole and the cognition of its contradictory parts...is the essence (one of the 'essentials,' one of the principal, if not the principal, characteristics or features) of dialectics.... The struggle of mutually exclusive opposites is absolute, just as development and motion are absolute...." [Lenin (1961), pp.357-58. Quotation marks altered to conform with the conventions adopted at this site. Paragraphs merged; bold emphasis alone added.]
So, "splitting" is an "essential", if not "the principle" aspect of this theory, with "struggle" an "absolute". Plainly, this "essential" feature must also involve the relations between 'comrades'. That was something Engels also emphasised, and he openly connected it with 'dialectics':
"It would seem that any workers' party in a large country can develop only through internal struggle, as indeed has been generally established in the dialectical laws of development." [Engels to Bernstein, October 20, 1882; MECW Volume 46, p.342. Bold emphasis added.]
[All of the above have been fully documented and substantiated in Essay Nine Part Two. Readers are directed there for more details. I have also posted many more examples of the odd things DM-fans say about the 'contradictions' they seem to see everywhere, in Essay Eight Part Two -- here and here, for instance.]
So, this isn't 'pedantry', nor is it merely 'academic' point-scoring. "Contradiction", as it has been, and still is being used by DM-fans, possesses disastrous political and ideological implications.
Be this as it may, DM-theorists themselves would be the first to point out that their interest doesn't lie in contradictory propositions, per se, but with real material forces that express or even constitute conflict in nature and society (but only if they have been confirmed in practice, etc.). Furthermore, since the vast majority of classical DM-theorists believe that reality itself is fundamentally contradictory, then, according to them, propositions which accurately describe or picture the world ought to be contradictory, too -- i.e., they should truthfully reflect the contradictions that exist in nature and society.
However, because (contradictory) propositions are, manifestly, linguistic expressions they clearly aren't material forces as such. That must mean they aren't oppositional per se, even though they supposedly reflect, or can be used to reflect (at some level), the dynamic nature of reality -- again, according to dialecticians.
On the other hand, even if contradictory propositions were oppositional, they would only be so in a derivative sense. In any case, the idea here appears to be that while objects and processes in nature are contradictory (or their inter-relationships/inter-actions are), and subject to change, any use of language capable of depicting reality must reflect this both accurately and adequately if it is to be precise and objective.
Or, so a (very brief) case for the defence might proceed...
'Resolving' Contradictions
Nevertheless, the principles that underlie FL merely commit us to the view that two contradictory propositions can't both be true and can't both be false at the same time. Hence, on this basis any supposition or claim that two supposedly contradictory propositions can be, or, indeed, actually are both true at once (or can be, or are both false at once -- as noted above, dialecticians appear to be unaware of that particular caveat) would automatically be regarded as in some way mistaken or confused.
Indeed, that fact alone would provide sufficient grounds for questioning whether one or both of a pair of allegedly true 'contradictory' propositions so described were in fact propositions to begin with. If it is unclear what is being proposed (in the sense that something determinate has been put forward for consideration), then anyone attempting to do this can't be proposing anything determinate -- that is, this side of their words being disambiguated. At least, no more than a door can be (literally) opened and shut at the same time.
[Examples of disambiguation in action will be given below and later in the main body of this Essay. See also here.]
Be this as it may, several factors might contribute to this apparent impasse:
(a) The said 'propositions' could contain typographically similar words that have different denotations;
(b) They could be using ambiguous, vague, or figurative language;
(c) They might be drawn from different areas of discourse; or,
(d) They might have been taken out of context, and so on.
Based on one or more of the above considerations, the presumption would always be that both 'halves' of an alleged contradiction (i.e., at least two supposedly true contradictory indicative sentences) could only be held true by someone in the grip of some form of linguistic, interpretative or psychological confusion. 'Contradictions' that have been generated in this way wouldn't normally be viewed as capable of revealing 'fundamental truths about reality'. In fact, it is far more likely that any such claim would merely underline the linguistic naivety of the individual that had been so easily misled.
In that case, the expectation would be that a disambiguation or a clarification of any such alleged 'contradiction' would resolve the 'problem'. Only an exceedingly naive person (or worse, a Mad Dog Idealist, like Hegel) would conclude that just because certain 'concepts', or sentences appeared to be contradictory, nature and society must be contradictory, too.
Indeed, under normal circumstances, one would be forgiven for concluding that the above 'austere' approach to what seem (to some) to be 'contradictions' would recommend itself to those who at least claim to be materialists. Not only was the alternative view -- that there really are 'contradictions' in nature and society -- invented by card-carrying mystics and Idealists, it clearly 'implies' that the natural world possesses properties that are only rightly to be attributed to human beings -- such as, the ability to converse, argue, and disagree. In short, it implies that extra-mental objects and processes are capable of contradicting one another, which in turn would suggest that 'dialectics' may only 'get off the ground' by anthropomorphising 'reality'.
In addition, the 'austere' approach adopted at this site (which advocates the consistent disambiguation of putative contradictions) undermines another Idealist doctrine, that fundamental truths about reality may be inferred solely from the (supposed) logical and grammatical properties of language. Or, to be more accurate (in this particular case), that they may only be derived on the back of a series of sophomoric errors concerning the nature of contradictions themselves outlined a few paragraphs back (but in much more detail, here).
Naturally, DM-apologists will view counter-claims like these with no little suspicion. Indeed, the above remarks might even appear to be both dogmatic and aprioristic. Furthermore, it could be argued that this obsession with the fine detail of linguistic usage itself collapses into LIE, since it presumes to offer linguistic solutions to what are in fact philosophical, scientific and practical problems.
[LIE = Linguistic Idealism; follow the link for an explanation.]
The opposite is in fact the case. The approach adopted at this site seeks to undermine a longstanding metaphysical dogma (which dialecticians themselves have adopted) that fundamental truths about reality may be inferred solely from language, from 'thought', or even from certain 'concepts' -- what Engels had to say about motion being a classic example. Clearly, it is the world (or, rather, our appeal to the facts) that makes what we say true or false; it isn't what we say, or how we say it that determines the nature of reality. Nor does what we think dictate to nature and society what either or both must be like. It is the opposite approach -- the traditional view of Philosophy --, that such truths can be inferred from though/language alone, which is integral to Idealism, 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 emphases added.]
[As Essay Seven will show, DM-'contradictions' can't be confirmed either in or by experience, nor can they be verified in any other way. (The accusation that this view of confirmation -- coupled with the emphasis placed on verification in these Essays -- smacks of 'positivism', or even 'empiricism', has been neutralised, here.) In Essay Twelve, the ideological motivation underlying the contrary, traditional view will be exposed for what it is: a form of LIE itself (summary here).]
Nevertheless, it is important to recognise when the descriptive, representational or expressive capacities of language begin to break down. Those concerns certainly implicate and involve the entire range of DM-theories since they have the disconcerting habit of breaking down alarmingly quickly when examined closely. They invariably turn out to be hopelessly vague, terminally confused, or even non-sensical and incoherent -- as several Essays at this site have amply demonstrated.
Furthermore, it is equally important to be able to distinguish spurious attempts to depict 'reality' from the genuine article. DM-theorists themselves attempt to do this when they highlight the confused or self-contradictory nature of rival theories, advocating their rejection on that basis alone. [That claim has been fully documented and substantiated in Essay Eleven Part One.]
Despite this, DM-theorists certainly believe that their approach begins with reality (albeit 'mediated' by the conceptual and practical resources available to human beings at any given time). They then require our linguistic resources, our vocabularies and concepts be adapted, modified or even upgraded accordingly. On that basis, if nature is contradictory and ordinary language (or even FL ) can't accommodate this (assumed) fact, that must be because those resources are either limited or defective in some way. In that case, they require supplementation, revision or even reinterpretation, fortified by concepts drawn from 'Materialist Dialectics' -- or, where necessary, from the Mother Lode Itself, Hegel's 'Logic' (albeit, put 'back on its feet').
It isn't easy for any (effective) rebuttal of the above claims to avoid appearing dogmatic. Language has been moulded throughout history by an evolving set of social norms, practices and conventions, which were themselves refined by factors that have operated across different Modes of Production for millennia. Because of this, it might seem possible to argue that when faced with situations which appear to be 'contradictory' human beings not only could, they actually did, develop and then adopt words, categories and concepts that could rightly be described as "dialectical".
[However, the 'factual basis' underlying that supposition will be undermined in Essay Twelve Parts Two, Three and Seven and Essay Fourteen Part One (summaries here and here), and again briefly, below.]
Even so, given other conventions that were actually adopted -- that is, in practice; no one supposes that overt decisions were taken -- the above scenario is extremely unlikely, if not impossible.
As the word itself suggests, to contradict someone is to gain-say or deny that what they have uttered is true (or false, as the case may be). So, to take a very simple example, if NN says it is raining and MM says it isn't, then (all things being equal) they would be contradicting one another. Furthermore, neither statement would be affected in the slightest if either one of the following were the case (in the local vicinity of these two individuals):
(i) It is pouring down with rain; or,
(ii) It is dry as a bone.
To be sure, those two sentences use the indexical expression, "it". Hence, it could be objected that the ambiguity and relativity of this particular word undermines the status of those two assertions as contradictories. However, that wouldn't be so if it were also stipulated that NN and MM both agree over the meaning and reference of "it". In that case, these assertions would count as genuine contradictories. If so, what they had to say would now become something like the following (illustrated in more detail by J3 and J4):
J1: It is raining.
J2: It isn't raining.
J3: Right now, right here, or near where we are stood/sat/walking/driving (etc.), rain is pouring down.
J4: Right now, right here, or near where we are stood/sat/walking/driving (etc.), there is no rain at all.
As with much else in the vernacular, much greater precision is relatively easy to secure (but, of course, at the expense of increased pedantry).
However, whether or not "It is raining" is actually true in no way affects the fact that these two sentences are contradictory. All that is required is that if one of them is true, the other is false, and vice versa. Moreover, we can say this in advance of knowing which one of these is the case, and even if we never find out or wish to find out. We wouldn't be able to understand anyone who claimed that both NN and MM were mistaken and both J1/J2, J3/J4 were false -- except in the circumstances covered below. Fanciful situations to one side (which was partially the point of the "all things being equal" clause added to the above), how, for example, would it be possible for it to be false that it is raining and false that it isn't raining at the same time, in the same location, in the same respect?
[Recall: DM-fans are oblivious of this additional necessary condition for two sentences to be contradictory -- i.e., that they can't both be false.]
Some might point to the vagueness of sentences like "It is raining". That would seem to mean both of the above sentences could in fact be false, since it might be indeterminate whether or not it is raining. Perhaps the weather is clearing up, so that anyone who said it was raining would be wrong, just as anyone who said it wasn't would be mistaken, too. Maybe someone has turned on a powerful fire hose or rain machine like they use in movies. Undeniably, sentences like these are vague, but just as soon as it had been decided that it is actually raining, then just one of the following sentences would be false and the other true: (a) "It is raining", (b) "No, it isn't raining". The same is the case in reverse -- i.e., if it had been decided that it isn't in fact raining: one of (a) or (b) would be false, but not both. In circumstances like these, we wouldn't be able to make sense of anyone who said both were false, or both were true -- when the truth-status of at least one of them had been decided upon in the manner just specified.
But, what if we can't in principle decide whether or not it is or it isn't raining? In that case, sentences like these would (in principle) lack a truth-value; neither could be deemed true or deemed false -- that is, until a decision either way became possible. In such circumstances, these two sentences would fail even to be propositions. If, in principle, we couldn't decide whether or not it is raining then nothing determinate will have been proposed (i.e., put forward for consideration) by saying it is, or by saying it isn't. I am of course speaking about a radical failure to decide, here; that is, where no one could decide, even in theory, whether or not it was raining in the vicinity of those attempting to determine whether or not it was the one or the other. If it were in principle impossible to decide in such cases, and it had always been impossible to so decide, then there would be no point to uttering such sentences and they wouldn't have entered the language. "It is raining" would lack both a sense and a use. Radically unusual circumstances like this would even call into question the concept of rain itself. If it were impossible to decide in this manner then the word "rain" itself would lack meaning.
Compare this with what was said about 'meskonators' in Essay Eleven Part One. If it is impossible for you, dear reader, to decide if something is or isn't a meskonator, and, indeed, it turned out that no one could so decide, that word would surely lack a meaning.
[This brings in factors associated with what Wittgenstein called "criteria" and "symptoms". I have said more about that topic in Essay Twelve Part One; readers are directed there for more details.]
However, in what might be described as non-radical circumstances, where it still can't be decided whether or not it is training for contingent reasons -- maybe the interlocutors in question are trapped underground, are locked away in a dungeon, can't see outside, are unable to receive any information from the outside world for whatever reason, or can't distinguish rainfall from water cascading from a fire hose or a rain machine, etc., etc. -- then these two sentences would still be contradictory, since if one of them were true (whether or not that fact is actually known), the other would automatically be false, and vice versa.
However, in everyday life (i.e., outwith the use of aesthetic, ethical, political and religious language (etc.) where the meaning of words is often "essentially contestable"), problems like this don't normally arise. So, when in doubt we say things like "It's trying to rain...", "It's spitting, I think...", "I reckon it's clearing up..." or even, "Well, it looks like rain to me!". Only a hardcore contrarian would come out with statements like "It is and it isn't raining" -- perhaps on the basis that there are gaps between the raindrops, or because it is raining in the vicinity, but not, say 100 metres down the road or in the next county. If someone were consistently to adopt such a contrarian approach to all such (indicative) sentences, they would either have very few friends or they would enjoy a severely limited social life. Either that, or they would be diagnosed with a Personality Disorder of some sort. If we all adopted such an attitude, inter-communication would soon grind to a halt. [On that, see here.]
[It is also worth noting that contradicting someone can be aimed at challenging truth and not always confronting falsehood, as many suppose.]
It could be objected that it was earlier claimed that:
...if NN says it is raining and MM says it isn't, then (all things being equal) they would be contradicting one another. Furthermore, neither statement would be affected in the slightest if either one of the following were the case (in the local vicinity of these individuals): (i) It is pouring down with rain, or (ii) It is dry as a bone...
...if NN says it is raining and MM says it isn't, then (all things being equal) they would be contradicting one another. Furthermore, neither statement would be affected in the slightest if either one of the following were the case (in the local vicinity of these two individuals):
(i) It is pouring down with rain; or,
(ii) It is dry as a bone...
whether or not "It is raining" is actually true in no way affects the fact that these two sentences are contradictory.
When it was asserted a few paragraphs later:
But, what if we can't in principle decide whether or not it is or it isn't raining? In that case, sentences like these would (in principle) lack a truth-value; neither could be deemed true or deemed false -- that is, until a decision either way became possible. In such circumstances, these two sentences would fail even to be propositions. If, in principle, we couldn't decide whether or not it is raining then nothing determinate will have been proposed (i.e., put forward for consideration) by saying it is, or by saying it isn't. I am of course speaking about a radical failure to decide, here; that is, where no one could decide, even in theory, whether or not it was raining in the vicinity of those attempting to determine whether or not it was the one or the other. If it were in principle impossible to decide in such cases, and it had always been impossible to so decide, then there would be no point to uttering such sentences and they wouldn't have entered the language. "It is raining" would lack both a sense and a use. Radically unusual circumstances like this would even call into question the concept of rain itself. If it were impossible to decide in this manner then the word "rain" itself would lack meaning.
Which is it to be? If we can't decide whether sentences like these are true or they are false, then how can they be contradictory?
The (hypothetical) objector forgot to quote this caveat:
All that is required is that if one of them is true, the other is false, and vice versa.
And we can arrive at that conclusion well in advance of knowing whether one of them is in fact true or one of them is in fact false. As noted below, those options are based on rules we have for the use of the negative particle, and, as with any rule, it is possible to decide how that rule can or can't, must or mustn't, be applied in advance of actually applying it. For instance, we can decide ahead of time what would and what wouldn't count as offside in football (soccer) even if there is no game actually being played at the time, and even if no more games were ever played --, and even if, during a game, we lost sight both of the pitch and the alleged offence itself (if the pitch were fogbound, for example). Plainly, that is because rules aren't capable of being true or false themselves; they are practical or impractical, useful or useless, applied or mis-applied, etc., etc. Hence, this particular rule (connected with the ordinary use of "contradiction" and the negative particle) is independent of any alleged truth or falsehood, as such.
This topic is, of course, connected with the so-called 'Law of Excluded Middle' [LEM], as that 'law' supposedly features in ordinary discourse. In that case, some might find they agree with Hegel when he asserted the following:
"Instead of speaking by the maxim of Excluded Middle (which is the maxim of abstract understanding) we should rather say: Everything is opposite. Neither in heaven nor in Earth, neither in the world of mind nor of nature, is there anywhere such an abstract 'either-or' as the understanding maintains. Whatever exists is concrete, with difference and opposition in itself. The finitude of things will then lie in the want of correspondence between their immediate being, and what they essentially are." [Hegel (1975), p.174; Essence as Ground of Existence, §119. Bold emphasis added.]
To In relation to which Engels had this to say:
"To the metaphysician, things and their mental reflexes, ideas, are isolated, are to be considered one after the other and apart from each other, are objects of investigation fixed, rigid, given once for all. He thinks in absolutely irreconcilable antitheses. 'His communication is "yea, yea; nay, nay"; for whatsoever is more than these cometh of evil.' [Matthew 5:37. -- Ed.] For him a thing either exists or does not exist; a thing cannot at the same time be itself and something else. Positive and negative absolutely exclude one another, cause and effect stand in a rigid antithesis one to the other.
"At first sight this mode of thinking seems to us very luminous, because it is that of so-called sound common sense. Only sound common sense, respectable fellow that he is, in the homely realm of his own four walls, has very wonderful adventures directly he ventures out into the wide world of research. And the metaphysical mode of thought, justifiable and even necessary as it is in a number of domains whose extent varies according to the nature of the particular object of investigation, sooner or later reaches a limit, beyond which it becomes one-sided, restricted, abstract, lost in insoluble contradictions. In the contemplation of individual things it forgets the connection between them; in the contemplation of their existence, it forgets the beginning and end of that existence; of their repose, it forgets their motion. It cannot see the wood for the trees.
"For everyday purposes we know and can say, e.g., whether an animal is alive or not. But, upon closer inquiry, we find that this is, in many cases, a very complex question, as the jurists know very well. They have cudgelled their brains in vain to discover a rational limit beyond which the killing of the child in its mother's womb is murder. It is just as impossible to determine absolutely the moment of death, for physiology proves that death is not an instantaneous momentary phenomenon, but a very protracted process. In like manner, every organic being is every moment the same and not the same, every moment it assimilates matter supplied from without, and gets rid of other matter; every moment some cells of its body die and others build themselves anew; in a longer or shorter time the matter of its body is completely renewed, and is replaced by other atoms of matter, so that every organic being is always itself, and yet something other than itself." [Engels (1976), pp.26-27. Bold emphases added; quotation marks altered to conform with the conventions adopted at this site. Some paragraphs merged.]
However, as I have argued in Essay Nine Part One (slightly edited):
Nevertheless, it is difficult to see what Hegel was trying to say here. That is because any attempt to interpret him requires the implicit or explicit use of the very terms he claims are misleading. The construal of his work requires decisions be taken about whether he meant either this or that by what he actually said. If an author always means both -- or maybe even neither -- then interpretation is rendered impossible and any attempt to unravel their meaning becomes self-defeating (as we are about to discover).
So, if Hegel were correct, if absolutely "everything is opposite" and there is no "either-or" anywhere in the universe, it would be impossible to disentangle what he meant from what he didn't, since we would be unable to decide whether he believed of, say, any two sentences, P and Q, one or more of the following:
H1: (i) Both P and Q; (ii) either P or Q; (iii) neither P nor Q; or (iv) either P or Q, but not both.
But, if, say, P and Q were inconsistent (that is, if, for instance, Q implies not P, or vice versa -- for clarity's sake an example will be given below), and we interpreted his words one way -- perhaps that he believed both P and Q, since to do otherwise would involve the implicit or explicit use of the dread 'either-or' --, then, plainly, we would have to conclude that he accepted both as part of an "unfolding of truth" here (as he might have put it). By his own lights that would mean, of course, that he would be unfolding error in place of truth!
Hence, in order to reject one or other of the above options, we, too, would be forced to appeal to, or employ, an "either-or" -- that is, we would have to conclude that Hegel accepted P or he accepted Q, but not both.
On the other hand, if we were to remain true to Hegel's dictum -- that "neither in heaven nor in Earth, neither in the world of mind nor of nature, is there anywhere such an abstract 'either-or' as the understanding maintains" --, we would have to conclude he accepted both.
So, any attempt made now to specify exactly what Hegel meant would undermine what he actually said about the use of the "either-or of understanding", for we would have to accept that Hegel asserted one thing, P, or he asserted something else, Q, but not both. Without that assumption it would become impossible to comprehend or defend him. If Hegel genuinely cast doubt on the "either-or of understanding" (and he wasn't being deliberately enigmatic, disingenuous, mendacious or merely playful) -- and assuming he was correct doing so --, then any attempt to interpret him as asserting P or asserting Q would have to conclude that he asserted both. [Again, I give a clear example of this, below.]
In that case, any determinate interpretation of Hegel (that is, any interpretation that settled on one option, not both) would have to ignore his own advice, by reluctantly accepting the protocols expressed in and by the "either-or" of ordinary language (or of 'commonsense', along with its corollaries), and acknowledge that, concerning either P or Q, Hegel accepted only one of them, not both -- that is, that he was a fully paid-up member of The Society For The Promotion Of The Either-Or Of Abstract Understanding.
In that case, truth would advance (as a result of yet another dialectical inversion) by forcing us to disregard Hegel!
In order to make this more concrete, let us suppose that:
"P" is: "Neither in heaven nor in Earth, neither in the world of mind nor of nature, is there anywhere such an abstract 'either-or' as the understanding maintains";
and,
"Q" is: "There is in fact an abstract 'either-or' somewhere in the world of mind or of nature (etc.)."
[As above, Q implies not P, and vice versa.]
So, either Hegel accepted P or he accepted Q -- which would, of course, imply that there is at least one 'either-or' "in heaven or in earth (etc.)" -- i.e., here, in front of us, right here, right now.
On the other hand, if Hegel took his own advice and accepted both P and Q -- thereby rejecting this particular "either-or" --, then not much sense could be made of what he was trying to say.
Incidentally, the above criticism isn't affected by Hegel's own interpretation of these controversial words, nor any technical meaning his epigones might want to attribute to them, since they, too, would have to conclude that he meant this or he meant that, not both. The issue here solely concerns how we are to understand him now, in this world, by our consideration of those very material words (in print, or reproduced on a screen), quoted earlier.
Hence, it is beside the point whether the rationale for Hegel's criticism of the use of such words by the "abstract understanding" is legitimate or not (irony intended). His writings now appear before us as phenomenal objects, hence, given the additional fact that they aren't self-interpreting (especially when we recall that Hegel is no longer alive to explain himself -- but, even then we would have to accept he meant either P or Q, not both), his words face the ordinary cannons we employ elsewhere to understand anyone's speech. In order to read and perhaps interpret Hegel as believing this or that, but not both, we are forced to ignore his advice and employ the dread "either-or".
Naturally, this is just one more reason why ordinary language can't be by-passed or undermined, no matter which 'genius' tries to fool some of us into thinking otherwise.
Once again, it is little use complaining that this is not how Hegel wanted his use of the "either-or" of "understanding" to be interpreted (i.e., we should perhaps view it ironically -- that is, that we should interpret it this way but not that), since he himself holed that complaint well below the water line when he asserted:
"Instead of speaking by the maxim of Excluded Middle (which is the maxim of abstract understanding) we should rather say: Everything is opposite. Neither in heaven nor in Earth, neither in the world of mind nor of nature, is there anywhere such an abstract 'either-or' as the understanding maintains. Whatever exists is concrete, with difference and opposition in itself. The finitude of things will then lie in the want of correspondence between their immediate being, and what they essentially are. Thus, in inorganic nature, the acid is implicitly at the same time the base: in other words, its only being consists in its relation to its other. Hence also the acid is not something that persists quietly in the contrast: it is always in effort to realise what it potentially is." [[Hegel (1975), p.174; Essence as Ground of Existence, §119. Bold emphasis added.]
Hence, if "everything is opposite", and Hegel's works were written somewhere on this planet, and copies of them still take on a physical form in this universe(!), then anything he committed to paper must be its own opposite, too -- or, he was wrong.
[Irony intended again.]
Either way, it would be foolish to believe Hegel was serious (or, and what is far more likely, that he had thought things through with due care) when he wrote the above words, while also agreeing with what he said about the LEM, the dread "either-or".
So, following Hegel's own advice, the above passage should in fact be re-written -- more consistently -- along the following 'Hegelian', deny-there-is-an-'either-or', lines:
"Instead of both speaking and not speaking by the maxim both of Excluded Middle and not Excluded Middle and (which is and is not the maxim of abstract understanding) we should and we shouldn't rather say: Everything is, and some things are not, opposite. Neither in heaven nor in Earth, and both in heaven and in earth, neither in the world of mind nor of nature, and both in the world of mind and of nature, is there anywhere such an abstract 'either-or' as the understanding maintains, but there is, and it is everywhere, too, while it is nowhere as well. Whatever exists is concrete, and it isn't, with difference and opposition, and also without difference or opposition, in itself, and not in itself, too. The finitude of things will and will not then lie in the want of correspondence, but also with actual correspondence, between their immediate being, and what they essentially are, or are not, and, indeed, both. Thus, in inorganic nature, and outside it, the acid is and is not implicitly at the same time, and at other times, the base, but it isn't the base, either: in other words, but also in the same words, its only being, and its many other beings, consist, and do not consist, in its relation, and absence of any relation, to its other, and whatever isn't its other. Hence also the acid is not something, and it is something, that persists quietly, and not quietly, in the contrast, or the accord: it is always, and is it is never, in effort to realise what it potentially is, and what it actually is not." [Hegelianised version of Hegel (1975), p.174; Essence as Ground of Existence, §119.]
Everyday, boring old non-abstract understanding will, I think, readily see what arrant nonsense results from Hegel's 'genius' when we apply his ideas to his own words -- providing we remain in this universe.
Any who object to the above re-write can, of course, neutralise its implications by demonstrating that Hegel's work wasn't actually written in this universe, or on real paper, but was written on Ideal paper, neither in heaven nor on earth -- and that they themselves don't exist anywhere, either (or both, or neither), in order to do that (or not).
[On the 'acid and base' example -- even if we were to take Hegel's comments about such reagents seriously -- see here.]
In a recent book [Stewart (1996)], several misinterpretations and misrepresentations of Hegel's work were 'corrected' by a handful of Hegel scholars. However, there would seem to be little point to such an exercise if Hegel's ideas about "either-or" are to be believed. If he were right -- that in the entire universe there is no "either-or" -- there would be some truth even in the wildest allegations about him and his work.
[LOI = Law of Identity.]
For instance, these: that (i) Hegel fully accepted without question the unlimited applicability of the LOI in every conceivable circumstance, without any qualifications whatsoever (and that includes its use in dialectical and speculative thought, as well as in relation to change, conceptual or material), and he did not; that (ii) he flatly denied that reality or thought is contradictory in any sense at all, and he did not; that (iii) he doubted the truth of every single one of his own ideas all the time, and he did not; that (iv) he wrote nothing at all in German in his entire life, and he did not; that (v) everything he wrote was actually written by Schelling -- in fact it was published only yesterday, and it wasn't --; that (vi) he was a Shape-shifting Martian, and he wasn't...
[Anyone who attempts to reject one or more of the above alternatives -- on the grounds that Hegel must have accepted one of them, or one of them must be true, but not both, or, indeed, that such objectors must do likewise, too -- will, alas, have to employ the dread LEM in order to do so, vitiating Hegel's challenge, as well as their own objections to the above argument.]
It could be objected that this completely misunderstands the nature of DL, at least as Hegel himself conceived it. Unfortunately, even that response is framed in ordinary language -- and, it was foolishly written in this universe! --, so, since a decision has to be taken over whether or not it is valid, a quick reference to DL will indicate it is both.
[DL = Dialectical Logic.]
This means that until DL-fans commit themselves to one or other view (but not both), it is impossible even to begin to evaluate anything they say -- and neither can they!
However, just as soon as they specify what they mean (i.e., that they genuinely intend this but not that), we must cease to take them seriously, since they would then have employed the dread LEM, thereby undermining their own criticisms of it!
Either way, such defenders of Hegel may be ignored even before they decide whether they agree with the above critical comments, or not (or both).
It could be countered that the above conclusions are ridiculous and fail to follow from a consistent application of the dialectical method; hence Hegel can't be saddled with any of them.
Once more, these 'ridiculous conclusions' either do or they do not follow from what Hegel wrote. If the above DM-rebuttal is correct, and they don't follow, then there is at least one either-or at work here, namely this one -- since, in that case, both options wouldn't be correct -- only one option would be the right one, namely, that they don't follow. And, if that is so, these 'ridiculous conclusions' do indeed follow, after all, since Hegel would, in that case, be wrong to assert there is no either-or anywhere in existence when one such has just been used to reject one option in favour of the other!
So, taking each 'ridiculous conclusion' individually: if we maintain that one of them doesn't follow, we will have applied the LEM, once more. That is because we would thereby have denied that that particular 'ridiculous conclusion' does and does not follow, and thus that an either-or option obtains in this case. Hence, we arrive at the same result.
On the other hand, if they do follow, then they do anyway.
Either way, they follow.
The problem with sweeping claims like the one quoted above (which litter Traditional Philosophy and not just Hegel's ill-considered 'Logic') -- in this case, concerning the supposed limitations of certain principles of FL (and especially those that express patterns of inference mirrored in our use of ordinary language, such as the LOI, the LOC and the LEM) -- is that they invariably collapse into incoherence, as we have just seen.
[FL = Formal Logic; LOC = Law of Non-Contradiction.]
Which is why, once again, we can say with complete confidence that no one (not even Hegel) could possibly understand Hegel!
It is of course also possible to 'adapt' Engels's comments (from earlier):
"To the metaphysician, things and their mental reflexes, ideas, are isolated, are to be considered one after the other and apart from each other, are objects of investigation fixed, rigid, given once for all. He thinks in absolutely irreconcilable antitheses. 'His communication is "yea, yea; nay, nay"; for whatsoever is more than these cometh of evil.' [Matthew 5:37. -- Ed.] For him a thing either exists or does not exist; a thing cannot at the same time be itself and something else. Positive and negative absolutely exclude one another, cause and effect stand in a rigid antithesis one to the other.
"At first sight this mode of thinking seems to us very luminous, because it is that of so-called sound common sense. Only sound common sense, respectable fellow that he is, in the homely realm of his own four walls, has very wonderful adventures directly he ventures out into the wide world of research. And the metaphysical mode of thought, justifiable and even necessary as it is in a number of domains whose extent varies according to the nature of the particular object of investigation, sooner or later reaches a limit, beyond which it becomes one-sided, restricted, abstract, lost in insoluble contradictions. In the contemplation of individual things it forgets the connection between them; in the contemplation of their existence, it forgets the beginning and end of that existence; of their repose, it forgets their motion. It cannot see the wood for the trees.
"For everyday purposes we know and can say, e.g., whether an animal is alive or not. But, upon closer inquiry, we find that this is, in many cases, a very complex question, as the jurists know very well. They have cudgelled their brains in vain to discover a rational limit beyond which the killing of the child in its mother's womb is murder. It is just as impossible to determine absolutely the moment of death, for physiology proves that death is not an instantaneous momentary phenomenon, but a very protracted process. In like manner, every organic being is every moment the same and not the same, every moment it assimilates matter supplied from without, and gets rid of other matter; every moment some cells of its body die and others build themselves anew; in a longer or shorter time the matter of its body is completely renewed, and is replaced by other atoms of matter, so that every organic being is always itself, and yet something other than itself." [Engels (1976), pp.26-27. Bold emphases added; quotation marks altered to conform with the conventions adopted at this site. Some paragraphs merged.]
It might be instructive if we applied his advice to his words (but to save the reader's sanity, this tactic has been inflicted on only part of one of the above paragraphs):
"At first sight and not at first sight, this mode of thinking and of not thinking seems, and it doesn't seem to us, and not to us, very luminous and not at all luminous, because it is and it isn't that of so-called sound common sense and not so-called common sense. Only sound common sense, and anything other than common sense, respectable fellow that he is and isn't, in the homely realm of his own four walls and outside them too, has very wonderful adventures and slightly non-wonderful adventures directly he ventures out into the wide world of research, or not...." [Edited, 'Hegelianised', version of Engels's words.]
So, not even Engels could have taken his own advice and hope to have made sense.
[Incidentally, his argument concerning the status of living organisms has been critically analysed here and here.]
Any who still harbour doubts (about the use of "It is raining", etc.) might like to focus instead on sentence pairs like the following:
(i) "The Nile is longer than the Thames"; and,
(ii) "The Nile isn't longer than the Thames"; or,
(iii) "Hitler was a Nazi"; and,
(iv) "Hitler wasn't a Nazi".
Now, can both (i) and (ii), or both (iii) and (iv), be true and false at the same time and in the same respect?
Finally, some readers might object that an earlier example (concerning off-side in football (soccer)) in fact underlines the limitations of FL. So, in a live game, many players (in or near an off-side configuration) will be moving; hence, at any point they might be situated in a borderline case between on-side and off-side. FL insists there is an "either...or" here when it is often a "both...and".
Or so it might be argued...
Admittedly, there are occasions when even those who have access to video evidence can't decide if a player is actually off-side, or different referees and observers have divergent opinions about such things. But, that doesn't affect the fact that when it is decided that the player concerned is off-side, it then becomes false that he/she isn't off-side.
DM-fans might then be tempted then to respond: FL obviously breaks down when such things are on the point of change.
Or so it could be further maintained...
[DL = Dialectical Logic.]
Ok, so what if it can't be decided? How would DL help here? How does it help a game of football (soccer) for a 'dialectical referee' to declare that a player is both off-side and not offside at the same time? The question answers itself. DL is even more useless.
However, decisions are always made. Never in the history of the game has it been permanently left hanging without a decision (in such circumstances) being made. As noted above, such a decision, once made, will make one of these propositions true -- "Player NN is off-side" or "Player NN isn't off-side" -- and the other false. At no point would anyone come out with "NN is both on-side and off-side!". Not even a referee who is also a DM-fan would conclude this. And that will still be the case even if those reviewing video evidence still can't agree. Someone will arbitrate here (the third referee, perhaps?), and a decision will be made.
But, let us imagine there actually are some hardcore DM-fans who would happily claim there are situations where both "Player NN is off-side" and "Player NN isn't off-side" are both true. Well, we needn't indulge in such flights-of-fancy since there is a dialectician who fits that description, Graham Priest; he has argued that there are states of affairs where it is true to say an object is in both states at once. I have discussed his response in Note 18a. Readers are directed there for more details.
If no decision can in principle be made, then, as we saw earlier, neither of these 'propositions' (time stamped for the game in question -- so that they are now spoken token sentences, not type sentences) when combined as follows, "Player NN is off-side and player NN isn't off-side (location, date and time added)" is now a proposition (since it is unclear what is being proposed), and such non-propositions have zero to do with FL. In which case, this scenario presents no challenge to FL, contrary to what dialecticians imagine.
[I have said much more about the failure of sentences like this even to count as propositions in Essay Eight Part Three, here, here, here and here.]
It is also worth remembering that DL has no use for them either, as we have also just seen.
Despite this, there are other strategies that would in all likelihood be adopted in such circumstances, and it is to them that I now turn.
[Some of the points made in this subsection might appear to be rather dogmatic, but subsequent sections will fully substantiate them; they will also be defended from several obvious, and a few not so obvious, objections in this Essay and others at this site.]
The facility we have in language to contradict one another (which apparently goes back as far as records last, or as far back as human beings have been able to argue, never mind converse -- indeed, without it, we wouldn't be able to comprehend indicative sentences before we knew whether they were true or whether they were false (why that is so, and why it is so important, was explained in Essay Twelve Part One)), means that our ancestors clearly failed to take the DM-route. And it isn't difficult to see why. In fact, given current linguistic practices (in tandem with the social relations on which they are based), it is now impossible to make sense of the claim that a contradiction could be true (or, rather, that two contradictory propositions could both be true or could both be false at once -- that is, without (retrospectively) altering the meaning of the word "contradiction" itself). 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, of course.
[In order to prevent what follows from sliding off into some form of Linguistic Psychologism it should be read in conjunction with the distinctions established in Shanker (1998), particularly Chapter Three, especially pp.97-120. Of course, there is nothing wrong with anyone employing the word "contradiction" in a completely novel way, but that having been done any new use of a typographically identical word can't affect its current (ordinary) employment -- nor can it be related to ordinary use, let alone to the role it occupies in FL.]
In cases where disputants might appear to be doing this (i.e., where both parties to an argument are gain-saying each other and both also seem to be speaking the literal truth), the most likely response 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 (or, rather, how two contradictory propositions could both be true or both be false, at once). Not only that, but these conventions prevent us from understanding anyone who might think otherwise, or try to persuade us to think otherwise. Even worse still, they also prevent us from now understanding how our ancestors could have developed alternative conventions -- or, indeed, how we could make sense of anyone who supposed they might have.
This is one intellectual river we can't now step back into, even once -- to paraphrase Cratylus.
In fact, these observations are connected with: (i) The way that negation works in language, and (ii) The capacity language has for allowing us to understand an empirical proposition (i.e., a fact-stating indicative sentence) before we know whether it is true or whether it is false. [There is more on this in Essay Twelve Part One.]
[Incidentally, I have added the following codicil: "Or, rather, how two contradictory propositions could both be true or both be false, at once", since most logicians (particularly mathematical logicians) classify contradictions as false, whereas the LOC is a rule of language (or, even better, the LOC is an indirect expression of the rules we have for the use of the negative particle); it is neither a logical truth nor a logical falsehood. This means a contradiction can't be true or false. If, per impossible, a contradiction could be false, then it could be true (for reasons explained in Essay Twelve Part One), which would create problems for how we use the negative particle. It is far better therefore to regard contradictions as senseless. (The word "sense", as it is used in most of these Essays in such contexts, is explained here.)]
Once again, the above assertions might seem dogmatic and controversial, so I will now defend each in turn.
Take the first of these -- which was that we should fail to understand anyone who believed a contradiction could be true (or, rather, how two contradictory propositions could both be true or both false, at once), 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 both B1a and B1b were true. Faced with that we would all find it difficult to take this person or what they said either literally or seriously. That is because, as they stand, both halves of B1 (i.e., B1a and B1b) couldn't be true, nor could they both be false, together.
[Some might think that these aren't the type of contradiction of interest to dialecticians; that objection will be dealt with presently. Of course, if there were no such person as John Rees (and there never had been), or no such book had ever been published, meaning The Algebra of Revolution had never existed, the above three sentences would fail to be propositions, to begin with.]
However, if both B1a and B1b were still held true, then, trivial cases aside (such as the names "John Rees" and "The Algebra of Revolution" referred to two separate individuals or two different books), 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 would imply that John Rees was the author of the said work; in another quite ordinary sense it might suggest that the book wasn't hand-written, but was perhaps word-processed. [Or, even that Rees had used an amanuensis.] In that case, B1 would be expressing the fact that although John Rees authored the said book he didn't hand-write it (or he didn't do so himself); he, or someone else, typed it. It would then be clear that B1 only appeared to be contradictory because of a simple equivocation. We wouldn't automatically think that there were 'real material forces' at work behind the 'struggle' to produce the said book, no matter how well-confirmed each half of B1, or even their conjunction, happened to be.
This shows that observation/and/or empirical checks in such circumstances aren't relevant in relation to what is in fact a logical or conceptual issue.
Again, someone might object, arguing that the above considerations highlight the LIE implicit in caveats like this, for it seems to restrict the options available by appealing to logical or linguistic protocols.
[LIE = Linguistic Idealism; that term is explained here.]
But, that would be to mistake the approach adopted at this site for its opposite. The strategy employed here seeks to undermine the idea that substantive truths about reality can be derived (solely) from logical, conceptual or even contingent features of language. In this case, that has been done on the basis of what we would now try to do (prior to, or independently of, the adoption of a pet theory), in order to interpret or understand what appear to be contradictions, as and when they might arise. In that case, these Essays appeal to rules we already employ (or with which we comply -- i.e., normative social practices that shape how we use language), not a series of Supertruths that can supposedly be inferred from a misconstrual of their nature.
Hence, no 'philosophical truths' are being derived (by me) from the above observations, merely a denial that any such truths can be obtained from the misinterpretation of a string of words.
Indeed, it is the opposite (dialectical) view that collapses into LIE, for it confuses linguistic and logical rules with empirical -- or, what are in effect Super-Empirical -- truths. In DM, this occurs when, for example, dialecticians treat the LOC as a supposed truth that they think could be (and often is) false -- or which is at least only true 'within certain limits' -- especially in relation to motion and change. Their criticism of the LOC leads them to argue that contradictions themselves can be true (or even that they actually exist in nature and society). But, if, as noted earlier, the LOC is a rule (or it expresses a rule we ordinarily employ in relation to specific uses of the negative particle), it isn't the sort of thing that could be true or false, no more than orders or instructions can be.
[Further ruminations on this theme will be resumed in Essay Twelve Part One, where it will be argued in detail why the aforementioned confusion of rules with substantive truths about the world is endemic to Traditional Thought -- and DM. Spoiler: that is because this approach to 'philosophical knowledge' is predicated on the ancient, mystical idea that there is a hidden world anterior to experience, accessible to thought alone, that is more real than the world we see around us. It is from ideologically-inspired confusions like this that Metaphysics and 'dialectics' originally arose.]
Admittedly, B1 is exceedingly trite, but it was deliberately chosen so that the strategy of disambiguation could be made clear to all.
B1: John Rees wrote and did not write The Algebra of Revolution.
Nevertheless, it could be objected that DM-theorists' interest is restricted to the study of real material forces at work inside Capitalism in order to assist in its overthrow. In that case, trite examples like B1 aren't remotely relevant. Nor are they even dialectical contradictions, to begin with.
Or, so it could be argued...
In order to counter that response, the sort of contradictions DM-theorists are interested in will be analysed elsewhere at this site (and in unprecedented detail, too -- for example, here, here and here -- as well as later in this Essay, here). There, it will be shown that "real material contradictions" turn out not to be contradictions to begin with (in any sense of the word -- on that, see here and here), and they can't be turned into "real material contradictions" howsoever they are interpreted or even 'surgically enhanced'.
With respect to the other assertion advanced above -- that we would fail to understand alternative conventions given those 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. Typically, but not exclusively, that takes place in ordinary language. And that, too, can be asserted with some confidence since the word "understand" is already (and patently) an ordinary language term. [The significance of that specific point will emerge in Essay Thirteen Part Three.] Clearly, language isn't a free-floating phenomenon. As all Marxists agree (at least in principle), its invention and subsequent evolution were, and still are, a function of our social, historical and technological progress/development (albeit heavily constrained by class division, the class war and all that that entails). In addition, our use of language is subject to the constraints we inherited from previous generations, which we plainly had no hand in shaping (since we have no access to a time machine!). Indeed, every single one of us had to be socialised by parents, siblings, carers, teachers and peers (etc.) into using language within, and in compliance with, these constraints. As social beings, we manifestly didn't individually socialise ourselves (although each of us certainly adapt and mould these linguistic and social resources and conventions to our own ends).
Moreover, we reveal a mastery of this complex socio-linguistic tool (language) as we begin to communicate and interact with others. While we can form thoughts as we please, we can't do so under logico-linguistic and social conditions of our own choosing (to paraphrase Marx).
Now, it is tempting to think that these 'limitations' present some sort of physical barrier -- or, at least, that they merely represent contingent constraints on the use of language, but that, too, would be a mistake. There certainly are physical and contingent constraints on language (for example, no one could utter or understand a trillion word sentence, or one spoken over a millisecond), but those aren't the limitations intended.
[A clue concerning the nature of these limitations may be ascertained by anyone who reads the Essays posted at this site, especially where it has been demonstrated time-after-time how readily DM-theories fall apart and can't be repaired no matter what is done with them. That sort of limitation isn't physical; it is conceptual. Another such example was outlined, here; several more will be aired in this Essay. However, these limitations aren't those that words exercise upon us; the word "limitations" underlines how we collectively -- through our socialisation -- understand and thus use the vocabulary we already have. To suppose otherwise would be to fetishise language, turning it into the agent, and humanity into the patient. (Incidentally, I am using the word "patient" here in its older sense; that is, it relates to that which is acted upon, not that which acts.)]
B1: John Rees wrote and did not write The Algebra of Revolution.
Fortunately, however, the negative criticisms of DM laid out at this site do not depend on the validity of this latest batch of seemingly dogmatic assertions. Doubters need only think about how they themselves would interpret B1 (or, indeed, B2, below), and the point should become a little clearer.
In relation to understanding others who speak different languages, or even characters from the past, while we often (obviously) translate what they have to say into our own language we may do so only within the constraints that currently operate on our use of that language. [Unless, of course, we aim to restrict ourselves merely to transliteration.] This means that because we can't make sense of contradictory speech now, we would also find it equally difficult to comprehend how contradictions could ever have been held true by anyone in the past.
Of course, there have been, and there still are mystics who utter and promote all manner of odd, or even contradictory, ideas. Other than Hegel, this more typically includes, for instance, Buddhist logicians and 'teachers' -- even though it is still a moot point whether anyone has ever actually understands the peculiar things they come out with. Indeed, mystics themselves tell us they don't understand the conundrums they cough up, which is part of their superficial appeal. Would anyone listen to those claiming they were communicating the 'divine word' if their 'message' were straight forward and easy to grasp? Mysticism and obfuscation go hand-in-hand -- as, it seems, is also the case with DM.
Francis Bacon summed-up this mind-set admirably well (although he confined his criticism to the tangled verbal spaghetti weaved by Medieval Schoolmen, i.e., the Scholastics):
"This kind of degenerate learning did chiefly reign amongst the Schoolmen: who having sharp and strong wits, and abundance of leisure, and small variety of reading, but their wits being shut up in the cells of a few authors (chiefly Aristotle their dictator) as their persons were shut up in the cells of monasteries and colleges, and knowing little history, either of nature or time, did out of no great quantity of matter and infinite agitation of wit spin out unto those laborious webs of learning which are extant in their books. For the wit and mind of man, if it work upon matter, which is the contemplation of the creatures of God, works according to the stuff, and is limited thereby; but if it work upon itself, as the spider works his web, then it is endless, and brings forth indeed cobwebs of learning, admirable for the fineness of thread and work, but of no substance or profit." [Bacon (2001), pp.25-26. Bold emphasis added; Stuart/Elizabethan words have been replaced by their contemporary English equivalent.]
As one commentator noted about the reasoning behind the use of obscure jargon:
"Sociologist C. Wright Mills, in critically examining 'grand theorists' in his field who used verbosity to cover for a lack of profundity, pointed out that people respond positively to this kind of writing because they see it as 'a wondrous maze, fascinating precisely because of its often splendid lack of intelligibility.' But, Mills said, such writers are 'so rigidly confined to such high levels of abstraction that the "typologies" they make up -- and the work they do to make them up -- seem more often an arid game of Concepts than an effort to define systematically -- which is to say, in a clear and orderly way, the problems at hand, and to guide our efforts to solve them.'
"Obscurantism is more than a desperate attempt to feign novelty, though. It's also a tactic for badgering readers into deference to the writer's authority. Nobody can be sure they are comprehending the author's meaning, which has the effect of making the reader feel deeply inferior and in awe of the writer's towering knowledge, knowledge that must exist on a level so much higher than that of ordinary mortals that we are incapable of even beginning to appreciate it.... The harder people have to work to figure out what you're saying, the more accomplished they'll feel when they figure it out, and the more sophisticated you will appear. Everybody wins." [Quoted from here. Quotation marks altered to conform with the conventions adopted at this site. One link added; several paragraphs merged.]
I don't often quote Nietzsche, but these words of his seem uncannily relevant:
"Those who know that they are profound strive for clarity. Those who would like to seem profound to the crowd strive for obscurity. For the crowd believes that if it cannot see to the bottom of something it must be profound." [Quoted from here.]
Finally on this point, no less a DM-fan than Lenin agreed with the above about the use of obscure language, even as he quoted page-after-page of it from Hegel(!):
"The flaunting of high-sounding phrases is characteristic of the declassed petty-bourgeois intellectuals." ["Left-Wing" Childishness.]
It's a pity Lenin didn't take the implied advice the above comment seems to offer.
[There will be more on this in Essay Fourteen Parts One and Two.]
Furthermore, we are equally incapable of translating (note: not transliterating) any language, ancient or modern, into our own in comprehensible terms while attempting to depict its users employing contradictory speech -- also holding any such contradictions true, or even proceeding with the assumption that those who engaged in such speech also held them true. This doesn't imply that we have to reject the idea (as false) that such individuals actually believed these contradictions were true (we can suspend judgement, for instance), but we certainly can't hold them true. While we might acknowledge the fact that some individuals (in the past, or whenever) speak, or have spoken, in paradoxical ways, given what we currently mean by the words we use, it is now impossible to make sense of the supposed 'content' that these ancient or mystical 'sayings' could have presented to those who uttered or produced them. Or, indeed, determine whether or not they presented anything determinate, to begin with. Moreover, since odd individuals like this invariably fail to explain themselves (or in ways that aren't equally obscure), it is quite clear they couldn't make sense of their own words, either.
Of course, mystics often say that what they have to say deals with the "ineffable", which, by definition, can't be put into words.
But that just makes my point for me!
In like manner, DM-fans can't explain their 'contradictions', either, and regularly complain that critics don't "understand" dialectics. Or, as is often the case with Academic Marxists and HCDs, the 'explanations' they come out with are no less obscure, expressed in jargon that is, to coin a phrase, as 'clear as mud'. [A recent 'debate' I had with one such illustrates this point admirably well. I have also quoted several examples of the obscure use of language (by such academics) in Essay Nine Part Two.]
[HCD = High Church Dialectician; follow the link for an explanation.]
In which case, if it is now impossible to make sense of the claim that individuals in the past could have held certain contradictions true then we manifestly can't comprehend the supposition that contradictions could ever have been true, whether or not some might (now) imagine they had been viewed that way by such individuals.
Once again, the various 'true contradictions' to which DM-theorists appeal will be examined elsewhere at this site (for example, follow the links posted above). Graham Priest's much more detailed (and logically well-informed) attempt to defend the idea that there can be, and are, 'true contradictions' in nature and society will be examined in a later Essay. [In the meantime, readers are directed to the following critics of his: Berto (2007), Goldstein (1992, 2004), Field (2008) and Slater (2002, 2007a), as well as this review.]
Update: I have now added a few comments to Note 18a concerning Priest's much more sophisticated attempt to show that motion and change are contradictory; or as he puts it:
"I [have argued in support of] the idea that contradictions not only occur in certain sorts of change but actually are the states of change themselves." [Priest (2006), p.172.]
Some might take exception to many of the above assertions, claiming that they can imagine speakers holding certain contradictions true (and, what is more, those contradictions actually do represent real material forces or conflicts), namely themselves! In that case, is it possible that dialecticians themselves are living disproof of the sweeping generalisations made so far in this Essay?
Despite this, the present Essay will show that Hegel and Engels's theory (that motion is, or involves, a 'contradiction') is far too vague and confused for it to be assessed for its truth or its falsehood (it doesn't even make it that far!). This means that the 'contradiction' they claim to 'see' in moving bodies isn't a contradiction in any sense of that word -- nor is it even 'dialectical'! Other examples of dialectical 'contradictions' will similarly be dealt with in Essay Eight Parts One, Two and Three, as well as Essay Eleven Part One. In addition, the DM-theory that reality itself contains, or is composed of, countless trillion UOs in each kilogram of matter (namely, each sub-atomic 'particle') will be destructively criticised in Essay Seven Parts One and Three.
[UOs = Unity of Opposites.]
Hence, because it isn't possible to make sense of any of the examples of 'dialectical contradictions' offered up by DM-theorists, the above "sweeping generalisations" have everything going for them. The fact that dialecticians have shown that they themselves are incapable of explaining these mysterious 'contradictions' to anyone -- let alone one another -- provides further supporting evidence in its favour. [On that, see here.] Indeed, on Internet discussion boards, when Academic Marxists and revolutionaries alike are asked (often repeatedly) to explain exactly what 'dialectical contradictions' are they all fail to do so --, or they just ignore the question. [Links to many of those discussions have been posted here.]
To be sure, as noted earlier, there have been, and still are, mystics and religious believers who come out with, or even assent to, all manner of apparently contradictory ideas, but that doesn't undermine the above counter-claims. Their talk is often non-propositional -- indeed, it is frequently little more wall-to-wall incoherent non-sense, as will be demonstrated in a later Essay. The same comment applies to 'ideas' expressed by Buddhists (this links to a PDF) -- more specifically, Zen Buddhists -- who also seem to glory in paradox and the production of gobbledygook.
[Concerning the odd things Buddhists come out with, see my other comments below.]
In relation to the earlier claim that we wouldn't be able to make sense even of the possibility that there might have been past generations who believed, or who could have believed, there were true contradictions, 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. That isn't because it would be particularly difficult for them to do so, but because any claim to the contrary would undermine the meaning of the word "literally", at the very least.
But, even supposing a few Mad Dog Dialecticians [MDDs] could be found who did attempt 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 disambiguating it.
[Again, see below for a few instances of such.]
As noted earlier, trite examples like B2 were deliberately chosen to illustrate a point that is all too easily missed: when faced with the paradoxical things people sometimes say, we automatically make an effort to disambiguate their words or their actions; we adopt what Donald Davidson once called the "principle of charity" when trying to grasp their meaning or their intentions. [Davidson (2001).]
[Of course, in so doing we have to distinguish between speakers' meaning (i.e., what an individual hopes to convey or achieve by his/her words) and word meaning (i.e., what those words actually mean in the language). Failure to do so leads to the sort of confusion that undermines, for example, Voloshinov's work, as well as that of his epigones. (I have discussed this phenomenon in extensive detail in Essay Thirteen Part Three.)]
Hence, when confronted with someone who asserts an apparent contradiction we would normally employ the above policy -- trivial examples excepted, of course. That doesn't mean this approach will necessarily distort what the said individual has uttered or written; rather, it is that we wouldn't be able to understand such individuals if we didn't do this.
In any case, if there are any MDDs out there (i.e., extremist DM-supporters who reject some or all of the above points), they would be hard-pressed to explain to anyone else what they themselves took the sense of a true contradiction to be -- that is, without playing yet another Nixon card --, as the rest of this site aims to show.
And that comment also applies to any 'dialectically-inspired' responses elicited from those who might think to question the above claims.
Clearly, that doesn't mean we shouldn't exercise some level of sensitivity toward other belief systems (past or present), but we may only do so in terms of current linguistic and social protocols. When confronted with what appear to be weird or paradoxical beliefs, it would prove to be impossible to translate them and interpret them literally while at the same time claiming to understand them (disambiguation excepted, again). On the other hand, if someone claimed they could do this, it would automatically throw into doubt the validity of their translation (unless the meaning of the word "translate" itself had been modified/altered) -- always supposing, of course, that they hadn't merely transliterated the relevant words instead.
However, if what had been 'translated' were held to be literally true, and it still remained paradoxical, then whatever else could be made of it, all talk of its literal truth would have to be abandoned. Either that, or, once again, we would have to understand the words "literal" and "truth" non-literally!
[This topic is still under intense and lively debate; see Miguens (2019), Creary and Read (2000) and Cerbone (2000). See also Conant (1991) and Forster (1998).]
So, until and unless DM-theorists explain themselves, we are forced to conclude that 'dialectical contradictions' fail to depict, or express, anything in any meaningful sense (other than the confused state of mind exhibited by anyone who thought contradictions could be true). [On that, see Slater (2007a).]
The above isn't being asserted because I personally think that reality contains no contradictions, or because I have concluded that the world either is or isn't as these allegedly 'true contradictions' supposedly depict it -- or even because contradictions are always false (which is the classical view). To argue along those lines would be to fall into the same trap that ensnares DM-theorists, since it would amount to the derivation of the opposite dogmatic theory about reality to that adopted by DM-theorists based on an alternative linguistic convention (which I might, in this case, have found more acceptable).
On the contrary, contradictions fail to picture the world, not because they are false, but because they aren't pictures to begin with. They represent a breakdown in the depictive and representational capacities of language, since they violate socially-grounded rules we already have for the use of the negative particle. [On that, see Essay Twelve Part One.]
Finally, it could be argued that the above comments are misguided since dialecticians don't question the general application of principles drawn from FL, such as the LOC; they merely point to their limitations when it comes to motion and change. In that case, the sorts of contradiction illustrated by B1 and B2 are completely irrelevant.
B1: John Rees wrote and did not write The Algebra of Revolution.
B2: This four thousand year old inscription says that its author wrote and did not write it.
Such a critic might continue to object on the basis that since the above even don't depict change, they are beside the point.
Or, so it could be argued...
That particular response will be put under considerable pressure throughout this site, where it will be shown that it is dialecticians who can't actually account for motion and change, irrespective of the examples chosen.
Update 12/02/10: A story on the BBC website ("Do speedy elephants walk or run?") illustrates how an "either-or" question is actually answered by scientists without having to agree with, or even consult, Hegel:
"Instead of speaking by the maxim of Excluded Middle (which is the maxim of abstract understanding) we should rather say: Everything is opposite. Neither in heaven nor in Earth, neither in the world of mind nor of nature, is there anywhere such an abstract 'either-or' as the understanding maintains. Whatever exists is concrete, with difference and opposition in itself. The finitude of things will then lie in the want of correspondence between their immediate being, and what they essentially are. Thus, in inorganic nature, the acid is implicitly at the same time the base: in other words, its only being consists in its relation to its other. Hence also the acid is not something that persists quietly in the contrast: it is always in effort to realise what it potentially is." [Hegel (1975), p.174; Essence as Ground of Existence, §119. Bold emphasis added.]
The answer scientists give in this case is that elephants do both, they run and walk. Is this a contradiction? Does it refute any of the earlier claims? Can this anomaly be 'resolved' -- maybe DM-style, by means of a series of a priori, dogmatic assertions about all of reality, for all of time? Or, perhaps defused by some form of disambiguation? Which tactic is going to work? Which one was actually used?
Well, here is the article's explanation how this conundrum was in fact resolved:
"With their awkward, lumbering gait, elephants moving at high speed are not the most graceful of animals -- but are they walking or running? Now scientists believe they have an answer: new research confirms that they do both -- at the same time. By observing elephants moving across a hi-tech track, the team found the hefty creatures run with their front legs but walk with their back legs. The research is published in the Journal of Experimental Biology. Earlier research had suggested that elephants perform a strange, part-walk/part-run while travelling at speed. But a team from Belgium, Italy and Thailand was able to investigate this further by using a specially built track that was able to precisely measure (sic) the forces exerted with each weighty elephant step. Professor Norman Heglund, an author of the paper from the Catholic University of Louvain, Belgium, told BBC News: 'We had to build the plates -- you just can't go down to your local hardware shop and pick up an elephant-sized force plate.' Armed with these, the researchers headed to the Thai Elephant Conservation Centre to study the big beasts, which ranged from an 870kg baby to a four tonne adult. The Asian elephants were encouraged to move across the track, at speed, by their keepers....
"They were...filmed using high-speed cameras. By comparing the measurements from the sensitive force-measuring platform with each frame of the footage, the scientists were able to look at every tiny movement that the elephants were making. This enabled them to calculate the amounts of potential energy (stored energy) and kinetic energy (the energy that is associated movement), that the creatures were using. Measuring the relationship between potential and kinetic energy is the key to defining whether something is walking or running. For example, when walking, as an animal raises its foot from the ground and moves it forwards, it is converting the stored energy in its muscles and tendons -- the potential energy -- into kinetic energy. As its foot lands, the kinetic energy converts back into potential energy, and then back into kinetic energy as the foot is once again raised, and so on. All the time the creature is walking, the energy is transferred back and forth between potential and kinetic energy.
"But while running, the exchange between potential energy and kinetic energy is continuous -- rather than one form of energy being recycled into the other, back and forth, the energy exchange is happening all the time. Professor Heglund explains: 'The running gait, in most animals, is a bouncing mechanism. In this case, the potential and kinetic energy are in phase, they both hit a maximum at the same time and a minimum at the same time, so they cannot be transferred back and forth.' However, the researchers found that fast-moving elephants seem to both run and walk at the same time. Professor Heglund said: 'When an elephant goes at higher and higher speeds, the kinetic and potential energy shift and start to become more in phase. But when we looked in detail, we see that the animal appears to be running -- bouncing -- with the front legs, and walking with the back legs. It is as if he is getting up to a transition speed where he wants to transition from a walk to a run, but he can't quite do it. It's like he can't quite get up into second gear.'...
"The scientists now plan to look at other large animals, such as hippos and rhinos, to find out if they run or walk. This latest study confirms the findings of other research, published in the journal Nature and the Journal of Experimental Biology, that have previously shown that elephants perform a run-walk hybrid. However, there are some differences -- while this latest paper suggests the front legs run and the back legs walk, the other studies suggested the opposite." [Quoted from here. Bold emphasis alone added. Several paragraphs merged. Minor typo corrected.]
So, this apparent contradiction was resolved by detailed observations (coupled with an appeal to clear definitions, in tandem with a modicum of common sense), which led to a new discovery: that elephants run with their front legs and walk with their back legs (or the other way round!). Had these researchers been dialecticians, it is highly unlikely this advance would ever have been made; we would merely have been told to "grasp" this 'contradiction' and move on (no pun intended).3a
Update 06/09/2023: Well, we needn't invent problems for hypothetical DM-fans to try and solve, we have several they happily volunteer (in addition to Engels's theory of motion) -- we might even label this 'leading with your chin'. A handful were volunteered in an article co-authored by Graham Priest, which lists several contradictions Buddhists have come out with in the past. Here are two such:
W1: "What the realised one has described as the possession of distinctive features is itself the non-possession of distinctive features."
W2: "Everything is real and is not real".
[Both of the above come from an on-line article by Yasuo Deguchi, Jay Garfield and Graham Priest (this links to a PDF).]
With respect to W1, it would be interesting to see the above three authors make any attempt to explain what "distinctive features" means without that explanation itself having "distinctive features" of its own. [They didn't!]
Independently of that, W1 isn't even a contradiction! [It certainly isn't 'dialectical'!] That is because: (i) "What the realised one has described as the possession of distinctive features" is plainly not the same as what this refers to, (ii) "the non-possession of distinctive features". (i) refers to some other subject of the conversation, while (ii) refers to (i), not what (i) itself is talking about!
So, W1 is really saying this:
W3: "The realised one has described X as the possession of distinctive features, but 'The realised one has described X as the possession of distinctive features' is itself the non-possession of distinctive features."
The second half is talking about what "the realised one" is saying, while the first half is talking about "X". So, this is no contradiction, even if it is an odd thing to come out with, but it is, alas, standard fare for those whose aim seems to be to confuse the easily confused (and maybe even separate them from their money).
What about W2?
W2: "Everything is real and is not real".
That certainly looks contradictory, but can anyone hold W2 true? If so, it would be interesting to see them try explain how it could be true -- what state of affairs it could conceivably picture or represent. Certainly the above three authors didn't even attempt to do that. In fact, they said the following:
"Some may argue that none of these contradictions is meant to be accepted as true, that each should, in fact, be interpreted in some other way. Others may argue that the contradictions are meant to be taken this way, but that this shows that the views espoused are some kind of irrational mysticism. The point of the present note is to examine the matter. We will argue that at least some contradictions found in the texts are indeed meant literally and to be accepted as true. We will also argue that this is not a mark of irrationality, but, indeed, a consequence of rationality itself." [Quoted from here.]
Although they say some of these 'contradictions' were "meant literally" and were "accepted as true", they neglected to say what that truth consisted in, or in what way any of them were "literal".
So, this philosophical cheque that has yet to be cashed.
And we have as yet no idea what its cash value even is!
[By "cash value" I simply mean we have no idea what the sentence is even trying to propose. If true, what state of the world has made it true? (No answer is forthcoming from the authors of this article.) On the other hand, if it isn't true, we can ignore it.]
But, even worse: with respect to W2, "everything" is said to be "real", but in the next breath that is (supposedly) denied. But who is to say the first "everything" is quantifying over the same set or class as the second? If a shop has this notice stuck to its main window "Mammoth Sale Today!! Everything Must Go!" who in their left mind would interpret that "everything" as ranging over the same set or class as the same word in the following sentence? "The cops sealed the crime scene so that everything remained where it had been left." So, while it seems reasonably clear in relation to the shop and the crime scene example that the word "everything" doesn't always range over the same set or class, that appears to be less clear in relation to W2. But even if it is less obvious, it is still clear that with respect to W2 the two "everythings" can't be ranging over the same set or class since one such set/class is said to be "real", while that is denied of the other. The two sets/classes concerned are thus totally different, which means that the two occurrences of "everything" can't be equated, and hence W2 can't even be a contradiction.
[I have entered in to this topic in more detail in Essay Eight Part Three, here, here, here and here.]
Readers are invited to check the article (by Yasuo Deguchi, Jay Garfield and Graham Priest) for themselves to see if I have misrepresented what its authors said -- or didn't say.
They do say this, though:
"It might be suggested that although such contradictions are true, their truth is in comprehensible. Such truths, in this view, have the deictic function of ostending the incomprehensibility of ultimate reality, but cannot themselves be understood. This view concedes our point that such contradictions are intended as true, but we do not concede the view that they are incomprehensible. Those who hold that contra dictions are always and obviously only false will of course find supposing them to be true incomprehensible. However, despite various orthodoxies, East and West, the view that some contradictions are true is a perfectly coherent and intelligible view, as modern studies in dialetheism and paraconsistency have established." [Ibid.]
Well, until they succeed in explaining these 'contradictions', the conclusion must remain that they are indeed incomprehensible, and can in no way be true, or held to be true.
Finally, their closing appeal to paraconsistency and dialetheism should be taken with a large pinch of salt until those who promote such doctrines explain how these other 'contradictions' can also be true. So, far they have failed miserably.
[I deal with one such in Note 18a. See also my earlier comments about Priest's rather odd ideas.]
So, my claim still stands: it is impossible to hold any of these 'contradictions' true, or say the same about anyone who thinks they are even 'contradictions', let alone 'dialectical', to begin with.
Initial Problems With Engels's Theory
We are now in position to examine Engels's actual argument in support of his theory that motion is a contradiction:
"[S]o long as we consider things as at rest and lifeless, each one by itself, alongside and after each other, we do not run up against any contradictions in them. We find certain qualities which are partly common to, partly different from, and even contradictory to each other, but which in the last-mentioned case are distributed among different objects and therefore contain no contradiction within. Inside the limits of this sphere of observation we can get along on the basis of the usual, metaphysical mode of thought. But the position is quite different as soon as we consider things in their motion, their change, their life, their reciprocal influence on one another. Then we immediately become involved in contradictions. Motion itself is a contradiction: even simple mechanical change of position can only come about through a body being at one and the same moment of time both in one place and in another place, being in one and the same place and also not in it. And the continuous origination and simultaneous solution of this contradiction is precisely what motion is." [Engels (1976), p.152.]
However, there are five initial difficulties with the above passage.
(1) "Asserted" By Whom?
Engels's closing sentence is rather odd:
"Motion itself is a contradiction; even simple mechanical change of place can only come about through a body being both in one place and in another place at one and the same moment of time, being in one and the same place and also not in it. And the continual assertion and simultaneous solution of this contradiction is precisely what motion is." [Ibid. Bold emphasis added.]
Exactly who is supposed to do the "asserting" and who the "solving", here? It could be argued that these words were meant to be taken metaphorically. But, if that is so, what then is the force of Engels's use of "precisely"?
Even more to the point: if Engels was speaking figuratively, what has "assertion and simultaneous solution" got to do with motion? This isn't even a good metaphor!
Perhaps Engels intended to say that his words merely apply to the description of motion? In that case, the conclusions he reached will be limited to the language we use about motion, not 'motion itself'.4
An article by Thomas Weston [i.e., Weston (2012)] appears to have an answer to the above questions. His analysis will be tested later in this Essay. [The latter is still under construction; it should be available in the next few days.]
(2) "Solved" In What way?
How exactly are contradictions "solved"? Are they like puzzles, riddles, brainteasers or mysteries? If they are, do they disappear once they have been "solved"? Puzzles and mysteries cease to be puzzles or mysteries when they have been unravelled. Is this the same with these contradictions?4a If so, do new contradictions immediately take their place? In which case, is each "solved" contradiction replaced by the 'same' contradiction further along the trajectory of that moving body or by an entirely new one? How might any of this be confirmed? And, how do we know if there is only one contradiction present, or countless thousands (for each unit of time involved)? If there is more than one contradiction, how are they all connected with a given body in motion? Does each contradiction arise and fall as that body moves? Or is there a single, extended contradiction spread out, as it were, right along the entire trajectory? Is this 'extended contradiction' then perhaps the following: that a moving body is "here and not here, in general", so to speak? [Whatever that means!]
More puzzling still: Are these contradictions "solved" by some mind or 'intelligence' first comprehending them? 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' is required in the first place? This now mysteriously still helps further propel the moving object along (if that is what it does). If so, how does a 'solved contradiction' manage to do that? On the other hand, if a 'solution' is required, how was that achieved before human beings evolved?
[Again, Thomas Weston appears to have an answer to some of these questions. His response will be examined later in this Essay. (The latter is still under construction; it should be available in the next few days.)]
At first sight, Engels appears to be arguing that it is only our understanding of motion which is contradictory:
"[A]s soon as we consider things…then we…become involved in contradictions…." [Engels (1976), p.152. Bold emphases added.]
This might help explain why the passage refers to the "continual assertion" of such contradictions, since it is evident that only human beings can assert anything. If so, it looks like Engels thought that human observers can't avoid "asserting" such contradictions, or maybe asserting there are contradictions present whenever they attempt to describe or conceptualise motion. That in turn might itself be a consequence of a partial understanding of the 'absolute truth' about motion (if such exists). On the other hand, the fact that this presents humanity with a conundrum could be a fault of logic, or even of language, both of which are said by some to be inadequate to the task (i.e., with respect to change, etc.). But, that would fail to explain how and why contradictions, upon being "asserted", are immediately "solved" and then promptly re-"asserted". If we don't understand such contradictions, how can they be 'solved'? On the other hand, if they are 'solved' why re-assert them?
The above considerations would appear to mean that it is only human understanding of motion that is contradictory, not 'reality itself' -- unless, of course, we are to suppose that nature itself is Mind (or the product of Mind). If that were the case, it would certainly help explain why Engels said such contradictions can be "asserted". Maybe he meant that it is the 'self-development of Mind' that propels bodies along (a faint echo of Hegel's theology)? After all, Engels was brought up in the strict Pietist faith, which was openly based on Jakob Böhme's (Hermetic) theology, who was also a formative influence on Hegel. [On Pietism, Engels, Böhme and Hegel, see Martin (2014), Boer (2013), especially Chapter Nine, Green (2008), Carver (1989), Hunt (2009) and Magee (2008).]
As Engels himself acknowledged in a letter:
"But...our good Lord God has given me an excellent sense of humour.... If I had not been brought up in the most extreme orthodoxy and piety, if I had not had drummed into me in church, Sunday school and at home the most direct, unconditional belief in the Bible and in the agreement of the teaching of the Bible with that of the church, indeed, with the special teaching of every minister, perhaps, I would have remained stuck in some sort of liberal supernaturalism for a long time." [Engels to Wilhelm Graeber, 30/071839, in Marx and Engels (1975b), pp.465-66. Italic emphasis in the original.]
Anyway, one of the alternatives aired above suggests that when reality is fully understood all such contradictions would cease, desist or disappear. Indeed, Engels himself believed they would:
"If one does not loiter here needlessly, but presses on farther into the immense building, one finds innumerable treasures which today still possess undiminished value. With all philosophers it is precisely the 'system' which is perishable; and for the simple reason that it springs from an imperishable desire of the human mind -- the desire to overcome all contradictions. But if all contradictions are once and for all disposed of, we shall have arrived at so-called absolute truth -- world history will be at an end. And yet it has to continue, although there is nothing left for it to do -- hence, a new, insoluble contradiction. As soon as we have once realized -- and in the long run no one has helped us to realize it more than Hegel himself -- that the task of philosophy thus stated means nothing but the task that a single philosopher should accomplish that which can only be accomplished by the entire human race in its progressive development -- as soon as we realize that, there is an end to all philosophy in the hitherto accepted sense of the word. One leaves alone 'absolute truth', which is unattainable along this path or by any single individual; instead, one pursues attainable relative truths along the path of the positive sciences, and the summation of their results by means of dialectical thinking. At any rate, with Hegel philosophy comes to an end; on the one hand, because in his system he summed up its whole development in the most splendid fashion; and on the other hand, because, even though unconsciously, he showed us the way out of the labyrinth of systems to real positive knowledge of the world." [Engels (1888), p.590. Spelling modified to agree with UK English; quotation marks altered to conform with the conventions adopted at this site. Minor typo corrected.]
The above passage appeared in a published work, so it represents Engels's more considered thoughts. Here he concludes that "if all contradictions are once and for all disposed of, we shall have arrived at so-called absolute truth...". That would appear to mean contradictions aren't 'objective' features of the world but are the product of our limited knowledge. Even though 'absolute truth' will never be attained, the fact that there is such a thing as, or there is a possible state of knowledge that can be described as "absolute truth", implies contradictions aren't really real but are a consequence of humanity's imperfect knowledge. Why else would they disappear? If they were 'objective' features of 'reality', they would still exist even if humanity attained 'absolute truth'. Engels wouldn't have surmised that "all contradictions" could be "once and for all disposed of" if contradictions were 'objective'. That is because only 'subjective contradictions' (those that are a result of limited knowledge) can be "disposed of". Engels pointedly speaks about "all contradictions", which must include those supposedly involved in motion. This further implies that the more we know the fewer contradictions we should observe in nature and society, or the fewer we should assert actually exist.
Plainly, this in turn implies that motion could one day come to a halt, all contradictions having been "solved"/"disposed of"! Indeed, if contradictions actually 'cause' motion (or they are a consequence of it), then their complete resolution/disposal should freeze nature in its entirety. On the other hand, maybe motion will just stop being (or appearing to be) contradictory and will simply carry on as normal? Or, does this mean that nature will simply slow down as it is better understood (i.e., if what we know about motion and change becomes less and less partial/relative and hence less and less 'contradictory-looking')?
Who can say? Certainly not DM-fans. In the 150 or so years since Engels wrote these enigmatic words they have been more content merely to regurgitate them than they have been concerned to raise, let alone consider or attempt to answer, these glaringly obvious questions.
Admittedly, DM-theorists distinguish between subjective and objective dialectics -- the former relating to our (perhaps decreasingly) partial grasp of the 'nature of reality', the latter referring to processes in the 'objective world' independent of our will or our knowledge. Even so, it is still unclear how this helps answer the above questions. If the human mind "solves" the contradictions involved in motion, wouldn't that mean things just stop moving? Or wouldn't it confirm the suspicion that movement only seems to be contradictory because of the partial nature of human knowledge, implying that it isn't really contradictory? Clearly, that is because these 'subjective contradictions' ought to disappear as knowledge grows, which in turn means that (in the limit) 'reality' can't be 'contradictory', after all. In that case, it is only our 'one-sided'/'partial' knowledge of nature that fools us into concluding otherwise!
As should now seem obvious, this implies 'objective reality' is now contradiction-free, which it must be if knowledge is only slowly catching up with that fact.
Alternatively, this might suggest we don't really understand these 'contradictions'. But, if that were so, it would fail to explain why contradictions are promptly reasserted upon being "solved". Nor is it at all clear how they could be "solved" if no one understands them, or if no one fully understands 'reality' (since they aren't in possession of 'absolute knowledge').
Perhaps even more alarmingly, this might mean that the objects in question aren't really moving, as Zeno originally contended! That is, that there is no such thing as motion! Reality is thus the opposite of what we perceive it to be -- which is another core principle Hegel dreamt up. Here is Herbert Marcuse expressing this odd idea as follows:
"Under the rule of formal logic, the notion of the conflict between essence and appearance is expendable if not meaningless; the material content is neutralised; the principle of identity is separated from the principle of contradiction (contradictions are the fault of incorrect thinking); final causes are removed from the logical order....
"Existing as the living contradiction between essence and appearance, the objects of thought are of that 'inner negativity' which is the specific quality of their concept. The dialectical definition defines the movement of things from that which they are not to that which they are. The development of contradictory elements, which determines the structure of its object, also determines the structure of dialectical thought. The object of dialectical logic is neither the abstract, general form of objectivity, nor the abstract, general form of thought -- nor the data of immediate experience. Dialectical logic undoes the abstractions of formal logic and of transcendental philosophy, but it also denies the concreteness of immediate experience. To the extent to which this experience comes to rest with the things as they appear and happen to be, it is a limited and even false experience. It attains its truth if it has freed itself from the deceptive objectivity which conceals the factors behind the facts -- that is, if it understands its world as a historical universe, in which the established facts are the work of the historical practice of man. This practice (intellectual and material) is the reality in the data of experience; it is also the reality which dialectical logic comprehends." [Marcuse (1968), pp.114-17. Bold emphasis alone added.]
"The doctrine of Essence seeks to liberate knowledge from the worship of 'observable facts' and from the scientific common sense that imposes this worship.... The real field of knowledge is not the given fact about things as they are, but the critical evaluation of them as a prelude to passing beyond their given form. Knowledge deals with appearances in order to get beyond them. 'Everything, it is said, has an essence, that is, things really are not what they immediately show themselves. There is therefore something more to be done than merely rove from one quality to another and merely to advance from one qualitative to quantitative, and vice versa: there is a permanence in things, and that permanent is in the first instance their Essence.' The knowledge that appearance and essence do not jibe is the beginning of truth. The mark of dialectical thinking is the ability to distinguish the essential from the apparent process of reality and to grasp their relation." [Marcuse (1973), pp.145-46. Marcuse is here quoting Hegel (1975), p.163, §112. Quotation marks altered to conform with the conventions employed at this site. Minor typo corrected.]
George Novack also weighed in on this with his very own brazen example of dogmatic apriorism:
"What distinguishes essence or essential reality from mere appearance? A thing is truly real if it is necessary, if its appearance truly corresponds to its essence, and only so long as it proves itself to be necessary. Hegel, being the most consistent idealist, sought the source of this necessity in the movement of the universal mind, in the Absolute Idea. Materialists, on the other hand, locate the roots of necessity in the objective world, in the material conditions and conflicting forces which create, sustain and destroy all things. But, from the purely logical standpoint, both schools of philosophy agree in connecting reality with necessity.
"Something acquires reality because the necessary conditions for its production and reproduction are objectively present and operative. It becomes more or less real in accordance with the changes in the external and internal circumstances of its development. It remains truly real only so long and insofar as it is necessary under the given conditions. Then, as conditions change, it loses its necessity and its reality and dissolves into mere appearance.
"Let us consider a few illustrations of this process, this contradiction between essence and appearance, resulting from the different forms assumed by matter in its motion. In the production of the plant, seed, bud, flower and fruit are all equally necessary phases or forms of its existence. Taken separately, each by itself, they are all equally real, equally necessary, equally rational phases of the plant's development. [We see here that Novack isn't ashamed to cite Hegel's batty idea about blossoms which we met earlier -- RL.]
"Yet each in turn becomes supplanted by the other and thereby becomes no less unnecessary and non-real. Each phase of the plant's manifestation appears as a reality and then is transformed in the course of development into an unreality or an appearance. This movement, triadic in this particular case, from unreality into reality and then back again to unreality, constitutes the essence, the inner movement behind all appearance. Appearance cannot be understood without an understanding of this process. It is this that determines whether any appearance in nature, society or in the mind is rational or non-rational." [Novack (1971), pp.86-87. Bold emphasis added.]
As I have pointed out Essay Three Part Two about the above passage:
It isn't my immediate concern to criticise this (almost classic) example of Mystical Natürphilosophie (however, it will be later), but merely to note: (a) The fanciful way that the term "contradiction" has been employed by Novack, and (b) His idiosyncratic use of the word "appearance". Exactly why a seed turning into a plant makes the seed an "appearance" Novack failed to say (except he regards Hegel's word on such issues as Gospel Truth), but why any of this is a 'contradiction' he left no less obscure. Of course, this might be a faint echo of an idea Hegel toyed with that anything that is transient or which lacks permanence is an 'appearance'. [Inwood (2002), pp.408-13.] Indeed, in relation to this it is worth asking how Novack knows that something is real only if its "appearance" coincides with its "essence" (always assuming that there are such things as 'essences', to begin with), that is, over and above merely accepting Hegel's diktat, once more.
This is in turn connected with the idea that some things appear for a short time and then disappear or fade away, like someone who (i) Has a part in a play (as in "NN, now appearing in Death of a Salesman on Broadway"), (ii) Occupies an official position for a year, (iii) Testifies in court (as in "NM is appearing for the prosecution"), or (iv) Is famous only for fifteen minutes. Or, maybe even when we (v) Describe how someone looks (as in "Her appearance gave her away; she was clearly terrified", or "His appearance changes from day-to-day; he is a master of disguise.") In this sense we might at a stretch say that a plant or a flower is "an appearance". At a stretch that is a valid point, but it is still unclear what this has to do with 'essence' and 'appearance'. Originally, the point here was, of course, to contrast the transient existence of certain phenomenal objects and processes when compared with others that are perhaps more permanent. For example, the play mentioned above might be on Broadway for a season, but Broadway will still be there after the play is well gone. So, it looks like 'essence' is somehow connected with permanence, 'appearance' with transience (no pun intended). And yet, do these more permanent features of the world have the 'ground of their being' within themselves, or do they, too, not 'rely on God'? If the latter is the case, then even they are also 'appearances'. Will Broadway still be there in five billion years time? I think there is room to suppose it might not. So, it too is an 'appearance', according to Hegel.
Furthermore, what connection is there between 'appearances' that might deceive us -- like the way that sticks appear to bend when partially immersed in water or the way the Sun appears to rise in the East and fall in the West -- and the sort of 'appearances' mentioned in the previous paragraph, those associated with a lack of permanence? Presumably sticks will still look bent when partially immersed in water in ten million years' time, just as the apparent motion of the Sun will remain the same as long as the Sun, the Earth and human beings still exist. Given the considerations mentioned above, these 'appearances' are also really 'essences' since they look like permanent features of the natural world --, which means, of course, that this distinction itself has become absurd. [I will return to consider these phenomena again, here, here and here.]
[Several passages from Hegel and others (including Marxist dialecticians) who promote the idea that there is a contradiction between underlying 'essence' and superficial 'appearance' (a distinction that goes back as far as Parmenides and Plato -- ruling-class hacks, if ever there were any) are also quoted in Essay Three Part Two.]
So, this aspect of Hegel's loopy 'logic' seems to imply motion is an illusion, the opposite of the way it appears in everyday life. If so, that will explain why, for anyone (or any 'being') that has 'absolute knowledge', these 'contradictions' will have disappeared (indeed, as we saw Engels confirm earlier).
That also helps explain why he then said this:
"…the continual assertion and simultaneous solution of this contradiction is precisely what motion is…." [Engels (1976), p.152. Bold emphasis added.]
This appears to confirm the idea that motion isn't really 'contradictory-in-itself', it is simply our 'one-sided'/'relative' perspective that misleads us into concluding otherwise. Here, Engels tells us that the "continual assertion" and "solution" of this contradiction is "precisely what motion is".
There is one small, lingering problem with that interpretation: Why then does he say this reveals "precisely" what motion is, as opposed to arguing that it merely depicts what we subjectively think it is? [It is a pity Engels didn't employ a sub-editor to check the consistency of his wording! Or maybe, DM is meant to be full of inconsistencies -- as a sort of indirect 'reflection' of the way the world is supposed to be?]
Be that as it may, an appeal to "objective dialectics" can't help us comprehend Engels, either. That is because neither assertions nor solutions occur in nature (apart, that is, from the intelligent beings who make or who provide them). And, if that is so, these non-objective assertions and solutions can't have been reflected in the mind of observers as part of an 'objective scientific theory' -- or, indeed, as part of 'objective dialectics'. If assertions and solutions don't exist in the world independent of the individuals who make or invent them, there would be nothing there, in 'extra-mental reality' for the minds of scientists and dialecticians to reflect or latch onto. As Lenin pointed out, objectivity is connected with "truth independent of man":
"To be a materialist is to acknowledge objective truth, which is revealed to us by our sense-organs. To acknowledge objective truth, i.e., truth not dependent upon man and mankind, is, in one way or another, to recognise absolute truth." [Lenin (1972), p.148. Bold emphasis added.]
"Knowledge can be useful biologically, useful in human practice, useful for the preservation of life, for the preservation of the species, only when it reflects objective truth, truth which is independent of man." [Ibid., p.157. Bold emphasis added.]
Since 'assertions' and 'solutions' are dependent on 'man', they can't be objective (if Lenin is to be believed).
If so, what has assertion and solution got to do with motion in the real world, in the first place? And why did Engels think they were at all relevant?
So many questions -- so few answers...
(3) Yet More Vagueness
As we have seen, Engels informed his readers that:
"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. Bold emphasis added.]
More specifically, in relation to moving bodies, it is pertinent to ask: How far apart are the two proposed "places" that a moving object is supposed to occupy while at the same time not occupying one of them? Is there a minimum distance involved?
The answer can't be "It doesn't matter, any distance will do." That is because, as we will see, if a moving object is in two places at once, then it can't truly be said to be in the first of these before it is in the second, since it is in both of them at the same time. So, unless great care is taken specifying how far apart these "two places" are, the DM-theory-of-motion would imply, for instance, that an aeroplane lands at its destination the same moment it takes off from the departing airport! If any distance will do, then the distance between the two airports involved is as good as any. [I return to this topic and discuss it in much more detail later in this Essay.]
Indifference here, in this respect, would have you arriving at your destination at the moment you left home!
Anyway, whatever the answer to that annoying question happens to be between any two locations there is a potentially infinite number of intermediate points (that is, unless we are prepared to impose an a priori limitation on nature by denying this). As we will see, even Hegel acknowledged this point (no pun intended).
Does a moving body, therefore
(i) Occupy all of these intermediate points at once? Or,
(ii) Does it only occupy each pair of such points successively? And which privileged pair is this, then?
If (i) were the case, would that not imply a moving object can be in a potentially infinite number of places at the same time, not just in two, as Engels asserted? On the other hand, if Engels's words are meant to be interpreted strictly and literally, implying that a moving body occupies at most two places at once, wouldn't that suggest motion is discontinuous? As we are about to find out, it seems it does because that would picture motion as a peculiar stop-go, staccato sort of affair (that is, if a moving 'dialectical' object is restricted to being in at most two places at any one time). That in turn, also means it must be stationary at the second of those two locations, even if only momentarily.
This is why (the following argument is based on the uncontroversial observation (explicitly accepted by Hegel, Lenin and also, it seems, by Trotsky (e.g., Trotsky (1971), pp.65-66)) that if a body is located at the same point for at least two contiguous instants in time, it must be stationary there, even if only momentarily):
Let us first of all suppose that body, B, is moving and occupies two points -- say p1 and p2 -- at the same time, t1 (in accord with Engels's claim).
But, if B continues to move when it is at p2, it must still occupy two points at the same instant, t1, otherwise it will be motionless there (according to the "uncontroversial observation" noted earlier) -- i.e., in that case, B would be located at p2 during two instants, t1 and t2, not one (here assuming these two 'moments in time' are contiguous). But, if B is in that second place, p2, during these two instants it must be stationary there (even if only momentarily).
On the other hand, if we reject the above conclusion and continue to assume B is still moving while it is located at p2, then, according to Engels, it must be the case that it occupies two places at once, p2 and p3, also at t1! But, as we will see later on in this Essay, that result will prove to be even more disastrous for Hegel and Engels's theory. So, in order to avoid that (fatal) result, we might now try to argue that B will be at p2 and p3 at a later moment, t2 -- since B has to be in those two locations at the same time if it is still moving (according to Engels), and we have just rejected the possibility that B is in p2 and p3 at t1. But, that means B must be located at p2 during two instants, t1 and t2, which, as we have also seen, implies it would now be motionless there (even if only momentarily).
The bottom line here is that if B is still moving in the second of these two locations, it must also occupy a third place at the same time, otherwise it would be stationary in that second location, since it would be there during two moments in time.
Unfortunately, the restrictive "in at most two places at once" qualifier mentioned earlier rules out any possibility that B can occupy a first, second and third place at the same time. That is why this means B must occupy the second and third of these locations at a later time, implying once again that B will be located at p2 during two instants, t1 and t2, meaning it will be motionless there (even if only momentarily).
However, the same argument applies to all the points along B's trajectory. The "in at most two places at once" restriction implies that B will occupy each successive point for two instants, not one, meaning its motion will be discontinuous, a stop-go sort of affair (suggested earlier). But, that runs contrary to the hypothesis that motion is continuous and therefore contradictory -- or, it does so if we accept the "at most two" caveat.
Any attempt to reject the "in at most two places at once" caveat will only succeed in re-introducing all the problems we met earlier this restriction was meant to avoid (and, as it turns out, sidestep several even more problematic implications we will meet later on in this Essay), namely that a moving object must occupy a potentially infinite number of points in the same moment, not two, contrary to Engels, once more!
But, it was surely the continuous nature of motion that (supposedly) presents logic (i.e., FL) with insoluble problems, which system -- so we have been informed by DM-fans -- is built on a static, discontinuous view of reality, a tall tale they never tire of spreading and which they always fail to substantiate.
Any who still find the above argument difficult to follow might find the following of some assistance (below, all the 'moments in time' mentioned are contiguous):
[1] Let us track moving object, B, along its path.
[2] Let assume that B begins its journey at point, p1, at time, t1.
[3] Let us further assume this journey takes B through the following points: p1, p2, p3,..., pi-1, pi, pi+1,..., pn-2, pn-1, pn, where it finally stops.
[4] Normally, we would say that B occupies each of these points at successive moments in time.
[5] So, B would be in p1 at t1, p2 at t2, p3 at t3, p4 at t4, and so on.
[6] But, if Engels is to be believed, we can't say that; we have to say something like this: B is in p1 and p2 at t1.
[7] The problem now becomes one of trying to decide what happens at all the other points along B's path.
[8] For reasons aired above, let us now restrict what Engels meant by (i) "a body being both in one place and in another place at one and the same moment of time" to the following, (ii) "a body being in at most two places at one and the same moment of time".
[9] We will also assume that if an object is located in one place for two or more contiguous moments, it will be at rest there.
[10] With that in mind, let us try and make sense of the movement of B from p2 to p3.
[11] One and only one of these must be the case:
(α) B is in p2 and p3 at t1.
(β) B is in p2 and p3 at t2.
(γ) B is in p2 at t1 and in p3 at t2.
[12] If (β) were the case, then from [6] above, B will be in p2 at two times, t1 and t2. But [9] tells us this would mean B is now stationary at p2.
[[6] But, if Engels is to be believed, we can't say that; we have to say something like this: B is in p1 and p2 at t1.]
[[9] We will also assume that if an object is located in one place for two or more contiguous moments, it will be at rest there.]
[13] If (γ) were the case, then Engels was wrong, since he held that all moving bodies occupy two places at the same time, not two places at successive moments in time, which is what (γ) implies.
[14] If (α) were the case, then, also from [6], B would occupy three places at the same time: p1, p2 and p3, all at t1.
[15] But [14] contradicts [8](ii), which was: "a body being in at most two places at one and the same moment of time".
[16] So, if we hold on to [6] and [8](ii), (α) and (γ) must be rejected. Hence, (β) must be the case. So B does come to rest at p2, since it is there for two moments. [Based on [9].]
[17] However, the same argument applies when B moves from p3 to p4, p4 to p5, p5 to p6,..., pn-1 to pn. Hence, B must come to rest at all those points!
[18] This means that while B might move from one point to the next, it does so in a stop-go, staccato sort of way, halting at every point along its path.
I trust that that makes the argument a little clearer!
[Later on in this Essay, I will return to this argument and derive even more weird results from it -- and where I also consider every conceivable response and objection.]
It could be countered 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 of them, a moving body must occupy more than two at once, contrary to what Engels said:
"[A]s soon as we consider things in their motion, their change, their life, their reciprocal influence…[t]hen we immediately become involved in contradictions. Motion itself is a contradiction; even simple mechanical change of place can only come about through a body being both in one place and in another place at one and the same moment of time, being in one and the same place and also not in it. And the continual assertion and simultaneous solution of this contradiction is precisely what motion is." [Ibid. Bold emphasis added.]
Hence, between any two points, P and Q -- located at, say, (Xp, Yp, Zp) and (Xq, Yq, Zq), respectively -- which a moving object, B, occupies (at the same "moment in time", t1), there are, for example, the following intermediary points: (X1, Y1, Z1), (X2, Y2, Z2), (X3, Y3, Z3),..., (Xi, Yi, Zi),..., (Xn, Yn, Zn) -- where n itself can be arbitrarily large. Moreover, the same applies to (X1, Y1, Z1) and (X2, Y2, Z2): there is a potentially infinite number of intermediate points between those two, and so on (again, as even Hegel acknowledged).
So, if Engels is to be believed, B must occupy not just P and Q at the same instant, it must occupy all these intermediary points, as well -- all at t1. That can only mean that B is located in a potentially infinite number of places at the same "moment". It must therefore not only be in and not in P at t1, it must be in and not in each of (X1, Y1, Z1), (X2, Y2, Z2), (X3, Y3, Z3),..., (Xi, Yi, Zi),..., and (Xn, Yn, Zn), at t1, just as it must be in all the intermediary points between (X1, Y1, Z1) and (X2, Y2, Z2), if it is also to be in Q at the same "moment" -- if we reject the "in at most two places at once" caveat.
And, what is worse: B must move through (or be in) all these intermediate points with time having advanced not 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!
Unless, of course, we decide to re-define "velocity" so that it is no longer the expression of a functional relation between distance and time -- calculated by dividing the former by the latter.
But, if not, what then is it?
[An appeal to the Calculus here -- or, rather, to a DM-reinterpretation of the Calculus -- would be to no avail, as we will see in Essay Seven Part One. See also this sub-section of the present Essay.]
Of course, we could always claim that by "same moment" Engels meant "same temporal interval", but as we will soon see, that reply would scupper his theory even faster. [No pun intended.] That is because, if by the "same moment" Engels did mean the "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. [Again, no pun intended!]
[Why that is so will be explained below. Indeed, we will also see that this alternative (i.e., that a moving body occupies all the intermediate points between any two points at the same time) poses even more serious problems for Engels's theory than this --, that is, over and above implying that 'dialectical' objects move with infinite velocities. For some of the social and political consequences of the idea that between any two points there is a third point, or that any point can be divided into two points -- i.e., that there are no "indivisibles" -- and the controversy over "infinitesimals" in the post-Renaissance world, see Alexander (2016).]
However, if B moves from P to Q in temporal interval, t, comprised of sub-intervals, t1, t2, t3, ..., tn, each of which is also comprised of its own sub-intervals, then B will be located at P at t1 and then at Q at tn, 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. The 'contradiction' Engels claims to see here has now 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. Hence, it will have been in two locations during the same temporal interval (spanning three hours), but not in two places in the same moment in time. Once again, 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 (i.e., until it reaches the city boundary). So, in this example, the car isn't in one place and not in it in this specific sub-interval of the longer 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'. That is probably why Engels didn't refer to them, and, as far as can be ascertained, no DM-theorist has done so since.
[Graham Priest has argued that changes from one state to another -- in the above example, the actual moment the said car left the city boundary -- are contradictory (in Hegel and Engels's sense of that word -- if it is granted, for the purpose of argument, that this use of "contradictory" makes some sort of sense!). I have neutralised his argument in Note 18a. (The car example is, of course, mine not Priest's!)]
On a different tack: Do these contradictions increase in number or stay the same if an object speeds up? [This is a problem that, for example, exercised Leibniz; more on that 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 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 is difficult to see how, in a DM-universe, moving bodies can possibly accelerate if they are in these two places at once.
[I am of course using "accelerate" here as it is employed in everyday speech, not as it is used in Physics and Applied Mathematics!]
Accelerated motion (in the above sense of the phrase) involves a body being in (or passing through) more places in a given temporal 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?
[For some of the complexities involved here, see Note 18c.]
Hence, as we have seen, if we insist on analysing motion this way, a moving object must be in an 'infinite number' of points all at the same time -- in which case it can't speed up. This conundrum was brought out rather well by Professor Joseph Mazur:
"Consider three adjacent points labelled A, B, and C. By this I mean that B is immediately to the right of A and that C is immediately to the right of B. In one indivisible instant, an object cannot travel from point A to point C. If it could, there would be no instant when it could be at point B. Of course, this is absurd, because that would mean all motion must take place at the same speed. The only way out of this is to reject the thought that points or instants are consecutive, i.e., arranged in a hierarchy from left to right and vice versa. This leads to equally puzzling thoughts about how a moving body gets from one point to another. If an object moved from A to C, there must have been a moment when it was at a point B between A and C. And there must have been a moment when it was at a point between A and B. This can go on indefinitely." [Mazur (2007), pp.29-30. Spelling modified to agree with UK English. Bold emphasis alone added.]
A B C
Alternatively, if the above remarks are correct, a moving object must be in these intermediate points 'outside of time'. Hence, if Trotsky is to be believed, such an object must cease to exist between any two points!
"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." [Trotsky (1971), p.64.]
There thus seems to be no way of making sense of the everyday phenomenon of movement/locomotion if we insist on using language this way.
(4) Yet More A Priori Dogmatics?
Quite apart from this, Engels's attempt to provide an overtly linguistic -- or even a 'conceptual' -- solution to the 'problem of motion' suggests that there is more than a hint of LIE to his theory. No wonder given the fact that he imported it from Hegel, an Idealist of the worst possible kind.
[LIE = Linguistic Idealism; that term is explained here.]
This purely 'conceptual' approach to motion is plain from the way that Engels's attempt to depict it depends on a 'one-sided' consideration of a handful of the concepts that seemed relevant to both him and Hegel -- albeit expressed with ordinary-looking language, the meaning of which both simply took for granted (more on that later).
So, based on thought alone, Engels imagined he could conclude what must be true of every moving object in the entire universe, for all of time, without exception. But, how could he possibly have known all this with so little evidence -- in fact, no evidence at all -- to back it up?
"[S]o long as we consider things as at rest and lifeless, each one by itself, alongside and after each other, we do not run up against any contradictions in them. We find certain qualities which are partly common to, partly different from, and even contradictory to each other, but which in the last-mentioned case are distributed among different objects and therefore contain no contradiction within. Inside the limits of this sphere of observation we can get along on the basis of the usual, metaphysical mode of thought. But the position is quite different as soon as we consider things in their motion, their change, their life, their reciprocal influence on one another. Then we immediately become involved in contradictions. Motion itself is a contradiction: even simple mechanical change of position can only come about through a body being at one and the same moment of time both in one place and in another place, being in one and the same place and also not in it. And the continuous origination and simultaneous solution of this contradiction is precisely what motion is." [Engels (1976), p.152. Bold emphasis added.]
"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. Paragraphs merged.]
Notice, Engels explicitly contrasts what we can see (when he refers to the "limits of this sphere of observation") with how things seem when we "consider things". In other words, his only 'evidence' is based on what we think about motion not what we actually observe.
Clearly, Engels was in possession of a truly remarkable skill: the ability to uncover fundamental truths about reality, valid for all of space and time, from the presumed meaning of a few words (or 'concepts')! Indeed, Engels's claims about motion are all the more impressive when it is recalled that he hit upon these ideas in abeyance of any supporting evidence, let alone a significant body of it. As it turns out (and as this will also be demonstrated in what follows), even had any evidence been available to him it would have been unnecessary, anyway.
As we have already seen (in Essay Two), all that an aspiring dialectician like Engels need do in such circumstances is briefly 'reflect' on the supposed meaning of a few words, or 'concepts', and substantive truths about fundamental aspects of 'reality', valid for all of space and time, effortlessly spring to mind.
Or, to be more honest, all they have to do is read Hegel's 'Logic' (or the work of some other mystic, such as Heraclitus). This a priori approach to 'knowledge' is the unifying thread that runs through the entire history of ruling-class thought, unfortunately imported into the workers' movement by incautious non-workers like Engels. [On that, see Essays Nine Parts One and Two, Twelve Part One and Fourteen Part Two.]
So, the only 'evidence' that 'supports' Engels's interpretation of motion is this highly compressed (and, as we will also see, rather badly formulated) 'argument' -- or, rather, this superficial 'thought experiment'. Pressed for a justification of the conclusions he reached, all that Engels could offer in response would be a rather weak claim that this is what the word "motion" really means. Such a rejoinder would clearly give the game away, since it would confirm the accusation that substantive truths about motion had indeed been derived from the supposed meaning of a few words (or in this case, perhaps just one), and nothing more.
[The significance of that observation will emerge in as this Essay unfolds, but more extensively in Essay Twelve Part One.]
As noted above, an appeal to evidence would be irrelevant, anyway. That is because the examination of a finite set (no matter how large) of moving objects would fail to confirm Engels's assertion that they occupy two places at once. That would still be the case irrespective of the instruments or devices chosen to help effect these observations and regardless of the extent of the magnification used to that end. Or, indeed, independently of 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), in one of them and not in it, at the same time. That explains why Engels offered no scientific evidence whatsoever in support of his belief that motion is contradictory. That picture hasn't changed in the intervening years; indeed, the author of no book, article or speech devoted to DM (by one of its supporters) even so much as thinks to quote or cite any such evidence, and that situation isn't ever likely to change.5
What is perhaps even more peculiar -- when we recall that DM-fans never tire of telling us that their theory enjoys convincing support from the available evidence and that they would never dream of imposing their ideas on the facts (on that, see Essay Two and below) -- is that not one of them has noticed this core part of their theory enjoys absolutely no evidential support.
Of course, it could be objected to such an accusation that if, say, a photograph were taken of a moving object, it would show by means of the recorded blur that such a body had occupied several places at once. In that case, therefore, there is, or could be, evidence in support of Engels's claims.
The problem with this is that no matter how fast the shutter speed, no camera (not even this one, or this) can record an instant in time, merely a temporal interval -- that is, such devices record what happens in the time interval between opening and closing the shutter, or other light permitting aperture. Clearly, in order 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. However, since instants (i.e., in the sense required) are mathematical fictions, it isn't possible to record them!
Update December 2016: The New Scientist recently reported this:
"For the first time, physicists have measured changes in an atom to the level of zeptoseconds, or trillionths of a billionth of a second -- the smallest division of time yet observed. In this case, the speed demon was an electron escaping the bonds of its parent atom when struck by a photon. This electron ejection is known as the photoelectric effect, and was described by Albert Einstein in 1905. Previous experiments could only measure what happened after the electron was kicked out, says Martin Schultze at the Max Planck Institute of Quantum Optics in Garching, Germany. Now, he and his colleagues have measured the ejection of electrons from a helium atom from start to finish with zeptosecond precision (10-21 seconds), marking the smallest time slot ever measured. To do this, they fired ultraviolet laser pulses lasting 100 to 200 attoseconds (10-18 seconds) at a helium atom to start exciting its pair of electrons. By making many readings and calculating their statistical spread the team could measure events with a resolution of 850 zeptoseconds. They found the ejections took 7 to 20 attoseconds (Nature Physics, doi.org/bszd). The results are an important window into the quantum behaviour of atoms, especially how their electrons interact with each other, says Schultze." [New Scientist, 19/11/2016, p.14. Paragraphs merged. One link added.]
Not even this ultra-precise measurement captures an 'instant', just an interval, albeit extremely brief.
It could be countered that as we increase a camera's shutter speed any photographs taken will always show some blurring. This supports the conclusion that moving objects are never located in one place at one time. Despite this, it still remains the case that no photograph can catch an instant, and thus none such can verify Engels's contention. Naturally, the situation hasn't been helped by the fact that neither Zeno, Hegel nor Engels were very forthcoming about how long they thought a "moment" or an "instant" in time was supposed to last. Indeed, it would seem that one of these "instants" is in fact a zero of time (i.e., they have no duration), which means, at least according to Trotsky, they don't actually exist!
Again, it could be argued that it is reasonable to conclude from the above that moving objects occupy two locations at the same moment. Once more: since an 'instant in time' is a mathematical fiction, it isn't reasonable to conclude this.
However, it isn't reasonable to conclude this since even that thought experiment has a body moving in a temporal interval, not a durationless 'instant'. Moreover, not even a mathematical limiting process could capture such ghostly 'entities' in the physical world, whatever else it might appear to achieve in theory. And, even if it could, no camera (radar device or other equipment) could capture it. Hence, even if an appeal to a mathematical limiting process were viable (or available), it would be of no help. No experiment or observation is capable of substantiating any of the conclusions Engels and Hegel reached about moving bodies.
And that explains why they (and those who accept these ideas) have had to foist this theory of motion onto nature.
But, as we will see later, the idea that a moving object is in two places at once possesses rather nasty consequences of its own (for this theory), so DM-fans had better hope that no camera will ever be able to record this alleged fact. Of course, there were no such cameras in the 19th century, but Hegel and Engels still seemed happy to assert the truth of something that was impossible to confirm in their day -- and now even in ours!
Hence, Engels's conclusion about moving bodies wasn't derived from a consideration of the facts, it has been imposed on them, in defiance of what Engels himself said:
"Finally, for me there could be no question of superimposing the laws of dialectics on nature but of discovering them in it and developing them from it." [Engels (1976), p.13. Bold emphasis added.]
"All three are developed by Hegel in his idealist fashion as mere laws of thought: the first, in the first part of his Logic, in the Doctrine of Being; the second fills the whole of the second and by far the most important part of his Logic, the Doctrine of Essence; finally the third figures as the fundamental law for the construction of the whole system. The mistake lies in the fact that these laws are foisted on nature and history as laws of thought, and not deduced from them. This is the source of the whole forced and often outrageous treatment; the universe, willy-nilly, is made out to be arranged in accordance with a system of thought which itself is only the product of a definite stage of evolution of human thought." [Engels (1954), p.62. Bold emphasis alone added.]
"We all agree that in every field of science, in natural and historical science, one must proceed from the given facts, in natural science therefore from the various material forms of motion of matter; that therefore in theoretical natural science too the interconnections are not to be built into the facts but to be discovered in them, and when discovered to be verified as far as possible by experiment. Just as little can it be a question of maintaining the dogmatic content of the Hegelian system as it was preached by the Berlin Hegelians of the older and younger line. Hence, with the fall of the idealist point of departure, the system built upon it, in particular Hegelian philosophy of nature, also falls. It must however be recalled that the natural scientists' polemic against Hegel, in so far as they at all correctly understood him, was directed solely against these two points: viz., the idealist point of departure and the arbitrary, fact-defying construction of the system." [Ibid., p.47. Bold emphasis alone added. Paragraphs merged. Unfortunately, this passage is longer available at the Marxist Internet Archive, but it can nevertheless be accessed here.]
From recently published Preparatory Writings for Anti-Dühring, we find the following entirely reasonable comment, also by Engels:
"The general results of the investigation of the world are obtained at the end of this investigation, hence are not principles, points of departure, but results, conclusions. To construct the latter in one's head, take them as the basis from which to start, and then reconstruct the world from them in one's head is ideology, an ideology which tainted every species of materialism hitherto existing.... As Dühring proceeds from 'principles' instead of facts he is an ideologist, and can screen his being one only by formulating his propositions in such general and vacuous terms that they appear axiomatic, flat. Moreover, nothing can be concluded from them; one can only read something into them...." [Marx and Engels (1987), p.597. Bold emphases alone added. Quotation marks altered to conform with the conventions adopted at this site.]
Again, as we will see, Engels is guilty of doing precisely what he accused Dühring of doing. In which case, the following characterisation of Idealism clearly applies to his '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.]
That is also what Zeno and Hegel did; 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." None of them "verified [this theory] by demonstration in practice...."
Of course, part of the problem here depends on what the word "instant" means. [I am taking it to mean the same as the phrase "moment in time", used by Engels.] In that case, some might think this 'problem' could be resolved by re-defining our terms. However, even if that were possible, such an 'adjustment' would merely amount to the adoption of a new linguistic convention, which would have no bearing on 'the nature of reality'. It would also further confirm the suspicion that this 'theory' had been imposed on nature, not 'read from it'. What else is the introduction of a new linguistic convention, adopted for the sole purpose of making a given theory 'fit the facts', but an imposition?5a
Again, as Trotsky argued:
"How should we really conceive the word 'moment'? If it is an infinitesimal interval of time, then a pound of sugar is subjected during the course of that 'moment' to inevitable changes. Or is the 'moment' a purely mathematical abstraction, that is, a zero of time? But everything exists in time; and existence itself is an uninterrupted process of transformation; time is consequently a fundamental element of existence. Thus the axiom 'A' is equal to 'A' signifies that a thing is equal to itself if it does not change, that is if it does not exist." [Trotsky (1971), p.64. Bold emphasis added.]
Unfortunately for Engels, if motion were to take place in one of these "moments", that would clearly mean it couldn't exist -- unless, of course, we're also prepared to reject the dogmatic, a priori opinion Trotsky himself expressed in the above passage!
But, if motion actually takes place -- as it most 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 (according to Trotsky) the latter don't exist? 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?
Some might claim that the above points are all rather abstract and 'academic', but that (proffered) deflection can't rescue Engels's theory. His analysis of motion is no less abstract! Even worse, his concept of motion can't have been derived by 'abstraction' from all (or any) of the forms of motion hitherto experienced by himself or by humanity in general -- or from a finite sub-set of either --, or even from what had been observed by scientists and philosophers in his day, or now even in ours. That is because Engels's theory clearly appeals to objects and processes that, according to Trotsky, don't exist -- such as "moments" in time and changes of place that take place 'outside of time'. What is more, even if they did exist, we couldn't experience or observe them, and hence we couldn't use them to confirm what Engels asserted. As seems plain, observations take place in time, and have a duration (and, in theory, can be observed); "instants" do not (and can't, even in theory).
Clearly, it isn't possible to 'abstract' from such non-existent 'instants' in order to agree with Engels!
So, whichever way we turn we hit yet other non-dialectical brick wall.
"[S]o long as we consider things as at rest and lifeless, each one by itself, alongside and after each other, we do not run up against any contradictions in them. We find certain qualities which are partly common to, partly different from, and even contradictory to each other, but which in the last-mentioned case are distributed among different objects and therefore contain no contradiction within. Inside the limits of this sphere of observation we can get along on the basis of the usual, metaphysical mode of thought. But the position is quite different as soon as we consider things in their motion, their change, their life, their reciprocal influence on one another. Then we immediately become involved in contradictions. Motion itself is a contradiction: even simple mechanical change of position can only come about through a body being at one and the same moment of time both in one place and in another place, being in one and the same place and also not in it. And the continuous origination and simultaneous solution of this contradiction is precisely what motion is." [Engels (1976), p.152.]
In the above passage, Engels promptly changed direction (no pun intended) arguing that it is motion itself that is contradictory, not just our thoughts about it that are:
"Motion itself is a contradiction…." [Ibid. Bold emphasis added.]
In which case, it could be argued that Engels was merely pointing out that our thoughts about motion are contradictory because motion itself is. That is, our theories depict the world more fully, accurately and truly when they faithfully reflect its contradictory nature. In that case, substantive claims about the universe are fully justified --, indeed, are objective -- when our ideas capture changing reality more precisely (but, only if they have been tested in practice).
Unfortunately, if that (proffered) response were correct, it would be inimical to DM itself; that is because it would mean DM contains contradictions, which would clearly imply it is a contradictory theory!7
[The disastrous implications that that particular observation has for DM were set out in Essays Seven Part One and Eleven Part One.]
Despite this, a reply along those lines would give the game away since it confirms the validity of an earlier accusation that this theory has been imposed on nature. That is because there is no way Engels could know, or have known, that nature is contradictory and that all motion in the entire universe, for all of time, is as he says it is. The very best he could claim is that our thoughts about motion are contradictory and this suggests that motion in nature might be, too.
However, as will become apparent by the end of this Essay, the insurmountable problem that confronts the above suggested fall-back position is that our thoughts about motion aren't the least bit contradictory, either!7a
Be this as it may, the above (proffered) response fails to neutralise the serious difficulties these ideas face, outlined earlier. That is because Engels's philosophical theory, which was the result of an extrapolation from what he thought were the meaning of a handful of words (and/or 'concepts') to a conclusion about fundamental aspects of reality, is itself overtly Idealist (on that, see Essays Two and Twelve Part One). Indeed, as Engels himself pointed out (quoted earlier):
"The general results of the investigation of the world are obtained at the end of this investigation, hence are not principles, points of departure, but results, conclusions. To construct the latter in one's head, take them as the basis from which to start, and then reconstruct the world from them in one's head is ideology, an ideology which tainted every species of materialism hitherto existing.... As Dühring proceeds from 'principles' instead of facts he is an ideologist, and can screen his being one only by formulating his propositions in such general and vacuous terms that they appear axiomatic, flat. Moreover, nothing can be concluded from them; one can only read something into them...." [Marx and Engels (1987), Volume 25, p.597. Italic emphases in the original; bold emphases added. Quotation marks altered to conform with the conventions adopted at this site.]
Compare those remarks (again) with George Novack's:
"A consistent materialism cannot proceed from principles which are validated by appeal to abstract reason, intuition, self-evidence or some other subjective or purely theoretical source. Idealisms may do this. But the materialist philosophy has to be based upon evidence taken from objective material sources and verified by demonstration in practice...." [Novack (1965), p.17. Bold emphasis added.]
Worse still, and for reasons aired earlier, not only is there no way this 'theory' can be confirmed (by an appeal to evidence), its subject matter (i.e., the theory that a moving body occupies and does not occupy a given location in the same moment, and is therefore in two places at once) resists all attempts to make sense of it, as we will soon see.
Substantive philosophical 'truths' like this (about motion, for example) are ambitiously universal in intent but are at the same time embarrassingly parochial in origin. Indeed, their promulgators' epistemologically expansive intentions (which purport to stretch across all regions of space and time) remain stubbornly unmatched by any capacity to satisfy such hyper-bold philosophical goals with adequate supporting evidence --, or, in this particular case, any at all.
More to the point: how could this theory possibly be 'tested in practice'? This isn't an academic point, since DM-theorist also never tire of telling us things like this:
"From living perception to abstract thought, and from this to practice, -- such is the dialectical path of the cognition of truth, of the cognition of objective reality." [Lenin (1961), p.171. Bold emphasis alone added.]
"Marxists hold that man's social practice alone is the criterion of the truth of his knowledge of the external world. What actually happens is that man's knowledge is verified only when he achieves the anticipated results in the process of social practice (material production, class struggle or scientific experiment)." [Mao (1961b), p.296. Bold emphasis added.]
Our old friends, Woods and Grant, agree:
"The validity of any theory must be demonstrated, sooner or later, in practice." [Woods and Grant (1995/2007), p.85/89.]
So does John Rees:
"[H]ow are we to be sure that our theory is correct? The answer is that there is a point where the theory and the consciousness of the working class meet -- in practice." [Rees (1998), p.236.]
They aren't alone; here are two STDs who concur:
"We now conclude: practice, the activity of man, is the test of the possibility and extent of his knowing things. If from oxygen and hydrogen I can compose water, then to this extent I have correct knowledge of the nature of water." [Thalheimer (1936), p.153. Bold emphasis added.]
"Dialectical materialism is a philosophy of practice, indissolubly united with the struggle for socialism.... This is the source of all its teachings, and in that service its conclusions are continually tried, tested and developed." [Cornforth (1976), p.125. Bold emphases added. Paragraphs merged.]
[STD = Stalinist Dialectician.]
But, has a single DM-fan ever wondered (out loud or even during episodes of 'inner speech') exactly which examples of practice have ever, or could ever, confirm what Engels had to say about moving bodies? According to the above, therefore, this theory can't be true. Why on earth then is it accepted by DM-fans?
As we have seen, throughout history Traditional Theorists -- like Engels, and more particularly, Hegel -- privileged speculation ahead of even a perfunctory search for supporting evidence. Indeed, they assumed that all of nature must be as their 'word-magicked-ideas' appeared to depict it. The world had to conform to what their theories said, not the other way round. Engels's thoughts on this topic (and others) dictate to the world how it must be and how it must behave, the exact opposite of what he said he would do:
"Finally, for me there could be no question of superimposing the laws of dialectics on nature...." [Engels (1976), p.13. Bold emphasis added.]
When what he should have said is the following:
"Finally, for me there could be no question of not superimposing the laws of dialectics on nature...." [Engels corrected.]
(5) Explanation Or Re-Description?
Here is the passage again:
"[S]o long as we consider things as at rest and lifeless, each one by itself, alongside and after each other, we do not run up against any contradictions in them. We find certain qualities which are partly common to, partly different from, and even contradictory to each other, but which in the last-mentioned case are distributed among different objects and therefore contain no contradiction within. Inside the limits of this sphere of observation we can get along on the basis of the usual, metaphysical mode of thought. But the position is quite different as soon as we consider things in their motion, their change, their life, their reciprocal influence on one another. Then we immediately become involved in contradictions. Motion itself is a contradiction: even simple mechanical change of position can only come about through a body being at one and the same moment of time both in one place and in another place, being in one and the same place and also not in it. And the continuous origination and simultaneous solution of this contradiction is precisely what motion is." [Engels (1976), p.152.]
In addition to the problems concerning the above quotation that were raised in the first few sub-sections of this Essay, the following questions are also worth asking:
Q1: What exactly is the point of this theory?
Q2: How does the 'contradictory nature of motion' in any way help explain it?
At best, it merely seems to re-describe this phenomenon (and in a paradoxical way, too). There is no obvious way in which it helps explain motion. How then can it form part of a scientific theory?
The answer often given is that the point of looking at motion this way illustrates:
(i) How reality is fundamentally dialectical;
(ii) How ordinary thought, commonsense and/or FL misleads us; and,
(iii) The superiority of DL.
[FL = Formal Logic; DL = Dialectical Logic; UO = Unity of Opposites.]
Responses (i) and (ii) will be tackled throughout the rest of this Essay and this site, while (iii) will be examined in detail in this sub-section (and, indeed, the rest of this site, too).
If DL is quite as 'superior' as DM-theorists seem to think it is we should be able to answer the second of the above questions, based on what Engels (or Hegel and Lenin) had to say, namely:
Q2: How does the 'contradictory' nature of motion in any way help explain it?
More specifically:
Q3: How is one 'part' of this supposed 'contradiction' capable of exercising a causal influence over any other 'part' of it?
Q4: How can one or both of the UOs involved in this phenomenon -- presumably, the "here" and the "not here" (or more accurately, presumably, a moving object being "in one place" and "not in it" at the same time) -- actually make anything move?
[A more generalised objection to this way of seeing movement and change has been aired here.]
The above questions, of course, assume there is a UO of some sort at work here, which there would have to be if this is accurately to be described as a 'dialectical contradiction', and not just an 'ordinary contradiction'. As noted in Q4, the only viable candidates for such 'dialectical opposites' seem to be the "here" and the "not here" (or more accurately, a moving object being "in one place" and "not in it" at the same time). Even so, exactly how these UOs are supposed to 'struggle' with and then turn into each other-- which the DM-classics tell us is an "absolute" -- is something of a mystery. How does a "here" and a "not here" engage in any sort of 'struggle'? How can a moving object being "in one place" and "not in it" (at the same time) do what the DM-classics tell us always happens with such UOs? How does "in one place" 'struggle' with "not in it"?
Again, has a single DM-fan in the entire history of Dialectical Marxism asked these rather obvious questions? Or even tried to answer them?
Are you serious!?
DM-supporters no more ask such questions than theists wonder why a beneficent 'deity' put humanity on a planet that is 99.9% molten rock in a universe full of lethal radiation and exploding stars! Or, indeed, why they were put on a planet so full of dangerous organisms/viruses that they would need a complex immune system just to stay alive.
However, as Engels depicts things, both 'parts' of the above UO appear to operate together. That is, a moving body is "here" and "not here" -- "in one place" and "not in it" -- all at once, as it were:
"Motion itself is a contradiction; even simple mechanical change of place can only come about through a body being both in one place and in another place at one and the same moment of time, being in one and the same place and also not in it." [Engels (1976), p.152.]
In that case, it looks like such awkward questions (concerning the proximate cause of motion) can't actually be answered by anyone who accepts this theory That is because the mere fact that a moving body is "here" doesn't appear to be capable of making it become "not here" -- or, more accurately, how a moving body being "in one place" is capable of making it move to "another". [Henceforth, for simplicity's sake I will just call these two locations, "here" and "not here".] Clearly, there is no 'struggle' going on between this "here" and this "not here" (or none that Engels and Lenin cared to mention). Indeed, this 'contradiction' seems to lack any causal power, any capacity to make something happen.
It isn't as if the 'dialectical batteries', so to speak, have run down as it is that there don't appear to have been any supplied with the original article.
More problematic, as we have already seen: 'dialectic objects' don't move from one place to another, since that would take time. Such objects are in both places at the same time!
[On this, see also Note 22b.]
This probably explains why Engels didn't even attempt to construct a causal theory of motion based on the contradiction he claims to have identified here -- and, as far as can be ascertained, no subsequent DM-theorist has made any effort to fill in the gaps (and that includes Graham Priest!). But, even if a causal account were eventually to be provided (by a DM-fan, one day!), it still wouldn't be easy to see how these 'contradictions' could help explain motion. After all, how does being "here" and "not here" (all at once) explain why anything actually moves? What work does such a 'contradiction' do? Even if you believed there were any at work here?
It could be objected that this radically misconstrues DM, since the above argument misleadingly splits the assumed 'parts' of a contradiction, one from the other, 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. Contrary to the above, DM doesn't depict motion (or change) in such mechanical, causal terms. Dialecticians' various discussions of causation are specifically aimed at countering mechanistic and reductionist accounts like this.
Or, so a response might go...
Nevertheless, even if such a reply were acceptable, no attempt was made by Engels -- and, to my knowledge, none has been made by anyone else since -- to explain how contradictions can have any effect on anything at all, anywhere, anyhow or in whatever preferred causal or 'mediational'/'dialectical' language they are expressed (that is, other than perhaps figuratively). [There is more on this in Essay Eight Parts One and Two.] And, contrary to the (proffered) DM-objection, this supposed contradiction (in motion) doesn't appear to be relational at all. What precisely is being related to what? What "relation" is this particular example meant to picture or reflect? Is a body related to itself as it moves? Even if it were, how would that make it move?
[One of the best 'dialectical' attempts that I have so far encountered (written by a Marxist Dialectician) that attempts to explain the rationale supposedly underlying this view of motion and change has been taken apart here. In Note 18a I have done something similar (but on a smaller scale) to another attempt to account for motion along Hegelian/Engelsian lines (this time by Graham Priest), but, alas, in connection with something that might not actually be a 'dialectical contradiction', to begin with!]
Of course, it could be argued that it is the relation between bodies and processes that makes objects move and change; that response will be examined below and in more detail in Essay Eight Part Two, as will the idea that contradictions can be accounted for in terms of "opposing forces".
Moreover, it is difficult to see how a contradiction could exercise any sort of effect on anything at all unless it was translated into, or was expressed somehow in, physical or material terms. [That will be attempted below.] At some point, material bodies are just going to have to be moved about the place, and something else material is going to have to make that happen. But, a physically inconsequential word (such as "contradiction") doesn't seem to have the required power -- the necessary oomph, as it were -- that would allow it to carry out such a menial task.8
[HM = Historical Materialism.]
Furthermore, if the volunteered DM-response above were correct (but see below), contradictions wouldn't be 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 else), then they certainly can't serve in such a capacity in HM. And if that were so, the (alleged) contradictions at work in Capitalism, for example, couldn't themselves make anything actually happen. At best, they would be the result of other things happening, or having happened.
[Incidentally, DM-theorists would now have no explanation for these 'other things', since they won't have been caused by contradictions, either; they would be the result of specific social relations. Again, I have dealt with whether even they could be labelled 'contradictions' in Essay Eight Part Two.]
Given the above (proffered) DM-rejection of any causal role for contradictions in 'dialectics', the cause or causes of social development would now be totally mysterious. In that case, we are forced to conclude that if there are any contradictions in 'reality', they must play some sort of causal role, at some level, in some form, otherwise dialecticians wouldn't be able to explain why anything actually happened in nature or society.
[Of course, that might be the real reason why dialecticians can't actually explain anything, but they certainly don't see things that way, to state the obvious!]
Conversely, it could mean that if the development of class society is still to be accounted for in terms of the supposed contradiction between the forces and relations of production -- or even the alleged contradictions between opposing classes -- contradictions themselves could be dispensed with at no loss to HM, since (given the above (proffered) DM-response), contradictions would do no work in HM, either, playing no causal role there, too! In that case, the sooner they are pensioned-off the better. Attention could then be focussed on the genuinely causal nature of the above social relations, suitably expressed in appropriately phrased historico-materialist terms. Naturally, that would involve a radical re-write of HM, abandoning much of the traditional, Hermetically-inspired jargon Hegel employed, which has only succeeded in enveloping much of Marxist theory in a suffocating philosophical fog.
If so, this means that dialecticians need to specify -- as a matter of some urgency -- what, if anything, is so causal about the contradictions they see (literally) everywhere, so that these Hegelian Chimeras can at least do some genuine work in HM. At present they don't appear to be part of the action. At best, they look merely ornamental.
On the other hand, the assignment of a causal role to contradictions in HM or DM -- so that they cease to be merely decorative -- would generate insuperable problems for both theories, as we are about to find out.
As hinted 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 fail to help DM-theorists account for motion. That is because (according to Engels) motion involves a body being in one place and not in it, all the while being in two places at one and the same 'moment'. The problem is: How does that actually explain motion causally -- or, indeed, in any other way? What exactly does it add to a scientific account/description of the same phenomenon? All it appears to offer is a paradoxically-worded re-description.
In order to make the last point a little clearer, it might be worth pondering once again (possible) DM-answers to the following questions:
(a) Do contradictions cause motion (i.e., do they make objects move)?
Or:
(b) Does motion merely reveal the presence of contradictions as it unfolds?
Here is Engels, again:
"[S]o long as we consider things as at rest and lifeless, each one by itself, alongside and after each other, we do not run up against any contradictions in them. We find certain qualities which are partly common to, partly different from, and even contradictory to each other, but which in the last-mentioned case are distributed among different objects and therefore contain no contradiction within. Inside the limits of this sphere of observation we can get along on the basis of the usual, metaphysical mode of thought. But the position is quite different as soon as we consider things in their motion, their change, their life, their reciprocal influence on one another. Then we immediately become involved in contradictions. Motion itself is a contradiction: even simple mechanical change of position can only come about through a body being at one and the same moment of time both in one place and in another place, being in one and the same place and also not in it. And the continuous origination and simultaneous solution of this contradiction is precisely what motion is." [Engels (1976), p.152. Bold emphasis added.]
On one reading of Engels's words, it looks like it is motion that causes (or creates) these contradictions. So, according to this way of reading the above passage, something must be in motion first for it to bring about a contradictory, simultaneous occupancy and non-occupancy of successive locations (with time having advanced not one instant). But, as we will soon see, that would mean one (or even both) of the following hypotheticals would have to be true:
(i) If there were no contradictions, movement could still take place. [In other words, there could be movement with no contradictions implied.]
(ii) If movement ceased, there would still be contradictions. [In other words, stationary bodies could still imply what appear to be contradictions.]
Taking each in turn:
(A) The relevance here of option (i) is brought out by the fact that unless motion was already present no contradiction could be inferred or would have occurred.
At the very least, option (i) prompts a further question: Which came first, the movement or the contradiction? One possible answer might involve what seems to lie behind Engels's comment that such contradictions could be "solved", 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 factors (i.e., contradiction and motion) go hand-in-hand. In that case, it makes no more sense to ask which came first, movement or contradictions than it would to wonder: "Which came first, counting or numbers?"
But, as we will see later on in this Essay, there are actual examples of motion (in the real world) where no 'contradiction' is implied, directly or indirectly. So, perhaps that is the case here, too.8a
(B) The second option above (i.e., (ii)) follows from the simple observation that a stationary body can also occupy two places at once, just as it can be in one place and not in it at the same time. [Examples of both of these possibilities are given below.]
In that case, option (ii) suggests that contradictions aren't a sufficient cause of motion, while (i) implies they aren't even necessary.
(i) If there were no contradictions, movement could still take place. [In other words, there could be movement with no contradictions implied.]
(ii) If movement ceased, there would still be contradictions. [In other words, stationary bodies could still imply what appear to be contradictions.]
Furthermore, and with respect to (i), once more: Engels himself appears to have reasoned from what he thought was the case with respect to motion to its alleged contradictory implications. In that case, it looks as if there is no causal role for contradictions to play with respect to 'motion itself', at least, as far as Engels was concerned. That is, there seems to be no way that a contradiction could make anything move. At best, as noted above, such contradictions appear to be conceptually derivative, not causal; they depend on motion, not the other way round. Hence, as things now stand, it looks like bodies first of all move, and only then do contradictions arise -- and, even then, that only applies to our depiction of this phenomenon!
If so, it might be correct to say that contradictions operate solely at the conceptual level; they appear to have no part to play in the physical action, on the ground, as it were.
Given this 'modified' view, it would seem that objects in the world just move, but they don't do so because they (first) become embroiled in literal contradictions.
[So, for example, moving bodies don't argue among themselves about the occupancy or non-occupancy of this or that particular "place", which would be the clear implication of the ordinary, literal use of the verb "to contradict". Nor do they become entangled in 'time-and-motion' wrangles about who or what was where, when and why. Again, they would have to do that if literal contradictions (as opposed to a figurative, DM-extension to this word) were implied in such circumstances. (On this, see an earlier sub-section, as well as Essay Eight Parts One and Three.)]
In fact, given Engels's theory 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 and society.
In other words, according to this interpretation of Engels's views, it looks like the 'fault' lies in us (as it were), not in objects and processes themselves.
Nevertheless, this way of depicting motion is clearly unacceptable to DM-theorists. They insist that we must begin with material reality (or our perception of, and interaction with, the world), and not simply start with a description. From there, according to them, we must postulate only those contradictions that actually exist in nature and society -- based perhaps on their reflection in human thought, confirmed in practice. Clearly, human beings study motion and its attendant contradictions, using whatever conceptual resources they have available to them, which, unfortunately, might not always be up to the job.
Or, so a counter-claim might go...
But, even this (proffered) response is no help. That is because there seems to be nothing in reality that thought could latch onto, or reflect -- and hence, nothing for anyone to abstract from, or to, and then test in practice -- that even remotely resembles the contradictions postulated by dialecticians.
[Why that is so will occupy the last three quarters of this Essay -- as well as this one.]
In relation to Engels's account of motion, as will soon become apparent, there is no clearly specifiable set of possibilities -- or even actualities -- in nature and society with which his description could conceivably correspond. In fact, his words turn out not to be a depiction of the physical world in any shape or form. That isn't because he got the details wrong, or because he failed to capture nature accurately enough --, nor yet because 'reality' is too complicated for us to describe or conceptualise -- it is because his words fail to be a description, to begin with.
Hence, Engels's 'description' of motion isn't just empty or devoid of content, it isn't even a description!
It turns out to be far too vague and incoherent to count as one.
Again, it could be objected that the analysis presented in this Essay is completely misguided since it compartmentalises reality, distorting DM as that theory is laid out by its theorists.
In response, it is worth pointing out that we don't have to divide the 'parts' of a contradiction, one from another (or from other relevant aspects of 'reality'), to make the arguments presented above 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", as required by the theory, and verified in practice, etc., etc.), that still wouldn't amount to an explanation of the causal or the "mediated" links their theory requires. Widening the domain (to the entire "Totality" if need be) can't suddenly provide an explanation of how the simultaneous presence and absence of an object in one and the same place at the same time could possibly make it move -- or even how it could account for its movement in any way.
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, can't account for movement and change in DM-terms.
[That cryptic comment will also be expanded upon in Essay Eight Parts One and Two.]
Are These Even 'Dialectical' Contradictions?
Furthermore, the supposed reflection of contradictions 'in the mind', which might be thought capable of providing the 'conceptual connection' that is imagined to exist between a cause and its effects (or between various mediated items, objects and processes in "the Totality", or even a part of it), can't establish a genuine connection if there aren't any contradictions in reality for it to reflect. Contradictions must have some sort of material basis, constitution or presence if they are to be reflected in thought. As far as materialists are concerned, they can't just be conceptual. And yet, what physical form do the contradictions that are supposed to be involved in motion take?
Of course, it could be objected once more that this is all woefully mistaken. Contradiction arise from a relation; they don't assume an 'independent material form'. In which case, the above paragraph is misguided in the extreme.
Or so it could be claimed...
However, when we ask what this supposed relation consists in, no answer returns. Certainly DM-theorists have yet to say what this "relation" amounts to with respect to moving objects. As noted above, since this contradiction appears to revolve around the supposed fact that a moving body is here and not here at the same moment, and in two places at once, the relation can't simply be these two places, this "here" and that "not here". The DM-classics are quite clear: for something to count as both dialectical and contradictory, (a) There must be a 'dialectical relation' between a pair of 'dialectical opposites', such that they imply one another to the extent that one can't exist without the other -- like the relation between the proletariat and the capitalist class; (b) They must (at some point) struggle with each other; and (c) They must turn into one another.
[Dozens of proof texts from those DM-classics, along with even more from 'lesser' DM-works, that support all three contentions have been posted here.]
This now highlights a serious problem: Is what Engels speaks about here (in relation to moving objects) even a 'dialectical relation' to begin with? How can a "here" possibly struggle with a "not here"? How can the two places a moving body occupies at the same moment 'struggle' with each other? Even worse, how on earth do they turn into one another? If a moving body is located at P1 and P2 at the same time, how does P1 manage to struggle with and then change into P2? Surely, P2 remains P2 throughout. Even if P2 were to change into P1, that would imply the moving object in question had actually gone backward!
Consider moving object, B, again: If the two opposites are, "B is here" and "B is there", at the same time, or even "B is here" and "B isn't here", at the same moment, how on earth do these struggle with and then change into each other? If "B is here" were to change into "B is there" and "B is there" were to change into "B is here" (which is what the DM-classics say must happen with all such opposites) then, clearly, nothing will have actually changed! Or as noted above, the object will have reversed direction!
Furthermore, do the above candidates in this presumed relation even count as 'dialectical opposites'? The latter are supposed to imply each other such that they can't exist without one another -- again, rather like the proletariat implies the capitalist class (and vice versa), such that the existence of one supposedly presupposes the existence of the other. How do two locations imply one another, such that the existence of one presupposes the existence of the other?
It could be countered that if we consider the Cartesian Plane, each point implies all the rest. That is undeniable, but the Cartesian Plane is a mathematical structure. No such structure exists in the material world, so the question remains: How do two locations imply one another? There is no obvious way they can. [If anyone knows how they can, please email me with the details.]
That being the case -- if these locations don't struggle with and then change into one another, and don't even seem capable of implying each other --, then whatever else this is, it can't be a 'dialectical contradiction'.
If so, why is it even part of DM?
[I will have much more to say about this below.]
Are These Contradictions Real Or Are They Merely Fictional?
Returning to an earlier point (no pun intended), unless some sort of physical sense can be given to the idea that contradictions are capable of affecting anything in the required way -- i.e., in reality, not just 'in the mind', in order to provide some grist for the DM-causal, or -mediational, mill to grind away at -- unless that were possible, an appeal to 'reflection' would fail even to advance the DM-explanation of motion one millimetre.
Assuming for the purposes of argument that it could be shown that contradictions do in fact represent or constitute a material (or physical) relation of some sort (between objects or between processes), and which have been abstracted from (or read into) the phenomena (in an as yet unspecified way!) -- they still couldn't account for motion. That is because this would (once more) simply amount to a re-description of the phenomena. We still await the explanatory punch-line: how do contradictions actually make anything move or affect movement? What is the material point to this Hegelian 'thought experiment'? Where does the rubber actually hit the road (to use an Americanism)?
If it is now claimed that a causal (mediational) link of some sort between events must be postulated (i.e., if it is just assumed that one exists in order to make the theory work), then that would merely provide a conceptual link between the said events, and such it would remain until the physical details had been filled in. Without the latter, the contradictory nature of motion would remain, at best, a conceptual, not yet a material, part of 'reality'.
[Of course, that conclusion should come as no surprise to anyone cognisant of the Idealist origin of this odd use of the word "contradiction".]
If, on the other hand, it is claimed that the mere presence of the said conceptual connection indicates that these causal links must exist in reality -- that is, if the Complex Reflection Theory of Knowledge is assumed to be true (wherein the human mind actively acquires knowledge in practice, etc.) --, then that would still fail to explain how contradictions are actually capable of causing motion. Precisely how do contradictions succeed in moving things about the place? It would seem that here the dialectical spade isn't just turned, it snaps in two.
Anyway, as should seem clear, any such hasty attempts to repair this theory are the equivalent of imposing it on the facts, which is something DM-theorists at least say they never do.
Clearly, the above difficulties will only be resolved if a clear explanation is given of exactly how contradictions can make anything move (or even keep things moving). The only other way to avoid, or circumvent, this 'problem' would be to show how and in what way the above anti-DM argument is itself defective. But there isn't much chance of that if we have to rely on DM-fans. They either (i) retreat into a prolonged dialectical sulk (whenever such 'difficulties' are brought to their attention), (ii) say they have 'better things to do', or (iii) they simply become abusive.
However, as should now also seem reasonably clear, the role that contradictions supposedly play in motion hasn't been helped by a theory that depicts them as: (a) The product, but not the cause, of motion (implying they are derivative, at best); or (b) A consequence of human reflection on 'the nature of motion', or on 'motion in itself' (even if there were such a thing) -- which would suggest such 'contradictions' are merely conceptual, and hence 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 ritual assumes in their theory. Why call anything "contradictory" and claim so much for that term if no account can be given of how it explains why or how anything actually changes or moves?
[DM-theorists who even bother to tackle such questions generally point to "opposing forces", or even "instabilities" in a body, process or system, in order to explain how contradictions actually result in change. Those issues have been examined in depth in Essay Eight Parts One, Two and Three. Also see the next sub-section.]
'Internal Contradictions' And Motion
It could be argued that the above objections are irrelevant since DM-theorists are committed to the theory that motion and change are caused by internal contradictions. The above sub-sections seem to be fixated on external causation.9
Unfortunately, in connection with motion there don't appear to be any internal contradictions capable of impelling objects along. No one supposes -- it is to be hoped! -- that an 'internal contradiction' works like some sort of metaphysical motor, humming away inside a moving object, powering it on its way!9a Nor do there appear to be any 'dialectical struggles' taking place within moving bodies that drive them ever onward. And, that would still be the case even if it were true that every body/process is in fact a UO. No matter how intense this supposed 'internal battle' is supposed to be, a 'metaphysical boxing match' of this sort seems incapable of generating, or maintaining, self-propulsion.
[UO = Unity of Opposites.]
Lenin's "demand", therefore, looks rather impotent (if this is what he meant):
"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 (1921), p.93. Bold emphases added. This entire topic is examined in much greater detail in Essay Eight Parts One and Two.]
Furthermore, there don't appear to be any identifiable 'contradictions' situated at the leading edge of a moving body 'dragging' it along, as it were, just as there seem to be none at the back, 'pushing'.
Worse still: both of those scenarios (even if they were remotely plausible) would clearly involve the creation of kinetic energy out of thin air. For example, precisely which 'internal contradictions' are capable of keeping, say, a billiard ball moving?
In that case, with regard to individual bodies, at least, motion can't be an example of change through "internal contradiction".
However, as we will see in Essay Eight Part One, part of the problem here is that DM-theorists continually equivocate between two meanings of the phrase "internal contradiction". Sometimes, it refers to:
(i) A logical, "internal relation" between objects and processes.
Sometimes, it merely implies:
(ii) A spatial connection.
Hence, an "internal contradiction" of Type (i) could exist between two widely separated bodies; they would be 'logically' connected, or would 'mediate' and/or inter-define one another. So, for instance, a section of the working class in one part of the globe could still be locked in a contradictory relation with a group of capitalists thousands of miles away. When Marxists speak about class relations, spatial separation doesn't enter in to it.
By way of contrast, Type (ii) 'internal contradictions' would seem to require some sort of proximity in order to work inside a given body, process or system. For example contradictions inside an atom are supposed to be what hold them together. A proton separated from an electron by billions of light years would not normally be held to be 'internally contradictory' to one another.
However, parties/entities locked in relations of either type would still have to 'contradict' each other by 'struggling' among themselves (if the DM-classics are to be believed), but, with respect to those of Type (ii), there would appear to be no (necessary) logical connection implied between them. Such opposites would simply be spatially-, not logically-connected.
In which case, there appear to be at least four possibilities, here:
(a) Something or some configuration could be spatially-internal to an object or system without any 'opposites' involved being logically-internal to one another;
(b) Something or some configuration could be spatially-internal to an object or system while any 'opposites' involved are logically-internal to each other;
(c) Something or some configuration could be spatially-external to an object or system without any 'opposites' involved being logically-internal to each other; or, finally,
(d) Something or some configuration could be spatially-external while any 'opposites' involved are logically-internal to one another.
[In fact, there are far more possibilities than these, but further consideration is beyond the scope of this Essay. "Logically-internal" refers to the (supposed) fact that each item involved in the relation implies the other, such that one can't exist without the other. This part of theory is challenged in Essay Eight Part Two.]
However, as I have pointed out elsewhere (slightly edited):
The expressions "internal contradiction" and "internal relation" (or what they supposedly represent) clearly underpin the idea that there are, or can be, internal, 'inter-penetrated' opposites. We can perhaps illustrate what an internal opposite is by recalling what DM-theorists say about the relation between the two main classes under Capitalism, the Proletariat and the Bourgeoisie. It is quite clear that for DM-theorists the Bourgeoisie and the Proletariat presuppose, inter-define and condition one another; each provides the condition for the other's existence; without the one the other not only wouldn't, it couldn't exist. They are thus internally related, not externally or accidentally connected.
This is what dialecticians mean by "interpenetration"; they don't mean these factors spatially interpenetrate one another, but that the one can't exist without the other, nor vice versa; the existence of the one logically implies the existence of the other, and vice versa. And this is where the presumed "contradiction" arises; the Proletariat and the Bourgeoisie are logically locked together, they can't exist independently of one another. This means that they have diametrically opposed material interests which force them into unremitting class conflict. None of this is accidental or external; the interplay between capitalist and worker is both reciprocal and inter-dependent.
Plainly, an external relation doesn't possess these logical properties. Concerning any two items (i.e., objects and/or processes), if they are externally related, the one can exist without the other; they don't presuppose one another, nor do they inter-define each other.
But, as noted above, something can be (i) spatially-internal to an object or system without it being logically-internal, just as something can be (ii) spatially-external while also being logically-internal.
[Indeed, something can be spatially-internal to an object or system and logically-internal to it, too, just as something can be spatially-external while also being logically-external, as well.]
Here is an example that might illustrate (i), above: an Amazonian tribe is logically-external to capitalism (since there seem to be no internal opposites in the capitalist system that condition that tribe and which are conditioned in return by it, or which define it and which it defines in return). Capitalism can live without Amazonian tribes, but it can't live without the Bourgeoisie and the Proletariat. Even so, this tribe would still be spatially-internal to the capitalist system in that it still exists in a Capitalist country, Brazil.
Alternatively, to illustrate (ii): consider the relation between, say, tenants and their landlords. They presuppose and inter-define one another; each is the condition for the other's existence; so they are logically-internal to one another. However, no landlord lives inside his or her tenants, nor vice versa. In that case, landlords and tenants, while being logically-internal to each other are at the same time spatially-external to one another. [Naturally, this assumes each landlord has at least one tenant!]
Of course, one could always say that landlords and tenants are spatially-internal to whatever social or economic system they happen to exist within, and that is the problem. As we will see (in Essay Eight Part One), this ambiguity lies behind the equivocation mentioned above: When we consider wider economic, social, or even physical systems, it turns out that there are in the end no such things as spatially-external 'dialectical' opposites, and hence no spatially-external contradictions! Indeed, it is even arguable that there are no logically-external 'dialectical' opposites either! [See also here.]
Be this as it may, it could be argued that since locomotion and development in a system are the result of forces acting on bodies or processes at work in that system, the contradictory nature of motion can easily be accounted for on the basis of a network of internal, systematically-opposed forces, or "instabilities". This might therefore turn out to be an example of a Type-(ii) , or even a Type (b), "internal contradiction". That would make the unit within which contradictions (and thus motion) occur the whole not the part, which seems to be the assumption underlying the argument developed in earlier paragraphs/sub-sections of this Essay.
Or, so a DM-reply might proceed...
Naturally, that response would make a mockery of the claim that all objects change through self-development, or that they locomote because they are self-motivated. Just as it would make a mockery of Lenin's contrast between a mechanical, 'external' account of movement/change and a dialectical version of the same. Given this (proffered) modified 'theory', it now turns out that no object would be self-motivated -- never mind what Lenin demanded -- it would be moved by forces internal to the system of which it is a part, but external to any of the objects caught up in that system.
"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 (1921), p.93. Bold emphases added.]
"The identity of opposites...is the recognition...of the contradictory, mutually exclusive, opposite tendencies in all phenomena and processes of nature (including mind and society). 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 '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. Quotation marks altered to conform with the conventions adopted at this site.]
Despite this, even if systematically-opposed forces could somehow be interpreted as contradictions -- or if they could at least be regarded as constituting them in some way -- that would still fail to show how they could explain motion (or, rather, how they could account for any change in motion), let alone how they could initiate it. Nor would it explain 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, or changed, any motion already in the system. The fact that a moving body appears to be in at least two places at once (and hence 'contradictory in itself' while moving) is in no way connected to whatever allegedly initiated that motion, or even with whatever now maintains it (if anything does) -- at least not in any obvious way. Certainly, dialecticians have yet to connect contradictory forces themselves with the alleged fact that moving bodies appear to be in two places at once, in and not in at least one of them at the same time. Nor is it easy to see how that might even be done on their behalf (since they appear to have given precious little thought to this problem over the last 140 years, or shown any sign they intend to address it).
Hence, whether or not it is true that movement is caused -- or even 'mediated' -- by a disequilibrium/instability that exists within a system of incipient forces ('internal' or 'external'), that still wouldn't affect the (supposed) fact that once set in motion a body appears to do contradictory things. Even given the truth of such an 'internalist', or even 'externalist', account of 'contradictions' and forces (i.e., assuming both Types (i) and (ii) senses of "internal" are correct), the fact that a body is in two places at once is a consequence of this. But, the "in two places at once" (etc.) descriptor -- or its physical correlate -- doesn't also cause motion in addition to the forces at play in the system. Indeed, while forces might cause a change in motion, the alleged contradictory nature of any subsequent movement has no part to play in the action.
So, even if both the 'internalist' and the 'externalist' models were correct, Engels's analysis of motion would still amount to nothing more than a re-description of that phenomenon; it would remain the case that motion makes bodies do allegedly contradictory things, not the other way round. Hence, the 'contradiction' that Engels highlights is still derivative, not explanatory.
It is worth re-emphasising this point: even if opposing forces could explain contradictory motion (which theory has been demolished in Essay Eight Part Two, anyway), the nature of the connection between the supposedly contradictory nature of motion itself and the forces operating on moving bodies has still to be established. All that the addition of opposing forces has achieved is to account for the origin of one (supposed) contradiction (motion) in terms of another (oppositional forces). The contradictory nature of motion itself is still locked in the descriptive mode -- it does no work. Whether or not forces can explain change in motion isn't 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, and once again, even supposing this theory were correct, change in motion would be causally related to the action of forces, but that just divorces the latter from the contradictory behaviour of moving bodies (a point Engels himself seems to have conceded -- on that, see Note 10). So, even if it were the case that opposing forces caused motion (or changed it), they would still provide no useful role in any the theory that modelled motion itself as contradictory. As far as DM is concerned (that is, on the basis of one particular interpretation of it that appears to be inconsistent with what Engels himself said about forces -- again, see Note 10), what seems to be important here 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, once more, it plays no effective role 'in the action'.10
[As will be argued at length in Essay Eight Part Two, an appeal to oppositional forces in order to account for contradictions, or even contradictory 'totalities', is no less misguided. There, it will be argued (in detail and at length) that not only is there no conceivable interpretation of opposing forces that could account for contradictions (in FL or DL), there is no viable literal or figurative way of modelling contradictions as opposing forces, nor vice versa, either.]
[DL = Dialectical Logic; FL = Formal Logic.]
But even worse: contradictory forces can't account for contradictory motion, anyway. Indeed, they have nothing to do with it. We can see that from the simple fact that where no forces at all are required to keep a body moving (for example, a billiard ball, or any object travelling at constant velocity), dialecticians still view such motion as contradictory.
So, the alleged contradictory nature of a moving body has nothing to do with the forces that set it in motion.
Of course, even more revealing is the fact that in Classical Physics, forces are supposed to change the motion of bodies (i.e., their velocity); this means that the idea that something has to maintain movement (whether that "something" is contradictory or not) depends on an obsolete, Aristotelian theory of motion. That being the case, the fact that contradictions can't provide a causal explanation of motion is all to the good, for if the supposedly contradictory nature of motion caused and maintained movement, much of post-Aristotelian (i.e., Newtonian/Lagrangian/Hamiltonian) mechanics would have to be binned.11
But, if 'contradictions' don't, or can't, explain motion (i.e., if they don't change or initiate it), why put them at the centre of your theory?
Despite the above, it could be objected that this whole line-of-argument seriously misunderstands the nature and role of contradictions in dialectics. As John Rees pointed 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, anti-DM criticisms is that they substitute an abstract analysis of motion and change for one that should have been focused on real material forces.
That (partially valid) objection is considered in detail elsewhere at this site (for example, here, here, here and here), where Rees's and other dialecticians' epistemological and methodological claims are examined in detail, alongside a consideration of actual examples of "real material contradictions" (to which most DM-theorists appeal in order to illustrate, explain or render their theory 'concrete'). That will be carried out in tandem with the additional claim that DM isn't a "master key" that unlocks all of reality -- when clearly it is intended to be just that! [On that, see Essay Two.]
[The other (anti-DM) claim will also be revived and re-examined -- i.e., the objection that 'material contradictions' can't account for change since they, too, are locked in 'descriptive mode' -- for instance, here and here, but, more specifically here, here and here.]
"[S]o long as we consider things as at rest and lifeless, each one by itself, alongside and after each other, we do not run up against any contradictions in them. We find certain qualities which are partly common to, partly different from, and even contradictory to each other, but which in the last-mentioned case are distributed among different objects and therefore contain no contradiction within. Inside the limits of this sphere of observation we can get along on the basis of the usual, metaphysical mode of thought. But the position is quite different as soon as we consider things in their motion, their change, their life, their reciprocal influence on one another. Then we immediately become involved in contradictions. Motion itself is a contradiction: even simple mechanical change of position can only come about through a body being at one and the same moment of time both in one place and in another place, being in one and the same place and also not in it. And the continuous origination and simultaneous solution of this contradiction is precisely what motion is." [Engels (1976), p.152.]
However, one further possibility hasn't yet been examined (and this introduces a concern that will dominate much of the rest of this Essay): What if it is completely unclear what Engels was trying to say in the above passage?
Indeed, what if it could be shown that he was in fact saying nothing at all comprehensible?
If so, it would be completely beside the point whether or not there are any genuine examples of "material contradictions" in nature and society (at least, not so far as Engels conceived 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 difficulty 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 or portrayal of the problem itself. That is, that something, anything, that could conceivably answer to, or 'reflect', what turns out to be an incoherent description to begin with, and hence actually be searched for. If we are offered nothing comprehensible to explore, plainly no search can either commence or even be contemplated.
[As noted in Essay Six, you can look for your keys if you don't know where they are, but not if you do not know what they are.]
But, is there any substance to these latest (seemingly wild) allegations?
The next few sections will aim to show that there is -- and plenty more than enough, too.
Is Engels's Theory At All Comprehensible?
Before an empirical investigation into the 'real' cause and nature of motion can even begin we need to be clear about precisely what it is we are being asked to examine, consider or seek out. As we are about to discover, it isn't possible to determine what Engels was even trying to say 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.]
Before any attempt is made to substantiate or clarify the above allegations, several further ambiguities in Engels's account will need to be examined and resolved, 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 don't 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 that second place at the same, or some later, time -- or even whether it could be in more than two places at once. To be sure, it could be argued that it is implicit in what Engels wrote that these events occur in the "same moment of time", and, moreover, that if an object isn't in a given location, or in some specific spot, it must be in a second place, since it has to be somewhere. However, since I am trying to consider every conceivable possibility connected with Engels's words, it is possible that he not only didn't say any of the above, he didn't even intend it. [The significance of those comments will emerge as this Essay unfolds.]
It is also difficult to see how a moving body can be "in one place and not in it", and yet still be in two places at once. If moving object, B, isn't located at X -- that is, if it is not in X (and we have just been told it isn't) --, then it can't also be located at X (contrary to what Engels asserts). 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 then did he mean?
At this point, we might be reminded that there is a special sort of 'dialectical' "not" [henceforth, "notD"] at work here, and it is totally different from our ordinary "not" [henceforth, "notV", short for "vernacular 'not'"], which seems to connote something like this: "NotD = This isn't a 'notV' at all, it is in fact the exact opposite of 'notV'". But, if the meaning of "notD" is quite so malleable, so accommodating, such that it in fact means the exact opposite of "notV", how can we be sure we know what the words "motion" and "place" mean, let alone "dialectical"? If "notD" can mean the opposite of the everyday, ordinary "notV", then perhaps "motion" can also mean "stationary", and "dialectical" can mean "metaphysical" (in the sense of that word as it was understood by Hegel and Engels).
But, when a DM-theorist tells us that "notD" does not mean "notV", what are we to say of the "not" in the middle (the one coloured red)? If "not" can slide about effortlessly in this manner, then perhaps this red "not" might do likewise, and mean its opposite, too? If so, when a DM-theorist tells us that "notD" does not mean "notV", who can say whether or not they actually mean the following: "'NotD' does not not (sic) mean 'notV'" -- which, of course, pans out as "'NotD' means 'notV'", at which point the 'dialectical "notD" collapses back into an ordinary "notV"!
A rather fitting 'dialectical inversion' if ever there was one.
These worries are all the more pertinent given the DM-commitment to the following dogmatic assertion coming in from Hegel (which few dialecticians fail to quote without approval, and which we have met several times already):
"Instead of speaking by the maxim of Excluded Middle (which is the maxim of abstract understanding) we should rather say: Everything is opposite. Neither in heaven nor in Earth, neither in the world of mind nor of nature, is there anywhere such an abstract 'either-or' as the understanding maintains. Whatever exists is concrete, with difference and opposition in itself. The finitude of things will then lie in the want of correspondence between their immediate being, and what they essentially are. Thus, in inorganic nature, the acid is implicitly at the same time the base: in other words, its only being consists in its relation to its other. Hence also the acid is not something that persists quietly in the contrast: it is always in effort to realise what it potentially is." [Hegel (1975), p.174; Essence as Ground of Existence, §119. Bold emphasis added.]
If, as Hegel asserts, "Everything is opposite" then that, too, must apply to words like "move" and "dialectical" -- they must also be their opposites (unless by "everything" Hegel meant its colloquial opposite "Nothing", which it must do if his words apply to his own statements!) Hence, if Hegel is right, "move" must mean "stationary" and "dialectical" must mean "metaphysical"!
Anyone who objects to the above argument hasn't read the DM-classics, where we are told that everything in the universe -- and that must include words, which, it seems, do exist in the universe -- struggles with, and then turns into, its opposite. Nor have they read these passages (from other DM-theorists).
On the other hand, if this theory can only be made to work by fiddling about with the meaning of certain words, how is that different from imposing it on the facts, something Engels, at least, affected to disavow?
But, of course, no one in their left mind actually believes a word of this (that all words mean their opposite!). So, why does anyone on the left take Hegel seriously? Why have so many been conned into believing that "notD" actually means the opposite of "notV"?
Until DM-theorists come up with non-question-begging criteria that inform us unambiguously which words don't 'dialectically' develop into, or mean, their opposites, and which do, the above 'reminder' can be filed away in that rather large and ever-growing waste bin labelled "Dialectical Special Pleading".
Be this as it may, and as we have already seen, if B is in two places at once -- e.g., in X and Y at the same time --, then it can't just be in Y, but must be in Y and a third place at the same time -- otherwise it will be stationary at Y!
[Later on we will return to the above 'problem' in order to see if there is some way, any way, of avoiding its disastrous consequences.]
L1: Motion involves a body being in one place and in another place at the same time.
Returning to the main feature: it is important to be clear what Engels meant here because L1 is actually compatible with the relevant body being at rest! That can be seen if we consider a clear example -- i.e., 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 were 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 -- or more colloquially, it would occupy some space, or take up some room). But, since all real, material bodies are extended in this way, the mathematical point option doesn't appear to be relevant. [Anyway, it, too, will be considered below, as will the motion of 'point masses'.]
A commonplace example of this would be where, say, a train is at rest relative to a platform. Here, the train will be in many places at once, but still stationary with respect to some inertial frame. Of course, that depends on what we mean by "place"; I will return to consider that topic in more detail later -- here and here -- and again, immediately, below.
[There are countless examples of this everyday phenomenon, as I am sure the reader is well aware. In this and subsequent paragraphs I will endeavour to illustrate the alleged ambiguities in Engels's account by an appeal to everyday situations (for obvious, materialist reasons). However, these can all be translated into more rigorous form using vector algebra and/or set theory. In the last case considered below, just such a translation will be given in order to substantiate that particular claim.]
Unfortunately, as noted above, even this ambiguous case (concerning that train) could involve a further equivocation regarding the meaning of the word "place" -- the import of which Engels simply took for granted (as did Hegel and Zeno before him).
As seems plain, "place" could either mean the general location of a body (roughly identical with that body's own topological shape, and equal in volume to that body --, or, on some interpretations of this word, very slightly larger than its volume so that the body in question can fit 'inside' its containing volume interval!), or something much more general and far less precise (such as the place where you, dear reader, live --, that is, the planet, hemisphere, continent, country, state, county, city, town, village, precinct, neighbourhood, street, building, or even flat/room where you happen to reside -- all of these are places -- as, indeed, is where you are now sat (if you are seated), stood or lying down (if not!)). Alternatively, it could mean something even more precise, involving the use of a system of precise spatial coordinates (which would, naturally, achieve something similar), perhaps even pinpointing its centre of mass, using that to locate the body in question, etc.
But, the word "place" is even more vague/polysemic than the above might suggest (on that, see here), something that will be used to great effect throughout the rest of this Essay.
So, if we ignore the verb form of "place" (as in "Place you luggage in the rack above your head!", or "Place your bets!"), "place" can mean all sorts of things. For example, it can connote a position in a queue (which might or might not be physically occupied by someone -- for example, it might be a queue on the phone, when one is "put on hold"), or in a team (as in "She regained her place in the squad last week!"). It could refer to the order in which someone was positioned in a race (as in "She finished the marathon in second place"), or to a page in a book (as in "I lost my place in the novel I was reading because the damn bookmark fell out!"). It could even mean something far less tangible (as in "There's a special place for her in my life", "There's a time and a place for that, and this isn't it!", "This might be a good place to end the meeting", "It's not your place to raise objections. You're not even in the union!", "You're obviously confused. Your argument is all over the place!", etc. etc.).
However, it might seem perfectly obvious what Engels meant by "place" -- but as we will see, it isn't. In fact, this is just one more reason why little or no sense can be made of anything he was trying to say in the passage under review, as we will also find soon out.
Alternatively, as noted earlier, 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 movement of ordinary (gross) material bodies -- and, how the latter relate to the former. Anyway, since DM-theorists hold that their theory can account for motion in the real world, the movement of mathematical points -- even where literal sense can be made of such 'abstractions' or, indeed, of the idea that they can move -- won't in general be entered into in this Essay.
[After all, if such points don't exist in physical space, they can hardly be said to move. And even if they could, what on earth do they move into? Other points? How does one point move into another point? In connection with this, it is worth adding that Graham Priest's otherwise sophisticated attempt to defend Hegel and Engels (in, for example, Priest (2006)) largely depends on (i) The use of mathematical and metaphysical idealisations like these (i.e., mathematical points, planes, manifolds, 'instants' in time, etc., etc.), and (ii) Interpreting the material world as a mathematical object or model of some sort -- which makes much of what he has to say of little or no relevance to any defence of Hegel or Engels. Quite the reverse, in fact; it would make movement itself either impossible, or far more paradoxical than even Hegel himself imagined -- as we will also discover as this Essay unfolds, for example, here and here.]
Turning to L2 (quoted again, below): this particular option involves further ambiguities that similarly fail to distinguish moving from stationary bodies. Thus, a body could be located within an extended region of space and yet not be totally or wholly inside/in it. In that sense, it would be both in and not in that place (at once), and it could still be motionless with respect to some inertial frame.
Here, the equivocation would centre on the use of "in" in L2. Of course, it could be objected that "in" has been illegitimately replaced by "(not) totally or wholly inside/in", in the previous paragraph. Nevertheless, it is worth noting that Engels's actual words imply that that could be a legitimate interpretation of what he said/meant:
L2: Motion involves a body being in one and the same place and not in it.
If a body is "in and not in" a certain place it can't be totally in that place, on one interpretation of those words, since it is somewhere else also at that time. So, Engels's own words allow for his "in" to mean "not wholly in".
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. In that case, it would be perfectly natural to say that the said pencil was in, but not entirely in, the pocket -- that is, it would be both "in and not in" the pocket at the same time (thus fulfilling Engels's definition) --, but still at rest with respect to some inertial frame. No one would think that NN was lying if she said she had a pencil in her pocket, if this were the case. L2 certainly allows for such a situation, and Engels's use of the word "in", alongside the rest of what he asserted, plainly carries such an interpretation.
If so, it seems that Engels's words are compatible with a body being motionless relative to some inertial frame!
What is more, that would still be the case even if L1 and L2 were combined, in the way Engels intended; even then his words would be compatible with there being no movement at all (with reference to some inertial frame):
L3: Motion involves a body being in one place and in another place at the same time, being in one and the same place and not in it.
An example of an 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 driveway of a given house), even while it is at rest relative to a suitable inertial frame.
In which case, the alleged contradiction that interested Engels can't be the sole result of movement, since his own words are compatible with a body being at rest. Hence, what he argued isn't unique to moving bodies.
Hence, this 'contradiction' is plainly a consequence of vagueness and ambiguity in Engels's sketchy, Hegelian, attempt to describe moving bodies.
Or it might even be the result of the polysemic meaning of many of the words he used, which he simply conflated.
As we have seen, and will see again as this Essay unfolds, objects at rest relative to some inertial frame can and do display the same apparent 'contradictions' as those that are in motion (and with respect to the same inertial frame, too). Naturally, if bodies at rest share the very same vague or ambiguous features/'properties' as those that are in motion, then Engels's description clearly fails to pick out what is unique to moving bodies.
This isn't a good start.
Alas for DM-fans, it only gets worse...
So, we are still in want of a clear and unambiguous DM-description of motion!
Or, indeed, any indication that these 'contradictions' aren't an artificial consequence of a sloppy and careless use of language.
Of course, it might be possible to repair Engels's attempt to depict 'dialectical motion' by the use of more precise formulations; I will leave that for others to decide. However, given what we are about to find out in connection with the sort of language that has traditionally been associated with previous attempts to study motion (especially when that language has been incorporated into a 'philosophical theory'), global scepticism is perhaps the best policy.
Again, at best, L3 depicts the necessary, not the sufficient, conditions for motion. [But, as we will also see, not even that is true!]
If so, the alleged contradictory nature of L3 has nothing to do with any movement actually occurring, since Engels's words also apply to bodies at rest, which plainly share the same 'necessary conditions':
L3: Motion involves a body being in one place and in another place at the same time, being in one and the same place and not in it.
As already noted, 'paradoxes' like this arise from the ambiguities implicit in the language Engels himself used -- and, as it turns out, in the language he also misused.
[That will be discussed in greater detail below.]
Nevertheless, in the next few subsections several (genuine) attempts will be made to resolve these equivocations in order to ascertain what, if anything, Engels could possibly have meant by the things he tried to say about moving bodies.
A First Attempt At Disambiguation
As was also demonstrated in Essay Six in relation to Trotsky's (and indirectly Hegel's) attempt to analyse the LOI, Engels's theory of motion is far too vague and ambiguous to be of much use.11a
[LOI = Law of Identity.]
It might be a good idea at this point (no pun intended!) to remind ourselves (again!) what Engels tried to assert about motion:
"[S]o long as we consider things as at rest and lifeless, each one by itself, alongside and after each other, we do not run up against any contradictions in them. We find certain qualities which are partly common to, partly different from, and even contradictory to each other, but which in the last-mentioned case are distributed among different objects and therefore contain no contradiction within. Inside the limits of this sphere of observation we can get along on the basis of the usual, metaphysical mode of thought. But the position is quite different as soon as we consider things in their motion, their change, their life, their reciprocal influence on one another. Then we immediately become involved in contradictions. Motion itself is a contradiction: even simple mechanical change of position can only come about through a body being at one and the same moment of time both in one place and in another place, being in one and the same place and also not in it. And the continuous origination and simultaneous solution of this contradiction is precisely what motion is." [Engels (1976), p.152. Bold emphasis added.]
I now propose the following disambiguation of Engels's rather brief comments in order to ascertain if any sense can be made of them:
L5: A moving body, B, involves a 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) isn't the same place as (X2, Y2, Z2).
[Where, (Xi, Yi, Zi), etc., represent coordinate triples, and ti is a temporal variable. These can, of course, be combined to yield (Xi, Yi, Zi, ti).]
L5-L7 look a little 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 that expression succeeds 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. Again, I will leave that for others to decide.
Still others, of course, might wonder exactly how the word "change" could be explicated (given DM) without an appeal being made to a definition that involved the word "motion" (a definition, it is worth remembering, that has yet to be attempted by dialecticians -- Graham Priest excepted, of course). Naturally, the use of this term wouldn't alter the 'truth' of L5, but it would make it entirely circular.
However, even if this minor glitch were avoidable in some way, the initial promise L5-L7 seemed to hold out soon vanishes when it is remembered that propositions like these 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, occupying a volume interval -- i.e., it "takes up room"), and is at rest with respect to some inertial frame. Subsequent motion could then take place at t2, not at t1 -- as we saw above with that car.
[What is worse, even a "change of place" can occur where there is no motion involved (examples of which will be given later in this Essay).]
It is no use objecting that Engels had referred to the "same moment" in which all this takes place since we don't know if this same moment is t1 or t2, or is, perhaps, even a temporal interval. The significance of those observations is all too easily lost, but it revolves around the fact that Engels's account is compatible with an object being stationary at t1, and it is no reply to be told that the said object moved later when we are still owed a 'dialectical' description of motion that captures its necessary and sufficient conditions, not a promissory note that the said object will move at some later time.
Anyway, attempts to capture the necessary and sufficient conditions related to the future (predicted or hypothesised) motion of this object will only attract the same objection -- that is, if L5-L7 were replaced with propositions that simply changed the temporal variable to t2, no other adjustments having been being made. In that case, questions will only arise as to why this minor alteration is capable of turning L5-L7 into necessary and sufficient conditions when the use of t1 had failed to do that earlier.
Any who might still be puzzled by this need only reflect in the fact that L5-L7 are fully compatible with B remaining perfectly motionless at t1, and at any subsequent time.
L5: A moving body, B, involves a 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) isn't the same place as (X2, Y2, Z2).
L6-L8 below will attempt to fix this annoying 'difficulty'. The problem, it seems, lies with L5, since it fails to connect the motion it mentions with the same instant recorded in L6 and L7. Hence, the following emendations seem to be required:
L8: A moving body, B, involves a 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) isn't the same place as (X2, Y2, Z2).
[L5: A moving body, B, involves a change of place such that....]
Of course, the same caveats could be applied to later instants so that such a description captures the movement of the body in question along its entire trajectory. That would entail the use of "tk" in the place of "t1" in L8 and L6. That complication will be ignored here since it doesn't seem to affect the points at issue. [No pun intended.]
Unfortunately, however, L6-L8 don't appear to imply a contradiction -- that is, not unless it is clear that B is no longer at (X1, Y1, Z1) at t1, since, as we have seen, it is possible for a (stationary) 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 at the same time (hence in two places at once), and stationary with respect to some inertial frame. Or, think about yourself, dear reader; while sat perfectly still in front of the screen you are now viewing (assuming you are seated!), your arms are in and not in the same place as your legs; while your limbs are in the same place (i.e., they are here you are sat -- no one has dismembered you!), they also aren't in the same place (i.e., they haven't been squashed into an amorphous lump of flesh and bone, unless you have been the subject of a horrendous accident involving the roof collapsing on you, or some such). In short, even you occupy several places and occupy only one place, at the same time (a seeming contradiction!), all the while remaining perfectly still, too! As we have seen, the word "place" can be highly ambiguous.
On the other hand, if a die-hard dialectician could be found who thought that the above scenario (depicted in L6-L8) was indeed contradictory, they would need to explain to the rest of us exactly what the alleged contradiction amounted to. That is: how, in virtue of B being in two such places at once, there was some sort of 'struggle' going on (which the DM-classics tell us must happen in all such cases), and then exactly what was 'struggling' with what. If we now switch to re-consider the cake example mentioned in the previous paragraph: What 'struggle' is taking place, and with what is this cake 'struggling'? As we will see in Essay Seven Part Three, the dialectical classics inform us that objects also turn into their opposites -- that is, they turn into that with which they have 'struggled'. In connection with the cake, once more: if this cake's being in two places at once was a indeed contradiction, that would involve it 'struggling' with and then turning into the tin, or maybe even the building, that contained it (if the DM-classics are to be believed)! Since no one in their left mind could reasonably be expected to believe this, cakes in supermarkets can't be viewed as in anyway contradicting the bricks, mortar and metal that contain them. Any who do so think are advised to seek professional help reasonably quickly.
If not, then this too can't be a contradiction and must be disambiguated along lines explored in earlier sections if this Essay.
Of course, it could be argued that since the first location of the said cake (i.e., inside a tin) is itself located inside the second (i.e., the building), that isn't at all what Engels meant by the two places a moving body will occupy at the same moment. But, on which set of words Engels committed to paper is that objection itself based? We have already seen that Engels didn't tell us what he meant by "place", so it isn't possible to rule out the above counter-example because of anything specific that Engels himself said. Indeed, as we have already seen, and will see again later, the word "place" is far more complex than Engels, Hegel, or even Zeno, imagined (in their theoretical deliberations).
Nor will it do to be told (again!) that these aren't the sort of 'contradiction' dialecticians are interested in, at least not until they produce a clear and unambiguous definition of those that do concern them, which, as we will see in Essay Eight Parts One, Two and Three they have yet to do.
Anyway, even if these aren't the sort of 'contradiction' of interest to DM-theorists, the whole point of the last few paragraphs (and, indeed, much of the rest of this Essay) was to show that it is only the careless use of words like "move" and "place" that artificially creates the 'contradictions' Engels and Hegel claim are generated by moving objects.
In order to rectify this latest 'glitch', we need to replace L6 with L9, and L7 with L7a, as follows:
L8: A moving body, B, involves a 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.
L7a: (X1, Y1, Z1) isn't the same place as (X2, Y2, Z2), nor is one contained by the other.
[L6: B is at (X1, Y1, Z1) at t1 and at (X2, Y2, Z2) at t1.]
This set (henceforth, "ℒ") certainly looks inconsistent. The question is: Can all of its constituent sentences be false at once? Only if we can rule that out 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 taken pair-wise from elements of S are contradictory just in case (i) Those elements are inconsistent and (ii) They can't also be false together. Or: in the simplest case, the elements of a binary sub-set of sentences taken pair-wise from elements of S are contradictory just in case they can't both be true and they can't both be false. That necessary condition is invariably overlooked by DM-fans, which, naturally, leads them into confusing contradictions with inconsistencies and contraries -- and, in many cases, with a whole host of other unrelated concepts, into the bargain. (Any who object to the 'pedantry' here should read this, and then maybe think again.)]
The question is: Can all of the elements of ℒ be false at once? If they can, then it won't be possible to construct a contradiction from all and only elements of ℒ. I propose to resolve this question by considering each of ℒ's constituent sentences in turn, but in reverse order:
(1) L9 would be false if at least one of its conjuncts was false. But, the first part of L9 ["B is at (X1, Y1, Z1)"] could be false in several ways: for example, if B is at (X3, Y3, Z3) at t1.
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.
In fact L9 is an inconsistent sentence anyway, and hence it is automatically false (either that, or it isn't a proposition to begin with (which is what I would maintain, anyway)11b -- depending on which branch of the Philosophy of Logic one accepts). However, since DL is based on the claim that an inconsistent sentence, or pair of sentences, can be true, I have ignored that complication 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.
L8: A moving body, B, involves a change of place only at t1, such that....
(3) L7a would be false if (X1, Y1, Z1) were the same place as (X2, Y2, Z2). This would make L9 false, as well.
L7a: (X1, Y1, Z1) isn't the same place as (X2, Y2, Z2), nor is one contained by the other.
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 isn't possible to construct a contradiction from all and only elements of ℒ.
Knowledgeable readers will no doubt have noticed the illegitimate way some of the schematic sentences of ℒ (and others) have been interpreted to derive the above spurious result. The reason for that particular ploy (and what its implications are) will be commented upon presently. Such readers are advised to shelve their qualms until then.
Finally, it could be objected that the above argument is fallacious anyway, since the contradiction to which Engels was referring here is a dialectical; it isn't a formal, contradiction. But, even if it could be shown that ℒ was a contradictory set (in the above sense), in no way could it be, or express, a 'dialectical contradiction'. None of the elements of this set imply one another (in a way that, for instance, the proletariat supposedly implies the capitalist class), such that any one element can't exist without the others. Nor is there a 'struggle' going on, which, as we have seen, the DM-classics label an 'absolute'. So, whatever else it is, this isn't a 'dialectical contradiction'.
[Readers are referred to earlier discussions of this topic (here, here and here).]
A Second Attempt At Disambiguation
From this point on it will be assumed that the difficulties with Engels's account noted in the previous section (whether or not they are legitimate) can be resolved, and that there exists some way of reading his words that does imply a contradiction, and which manages to distinguish moving from stationary bodies!
Perhaps the following will suffice?
L10: For some body, b, for 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 somewhat 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.
One point needs underlining: none of the strictures dialecticians impose on the LOI can be allowed to stand if L11 is to be of any use, otherwise we would lose the ability to talk about "the same body", "the same time" or "the same place". These concerns 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, note, as a rule of language not a 'logical truth' (or any sort of truth) -- why that distinction is important is explained in Essay Twelve Part One). Since protracted instances of motion (plainly!) take place over extended time periods, we can't appeal to the 'relative stability of language' to fix the reference of these variables (or, indeed, the reference of their ordinary language counterparts), if the LOI isn't applicable in all cases.
[Anyway, the 'relative stability' argument was batted out of the park in Essay Six; see below.]
[FL = Formal Logic; MFL = Modern FL; LOI = Law of Identity.]
But, if the LOI is still to be rejected then Engels's description would become hopelessly and irredeemably vague. Many of the 'spurious' objections rehearsed toward the end of the previous section (in relation to ℒ) depend on ignoring some or all of these conventions; as a result they were (obviously) illegitimate. Of course, that ploy was deliberately chosen since it highlights this very point: the use of variables in FL is based on conventions that DM-theorists must themselves accept/apply in ordinary discourse (and in informal logic) if Engels's analysis of motion is to be rendered at least minimally comprehensible. However, their acceptance of these conventions (ironically) undermines their own criticisms of the LOI! Naturally, it is a moot point which horn of this dilemma dialecticians will want to "grasp": (i) Accept Hegel's criticisms of the LOI and sink Engels's (and, indeed, Hegel's own) analysis of motion, or (ii) Accept Engels's theory and reject Hegel's criticism of the LOI.
It could be objected that the above comments represent a caricature of the points dialecticians make against the unrestricted acceptance of the LOI. The relative stability of both material bodies and linguistic expressions permits talk about such things as the "same body", "same word", "same place", "same variable", "same moment", and so on. Dialecticians don't flatly deny or reject the LOI; they just claim that it is true only within "certain limits". In addition, they hold that objects and processes undergoing change possess "identity-in-difference".
Those responses were examined in detail in Essay Six; the 'relative stability argument', for example, was neutralised here, here and here. 'Dialectical contradictions' themselves were analysed earlier in this Essay -- as well as: here, here, here, here and here.
Of course, hard-nosed dialecticians might choose to ignore MFL altogether. That is, of course, their right (not that they need my permission!). But, as a consequence of such an unwise move, they will find it rather difficult to say what Engels actually meant in the quoted passage above.
Be this as it may, that rather desperate move will also be blocked later on in this Essay.
Unfortunately, however, even as it stands, and despite the foregoing considerations (that is, if the contentious claims made above about the LOI and MFL are misconceived and were withdrawn as a result by the present author), L11 would still fail to be a logical contradiction, and that is because of several further, even more annoying, ambiguities.
In fact, this new batch of vagaries turns out to be far more intractable than the relatively minor quibbles we have so far encountered.
This new 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 (a translation into more ordinary language will soon follow!):
L12: For some b, during interval, T, and for two 'instants', t1 and t2, where both t1 and t2 are elements of 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 sets of nested sub-intervals themselves, which can be put into an isomorphism with suitably chosen intervals of real numbers; hence the 'scare' quotes around the word "instant" in L12. (Incidentally, t2 > t1 means that t2 is later than t1.)]
Clearly, the implication here is that the unanalysed variable, t, in L11 actually represents a temporal interval, T (as opposed to an instant in time, a mathematical 'abstraction' that, according to Trotsky at least, can't exist!) -- which alternative was expanded upon in and by L12 -- during which the supposed movement takes place. Plainly, this would licence a finer-grained discrimination among the sub-intervals of T (e.g., resulting in the introduction of t1 and t2) during which the action does take place.12
Two possible translations of L12 into less formal/intimidating 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 point, q, a millisecond later.
Or,
L12b: A body, b, observed over the course of a millisecond, is located at point, p in the first nanosecond, and is located at point, q, a nanosecond later.
And so on.
[Some might reply that the above analysis of motion would in fact freeze it, since it speaks about the body in question being "located" at a certain point at a certain time. Hence, it is claimed that if a body is located somewhere, it can't be moving. That is certainly a point both Hegel and Engels wanted to make. It will be addressed across much of the rest of this Essay.]
Indeed, L12, L12a and L12b actually express how motion is normally conceived: that is, as change of place in time, i.e., with time having advanced while the object in question moves.
[The "ordinary view", as I have called it, mustn't be confused with what Graham Priest has called "The Orthodox Account Of Motion", classically represented in Russell (1937), pp.469-74 (this links to a PDF of the 2010 Routledge edition, where this passage can be found on pp.476-80); cf., Priest (2006), pp.172-75.]
If this weren't so (i.e., if L12 -- and/orL12a/L12b -- were rejected for some reason), then L11 would seem to imply that the supposed change of place must have occurred outside of time -- or, perhaps worse, that it happened independently of the passage of time --, which is either incomprehensible (again, as even Trotsky would have admitted, see below), or would imply that for certain sub-sections of its trajectory a moving object (no matter how low its speed) actually moved with infinite velocity! [That 'inconvenient' consequence was pointed out earlier. Mathematical objections to this specific point will be considered below.]
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 both t1 and t2 are elements of 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.
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 so, a moving body would move from one place to the next outside of time -- that is, with time having advanced not one nanosecond (or even less). In that case, it would be in one place at one instant, and would 'move' to another place with no lapse of time. Clearly, such 'motion' would thus take place outside of time. But, according to Trotsky, that sort of 'motion' can't exist, for it wouldn't have taken place in time.
Indeed, if that were so, we would lose the right to say that a moving body was in the first of these Engelsian locations before it was in the second. That is because "before" implies an earlier time, which has just been ruled out in this case. Hence, by a suitable induction clause, and in relation to the entire trajectory of a body's motion, it would be impossible for a DM-fan to say that a moving body was at the beginning of its journey before it was at the end!
[The precise reasons for saying this have been set out in detail below, but the above conclusion depends on an argument presented here, which readers would be wise to consult first. Trotsky's entirely legitimate worries about 'instants' will also be re-examined, below. The contrary idea that if a body is located at a point at an instant, it must be stationary, will be re-considered below, too.]
Despite this, it might seem that this latest set of difficulties could be neutralised by means of a stipulation to the effect that whereas time isn't composed of an infinite series of embedded sub-intervals (or, rather, our depiction of it isn't) -- that condition perhaps depicted by suitably defined nested sub-sets of real numbers --, location is.
[Once more, such a stipulation would have to reject Trotsky's argument that events take place only in time.]
This would in turn mean that while we may divide the space occupied by a body as it moves along as finely, or as fine-grained, as we wish -- so that no matter to what extent we 'zoom in' on its location we would always be able to distinguish two contiguous points in its path, which would then allow a theorist to say that the body in question is in both of these places at the same time --, while we can do that with respect to location, we can't do the same with respect to time!
In short: it would be to stipulate that while time isn't infinitely divisible, space is.
Clearly, that would represent an inconsistent approach to the divisibility of time and space -- wherein we are allowed to divide one of them (space) as much as we like, we can't do the same with the other (time).
In fact, this is actually where the alleged 'contradiction' originally appears to have arisen; it was introduced into this 'problem' right at the start by just such an inconsistent (implicit) assumption. So, it is no big surprise to see it 're-emerge' later on.
This inconsistent protocol might at first sight appear to neutralise an earlier objection -- e.g., that even though a moving body might be in two places at the same time, we could always set up a one-one correspondence between the latter and two separate instants, because time and space can be represented in an equally fine-grained manner. But, plainly, it only achieves that result by stipulating, without any justification, that a successful mapping of occupied places onto nested intervals of real numbers (to give them the required density and continuity) is then denied of temporal intervals.
Continuing from the issues raised in the previous sub-section: there seem to be three distinct Alternatives with respect to these two variables (i.e., location and time):
(1) Time and space are both infinitely divisible.
(2) Infinite divisibility is true only of space.
(3) Infinite divisibility is true of either but not both (i.e., it is true of time but not space, or it is true of space but not time).
Naturally, these aren't the only alternatives, but they seem to be the only ones relevant to matters in hand.
Of course, one of the classical responses to this dilemma ran along the lines that the infinite divisibility of time and space implies that an allegedly moving body is actually at rest at some point. So, if we could specify a time at which an object is located at a given point in space, and only that point, it must be at rest at that point, at that time. This appears to be what Zeno himself concluded; it is at least what his argument implied or what he assumed must be the case given this line-of-thought. Here is Philosopher of Science, John Norton, on this:
"In ordinary experience, we see change everywhere. Flies buzz about. Apples fall from trees. Leaves slowly turn yellow in the fall and are blown off the trees. And so on in innumerable variation. Parmenides held that all this motion is an illusion. Nothing changes. We just have the mistaken impression that it does. This view is an instance of a perennially reappearing form of skepticism: that reality is other than what our senses overwhelmingly tell us. The enduring and fatal difficulty of this form of skepticism is that the evidence of our senses is powerful. Perhaps, with tenacity and even some clever sophistry, a skeptic can shake our confidence in the strength of that evidence. However that falls far short of what skeptics need. They must provide positive evidence for their alternative, fantastical conception: that nothing changes; or that we are brains in vats fed spurious perceptions; or whatever other bizarre imaginings they propose.
"Zeno's paradoxes of motion are targeted at one particular form of change: locomotion -- that a body changes (motion) its position (locus) in space. They seek to show that the idea of ordinary motion is internally contradictory. It is hard to believe that Parmenides and Zeno really believed that motion is impossible. The evidence of our senses is powerful, unrelenting and, I believe, irrefutable. Someone who genuinely believes that all change is illusion would seem to be massively deluded and in the grip of a mad fantasy.
"We can cast a kinder light on Parmenides and Zeno's project if we understand them not to be challenging change, but to be challenging the accounts we give of it. Can we really reason reliably about motion using the concepts we have? We think we can. Zeno says otherwise. Look at them more closely and you will find them to be an internal mess. If that was Zeno's goal, then his efforts have met with great success. In one form or another, his paradoxes involve infinities associated with our normal thinking about motion. His paradoxes have forced us to think with great rigor about these infinities and, in immunizing ourselves from his paradoxes, we have brought greater clarity to these notions....
"We do not have Zeno's wording for his paradoxes. Rather, we are in the unfortunate position that our best account of the paradoxes come from a critic of them, Aristotle. Nonetheless, that is what we have and that is what we must work with. Here is the totality of Aristotle's account in his work Physics, Book 6, Part 9:
'Zeno's reasoning, however, is fallacious, when he says that if everything when it occupies an equal space is at rest, and if that which is in locomotion is always in a now, the flying arrow is therefore motionless. This is false; for time is not composed of indivisible nows any more than any other magnitude is composed of indivisibles.'" [Quoted from here; accessed 10/09/2023. Several paragraphs merged. Norton is here quoting Aristotle (1995b), p.404; Book 6, Part 9. One link added. A minor typo corrected,]
Nevertheless, as Norton notes, it seems equally clear to others that moving bodies can't be depicted in this way, some arguing further that motion must be an 'intrinsic' (or even an 'inherent' property) of moving bodies. This means we can't depict moving bodies in any way that would imply they are also stationary during that incidence of movement. In turn, it implies that at all times and places a moving body must actually be in motion, and that is indeed how it later came to be argued, which meant, to some, that such a body must both be in and not in a given location, at one and the same time.
[This is Hegel's view of the matter, but good luck to anyone trying to find anything that clear in what he had to say about this topic! This theory has also been defended with great sophistication in Priest (2006); I aim to show in what follows that he is mistaken, too. So, it turns out he hasn't successfully defended Hegel; he has merely exposed the latter's incoherence even more starkly.]
And, here is Hegel himself on this:
"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....
"Now as regards the assertion that there is no contradiction, that it does not exist, this statement need not cause us any concern; an absolute determination of essence must be present in every experience, in everything actual, as in every notion. We made the same remark above in connection with the infinite, which is the contradiction as displayed in the sphere of being. But common experience itself enunciates it when it says that at least there is a host of contradictory things, contradictory arrangements, whose contradiction exists not merely in an external reflection but in themselves. Further, it is not to be taken merely as an abnormality which occurs only here and there, but is rather the negative as determined in the sphere of essence, the principle of all self-movement, which consists solely in an exhibition of it. 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.
"Similarly, internal self-movement proper, instinctive urge in general, (the appetite or nisus of the monad, the entelechy of absolutely simple essence), is nothing else but the fact that something is, in one and the same respect, self-contained and deficient, the negative of itself. Abstract self-identity has no vitality, but the positive, being in its own self a negativity, goes outside itself and undergoes alteration. Something is therefore alive only in so far as it contains contradiction within it, and moreover is this power to hold and endure the contradiction within it. But if an existent in its positive determination is at the same time incapable of reaching beyond its negative determination and holding the one firmly in the other, is incapable of containing contradiction within it, then it is not the living unity itself, not ground, but in the contradiction falls to the ground. Speculative thinking consists solely in the fact that thought holds fast contradiction, and in it, its own self, but does not allow itself to be dominated by it as in ordinary thinking, where its determinations are resolved by contradiction only into other determinations or into nothing
"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, §955-§960. Bold emphases alone added.]
Detailed comments about the above passage (as it has been interpreted by one particular DM-theorist, James Lawler) can be accessed here; several more remarks will be posted in Essay Twelve Part Five, at a later date. This Essay is focussed on what Engels had to say, not so much with what Hegel argued, hence I will say no more about the above passage in the present work.
If this is also Engels's view (although I know of nowhere in his writings where he is at all clear about this, but it seems to follow from what he has said), one or other of the above Alternatives must be rejected.
Based on what Engels has written on this, it seems that (1) and (3) must be dropped, leaving (2):
(1) Time and space are both infinitely divisible.
(2) Infinite divisibility is true only of space.
(3) Infinite divisibility is true of either but not both (i.e., it is true of time but not space, or it is true of space but not time).
Nevertheless, it is important to note that the paradoxical conclusions classically associated with these three Alternatives only arise if other, less well appreciated (but often implicit), assumptions are either left out of the picture or are totally ignored -- that is, in addition to those mentioned above concerning the continuity of space and the (assumed) discrete nature of time. As it turns out, and as we are also about to discover, the precise form taken by several of these suppressed and unacknowledged premisses depends on what view is taken of the 'real' meaning of words like "motion" and "place"/"space".
In Essays Three Part One and Twelve Part One, it was shown that philosophical 'problems' like these arise when ordinary words are twisted almost beyond recognition (which criticism, incidentally, was endorsed by Marx), or they are employed in contexts far removed from their ordinary, more normal surroundings. The problems false moves like these create were further compounded by misinterpreting the results, not as a new set of conventions governing this novel use of language -- which is what actually happened here --, but as Super-Empirical facts concerning 'the deep structure reality underlying appearances', valid for all of space and time.
[The justification for these seemingly dogmatic claims can't be entered into in this Essay; I have substantiated them in Essay Twelve Part One -- link above.]
In short, the 'classical' approach to this 'problem' only gets off the ground if linguistic conventions (or rules) are misconstrued as Super-Scientific, Mega-Truths, which express, reflect, or represent 'industrial strength facts'.
This approach to 'philosophy' interprets what is in fact a different use familiar words as if it were capable (on its own) of uncovering these super-truths instead of it merely being either the by-product of a set of novel linguistic conventions, at best, or plain and simple linguistic confusion/distortion, at worst.
Indeed, this is how ruling-class ideologues in Ancient Greece began to misread and misconstrue the linguistic by-product of social relations (i.e., the aforementioned rules and conventions) as if they were the real relations between things, thus fetishising language. Because of this, such theorists imagined they could 'derive' super-truths like these from the 'philosophical' jargon they had invented for that express purpose -- indeed, as the late Professor Havelock pointed out:
"As long as preserved communication remained oral, the environment could be described or explained only in the guise of stories which represent it as the work of agents: that is gods. Hesiod takes the step of trying to unify those stories into one great story, which becomes a cosmic theogony. A great series of matings and births of gods is narrated to symbolise the present experience of the sky, earth, seas, mountains, storms, rivers, and stars. His poem is the first attempt we have in a style in which the resources of documentation have begun to intrude upon the manner of an acoustic composition. But his account is still a narrative of events, of 'beginnings,' that is, 'births,' as his critics the Presocratics were to put it. From the standpoint of a sophisticated philosophical language, such as was available to Aristotle, what was lacking was a set of commonplace but abstract terms which by their interrelations could describe the physical world conceptually; terms such as space, void, matter, body, element, motion, immobility, change, permanence, substratum, quantity, quality, dimension, unit, and the like. Aside altogether from the coinage of abstract nouns, the conceptual task also required the elimination of verbs of doing and acting and happening, one may even say, of living and dying, in favour of a syntax which states permanent relationships between conceptual terms systematically. For this purpose the required linguistic mechanism was furnished by the timeless present of the verb to be -- the copula of analytic statement.
"The history of early philosophy is usually written under the assumption that this kind of vocabulary was already available to the first Greek thinkers. The evidence of their own language is that it was not. They had to initiate the process of inventing it.... Nevertheless, the Presocratics could not invent such language by an act of novel creation. They had to begin with what was available, namely, the vocabulary and syntax of orally memorised speech, in particular the language of Homer and Hesiod. What they proceeded to do was to take the language of the mythos and manipulate it, forcing its terms into fresh syntactical relationships which had the constant effect of stretching and extending their application, giving them a cosmic rather than a particular reference." [Havelock (1983), pp.13-14, 21. Bold emphases and links added; quotation marks altered to conform with the conventions adopted at this site. Spelling modified to agree with UK English. Several paragraphs merged.]
As a result of this philosophical 'wrong turn' (on that, see below, and here), Traditional Philosophers reasoned that the word "motion" itself presented some sort of 'problem'; apparently it implied a 'contradiction', even a 'paradox', which, of course, needed their good services to resolve -- indeed, as we saw John Norton point out earlier. All the while, they imagined they were talking about 'motion itself' and not (indirectly) about the distorted meaning of the words they had just used to talk about it (or, rather, what these words supposedly 'reflected'). But, as we will see, since they focused on a strictly limited (and unrepresentative) range of examples, in tandem with a severely restricted set of terms associated with the phenomena (which they also misconstrued), what they had to say about motion in the end was biased/coloured by this misconstrual and by their narrow choice of examples. Indeed, few, if any, questioned the original distortion, or fetishisation, that had been inflicted on ordinary words ordinarily used to describe motion, location, and change -- which linguistic chicanery had conjured into existence these 'philosophical problems', to begin with.
As Keith Thomas pointed out in relation to 16th century magicians:
"It would be tempting to explain the long survival of magical practices by pointing out that they helped provide many professional wizards with a respectable livelihood. The example of the legal profession is a reminder that it is always possible for a substantial social group to support itself by proffering solutions to problems which they themselves have helped to manufacture." [Thomas (1972), p.295. Bold emphasis added.]
The same could be said -- but perhaps with even more justification -- about the 'philosophical problems' invented over the centuries by Traditional Philosophers.
That is because these thinkers came from sections of society that were divorced from the world of collective labour and communal life, whose theories reflected an Ideal view of 'reality' that their privileged life-style seemed to embody. Their view of the world was also born out of an ideologically-driven denigration of the lives and experience of working people and hence of the vernacular and 'commonsense'. [Again, these allegations will be fully-documented in Essay Twelve (summary here).]
This then filtered into Marxism. As I have argued elsewhere at this site (slightly edited):
The founders of our movement weren't workers; they came from a class that educated their children in religion, the classics and philosophy. Almost from day one they were spoon-fed ruling-class ideas and forms-of-thought. These were an integral part of an ancient tradition which taught that behind appearances there lies a hidden (often 'spiritual') world, accessible to thought alone, which is more real than the material universe we see around us.
Ruling-class ideologues concocted this world-view because,
if you belong to, benefit from or help run a society that is based on gross
inequality, oppression and exploitation, you can keep 'order' in one or more of
the following ways:
The first and most obvious way is through violence. That will work for a time,
but it is not only fraught with danger, it is costly and stifles innovation
(among other things).
Another way is to win over the majority -- or, at least, a significant
proportion of "opinion formers"/"influencers" (i.e., bureaucrats, judges, bishops, generals,
'intellectuals', philosophers, editors, teachers, administrators, etc., etc.) -- to
the view that the 'present order' either (i) Works for their benefit,
(ii) Preserves and protects 'civilised values', (iii) Is ordained of the 'gods',
or (iv) Is 'natural' and thus can't successfully be fought against or reformed.
Hence, a world-view that helps rationalise one or more of the above is necessary for
a ruling-class to carry on ruling
"in the
same old way". While the content of this tradition may have
evolved in line with each change in the
mode of production, its
form has remained largely the same
for at least two-and-a-half thousand years: Ultimate Truth about this
'hidden world' underlying appearances -- often called "Being", or even a world of
'essences'/'abstractions' -- may be accessed by
thought alone, and hence can be imposed on reality dogmatically and
aprioristically....
So, the non-worker founders of our movement -- who had been educated from
childhood to believe there was just such a hidden world underlying appearances,
and which governed everything in existence --, when they became revolutionaries looked for 'logical' principles in
that abstract world that told them change was inevitable and part of the
'cosmic order'. Enter dialectics, courtesy of the dogmatic musings of that ruling-class mystic, Hegel. The dialectical classicists latched onto this
theory and were happy to
impose it on the world (upside down
or the "right way up"),
since -- because of their early education -- it seemed to them quite natural and
uncontroversial to do so. After all, that is what 'genuine' philosophers are
supposed to do -- or, so
they had been socialised to
believe....
Some might object to the above assertion that certain philosophical ideas have remained the same for thousands of years, across different modes of production, since that contention runs counter to core ideas expressed in HM.
But, we don't argue the same in relation to religious belief. Marx put no time stamp on the following, for example:
"The foundation of irreligious criticism is: Man makes religion, religion does not make man. Religion is, indeed, the self-consciousness and self-esteem of man who has either not yet won through to himself, or has already lost himself again. But man is no abstract being squatting outside the world. Man is the world of man -- state, society. This state and this society produce religion, which is an inverted consciousness of the world, because they are an inverted world. Religion is the general theory of this world, its encyclopaedic compendium, its logic in popular form, its spiritual point d'honneur, its enthusiasm, its moral sanction, its solemn complement, and its universal basis of consolation and justification. It is the fantastic realization of the human essence since the human essence has not acquired any true reality. The struggle against religion is, therefore, indirectly the struggle against that world whose spiritual aroma is religion. Religious suffering is, at one and the same time, the expression of real suffering and a protest against real suffering. Religion is the sigh of the oppressed creature, the heart of a heartless world, and the soul of soulless conditions. It is the opium of the people." [Marx (1975c), p.244. Italic emphases in the original. Paragraphs merged.]
The above comments applied back in Ancient Babylon and Egypt, just as they did in China and India, in Greece and Rome, and they have done so right across the planet ever since. The same is true of the core thought-forms that run through all of Traditional Philosophy -- that there exists an invisible, 'abstract' world, accessible to thought alone, which is more real than the world we see around us -- especially since Marx also argued that:
"[P]hilosophy is nothing else but religion rendered into thought and expounded by thought, i.e., another form and manner of existence of the estrangement of the essence of man; hence equally to be condemned...." [Marx (1975b), p.381. Bold emphasis added.]
And:
"[O]ne fact is common to all past ages, viz., the exploitation of one part of society by the other. No wonder, then, that the social consciousness of past ages, despite all the multiplicity and variety it displays, moves within certain common forms, or general ideas, which cannot completely vanish except with the total disappearance of class antagonisms." [Marx and Engels (1848), p.52. Bold emphasis added.]
This, of course, helps explain why Marx also thought that this entire discipline (Philosophy) was based on distorted language and contained little other than empty abstractions and alienated thought-forms -- and, indeed, why he turned his back on it from the late 1840s onward. [On that, see here.]
Hence, if the world is ultimately Ideal, it would be 'perfectly legitimate' to derive Super-Scientific 'truths' about it solely from language and/or 'thought' -- as we also saw George Novack point out earlier.
The classical 'paradox' of motion is based solely on a set of surreptitious and, as it turns out, illegitimate linguistic moves like these. That accusation is confirmed by the fact that the acceptance or rejection of one or more of the three Alternatives listed above (repeated below) can't be, and has never been based on any actual evidence. Severally or collectively, these Alternatives are founded on linguistic conventions, overtly/covertly accepted or imposed by all parties involved in this metaphysical con-trick. As noted above, these conventions are based on what is supposed to be the 'real' meaning of the word "motion" -- or, indeed, the 'real' meaning of "place", "space", "same", "time", "moment", and "instant" -- all of which are assumed to have one 'real meaning' (known only to the theorists involved, of course!), in order to derive a series of 'paradoxical' or 'contradictory' results.
(1) Time and space are both infinitely divisible.
(2) Infinite divisibility is true only of space.
(3) Infinite divisibility is true of either but not both (i.e., it is true of time but not space, or it is true of space but not time).
Moreover, the choice of one more of Alternatives (1) to (3) (as a way motivating any particular, or any favoured, 'solution' to this artificially-created 'problem') also depends on the acceptance of one or other of two further Choices (mentioned very briefly earlier):
(A) Even if the specification of the location of a moving body is in no way problematic (in that we can always and uncontroversially declare that a moving body is in two places at once), the specification of the time when this occurs is. So, while time can be divided as much as we like, space can't.
(B) Even if the specification of the temporal history of a moving body is in no way problematic (in that we can always and uncontroversially track a moving body and declare it to be wherever it is a particular 'instant'), the specification of the moment in time when it is there is -- in that it is both "here and not here" at some specific time. So, while space can be divided as much as we like, time can't.
As far as Choice (A) is concerned, it seems that the focus on (point) instants in time is what motivates or underlies the classical 'problem of motion', while an analogous specification for points in space hardly raises a eyebrow. The obverse of this, of course, provides the rationale for Choice (B).
With respect to DM, we can see the tension that exists between the above two approaches to this 'problem' from the way that Trotsky, for example, failed to draw the same conclusions about locations in space that he drew about 'instants in time'. How is it possible to declare that an instant in time is an abstraction -- which can't actually exist -- but fail to say the same about point locations in space? It can't be that objects have to be somewhere in order to exist, since they also have to be wherever they are at some time, too.12a If, according to Trotsky, instants in time don't exist (since they are mathematical fictions), how is it possible for points in space (i.e., mathematical points in space) to exist? If the one can't exist, how can the other? If so, what on earth are DM-fans talking about when they say things like this?
"[T]he position is quite different as soon as we consider things in their motion, their change, their life, their reciprocal influence on one another. Then we immediately become involved in contradictions. Motion itself is a contradiction: even simple mechanical change of position can only come about through a body being at one and the same moment of time both in one place and in another place, being in one and the same place and also not in it. And the continuous origination and simultaneous solution of this contradiction is precisely what motion is." [Engels (1976), p.152. Bold emphasis added.]
What exactly are the "places" or the "moments" they all speak about? Are they mathematical abstractions or are they somehow physical/extra-mental? Search as long and as hard as you like you will find no answer to such questions in the writings of these serial obfuscators.
And this is meant to be the cutting edge of science and philosophy?
Mathematical points are problematic in other respects, too: they have no shape. They aren't spherical, ellipsoidal, cubical or prismatic -- otherwise they would have parts and hence they wouldn't be mathematical points. Hence, they have no radius or circumference, and so can't be 'occupied' by moving bodies. Plainly, they aren't containers -- or, once more, they wouldn't be points. Again, which DM-theorist has ever expressed any reservations about such rather obvious facts? Of course, in modern Mathematics and Physics these issues are handled differently, where the functional relation between space and time (with respect to moving bodies) is expressed differently (in the Calculus, for example). But, that can't help us resolve this 'problem'. That is because it arose directly out of linguistic confusion and word-juggling stretching back over two thousand yeas --, and mathematics isn't a description of the world. If it were then nature would be Mind. [Why that is so will be explored in Essay Twelve. I return to this topic again, below.]
Be this as it may, it seems reasonably clear that DM-theorists have in general opted for these two: Choice (B) and Alternative (2):
(B) Even if the specification of the temporal history of a moving body is in no way problematic (in that we can always and uncontroversially track a moving body and declare it to be wherever it is a particular 'instant'), the specification of the moment in time when it is there is -- in that it is both "here and not here" at some specific time. So, while space can be divided as much as we like, time can't.
(2) Infinite divisibility is true only of space.
Nevertheless, Alternatives (1)-(3) appear to be among the fundamental issues that have exercised Traditional Philosophers for millennia, and now dialecticians. In the latter case, however, the preferred 'solution' appears to rule out the possibility of a moving object being in two contiguous places at two different times. This means, therefore, that DM-theorists have indeed opted for Alternative (2) (with the word "indefinite" perhaps replacing "infinite").
As has already been noted, such a choice was motivated by a surreptitious exclusion of other choices: the indefinite division of time having been ruled out, while that of location hasn't.13
Finally, but more importantly, the 'solutions' on offer over the last two millennia from Traditional Metaphysicians are similarly based on the rejection of at least one implication of the ordinary understanding of motion, part of which is that moving bodies are in different places at different times. [Other aspects of our ordinary concept of motion, ignored by Traditional Theorists, will be explored as this Essay unfolds. Suffice it to say at this juncture that there is no one sense to the verb "move" or the noun "motion" in the vernacular. This means that the phrase "concept of motion" denotes a range of expressions, not a singular or unique meaning typical of the 'Orthodox Account' mentioned earlier.] The broad span of meanings available in the vernacular is such a (seemingly) mundane aspect of our everyday grasp of different sorts of movement and change that it seldom features in classical discussions, except perhaps where it is rejected out-of-hand as far too 'crude' to be worthy of consideration (and that also appears to be the implicit view adopted by DM-theorists). [Or, it is erroneously conflated with the 'Orthodox Account'.]
However, as we shall soon see (indeed, as we will also discover in several other Essays posted at this site), the protocols and conventions of ordinary language and common understanding aren't so easily by-passed, ignored, dismissed, depreciated or hand-waved aside.
Here is Engels again:
"[S]o long as we consider things as at rest and lifeless, each one by itself, alongside and after each other, we do not run up against any contradictions in them. We find certain qualities which are partly common to, partly different from, and even contradictory to each other, but which in the last-mentioned case are distributed among different objects and therefore contain no contradiction within. Inside the limits of this sphere of observation we can get along on the basis of the usual, metaphysical mode of thought. But the position is quite different as soon as we consider things in their motion, their change, their life, their reciprocal influence on one another. Then we immediately become involved in contradictions. Motion itself is a contradiction: even simple mechanical change of position can only come about through a body being at one and the same moment of time both in one place and in another place, being in one and the same place and also not in it. And the continuous origination and simultaneous solution of this contradiction is precisely what motion is." [Engels (1976), p.152.]
However, there are and can be no a priori empirical constraints concerning the length of a temporal interval. In fact, as noted earlier, Engels's account of motion wasn't derived from observation or experiment, nor could it be -- whether or not it had been mediated via the naïve or the sophisticated version of the RTK. Hence, his conception of 'motion in general' can't have been materially-grounded, either, nor, indeed, could was his concept of 'abstract motion'/'motion-in-itself'.
[RTK = Reflection Theory of Knowledge.]
That is because human beings -- aided or not by the use of microscopes, computers, cameras or lasers -- do not possess powers of observation fine-grained enough to allow the study of movement at the level of microscopic detail required by Engels's theory. This means that our 'reflective-', or even our supposed 'abstractive-powers', have nothing useable to work with or upon in order for anyone to be able to decide what does or doesn't happen to moving bodies in an 'instant'. Nor do any of the machines or devices we employ.
And this isn't ever likely to change.
It is little use objecting that "such-and-such" must be true of 'motion itself', for that would simply concede the validity of the accusation that these ideas had been imposed on the facts, having been derived from the assumed, 'real' meaning of a handful of words -- the import of which is far less straight-forward than Traditional Theorists would have us believe, as we are about to find out.
It could be argued that the classical analysis of motion follows deductively from certain incontestable, if not self-evident premises/indubitable facts. There are only a handful of possibilities that the world could conceivably present us with. Engels's analysis, via Hegel, is based on several of these.
Or so it could be objected...
Once more, the problem here is that the deducibility or otherwise of these 'contradictory conclusions' (from such premises) depends solely on the use of a limited range of words, the meanings of which have been artificially modified, construed or constrained -- e.g., "place", "point", "space", "move", "time". "instant", and "moment". These words have either been idiosyncratically (re-)defined, or they have had their meanings (implicitly) altered in order to derive the required result. In that case, nothing reliable can follow from their use (as I hope to show as this Essay unfolds). That was, of course, the point Marx was trying to make -- as was George Novack:
"A consistent materialism cannot proceed from principles which are validated by appeal to abstract reason, intuition, self-evidence or some other subjective or purely theoretical source. Idealisms may do this. But the materialist philosophy has to be based upon evidence taken from objective material sources and verified by demonstration in practice...." [Novack (1965), p.17. Bold emphasis added.]
And yet, that is exactly what was attempted by the above (proffered) DM-response. It seeks to derive substantive conclusions about fundamental aspects of the reality from "abstract reason, intuition, self-evidence or some other subjective or purely theoretical source". The aforementioned "self-evident premises or indubitable facts" are an artificial bi-product of these linguistic moves, as will also be demonstrated in what follows.
Even worse, not only does nothing legitimately follow from distorted language -- as should seem obvious -- it is impossible to give a clear sense (or any sense at all) to the classical account of motion (nor, indeed, to more modern versions of the same, especially those that have yet to distance themselves from this ancient, defective tradition). In fact, as will be demonstrated in Essay Twelve Part One, all such accounts are non-sensical and incoherent; they not only fail to say anything comprehensible about the world, they can't say anything about anything.
In that case, if, for the sake or argument, it is conceded that humanity possesses an 'abstract' idea of motion (even that will be contested below), it can't have been derived by 'reflection', nor can it have been based on anything abstracted from the material world. And these observations become all the more pertinent when it is recalled that this traditional, 'abstract' idea of 'motion itself' originated from an inequitable constraint arbitrarily imposed on temporal intervals, but excused of spatial locations and a ruling-class view of reality (i.e., that there is an Ideal world underlying 'appearances' that is more real than the world we see around us, the nature and existence of which may be derived from the 'real' meaning of a handful of words that only Philosophers can access, mentioned by John Norton, earlier).
In short, Engels's theory wasn't based on 'reflection' (howsoever that word is understood), on evidence, or even on 'abstraction', it was based solely on 'concepts' that were themselves the product of a series of (age-old) stipulations and (covert) conventions, inequitably imposed on 'reality'.
I would be tempting retort "You just couldn't make this up!", but someone clearly did!
Returning now to a re-examination of several earlier approaches to this topic, consider L11 and L12 alongside Alternative (2):
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.
Alternative (2): Infinite divisibility is true only of space.
[L12a: A body, b, observed over the course of a second, is located at point, p, in the first millisecond, and is located at point, 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 point, q, a nanosecond later. And so on…]
However, if for some reason L12 were to be rejected as an alternative interpretation of L11 -- that is, if it is flatly denied that time is continuous and hence indefinitely divisible, while that is asymmetrically allowed of space; i.e., if Alternative (2) above is imposed on the phenomena --, then there would seem to be no consistent way of ruling out the following as another possible version (an everyday example, involving a ship in port, will also be given below to aid in comprehension):
L13: For some b, for just one instant, t, for three places, P1, pi and pk, b is at P1 at t, but not at pi at t, and b is at pk at t (where pi and pk are proper parts of P1).
Here, a finer-grained discrimination of location alone means that L13 isn't contradictory, after all. That is because a body can be in two places at once whether or not it is moving (as we saw earlier), with no implication that it both is and isn't 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 (xk, yk, zk), but not at (xi, yi, zi), where (xk, yk, zk) and (xi, yi, zi) 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 (xk, yk, zk), but not at (xi, yi, zi), where (xk, yk, zk) and (xi, yi, zi) are both located inside (X1, Y1, Z1).14a
[The obvious objection that mathematical points like (X1, Y1, Z1) aren't containers and so can't contain other points, has been neutralised in Note 14a (link above).]
In which case, this version also fails to distinguish moving from stationary bodies.
Here is an everyday example of L13: imagine a ship that has entered port. While there it could be extended across several locations, in at least two places at once. The ship could also be moving, but with no implication that it is entirely in any one of these locations at one and the same time, or that it is fully occupying any specific location, nor yet occupying every point in the entire port. This also means it needn't be occupying other areas of the port at that time. So, while it is still inside the port it could be being moored next to the dry dock (which is also part of that port), but it isn't in the staff canteen or the harbour master's office, or any of the many other places in this port.
Moreover, the same possibilities would still apply even if the ship were stationary with respect to some inertial frame inside this port. Here, this ship could be in one place and not (fully) in all of it, in two or more places at once and stationary, without this implying a contradiction. Plainly, that is because this specific example employs a finer-grained division of space to compensate for the arbitrary imposition of the opposite convention on time.14b
Hence, the alleged contradiction vanishes, once again.
[Any who object to my use of the phrase "not (fully) in" here in place of "in" should read this and then perhaps think again.]15
The following is an example of the above type of motion/non-motion partially expressed in vector algebra:
V1: Let B be a body moving in ℝ3 (or some Vector Space) with respect to a given reference frame.
V2: Let B be at 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 λw (where λ is a Real Number).
V9: Let B be moving at time t1 with velocity vector s, such that s = μw (where μ 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 μ = 0), and all the above considerations would still apply.
Here, we have a slightly more technical version of the ambiguous case mentioned above (concerning that ship). Translated, it could apply to the following scenario:
Ports are generally bigger than ships, and are composed of countless sub-spaces (land, water, buildings, shorelines, etc.). A ship can, therefore, be in port and be located at several points within that port, and yet not be located at every point there, with no implication that it is both in and not in the entire 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, at the same time. And these could all be the case independently of whether or not it is moving with respect to a suitable inertial frame (that is, if we set s above at zero). Furthermore, all these points could lie along the same line.
Figure One: A Ship Both In And Not In The Same Place -- In Dry Dock But Not In Those Buildings While Still In Port --,
And In At Least Two Places At The Same Time -- In Cornwall And In The UK, For Example
(Image Credit: Greg Martin/Cornwall Live)
So, L12 and L13 may only be rejected on the basis of an ad hoc stipulation -- to the effect that while space can be divided indefinitely, time can't --, but, even then, we have just seen that Engels's half-baked theory still doesn't work!
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.
L13: For some b, for just one instant, t, for three places, P1, pi and pk, b is at P1 at t, but not at pi at t, and b is at pk at t (where pi and pk are proper parts of P1).
In which case, of course, the allegedly contradictory nature of motion is, at best, a partial artefact of convention, and which itself only works by constraining the divisibility of time but not of space. In that case, this (implicit) convention isn't even based on any (supposed) 'objective' features of 'reality'.16
In fact, it is the product of a confused use of abstract, philosophical jargon.
[It should be noted that I don't think conventions are or can be based on 'objective reality', but those with whom I am taking issue certainly talk as if they think that is the case. Or, rather, they imagine their use of language is a 'reflection of reality', which becomes more 'objective' over time if it is 'tested in practice', etc., etc. As we have seen, the linguistic conventions underlying Engels's theory of motion were based on (i) an inequitable constraint arbitrarily imposed on temporal intervals but excused of spatial locations, and (ii) the unsustainable belief that he was dealing with the 'real meaning' of words like "motion", "moment", and "space", etc.]
Finally, it could be argued that no matter how much we partition time, no moving body can be located at a certain point (i.e., at one, and only one, point) at that time, otherwise it would be stationary.
It is to that core idea (one that Hegel accepted, and, it seems, so did Engels and Lenin) that I now turn.
The Background To Engels's Argument?
So, in response to the points raised in the previous sub-section, some might concede that while it might not be possible to express the contradictory nature of motion in ordinary (or even technical) language,17 nevertheless, motion in the real world must be contradictory.18
That in turn might involve the acceptance of one or more of the following (partly and partially suppressed) assumptions:
L14: An object can't be in motion and at rest at one and the same time (in the same inertial frame).
L15: If an object is located at a point it must be at rest at that point.18a, 18b
L16: Hence, a moving body can't just be located at a point, otherwise it wouldn't be moving, it would be at rest.18b1
L17: Consequently, given L14, a moving body must both occupy and not occupy a point at one and the same instant.
In which case, it could be maintained that L14-L16 (or their 'dialectical' equivalent) capture the rationale behind Engels's (and perhaps even Hegel's) analysis of motion.
Indeed, if that weren't so, it would suggest motion was either (a) impossible or (b) illusory, or even that (c) it is a 'stop-go', staccato sort of affair.18c
As far as (c) is concerned, dialecticians often point out that those who reject their particular theory end up talking as if motion is analogous to the way it is depicted in or by film. There, motion on the screen only appears to be continuous when it is in fact discontinuous, composed of rapidly sequenced 'freeze frames', as it were. When played at a certain speed this 'fools' the human eye into 'seeing' continuous movement where there really isn't any. If such a 'quasi-static' view of motion were the case, a 'moving' body (in the real world, not on film!) would occupy a point and be stationary at that point for a fraction of a second, occupy another point an instant later, be stationary there, too, and so on. Naturally, what the said object gets up to in-between each of these stages would be, on this view, entirely mysterious. But, on its own, that wouldn't be enough to falsify this view of motion. At least, no more than certain quantum 'leaps' (which are discontinuous in this way) would invalidate QM -- that is, given the way that motion is depicted in and by Traditional Philosophy.19
[QM = Quantum Mechanics.]
Interlude One -- Moving Pictures
In fact, the analogy with moving pictures creates problems of its own for dialecticians since even 'still' pictures of moving bodies capture motion in temporal intervals, not 'instants in time'.
Of course, this minor niggle might be neutralised somewhat by considering flip cards and cartoons. Consider this 'moving horse', for example:
Video One: Eadweard Muybridge -- The Film That
Confounded Artists
The appearance of motion here is created by a series of still photographs:
"Eadweard Muybridge's famous 'Motion Studies' was the product of the wealth and the whim of the railroad baron, Leland Stanford. Stanford came to Muybridge because he had a rich man's problem. A passionate race horse breeder, he wanted to prove that a horse lifted all four feet off the ground when it trotted -- something that had evaded human perception for millennia. On a specially whited out section of track, Muybridge placed a row of 24 cameras with electric shutters, which would be triggered in sequence, four every second, as the horse passed by. By this means, Muybridge did more than freeze the moment; he took a scalpel to time itself.
"'Muybridge's photographs were the first source of accurate information about the gait of a horse, and it's the beginning of this change where suddenly the camera allows human beings to see faster than our own eyes, to break down the world and dissect motion. It's part of that intrusion into the flow of time. For Stanford, the project was always about horses, whereas Muybridge understood that this was potentially about everything he could possibly find and really create an encyclopaedia of zoological motion.' (Rebecca Solnit)" [Quoted from here; accessed 10/04/2015. Quotation marks altered to conform with the conventions adopted at this site. Link added, several paragraphs merged. On this, see Solnit (2004).]
If anything, this analogy is more closely in tune with a view of change captured by the use of episodic language in ordinary life: that is, where motion takes place in time and has nothing to do with abstract metaphysical 'instants' or 'moments' that Engels, Trotsky and other dialecticians seem fixated upon. In that case, what little evidence there is (from this source -- i.e., from ordinary experience) is consistent with the approach adopted at this site.
Having said that, the 'picture' presented by our use of ordinary language is highly complex, so there is no such thing as the picture in this case. There are many such pictures, just as there many different ways of depicting motion and change -- indeed, as we will discover as this Essay unfolds. Be this as it may, I am certainly not advocating my own 'theory of motion', and that isn't just because I neither have one nor want one. I am merely pointing out that ordinary language isn't as obviously defective as many assume. In that case, Marxism doesn't need a theory of motion any more than they need a theory of postage stamps or Medieval Icelandic Pottery. There is no such thing as 'motion in itself' for anyone to theorise about.
Admittedly, a 'stop-go' view of motion would present problems for certain fundamental laws in Physics (for example, the conservation of momentum); but if this is indeed how nature behaves, those laws will need revising, anyway. Other significant advances in science have certainly been predicated on overturning what at one time seemed to be the fundamental laws of nature. One thing we can't do is lay down a priori caveats that nature has to obey --, unless, of course, we wish to emulate the approach adopted by notorious Idealists (and, of course, DM-fans).
~~~~~~oOo~~~~~~
In order to reject the 'quasi-static' view of motion (i.e., (c) from earlier -- which held that motion is a sort of 'stop-go', staccato affair), attention might be directed toward one or more of the (following) considerations described by Hegel (each defined in relation to a suitable inertial frame, as necessary). Now, there is no suggestion that dialecticians have actually argued this way (but, as the above link shows, Hegel, at least, seems to have had many of these issues in mind when he wrote what he did about motion). Nevertheless, what follows could (plausibly) underpin some of the assumptions and conclusions which DM-theorist might very well accept (even if only after having been informed of them by the present author, for the very first time!):
L18: If a body is located at a point it is at rest.
[Unless otherwise stated, "located" should be taken to mean the said body is situated at/in a certain (non-mathematical) point over a finite temporal interval with respect to a suitable inertial frame.]
L19: If that body is subsequently located at another point, it must be at rest there, too.
L20: Hence, if (c) were the case, motion would be little more than successive point location. In turn, this means it would be composed, or be the result, of one or other, but not both, of these two possibilities:
(i) Successive states of instantaneous rest; or,
(ii) 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 instance of motion, location and then rest, followed by the subsequent entry into existence of a new, but seemingly identical body, in the next moment at the very next point in line, giving only the impression of motion and continuous existence.
[(ii) above would, for example, resemble the way that neon lights in a complex sign can be turned on and off in sequence to create the illusion of motion (there is a graphic at this site that illustrates this specific point). It seems that for a while at least Leibniz held a version of this theory.]
L21: L20(i) above involves a body in discontinuous motion separated by periods of instantaneous rest, while L20(ii) pictures a body, or series of bodies, in discontinuous existence at contiguous locations.
L22: L20(ii) must be rejected as absurd.
L23: If L20(ii) is rejected then L20(i) implies that in between each successive point occupancy a body must pass through an indefinite (possibly infinite) number of intermediate points.
[Of course, L23 depends on the further assumption that there is an infinite, or a potentially infinite, number of points between any two points. Hegel appears to have accepted this principle.]
L24: Hence, even on the assumption that motion is discontinuous, there will 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. Plainly, this body won't be at rest in any of these intermediate points.
L25: Consequently, if motion takes place -- and it 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 the very least.
L26: Therefore, the assumption that a body is in motion only if it occupies and is at rest in successive locations at contiguous instants is false -- for even on that assumption, a body must violate this condition for an indefinite number of intermediate points between each successive instance of 'rest', at successive instants.
L27: Therefore, either motion is impossible or illusory (which is absurd), or motion can't be wholly discontinuous.
[It is possible to strengthen L27 by means of L27a, but that option won't be pursued any further here:
L27a: Therefore, either motion is impossible or illusory (which is absurd), or motion can't be discontinuous.]19a
[QM = Quantum Mechanics.]
Having said that, it is worth noting that Loop Quantum Gravity, which is one of the main competitor theories in Modern Physics that attempts to explain gravity, does so in QM-terms, picturing space and time as discrete -- about which we read:
"Unifying quantum mechanics with general relativity is the ultimate dream -- or nightmare -- of physics. It would be a way to finally describe the force of gravity with the tools of quantum mechanics, unlocking how gravity works when it's really strong and at really small scales. Einstein's theory of general relativity tells us that the warping of space and time is what we experience as the force of gravity. Quantum mechanics tells us that what we experience as the forces of nature really come in discrete, tiny chunks, known as quanta. So, if gravity is the bending of space-time, gravity is a force and all forces are quantized, maybe space-time itself comes in discrete little blocks. Maybe there are fundamental units of space-time at some unfathomably tiny scale.
"One of the most annoying things that general relativity and quantum mechanics disagree about is the role that space-time plays in the physics. For quantum mechanics, space-time is just a background, a stage, a floor, a container for all the interesting interactions that make up the physics of the universe. Yes, that stage may bend and warp, and that bending and warping affect the paths of particles -- but that's about it. All physics happens 'on top' of that background space-time.... For general relativity, however, space-time isn't a background stage for the actors; it is the actor. General relativity doesn't assume a background; it creates it. General relativity is the language of the warping of space-time, and that very warping generates the physics of gravity. So, in our quest to unite quantum mechanics with gravity, maybe we should take Einstein's theory at face value. If gravity simply is the mechanics of space-time, then to seek a quantum theory of gravity, we really need to seek a quantum theory of space-time. If we can crack that quantization, then by default, we'll end up with a quantum theory of gravity, and the problem will be solved.
"This is the approach known as loop quantum gravity. The word 'loop' appears in the name because the theory's foundation is based on a rewriting of Einstein's general relativity in terms of lines (instead of points as it's usually done). It doesn't change any of the physics but makes some calculations easier, especially when it comes to quantizing space-time. What does it mean to quantize space-time? It means there's a fundamental unit, a discrete chunk, of space-timey-ness that sits at some imperceptibly small scale. If you were to zoom in to this screen, the smooth curves and clean edges of the letters would be revealed as a vast number of little squares -- pixels. In much the same way, if you were to zoom in to space-time, you would see that time doesn't advance into the future continuously but in quick little tick-tick-ticks of a discrete clock. When you move, it wouldn't be a smooth motion; it would just consist of stuttering steps from one space-time pixel to another
"The biggest benefit of this quantization of space-time is that singularities simply go away. Singularities appear in Einstein's general relativity as places where densities go infinitely high and gravity becomes infinitely strong. We know that this really means that our understanding of the physics is going off the wall, and that we have no clue as to what's happening deep inside a black hole or at the beginning of the Big Bang, where singularities appear. In loop quantum gravity, though, those singularities get replaced with really, really tiny chunks of ultradense (and, presumably, ultra-exotic) matter. We would simply banish those singularity demons from our universe and replace them with something understandable. What do those ultradense chunks of matter look like? Well, we're not sure. You see, loop quantum gravity isn't exactly complete. Although we've managed to develop some of the mathematics of 'pixellated' space-time using a mathematical tool called spin networks, the biggest problem is that loop quantum gravity is a theory of strong gravity at small scales, which should automatically also be a theory of weak gravity at normal scales. That means that, if you use the mathematics of loop quantum gravity in non-crazy situations, like Earth orbiting the sun, you should get all the same results as you would from general relativity or old-fashioned Newtonian physics.
"In other words, loop quantum gravity should contain within itself Einstein's general relativity, and we don't yet know if it does. You should be able to zoom out from the pixellated, quantum space-time view at the smallest scales and recover the smooth, undulating fabric of general relativity's space-time -- and nobody knows how to do that. There are other issues, too. Special relativity tells us that perceptions of time and space depend on our velocity but that our perception of fundamental physics should be the same. But different observers will have different views of the sizes of the quantized pixels of space-time, which will radically alter their views of physics. So that's a problem. Loop quantum gravity is incomplete, and it may not work out. Just like its cousin string theory, which also claims to be a quantum theory of gravity, the mathematics of loop quantum gravity aren't revealing any workable solutions. Some future scientist could crack the code, paving the way to a full understanding of the force gravity. Or, we could just be…wait for it…going in circles." [Quoted from here; accessed 03/07/2023. Several paragraphs merged; links in the original -- however, two have been removed and three added. Spelling modified to agree with UK English; one minor typo corrected. Quotation marks altered to conform with the conventions adopted at this site. Bold emphases alone added.]
If the above theory pans out, we should finally be able to wave "Goodbye!" to any idea that motion is either continuous or 'contradictory'. The same can be said in relation to any success enjoyed by Causal Set Theory:
"The causal set theory...approach to quantum gravity postulates that at the most fundamental level, spacetime is discrete, with the spacetime continuum replaced by locally finite posets or 'causal sets'". [Suraya (2019); accessed 03/07/2023. Quotation marks altered to conform with the conventions adopted at this site. Bold emphasis added.]
Since these two theories have yet to be confirmed and/or generally accepted by scientists, I will say no more about them -- except to point out the obvious, that DM-fans will be looking over their shoulders for the next decade or so as these ideas are refined and tested, All I will add is that the conclusions drawn in this Essay in no way depend on either theory being correct. The idea that motion is 'contradictory' makes no sense to begin with, as this Essay aims to show, whatever theory of gravity Physicists finally end up with (if they do!).
However, it is worth noting that the above argument begins with the rejection of an apparent contradiction -- expressed in L14 (restated below, but re-numbered L28, and hence very slightly modified) alongside its supposed contradictory, L29:
L28: A body can't be at rest and in motion at the same time in the same inertial frame.
L29: A body can be at rest and in motion at the same time in the same inertial frame.
Naturally, this depends on whether these two are genuine contradictories; I will ignore that minor complication in what follows. On the other hand, if they aren't even propositions, then they can't be contradictories in the first place. Nevertheless, I will assume they are propositions for the purposes of this argument; however, their status as propositions will be questioned in Essay Twelve Part One.20
If these seemingly minor 'niggles' are put to one side, we can conclude that L29 is true if and only if L28 is false, and vice versa.
As is well-known, an analogous series of background assumptions motivated Zeno into trying to 'prove' that motion was either impossible or illusory. DM-theorists clearly reject Zeno's conclusion, but it seems they can only do so by accepting L28 (or its 'dialectical' equivalent), thus rejecting L29 (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 were false, and L29 were true that would imply that a body could be moving and at rest at the same time. [That certainly looks like a 'contradiction', one might think!] However, if L29 turned out to be true, and a body could be at rest and in motion at the same time, L17 might not look quite so compelling to DM-fans. At any rate, it is quite clear that dialecticians have to reject one 'contradiction' (expressed in L29) in order to derive their own (in L17).
L28: A body can't 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.
[In response, it could be argued that the contradiction in L29 isn't dialectical. But, as we have seen (here, here and here), the 'contradiction' Engels and Hegel claimed to have found in motion isn't dialectical, either! On that, see also Note 18a.]
When L17 is conjoined with L28 we obtain the following:
L17a: Since a body can't 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 that is so, it is now worth asking: Which of the following two 'contradictions' is it legitimate to accept or legitimate to 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 were the case, L17 can't be derived in any obvious way from L14-L27. That would in turn mean that Engels's conclusion (L17) must be false.
Nevertheless, it is clear from the way the above argument has been developed that L17/L17a depend on the truth of L28:
L28: A body can't be at rest and in motion at the same time in the same inertial frame.
L17a: Since a body can't 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.
[L14: An object can't be in motion and at rest at one and the same time (in the same inertial frame).]
That is because L14-L27 began with the assumed truth of L14 -- or, with its current equivalent, L28. The reverse implication doesn't appear to hold.
[I am not really too concerned with whether or not the reverse implication holds in this Essay. All I am trying to do here is make sense of the idea that motion is contradictory; beginning with the assumption that L14 is true appears to be the only way to do this. Again, since DM-theorists refuse to be clear about what they mean, it has been left to me to try to (i) make sense of what little they have committed to paper, (ii) understand how they arrived at the conclusions that finally emerged (even if only implicitly), and (iii) provide some sort of rationale for it.]
This means that it looks like L28 doesn't pre-suppose the truth of the conclusion drawn in L17a, whereas the conclusion drawn in L17a appears to depends on L28. This in turn suggests that L28 might be the more fundamental 'proposition' of the two. Indeed, because L17a physically contains L28 as its first clause (prefacing it with the word "since"), there is far more here than a simple "appears"; it is quite plain that L17a depends on the truth of L28, not the other way round.
L28: A body can't be at rest and in motion at the same time in the same inertial frame.
L17a: Since a body can't 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.
It could be objected that this is an artificial result because of the way the present author has worded L17a. In that case, DM-fans are welcome to re-cast/re-formulate the above argument (along with all its complexities) in a way that they feel doesn't produce the same result -- that L17a depends on L28, not the other way round.
L17a: Since a body can't 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.
Recall, L17 was the end-point of all this; L17a was merely quoted to make the entire argument a little more concise. In addition, L17 also depends on L28 not the other way round.
L28: A body can't be at rest and in motion at the same time in the same inertial frame.
L17: A moving body must both occupy and not occupy a point at one and the same instant.
Be this as it may, as we have seen L28 would itself be false if L29 were true:
L28: A body can't 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 doesn't preclude it. In order to eliminate this latest difficulty, L29 must be modified; perhaps along the following lines:
L30: With respect to the same inertial frame and the same instant in time, a body can be at rest and in motion.
It is worth noting that L30 'contradicts' L30a:
L30a: With respect to the same inertial frame and the same instant in time, a body can't be at rest and in motion.
L30 now certainly looks 'contradictory' -- especially if the phrase "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 'dialectical' equivalent) that led to the derivation of L17/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).
L28: A body can't be at rest and in motion at the same time in the same inertial frame.
L17a: Since a body can't 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.
L17: A moving body must both occupy and not occupy a point at one and the same instant.
Consequently, if we deny that a body can be at rest and moving at the same time (in the manner indicated above), Engels's conclusion does appear to follow!
That much seems reasonably clear.
Unfortunately, however, the following line of argument also shows that the derivation of L17a from the rejection of L30 isn't inevitable, and hence that Engels's conclusion doesn't automatically follow:
L31: A body can't 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 can't be wholly located 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 can't take place. Hence, by L31, and despite appearances to the contrary, all bodies are at rest!
Of course, L34 is somewhat analogous to the conclusion Zeno himself drew, and it flatly contradicts experience. It is therefore unacceptable -- that is, if we allow experience to be decisive in such matters (indeed, as John Norton from earlier also argued). However, it is now clear that L31-L34 demonstrate that L17a doesn't have to follow from the rejection of L30, even if the alternative result proves unpalatable for other reasons.
L30: With respect to the same inertial frame and the same instant in time, a body can be at rest and in motion.
So, a refusal to accept the 'contradiction' contained in L30 can lead off in separate directions, ending up with two distinct 'contradictory' conclusions. One of them is inconsistent with experience (the latter half of L34 -- i.e., L34b), while the other (i.e., L17a) is self-contradictory:
L17a: Since a body can't 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 the above 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, L17a might well be chosen. However, it is worth noting that neither option is empirically verifiable; in fact they both transcend any conceivable body of evidence and every possible deliverance of experience.21
Interlude Two -- 'Appearances To The Contrary'
In response, 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.
As should seem obvious, it isn't possible to test something "despite appearances to the contrary".
That is because, plainly, any test has to depend on the appearances delivered to us by cameras, instruments, computers and other recording devices. [There is more on this in Essay Three Part Two.]
It could be objected that the present author has just quoted an example where something was indeed tested "despite appearances to the contrary" -- namely the work of Eadweard Muybridge and the movement of horses. To the naked eye, these mammals appear to run one way even though photographic evidence shows they don't. But, those photographs are all 'appearances' (if we adopt for the moment this way of talking). So, if we really do have to embrace this way of speaking (i.e., about 'appearances'), what Muybridge in fact tested was one set of appearances (those clocked by the 'naked eye') against another (those recorded by a series of photographs -- also examined by the eye). Unless one day we manage to 'intuit nature directly', by-passing all those inconvenient 'appearances', there is no way out of this phenomenalist loop. As Essay Three Part Two shows (link above), I don't prefer this way of speaking, but when one finds oneself in the 'Land of the Idealists' one has to adopt their patois. The bottom line is that I utilise their way of speaking in order to undermine it.
That isn't to suggest there are no theoretical problems faced by either option (i.e., whether motion is continuous or discontinuous), but there is no way of experimentally testing these options or even discriminating between them. If a moving body occupied points in space (and was thus stationary) during an interval of the order of, say, 10-10,000,000,000 seconds (if that were even possible!), there is no way we would ever be able to detect it. At least, not without reference to yet more of those annoying 'appearances'.
On the other hand, if a moving body occupied at most two such places in the same 'moment' (in accord with Engels's analysis), we still wouldn't be able to tell. That shouldn't surprise us; as they stand, both options are metaphysical and aren't, therefore, based on any processes in this world, having been conjured into 'existence' by distorting the only language that secures our knowledge of it -- i.e., the vernacular (in conjunction with the everyday practices in which it is embedded) -- a defective strategy that was further compounded by imposing the results on reality, à la Engels/Hegel/Zeno.
Of course, there are certain protocols of modern Physics that postulate minimum times and distances:
Planck Mass: 2.17645(16) x 10-8 kg;
Planck Temperature: 1.41679(11) x 1032 K;
Planck Length: 1.61624(12) x 10-35 m;
Planck Time: 5.39121(40) x 10-44 s.
But, these are the result of convention, required by theory. All but the first of them can't be measured, nor are they even measurable. Hence, there is no way any of them can be shown to be universally or eternally valid maxima or minima. To be sure, certain well-confirmed theories might be based on these conventions, which might suggest they are valid extremes, but as we will see in Essay Ten Part One, that isn't a safe inference itself.
~~~~~~oOo~~~~~~
Of course, it could be argued that L32 begs the question, since, with respect to moving bodies, DM-theorists claim they can be wholly located at two points at once, and still be moving. In fact, both L32 and L33 beg the question.
L32: If a body is wholly located at a point it can't be wholly located 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.
Or, so it could be maintained...
Nevertheless, given the fact that dialecticians also believe that appearances 'contradict' underlying 'essences', they are the very last ones who can legitimately appeal to experience to refute Zeno-esque conclusions like L34b. In fact, if the DM-theory that underlying 'essences contradict appearances' were itself correct, then, since it appears to be the case that there are moving bodies, in 'essence' the opposite must be the case! The inescapable conclusion now seems to be that, if 'appearances' do in fact 'contradict reality', the following must be the case: essentially no bodies actually move --, which, would, of course, mean Zeno was right all along!
L34b: Despite appearances to the contrary, all bodies are at rest.
[I hasten to add that I don't believe Zeno was right all along! Once again, I am merely drawing out the ridiculous implications of this strand of DM.]
Putting this annoying corollary to one side for now, it is important to note that both of the above two 'derivations' rely on the sorts of ambiguities we encountered earlier with respect to L1-L13 -- alongside several more yet to be highlighted. As we will see, traditional, aprioristic 'arguments' like these only seem to work because they are shot-through with equivocation, ambiguity and linguistic distortion. Indeed, that is partly why both of the above conclusions finally collapse into absurdity and incoherence -- as we are about to see.
[Apologies are owed in advance to the reader: the next few sub-sections are somewhat involved and quite technical, but there is no other way of exposing just how confused the 'DM-view of motion' actually is. Where possible I have also translated parts of this material into more ordinary terms.]
The absurdity in L34b (below) is quite plain for all to see and needn't detain us any longer. However, the ludicrous nature of L17a isn't perhaps quite as obvious (although several clear pointers in that direction were outlined earlier).
L34b: Despite appearances to the contrary, all bodies are at rest.
L17a: Since a body can't 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.
The ludicrous nature of L17a may nevertheless be made more obvious by means of the following argument. [In fact, much of what follows depends on and develops an earlier argument, which showed that if Engels's theory were correct, 'dialectical motion' would be a stop-go, staccato sort of affair. The material in this sub-section derives several other absurd conclusions based on similar reasoning, but aimed in a new direction.]
In order to proceed it will first of all be taken for granted that L15b, L15c and L15d (below) are true and that the phrase "moment in time" is well understood -- or at least is as well understood as it was when Engels used similar language. Second, unlike earlier in this Essay, it will now be assumed that the word "located" doesn't automatically, or even always, imply a given object is stationary; for that to be the case, it has to be clear that the said object is located at a point for more than one successive moment (howsoever "point" and "moment" are defined):
L15b: If an object is wholly located at a point for at least two contiguous moments in time, it must be at rest at that point.
L15c: So, no moving body can be in one and only one location during two such moments.
L15d: Hence, if an object is located at a point during a temporal interval of arbitrary length it must be at rest at that point.
L35: Motion implies that a body is in one place and not in it at the same time; in one place and in another at the same moment.
L36: Let body, B, be in motion and at (X1, Y1, Z1), at t1.
L37: L35 implies that B is also at some other point -- say, (X2, Y2, Z2) --, at t1.
L38: But, L35 also implies that B is at (X2, Y2, Z2) and at another point at t1; hence it is also at (X3, Y3, Z3), at t1.
L39: Again, L35 implies that B is at (X3, Y3, Z3) and at another point at t1; hence also at (X4, Y4, Z4), at t1.
L40: Once more, L35 implies that B is at (X4, Y4, Z4) and at another point at t1; hence also at (X5, Y5, Z5), at t1.
[This is just a re-statement of a result obtained and explained in more detail earlier, but it is being used here to reach a totally different conclusion.]
By n successive applications of L35 it is possible to show that, as a result of the 'contradictory' nature of motion, B must be everywhere along its trajectory if it is anywhere, all at t1!22
Expressing the same argument in more detail, but perhaps with clearer language and less intimidating symbols, we have the following:
E1: Assume that body, B, is at rest. If so it will be in a given location -- say, pk -- for at least two successive moments (leaving the word "moment" as vague as Engels left it). Call these "moments", tk and t(k+1). [Where tk is "any moment in time" and t(k+1) is "any successive moment in time".) .]
E2: Assume further that B is now set in motion and hence that it is in two places at once -- say, p1 and p2, both at t1.
E3: If so, B can't be in p2 at a later moment, t2, otherwise it will be at rest there (by L15b and that earlier result).
[L15b: If an object is wholly located at a point for at least two contiguous moments in time, it must be at rest at that point.]
E4: That is because B would then be located at p2 during two moments, t1 and t2, which would mean it had stopped moving. In that case, B must be in a third place, p3, at the same moment, t1.
E5: If B isn't located at p3 at the same moment, t1, it must be there at a later time -- say, t2.
E6: But, according to E2 (i.e., according to Engels), B must be in p2 and p3 at the same time, since moving bodies must be in two places at the same time, and we have already established that B is in p2, at t1. [From (E2).]
E7: So, B must be in p2 and p3, at t1 -- otherwise we will have to abandon the claim that B is moving. [Here is where this argument diverges from that earlier one.]
E8: Hence, if B is in p2 and p3 at t1, and is still moving, it must be in three places at the same time, p1, p2 and p3.
E9: But, the same considerations apply to p3 and p4 as they did with p2 and p3; B has to be in those two places at the same time, too, which means that B is now in four places, p1, p2, p3 and p4, at t1.
E10: It takes very little 'dialectical logic' to see where this is going (no pun intended): if there are n points along its path, B will be in p1, p2, p3..., pk-1, pk, pk+1..., p(n-2), p(n-1), and pn, all at t1!
E11: So, the 'world-view of the proletariat' would have a moving object occupying every point along its trajectory, at the same time!
In order to aid those readers who aren't too familiar with technical arguments like the above, here it is again in summary form, with very few technicalities, employing much more ordinary language:
According to Engels, a moving object has to be in two places at the same time; call that moment, t1. But, if it is still moving at the second of those two locations, it must be there and in a third place at the same moment in time, t1. If that weren't the case, and it was there at a later moment, t2, that would imply it was in that second location during two moments, t1 and t2, not one moment (contradicting Engels). That in turn would mean it was at rest there, contrary to the supposition that it is moving. So, if this object is still moving, the same considerations apply: this body must be in a third place also at t1. Similarly, if it is still moving, the same must be the case with the third and fourth places occupied, as well as the fourth and fifth, the fifth and the sixth, and so on.... They area all occupied at the same time.
Hence, if Engels is to be believed, a moving object must be located at every point along is path at the same moment, t1!
But, that conclusion is even more absurd than L34b!
L34b: Despite appearances to the contrary, all bodies are at rest.
It might seem (to some) that there is a way to avoid that outlandish conclusion by arguing that L35 implies that a moving body is in no more than two places (i.e., it is in more than one but less than three locations) at once. In other words -- as argued earlier -- such a body must be in at most two places at the same time. But, that is no help, for, as noted above, if a body is still moving and in the second of those two places, it won't still be in motion there unless it were in a third place at the very same time (by L15b and L35).
L15b: If an object is wholly located at a point for at least two contiguous moments in time, it must be at rest at that point.
L35: Motion implies that a body is in one place and not in it at the same time; in one place and in another at the same moment. [Emphasis added.]
Once again, just as soon as a body is located in a given location for any length of time (i.e., two or more successive moments) it will be at rest there. Without assuming the truth of L15b (and hence without L35), Engels's conclusions simply don't follow. Given his view, if a body is moving, it has to occupy at least two points at once, or it will be at rest. But, that is precisely what creates the absurdity, for if that body is located at the second of these two points, it will be at rest there unless it is also located at a third point, at the same time.
That follows from L17 (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.
~~~~~~oOo~~~~~~
Interlude Three -- Terminology
The following remarks are intended for those not too familiar with the use of phrases like "at most two" and "at least two", which appear in mathematics and modern logic all the time (no pun intended).
[A] "At most two" means the same as "less than three" -- i.e., "two or less" --, which implies in this case, with respect to locations: (i) p1 on its own, (ii) p1 and p2, or (iii) p2 and p3 (etc.), but (iv) not p1, p2 and p3 (etc.).
[B] "At least two" means the same as "more than one" -- i.e., "two or more" --, which implies in this case, again with respect to locations: (i) p1 and p2, (ii) p1, p2 and p3, or (iii) p1, p2, p3 and p4 (etc.) but not, say, (iv) p1 only, (v) p2 only, or (vi) p3 only (etc.).
[C] Finally, a combination of "at most two" and "at least two" means "exactly two", which implies in this case, once more with respect to locations, just (i) p1 and p2, (ii) p2 and p3, or (iii) p3 and p4 (etc.), but not (iv) p1 on its own, nor (v) p1, p2 and p3, either, nor (vi) p1, p2, p3 and p4, either (etc.).
~~~~~~oOo~~~~~~
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). Hence, the conclusions drawn above are invalid.
L17b: A moving object must occupy at least two places at once.
Or, so it might be maintained...
The above anti-DM argument would indeed be misconceived if Engels had managed to show that a body can be in at most two (but not in at least two) places at once, which he not only failed to do, he couldn't do.
L17c: A moving object must occupy at most two places at once.
That is because, between any two points there is a third point (as we have seen, even Hegel conceded this!), and if the said body is in (X1, Y1, Z1) and (X2, Y2, Z2), at t1, it must also be in any point between (X1, Y1, Z1) and (X2, Y2, Z2), at t1 --, say, (Xj, Yj, Zj). But, just as soon as that is admitted, it becomes clear that a moving body must be in more than two places at once -- namely (X1, Y1, Z1), (Xj, Yj, Zj), and (X2, Y2, Z2), at t1. Hence, there seems to be no way of avoiding the conclusion drawn above: if a moving body is anywhere, it is everywhere in its trajectory at the same time.
[And that is one reason why the question was posed earlier about the precise distance between the points at, or in which, Engels concluded that moving bodies perform such 'contradictory' antics. Of course, whenever I use the phrase "a moving body is in a (certain) point", it should be taken to mean "a moving body is located at a (certain) point", since it has already been established that points aren't containers. (The reason that I have often used the first of these locutions (i.e., employing "in") in this Essay is that the word "located" tends to suggest (to some) a lack of motion.)]
Putting these annoying technicalities and quibbles to one side for now, some might think it unwise to assume Engels believed that a moving body occupies at most two points at the same time (or even that DM requires it), since, as we have just seen, if that body occupies the second of these two points, it would be at rest at that point unless it also occupied a third point at the same time. Given the truth of L15b, there seems to be no way to avoid that implication.
L15b: If an object is wholly located at a point for at least two contiguous moments in time, it must be at rest at that point.
However, we have already seen that if Engels did mean that a moving body occupies "at most two points" at once, then 'dialectical motion' would be discontinuous. If supporters/defenders of Engels want to maintain that 'dialectical motion' is continuous, they will need to reject the "at most two points" codicil. Unfortunately, as we have just seen, upon doing that the ridiculous conclusion reached above follows -- i.e., E11:
E11: So, the 'world-view of the proletariat' would have a moving object occupying every point along its trajectory, at the same time!
So, DM-fans are caught between a rock and a hard place. Either they admit 'dialectical motion' is discontinuous, or they acknowledge the truth of E11.
On the other hand, a combination here of "at least two places" and "at most two places" at once would be the equivalent of "exactly two places", at once.
L17d: A moving object must occupy exactly two places at once.
But, any attempt to restrict a moving body to the occupancy of exactly two places at once would only work if that body came to rest at the second of those two points! L15b says quite clearly that if a body is located at a point (even if this is the second of those two points) for any length of time, it must be at rest at that point. Hence, this seemingly promising escape route (i.e., restricting a moving body to the occupancy of exactly two points, at the same time) will only work if DM-theorists now reject their own characterisation of motion, partially captured by L15b:
L15b: If an object is wholly located at a point for at least two contiguous moments in time, it must be at rest at that point.
[That DM-option also falls foul of the intermediate points objection, outlined earlier.]
In that case, if L15b is still to be held true, then at the second of these two proposed DM-points -- in this case, (X2, Y2, Z2) --, if the said body is still moving, it will also be in and not in that second point at the same instant, too.
It is worth underling this conclusion: if L17d were accepted, and the said body were located at a second point -- say, (X2, Y2, Z2) --, at t1, it will be at rest there, contrary to the assumption that it is moving. So, for that body still to be moving at t1 it must be elsewhere also at t1, and so it must be at a third point -- in this case, (X3, Y3, Z3) -- at t1, contrary to L17d. Otherwise, the condition that a moving body must be both in a certain place and not in it at the very same moment will have to be abandoned. So, DM-theorists can't afford to accept L17d --, unless, of course, they are also prepared to admit that motion isn't dialectical, isn't contradictory.
L17d: A moving object must occupy exactly two places at once.
Consequently, we end up with the unacceptable outcome: that, as a result of the 'contradictory' nature of motion, a moving body must be everywhere along its trajectory all at once.
In response, it could be argued that when body, B, is in the second place at the same instant, a new moment in time would begin. So, while B is in (X2, Y2, Z2) at t1, a new instant, say t2, would start. B would then be in (X2, Y2, Z2) and (X3, Y3, Z3), at the same moment, t2, thus rescuing Engels's theory.
Admittedly, that hasty, ad hoc, 'repair' seems to avoid some of the disastrous implications obtained above (in this case, expressed in E11):
E11: So, the 'world-view of the proletariat' would have a moving object occupying every point along its trajectory, at the same time!
However, it only succeeds in doing that by introducing several serious problems of its own, since it implies that B would be located at (X2, Y2, Z2) at t1 and t2, which would in turn mean that B was located in the same place for two 'moments in time', and that would mean it was stationary at that point! That is why proposition L15b was introduced earlier:
L15b: If an object is wholly located at a point for at least two contiguous moments in time, it must be at rest at that point.
It could now be argued, again (!!), that B-like objects do in fact occupy two places at once, namely (X1, Y1, Z1) and (X2, Y2, Z2), so the above anti-DM argument is defective. If so, the 'derivation' that purports to show that a moving body must be everywhere along its trajectory, if it is anywhere at the same time -- E11, again --, is also fallacious.
E11: So, the 'world-view of the proletariat' would have a moving object occupying every point along its trajectory, at the same time!
We can perhaps clarify this (proffered) DM-reply by means of the following:
L38: L35 also implies that B 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; in one place and in another at the same moment.]
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 still be satisfied, and the above 'derivation' -- that a moving body must be everywhere along its trajectory if it is anywhere, at the same time -- fails. [This 'repair' was in fact considered earlier and rejected.]
L17c: A moving object must occupy at most two places at once.
Or, so it could be argued...
Unfortunately, this seemingly promising alternative soon self-destructs. Here is why:
The (proffered) DM-reply above is based on the counter-claim that Engels only needs a body to be in two places at once. He didn't specify where along that body's trajectory those two places were supposed to be. In that case, any two places will do. Hence, a third place introduced in the above attempted refutation of Engels -- i.e., (X3, Y3, Z3) -- isn't actually implied by his description of the 'contradiction' involved.
L38: L35 also implies that B 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; in one place and in another at the same moment..]
The (proffered) DM-counter-argument then goes something like this:
L38 only follows if we ignore certain facts, perhaps the most important one of which is that the other place where moving object, B, is located is (X1, Y1, Z1). Hence, B, can't also be located at (X3, Y3, Z3), at that time since it is at these two points, (X1, Y1, Z1) and (X2, Y2, Z2), at the same time. So, the requirement that B should be located at any two points is satisfied when the following is the case, B is located at:
(i) (X1, Y1, Z1) and (X2, Y2, Z2); or,
(ii) (X1, Y1, Z1) and (X3, Y3, Z3); or,
(iii) (X3, Y3, Z3) and (X7, Y7, Z7)...; or,
(n) (Xn, Yn, Zn) and (Xn+k, Yn+k, Zn+k), etc., etc.,
along its path. In that case, the said object will be located at two points at the same time, not every point along its trajectory at once (contrary to L38 and E11).
L38: L35 also implies that B 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; in one place and in another at the same moment.]
E11: So, the 'world-view of the proletariat' would have a moving object occupying every point along its trajectory, at the same time!
Or so it might be maintained...
But, the original anti-DM argument was quite specific and ended up deriving the following result (here re-phrased):
R1: If we select any two points a moving body occupies in any order [i.e., (i) (X1, Y1, Z1) and (X2, Y2, Z2), and (ii) (X1, Y1, Z1) and (X3, Y3, Z3)..., and (k) (X1, Y1, Z1) and (Xk, Yk, Zk), and..., (n)..., and so on], then the condition expressed in L17c will be violated, and E11 will still follow.
L17c: A moving object must occupy at most two places at once.
E11: So, the 'world-view of the proletariat' would have a moving object occupying every point along its trajectory, at the same time!
It could be objected that the above anti-DM response only works because an "and" has been surreptitiously substituted for an "or". The original (proffered) DM-reply in fact argued as follows (slightly modified and tidied-up):
R2: If we select any two points a moving body occupies in any order [either (i) (X1, Y1, Z1) and (X2, Y2, Z2), or (ii) (X1, Y1, Z1) and (X3, Y3, Z3)..., or (k) (X1, Y1, Z1) and (Xk, Yk, Zk), or.... (n)..., and so on], then L17c will be satisfied, ruling out E11.
L17c: A moving object must occupy at most two places at once.
E11: So, the 'world-view of the proletariat' would have a moving object occupying every point along its trajectory, at the same time!
But not:
R1: If we select any two points a moving body occupies in any order [i.e., (i) (X1, Y1, Z1) and (X2, Y2, Z2), and (ii) (X1, Y1, Z1) and (X3, Y3, Z3)..., and (k) (X1, Y1, Z1) and (Xk, Yk, Zk), and..., (n)..., and so on], then the condition expressed in L17c will be violated, and E11 will still follow.
Or so it could be objected, again...
Unfortunately, once more, this (proffered) DM-response simply catapults us back to an earlier untenable position, criticised along the following lines:
[B]etween any two points there is a third point (as we have seen, even Hegel conceded this!), and if the said body is in (X1, Y1, Z1) and (X2, Y2, Z2), at t1, it must also be in any point between (X1, Y1, Z1) and (X2, Y2, Z2), at t1 --, say, (Xj, Yj, Zj). But, just as soon as that is admitted, it becomes clear that a moving body must be in more than two places at once -- namely (X1, Y1, Z1), (Xj, Yj, Zj) and (X2, Y2, Z2), at t1.Hence, there seems to be no way of avoiding the conclusion drawn above: if a moving body is anywhere, it is everywhere in its trajectory at the same time.
In that case, the (proffered) DM-reply, encapsulated in R2, itself fails. So, if a body is in (X1, Y1, Z1) and (X2, Y2, Z2) at t1, it must also be in at least one of the intermediate points -- e.g., (Xj, Yj, Zj) --, also at t1. Hence, R1 is still a valid anti-DM objection.
R2: If we select any two points a moving body occupies in any order [either (i) (X1, Y1, Z1) and (X2, Y2, Z2), or (ii) (X1, Y1, Z1) and (X3, Y3, Z3)..., or (k) (X1, Y1, Z1) and (Xk, Yk, Zk), or.... (n)..., and so on], then L17c will be satisfied, ruling out E11.
In order to see this, a few of the subscripts in R1 only need to be altered -- somewhat as follows:
R3: If we select any two points a moving body occupies in any order [i.e., (i) (X1, Y1, Z1) and (X2, Y2, Z2), and (ii) (X1, Y1, Z1) and (Xj, Yj, Zj), and (iii) (X1, Y1, Z1) and (Xq, Yq, Zq)..., and..., (n)..., and so on), then the condition expressed in L17c will be violated, and E11 will still follow.
R1: If we select any two points a moving body occupies in any order [i.e., (i) (X1, Y1, Z1) and (X2, Y2, Z2), and (ii) (X1, Y1, Z1) and (X3, Y3, Z3)..., and (k) (X1, Y1, Z1) and (Xk, Yk, Zk), and..., (n)..., and so on], then the condition expressed in L17c will be violated, and E11 will still follow.
It is surely philosophically and mathematically irrelevant whether we label such points with iterative letters (i.e., "j" or "q") or with numerals ("1", "2" or "3"). [Recall, the variables labelled with iterative letters (i.e., "j" or "q") were meant to be intermediate points in R3.]
In which case, R3 implies that if a body is in, say, (X1, Y1, Z1) and (X2, Y2, Z2), at t1, it must also be in at least one of the intermediate points -- say, (Xj, Yj, Zj) --, at the same moment. R3 therefore implies L17c is false, and hence E11 still stands.
L17c: A moving object must occupy at most two places at once.
E11: So, the 'world-view of the proletariat' would have a moving object occupying every point along its trajectory, at the same time!
Since there is a potentially infinite number of points between any two points, there is no way that L17c could be true, even if you accept the veracity of DM.
Moreover, it is also worth posing the following question in relation to L38: Is B at (X2, Y2, Z2), at t1?
If it is, then it must be elsewhere at the same time, or it will be stationary there. So much is agreed upon (even by DM-supporters). In that case, the only way to stop the absurd induction (i.e., the one that derived the conclusion that if a moving body is anywhere it must be everywhere at the same time -- i.e., E11) would be to argue as follows:
L38a: L35 also implies that B is at (X2, Y2, Z2) and at another place at t1, hence it is also at (X1, Y1, Z1), at t1, but not at (X3, Y3, Z3), at t1.
[L38: L35 also implies that B 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; in one place and in another at the same moment.]
E11: So, the 'world-view of the proletariat' would have a moving object occupying every point along its trajectory, at the same time!
However, that 'straw', once clutched, has unfortunate consequences, which beleaguered DM-fans might want to mull over before they grab at it too frantically:
L38b: If B is at (X2, Y2, Z2) and (X1, Y1, Z1), at t1, but not at (X3, Y3, Z3), at t1, then it must be at (X3, Y3, Z3), at t2.
L38c: If so, B will be at two places -- (X2, Y2, Z2) and (X3, Y3, Z3) -- at different times (i.e., at (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 B will cease to be contradictory, cease to be 'dialectical' -- since it will not now be in these two places at the same time, but in two places at different times.
Finally, and perhaps more importantly, the above (proffered) DM-counter-argument also falls foul of an earlier result -- that is, that if a moving object is in at most two places at once, it must be stationary at the second of these two locations.
That will itself become clear if we re-examine the above pro-DM objection more closely -- i.e., that B-like objects occupy two places at once, namely (X1, Y1, Z1) and (X2, Y2, Z2), at t1.
The question now becomes: At what point in time does B move from (X2, Y2, Z2) to (X3, Y3, Z3)? If it does so at t1, that would imply B occupies more than two points at once -- namely, (X1, Y1, Z1), (X2, Y2, Z2) and (X3, Y3, Z3), at t1 -- which would in turn mean the above pro-DM objection itself fails. On the other hand, if B moves from (X2, Y2, Z2) to (X3, Y3, Z3) at a later moment, i.e., at t2, then B will have been located at (X2, Y2, Z2) for two moments in time, namely, t1 and t2, and that would mean B was stationary while it was at (X2, Y2, Z2).
Hence, it seems the only way that dialecticians can escape from this absurd consequence of their theory -- that a moving object is everywhere along its trajectory at the same time -- is by abandoning their belief in the contradictory nature of motion. That is, they will need to accept that these 'contradictions' cease to operate at an indefinite number of intermediate points in B's transit. For example, the alleged contradiction would disappear right after it left the first two places it occupied in its journey, since it would be stationary at each subsequent point. [Again, that result was established earlier.] That would, of course, concede the result that the said object was stationary at every point along its path!
In which case, the choice before DM-fans is now quite stark: a 'moving' dialectical object is either stationary at every point along its path, or it is everywhere in its trajectory at the same time!
So, it now looks like the only way to avoid the above fatal results -- and of maintaining the view that motion is 'contradictory' -- is if DM-fans are prepared to impose a series of ad hoc stipulations on nature (of the sort mentioned above), none of which seem to work, anyway!
But, as we have already seen several times, such a response would be inimical in another sense: it would undermine the belief that reality itself is contradictory (rather than: these results are merely a consequence of what we say or think about such things -- or the manner in which we do either -- that are), all the while confirming the suspicion that it is only certain ways of representing nature that appear to imply it is contradictory, which "ways of representing nature", incidentally, still await clarification.
Once again: As we will see throughout this site, the source of these (and similar) 'problems' lies in the repeated attempt made by dialecticians (and metaphysicians alike) to state, or deduce, 'necessary truths' about reality from language alone. Such theories are one and all based on an extrapolation from the supposed meaning of a few specially-selected words to fundamental truths about nature, valid for all of space and time, and nothing more. Clearly, with respect to Engels's 'analysis' of motion, his predicament was further compounded by an attempt to circumvent several core conventions expressed in or by our use of ordinary language --, such as those expressed in or by the LOC and the LOI.
[I will endeavour to substantiate these claims below, but in much more detail in Essays Four Part One and Twelve Part One.]
[LOC = Law of Non-contradiction; LOI = Law of Identity; FL = Formal Logic; DL = Dialectical Logic.]
It could be objected that the above criticisms beg the question since dialecticians don't reject the application of principles drawn from FL -- such as the LOC and the LOI --, they merely highlight their limitations with respect to motion and change. However, that response was neutralised in Essays Four Part One and Eight Parts One, Two and Three.
Suffice it to say that dialecticians themselves have yet to account for motion in anything like a clear and comprehensible manner -- or even depict it accurately, for goodness sake! So, whether or not it is correct to say that FL can't account for motion and change, it is clear that DL itself miserably fails in this respect.
Even more annoying: (again) as we saw in Essay Four Part One, and contrary to what dialecticians try to tell us, FL copes with motion and change with relative ease.
Yet Another Absurd Dialectical Consequence
Here is another, perhaps less well appreciated consequence of the 'dialectical' theory of motion and change -- which is, if this were possible, even more absurd than those outlined earlier: If Engels's theory of motion were correct, we would have no right to say that a moving body was in the first of these 'Engelsian locations' before it was in the second.
L3: Motion involves a body being in one place and in another place at the same time, being in one and the same place and not in it.
That is because such a body, according to Engels, is in both places at the same time, so it can't be in one of them before it is in the second.
"Motion itself is a contradiction: even simple mechanical change of position can only come about through a body being at one and the same moment of time both in one place and in another place, being in one and the same place and also not in it. And the continuous origination and simultaneous solution of this contradiction is precisely what motion is." [Engels (1976), p.152. Bold emphasis added.]
Now, if the conclusions drawn in the previous section are valid (i.e., moving 'dialectical objects' are everywhere along their path at the same time), then it follows that no moving body can be said to be anywhere before it is anywhere else in its entire journey! That is because such bodies are everywhere all at once. Hence, they can't be anywhere first and then somewhere else, second. In the 'dialectical universe', therefore, when it comes to motion and change, there is no before and no after -- hence there is no during or while, either!22a
Hence, according to the implications of 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 same time as it sets off! So, even though you might foolishly think, for example, that in order to go on your holidays, you have to board an aeroplane before you disembark at your destination, this 'path-breaking theory', DM, tells us you are sadly mistaken: you not only must get on the plane at the very same moment as you get off it at the 'end', in fact, you do!
And the same caveat applies to everything that has happened 'since' the 'Big Bang'. While foolish and benighted non-dialecticians might think that this event took place billions of years ago, they, too, are sadly mistaken, if this 'super-scientific theory' is correct. That is because, by the above argument, any two events involving motion and change in the entire history of the universe must have taken place at the same instant. Naturally, this means that as you, dear reader, are reading this, the 'Big Bang' is now taking place!
I rather think 'Duck and cover!' should be le mot du jour...22b
Admittedly, this is completely absurd, but that's Diabolical Logic for you!
[When confronted with the truly absurd consequences of their theory, like the above (alongside others covered in this Essay, as well as Essay Seven Part Three), DM-fans with whom I have debated these issues seem to think that if they just flatly deny them (without giving any clear or coherent reason why they should be rejected other than they are patently absurd) they will just disappear, which, of course, they won't. Others have tried to argue that since these are patently absurd consequences, we can't expect Hegel, Engels or Lenin to have accepted them, or, indeed, for their theory to imply them. Naturally, that is just a variation on the fallacious Argument from Authority. In fact, they regard it as a slur on the good name of Engels and Lenin (which it isn't, it is merely to question their philosophical judgment and expertise). When asked how these absurd consequences can actually be avoided or neutralised --, or, indeed, where my arguments have gone wrong --, either deafening silence follows or an attempt is made to deflect onto me and my assumed defects/quirks/peccadilloes, or, indeed, anything else that can be thrown in the air, any 'shiny' object dangled to distract the attention of onlookers. Failing that, they just become abusive. Having to face barrage after barrage of responses like these (across at least three decades!) has helped convince me that DM-fans (i) Are B.S. merchants; (ii) Don't really think about DM much beyond what they read in the classics (since they are so easily stumped by such rather obvious objections); or, (iii) Don't care what disrepute they bring to Marxism by their advocacy of such crazy ideas. (Other replies and objections from DM-supporters have been dealt with here.)]
And Therefore Never Send To Know For Whom The Bell Tolls, It Tolls For DM
Several of the points raised above require further elaboration -- in the course of which we will discover once again that Engels was in fact saying nothing at all intelligible. In fact, the opposite; yet more gobbledygook.
As we have seen, 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.]
However, in so doing he was clearly appealing to what he regarded were the established, inter-subjective meanings of terms like "motion", "change", "place", "moment" and "time". This can be seen from the fact that he didn't even think to define or explain what he meant by these words.
Engels did, however, offer an aside (in the above comment) to the effect that motion is a "simple mechanical change of place", an idea he reiterated in DN:
"All motion is bound up with some change of place, whether it be change of place of heavenly bodies, terrestrial masses, molecules, atoms, or ether particles. The higher the form of motion, the smaller this change of place. It in no way exhausts the nature of the motion concerned, but it is inseparable from the motion. It, therefore, has to be investigated before anything else." [Engels (1954), p.70. Italic emphasis added.]
[I will re-examine what Engels had to say in the above passage, later in this Essay.]
Ordinarily, this lack of precision wouldn't be a problem since we understand words like these perfectly well in our day-to-day lives, and typically without any need to check definitions, etc. But, in highly specialised areas of philosophy and science -- particularly those associated with attempts to revise or correct the way we understand, or even perceive, objects and processes --, a sloppy approach to the use of language like this isn't just unacceptable, it is counter-productive. Indeed, such a cavalier attitude to ordinary language has a tendency to backfire on anyone foolish enough to indulge. Again, this is especially true of those who try to press the vernacular into service way beyond its prosaic remit.
The ability to manoeuvre with apparent ease one's way around linguistic conundrums like this 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' such serial 'graspers' to ignore the internal contradictions this cavalier approach introduces into their own theory. [The serious problems that this tactic brings in its train have been explored and exposed here and here.]
However, as we will see in Essay Seven (and here), DM-theorists are highly selective when it comes to deciding which 'contradictions' they should "grasp", which they should simply drop -- or, and far more likely, which they should simply ignore, which they should try to blame on the defective nature of a rival theory. Hence, when dialecticians "grasp" the 'contradictions' they claim to see in motion and change, they readily attribute them to nature itself -- failing to blame them on Hegel's logical incompetence, Engels's lack of clarity, or, indeed, on Zeno's confused Idealist fantasies.
On the other hand, when a contradiction is detected in a rival theory, that becomes a handy excuse for berating anyone foolish enough to promote it, and which also provides a convenient excuse for rejecting it out-of-hand. By way of contrast, DM-theorists are remarkably forgiving of the contradictions implied by their own ideas, which aren't allowed to suggest -- under any circumstances -- that they are defective or in need of revision. Quite the reverse; these 'contradictions' must be worn as a badge of honour!
So, for example, we are told that by 'resolving' certain contradictions science has been able to progress. [I have covered this topic in detail in Essay Eleven Part One; readers are directed there for the relevant proof texts and analysis.] But, if science advances by rejecting or 'resolving' contradictions in and between theories, or in and between a theory and observation, then it would seem that the scientific theory of motion itself can't advance unless and until the 'dialectical contradiction' implied by a moving body (according to Engels) has also been resolved. However, just as soon as that has been done, dialecticians will surely have to abandon their belief in the 'contradictory' nature of motion -- or, of course, risk holding up the progress of science.
This self-inflicted quandary I have elsewhere called "The Dialecticians' Dilemma".
As seems obvious, 'dialectically grasping' a 'contradiction' doesn't make it disappear. Even if we grant for the moment the veracity of DM, motion would still be 'contradictory' whether or not anyone else viewed this phenomenon the same way. Hence, the significance of "grasping a contradiction" appears to be little more than this: Certain processes in nature and society, which might seem puzzling or paradoxical (to some) stop bothering others when they become dialecticians. They have "grasped" these oddities and can now move on (no pun intended). But, this tactic only works if it is accepted that this is the way the world actually is -- i.e., that it is indeed contradictory. In that case, and on this basis, DM-theorists seem to think they can stop 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 correctly -- where "viewed correctly" appears to mean "Ignore what you can't explain and then accuse critics of not 'understanding dialectics'". Rinse and repeat...
Despite the DM-spin, the above approach nevertheless implies that it is impossible to explain what it means for something to be in two different places at once (save in the ambiguous manner described earlier in this Essay, and again below). If that is so, the dialectical 'analysis' of motion will be of little use to anyone, least of all dialecticians. That is because it is clear that not even they can explain motion, since all their theory does is re-describe it in an equally perplexing manner. All that Engels's 'analysis' seems to have achieved, therefore, is to stop dialecticians worrying about their own defective theory (defective since it contains contradictions like this one!), all the while leaving motion, as they see it, no less 'paradoxical'.
We have also seen that, even if DM were a correct description of, or a valid theory about, 'reality', Engels's view of motion does no real work. How does it help anyone change the world to be told that motion is contradictory? How does it help scientists if they are informed that motion is a contradiction? Can they use it to predict anything? Can technologists and engineers use it to help control nature, or design and then construct something? How many bridges can be built on the basis of the belief that motion is a contradiction? How many strikes won? Or even leaflets printed?
What dialectical --, or, indeed, any --, use is this idea?
In that case, if there is in fact a rational solution to this 'paradox' -- if we but knew what it was --, it is no good looking to dialecticians for assistance. They gave up on that score the moment they leafed through Hegel's 'Logic' and began "grasping" 'contradictions'.
Left to DM-fans, the advance of at least this branch of Physics and Applied Mathematics would come to a grinding halt.23
[Irony intended.]
However, Engels did at least make some attempt to use everyday terms in his effort to show that they, or what they supposedly reflected, weren't all they seemed -- i.e., that when considered 'dialectically' the vernacular reveals more about reality than might otherwise have been suspected, especially by those who are mesmerised by 'commonsense' or blinded by 'formal thinking'. Or, indeed, those who have been bamboozled by that 'inner fifth-columnist', the "abstract understanding" (very helpfully identified for us by Hegel without the use of a single consulting couch, or even a brain scan, let alone a degree in psychology).
Nevertheless, anyone who disagrees with the 'dialectical' conclusions Engels drew would no doubt be reminded that these few words -- or, the 'concepts', objects and processes they supposedly 'represent' -- clearly and unambiguously imply the 'contradictions' that Engels and Hegel said they did. In that case, defenders of the 'dialectical view' of 'reality' could claim that Hegel and Engels had actually made explicit what were in fact implicit 'contradictions' in our knowledge of the world and how it works, and not just in the language we use to express that (assumed) fact. Hence, whether we know it or not we are all 'unconscious dialecticians'.
"Every individual is a dialectician to some extent or other, in most cases, unconsciously. A housewife knows that a certain amount of salt flavours soup agreeably, but that added salt makes the soup unpalatable. Consequently, an illiterate peasant woman guides herself in cooking soup by the Hegelian law of the transformation of quantity into quality…. Even animals arrive at their practical conclusions…on the basis of the Hegelian dialectic." [Trotsky (1971), pp.106-07. Italic emphasis in the original.]
[I have commented at length on this unfortunate passage, which does Trotsky few favours, in Essay Seven Part One, here, here and here.]
Intentionally or not, by arguing the way he did Engels succeeded in identifying this paradoxical idea with an ancient