Essay Five:
Motion Isn't Contradictory
[This Essay should be read in
conjunction with Essays
Four
and Eight Parts
One and
Two.]
Preface
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As is the case with all my Essays, nothing here should be read as an attack
either on Historical Materialism [HM] -- a theory I fully accept --, or,
indeed,
on 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
nearly thirty years ago. [The
difference between
Dialectical
Materialism [DM] and HM, as I see it, is explained
here.]
It
is
also worth pointing out that phrases
like "ruling-class theory", "ruling-class view of reality",
"ruling-class ideology" used at this site (in connection with
Traditional Philosophy and DM) aren't meant to imply 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 meant 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 approach had almost invariably been promoted by thinkers
who relied on ruling-class patronage, or who, in one capacity or another, helped
run the system
for the elite.
However, this 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.
It is also worth pointing out that a good 50% of my case
against DM has been relegated to the
End Notes.
Indeed, in this particular Essay, most of the supporting evidence and
argument is to
be found there. This
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 will have occurred to the reader) to my own arguments -- which I have then
answered.
[I explain why I have adopted this tactic in
Essay One.]
If readers skip this
material, then my answers to any qualms or objections readers might have will be
missed, as will my expanded comments and clarifications.
[Since I have been
debating this theory with comrades for over 25 years, I have heard all the
objections there are! Many of the more recent on-line debates are listed
here.]
Update 07/03/14: 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 [i.e., 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' fails miserably; I
will attempt to explain why over the next few weeks.
Finally, anyone
puzzled by the unremittingly hostile tone I have adopted toward DM/'Materialist Dialectics' in these Essays
should perhaps read
this first.
As of March 2014, this Essay is just under 68,000 words long; a
much shorter summary
of some of its main ideas can be found
here.
The
material presented below does not represent my final view of any of the
issues raised; it is merely 'work in progress'.
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(1) Introduction
(2) Initial
Problems
(a) "Asserted" By Whom?
(b) "Solved" In What Way?
And By Whom?
(c) Yet More Vagueness
(d) Yet More Dogmatism?
(e) Motion 'Itself'
(3)
Do Contradictions
Explain Motion? Or Merely Re-Describe It?
(a) The Problem Stated
(b) Are Contradictions
Causes?
(c) 'Internal Contradictions'
And Motion
(d) An Indistinct Note
(4) Is
Engels's Account Comprehensible?
(a) A Minimum Requirement
(b) An Initial Ambiguity
(c) First Attempt At Disambiguation
(d) Second Attempt At
Disambiguation
(e) Fatal Ambiguity
(5)
The Classical Response To Zeno
(6) Back to The
Drawing Board
(a) The Devil In The
Detail
(b) Space To Let
(7) Further
Problems
(a) Pick Your
Contradiction
(b) Theatre Of The Absurd
(c)
Samuel Beckett
Eat Your Heart Out
(8) No
Word Is An Island -- Philosophers Ignore Ordinary Language
(a) For Whom The Bell Tolls
(b) Ordinary
Language And Paradox
(c) Lack Of Imagination
(d) Ordinary Objects Regularly
Do The Impossible
(9)
Dialectical Objects Do The Oddest Things
(a)
Do They Move Or Simply Expand?
(b) Or
Do They Concertina?
(c)
Coordinates To The Rescue?
(10)
Everyday Miracles?
(11)
Inferences From Language To The World
(a)
Thought Experiment In Place of Scientific Experiment
(b) Metaphysical Con-Trick
(c) Exclusively Linguistic
(12)
Dialectical 'Contradictions'
(13) Conclusion
(14) Notes
(15) References
Summary Of My Main Objections To
Dialectical Materialism
Abbreviations Used At This
Site
Return To The Main Index
Page
Introduction
In this Essay, I aim to examine the role that 'contradictions' are supposed to play in
explaining motion and change.1
Several prominent
DM-theorists have attempted to illustrate the allegedly
contradictory nature of reality by appealing to a variety of examples, some of
which are based on variations of
Zeno's Paradoxes. For instance, in order to
highlight the limitations of
FL, Engels
directed our attention to the 'contradictory' nature of motion, depicting it in
the following way:2
"[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
In common
with other dialecticians -- indeed, as is well-known, he lifted these ideas
from Hegel
--, Engels here connects change with motion, and both with
"contradictions"
in nature and society.
However,
before this passage is examined in detail, there
are a
number of
serious problems it raises which need addressing since they influence the
overall interpretation of the
conclusions Engels
reaches. Left unresolved they threaten to undermine it completely.
Initial Problems
There are in fact five
general 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?
Of course, it
could
be argued that these words were meant to be taken metaphorically. But, if
that
is so, what 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 these phrases merely pertain
to
the
description
of motion? In that case, his conclusions were restricted to language
about motion, not motion itself.4
(2) "Solved"
In What way?
How
exactly are contradictions "solved"? Are they like puzzles, riddles and
mysteries? If they are, do they disappear once they have been "solved"? Puzzles
and mysteries cease to be such when they have been resolved.
Is
this the same with these contradictions? If it is, do new contradictions immediately take
their place? Is each "solved" contradiction then replaced by the
'same'
contradiction, or by an entirely new one?
How
might we conform this? 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 any given body in motion?
Does each contradiction arise and fall as that body moves?
Or is there a single, extended contradiction smeared,
or spread
out, as it were, right across its entire trajectory? Is this 'extended contradiction'
then
perhaps
this: that a moving body is
"here and
not here, in general",
so to speak?
More puzzling still: Are these contradictions "solved" by some mind or other
comprehending them first? If not, what sense can be given to the word "solved"? And, what precisely is there
to understand in a contradiction so that a 'solution' is required
in the first place, but which now mysteriously still helps propel the moving object further
along (if it does)? On the other hand, if a 'solution' is required, how was
this achieved before human beings evolved?
At first sight,
Engels appears
to be arguing that it is only our understanding of motion that is
contradictory:
"[A]s soon as we consider things…then we…become
involved in contradictions…." [Ibid.,
p.152. Bold emphasis added.]
This might help explain why the passage refers to the "continual
assertion" of contradictions, since it is evident that only human beings can assert
things. If so, it looks like Engels thought that human observers can't avoid "asserting" such contradictions whenever they attempt to describe
motion, and that could itself be a result of their partial understanding of the
'absolute truth' about motion.
On the
other hand, this
conundrum could be a fault of logic, or even language, both of which
are
said by some to be inadequate to the task. But, that would fail to explain how
and why contradictions, upon being "asserted", are immediately "solved", and
then promptly re-asserted again.
Anyway, but worse, this would mean that it is only human
understanding (of motion) that is contradictory, not reality itself --
unless, of course, we are meant to assume that nature is Mind, or even that
it is the 'self-development of Mind' that propels bodies along. But, the former
alternative suggests that when reality is
fully understood, all such contradictions should disappear. If so, this implies
that motion might one day cease, all contradictions having been 'solved'.
Moreover, if
contradictions actually 'cause' motion, then their total resolution should, it
seems, freeze nature in its entirety.
Or, is it
that motion will just stop being (or
appearing to be) contradictory one day, but otherwise
carry on as normal? Or does
this
mean that nature will just slow down as it is understood better (i.e., if
what we know about motion and change becomes less and less contradictory)? Who
can say? Certainly, in the 140 years since Engels wrote these enigmatic words, DM-fans
have been more content merely repeating them than they have been posing these
rather obvious questions, let alone answering them.
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 relating to processes in the 'objective world' independently
of our will. But, it is still
unclear how this helps answer the above questions. If the mind "solves" the
contradictions involved in motion, wouldn't this mean that things
actually stop moving?
And wouldn't
this indicate, too, that movement only seems to be contradictory because
of the partial nature of knowledge, implying that motion isn't really
contradictory?
Plainly, that is because these subjective contradictions ought to
disappear
as knowledge grows, meaning that (in the limit) reality isn't
'contradictory', after all. In that case, it is only our 'one-sided knowledge' of nature
that fools us into concluding otherwise.
Well,
perhaps then this just means that we don't really understand
such
'contradictions' to begin with?
But, yet again, that would fail to explain why contradictions are promptly
reasserted upon being "solved", nor is it at all clear how they could
be solved if no one
understands
them, or if no one understands nature fully. More alarmingly, this might mean that the
objects in question aren't
really moving,
as Zeno originally contended.
Why then does Engels
declare the following?
"…the continual assertion and simultaneous solution of this
contradiction is precisely what motion is…." [Ibid.,
p.152.
Bold emphasis added.]
This seems to confirm the view that motion isn't really 'contradictory-in-itself', and that it is simply our
'one-sided' perspective on it that misleads us. After all, Engels tells us that
the "continual assertion" and "solution" of this contradiction is "precisely what motion
is". Why does Engels say that this reveals "precisely" what motion is, as opposed to arguing that
it merely depicts what we subjectively think it is?
An appeal
to "objective dialectics" can't help us comprehend what Engels meant
here either, since 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 as part
of 'objective dialectics'. If
assertions and solutions don't exist in the
world
independent of the minds involved, there would be nothing there (in the material world)
for the minds of scientists and/or dialecticians to reflect.
And, if that is
so, what has assertion and solution got to do with motion in the
real world? And why did Engels think they were at all relevant?
So many questions -- so few answers...
(3) More Vagaries
"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.]
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 at
the same time). So, unless great care is taken
specifying how far apart these two places are, this view of motion would have,
say, an aeroplane landing at the same time as it took off! If any distance will do,
then the distance between the two airports involved is as good as any. [I
return to this topic
later in this Essay.]
Indifference in this respect would have you arriving at your
destination at the same time as you left home!
Anyway, whatever the answer to that question turns out to be -- as is well known
-- between any two locations there is a potentially infinite
number of intermediary points (that is,
unless
we are prepared to impose an a priori limitation on nature and deny this).
Does a
moving body, therefore, (1) occupy all of these
intermediate points at once?
Or
(2) does it occupy each of them successively?
If the former is the case, does this imply that a moving object can be in an infinite number
of places
at the same time,
and not just in two, as Engels said? On the other hand, if Engels is correct,
and a moving body only occupies (at most) two places at once, wouldn't that suggest that motion
is
discontinuous? That is because, such an account seems to picture
motion as peculiar a stop-go sort of affair, since a moving body would have to skip past
(but not occupy, somehow) the potentially infinite number of intermediary
locations between any two arbitrary places (the second of which it then occupies), if it is restricted to being in
at most two of them at any one time. But, that itself appears to run
contrary to the hypothesis that motion is continuous and therefore
contradictory --,
or, it does so at least
in any straight-forward sense. It is surely the continuous nature of motion that
poses such problems for a logic (i.e.,
FL) which is allegedly built on static,
discontinuous points in space and time, this being the picture that
traditional
logic
is supposed to
have painted
--,
at least, according to dialecticians.
It could be argued that no matter how much we
'magnify' the trajectory of a moving body, it will still occupy two locations at
once, being in one of these and not in it at the same time. But, that doesn't solve
the problem, for if there is a potentially infinite number of intermediary
places between any two locations, a moving body musty occupy more than two at
once, contrary to what Engels seems to be saying:
"[A]s soon as we consider things in their motion, their change,
their life, their reciprocal influence…[t]hen we immediately become involved in
contradictions. Motion itself is a contradiction; even simple mechanical change
of place can only come about through a body being both in one place and in
another place at one and the same moment of time, being in one and the same
place and also not in it. And the continual assertion and simultaneous solution
of this contradiction is precisely what motion is." [Ibid.
Bold emphasis added.]
Hence, between any two points P and Q
-- located at, say, (XP, YP, ZP)
and (XQ, YQ, ZQ),
respectively --
that a moving object M occupies (at the same
"moment in time", T1),
there are the following intermediary points: (X1, Y1, Z1),
(X2, Y2, Z2), (X3, Y3, Z3),...,
(Xi, Yi,
Zi),..., (Xn, Yn, Zn)
-- where n cam be arbitrarily large.
And the same applies to (X1, Y1, Z1)
and
(X2, Y2, Z2),
and so on.
So, if Engels is right, M must occupy not
just P and Q at the same instant, it must occupy all these
intermediary points too -- again, all at T1.
That can only mean that M is located in a potentially infinite number of
places, all at the same "moment". It must therefore not only be in and not in
P at 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
(and it must be in all those intermediary points between (X1, Y1, Z1)
and
(X2, Y2, Z2),
too),
if it is also to be in Q at the same "moment".
And, what is worse: M must move
through (or be in) all these points without time having advanced one instant!
It will
have done all this in zero seconds!
M 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 distance divided by time.
But, then, what is it?
[An appeal to the
Calculus
here -- or, rather, to a DM-interpretation 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.]
However, as we will
see later,
this alternative (i.e., that a moving body occupies all the intermediate points
between any two points, all at the same time) poses other
serious problems for Engels's
theory, over and above it implying that objects move with infinite velocities.
On a different tack, do these contradictions
increase in number, or stay the same, if an object speeds up? Or, are the two points
depicted by Engels (i.e., the "here" and the "not here") just further apart, in
that case? That is, are the two points that M 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. Hence it
isn't easy to see how, in a DM-universe, moving bodies can accelerate (or
even move!) if they are in these two locations at once.
[I am of course using "accelerated" here as it is
employed in everyday speech, not as it is used in Physics or Applied
Mathematics.]
Accelerated motion involves a body being in (or
passing through) more places in a given time interval than had been the case
before it accelerated. But, if M 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.]
So many more questions; even fewer answers...
(4)
Yet More
A Priori Dogmatics?
Quite
apart from all this, Engels's endeavour to provide an overtly linguistic/'conceptual' solution to the
'problem of motion' suggests
that
there is more than a hint of
LIE in his account. And no wonder:
he borrowed this approach from Hegel,
an
Idealist of the worst possible kind.
[LIE = Linguistic Idealism; this term is
explained here.]
This
'conceptual' approach
to motion
is evident from the way that Engels's depiction of it depends on a
'one-sided' consideration of just a few
of the
concepts that apply
in this area, expressed
though by means of some rather ordinary-looking words, the
meaning of which Engels simply took for granted (more on this later).
Based on thought alone, Engels imagined he was able to conclude what must be true
of every moving body in the entire universe, for all of time,
without exception. But, how could he possibly know all this
with so little evidence (in fact, none at all, as we will also see) to rely on?
"Motion is the mode of existence of matter.
Never anywhere has there been matter without motion, nor can there be….
Matter without motion is just as inconceivable as motion without matter.
Motion is therefore as uncreatable and indestructible as matter itself; as
the older philosophy (Descartes) expressed it, the quantity of motion existing
in the world is always the same. Motion therefore cannot be
created; it can only be transmitted….
"A motionless state of matter therefore proves to
be one of the most empty and nonsensical of ideas…." [Ibid.,
p.74. Bold
emphases alone added.]
Clearly, Engels possessed a truly remarkable skill:
the ability to determine fundamental features of reality, valid for all of space and time,
based on the alleged meanings
of a few words/'concepts'. Indeed, Engels's claims about motion are all the more
impressive when it is recalled that he hit upon them in abeyance of any
supportive evidence -- let alone a significant body of evidence. As it
turns out (and this will also be demonstrated below), evidence would have been
unnecessary, anyway.
As we have already seen (in Essay
Two), all that an aspiring dialectician
like Engels needs to do in such circumstances is briefly 'reflect' on the supposed meaning of a few words/'concepts',
and substantive truths about fundamental aspects of nature, valid for all
of space and time, spring instantly to mind.
Or, to be more honest, all he/she has
to do is read Hegel's 'Logic'. This is a
core feature of ruling-class forms-of-thought, imported into the workers'
movement by incautious non-workers like Engels. [On this, see Essay Nine
Parts One and
Two, Twelve
Part One and Fourteen Part Two.]
The
only 'evidence' that supports Engels's interpretation of motion is
this highly compressed argument, or rather, 'thought experiment', which is itself based on a consideration of what
a few innocent-looking words/'concepts' must mean. Pressed for a justification of
this line of reasoning, all that Engels could possibly have offered by way of substantiation would
have been a rather weak claim
that this is what the word "motion" really means. Clearly, such
a (imagined, but plausible) rejoinder gives the game away since it would reveal that
substantive truths about motion had indeed been derived from the meaning of
certain words, and
nothing more.
[The significance of that observation will emerge in Essay Twelve
Part One.]
As noted above, an appeal to evidence would be irrelevant,
anyway. That is because the examination of countless moving objects would fail
to confirm Engels's assertion that they occupy two places at once. This is so no matter what instruments or devices
are used
to carry out these hypothetical observations, and regardless of the extent
of the magnification used to that end, or the level of microscopic detail enlisted in
support. No observation could confirm that a moving object is in two places at
once (except in the senses noted below), and in one of these and not in it at the
same time.
This, of course,
explains why
Engels offered no scientific evidence whatsoever in support of his belief
in the contradictory nature of motion.
And this picture
hasn't altered in the intervening years -- indeed, no book or article on DM even so
much as thinks to quote such evidence in support of this thesis --,
and that situation isn't likely ever to change.5
It could be
objected
to this
that if,
say, a
photograph were taken of a moving object, it would show by means of the recorded
blur, perhaps, that such a body had occupied several places at once.
In
that case, therefore, there is, or could be, evidence 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. Clearly, to verify the claim
that a moving object occupies at least two places in the same instant, a
physical recording of an instant would be required. Plainly, since
instants (i.e., in the sense required) are mathematical fictions, it isn't
possible to record them.
It could be countered that as we increase the
shutter speed of a camera, any photographs taken will always show some blurring.
This supports the contention, then, that moving objects are never located in one
place at one time. Maybe so, but it still remains the case that no photograph
can catch an instant, and thus none can verify Engels's contention.
Again, it could be argued that it is
reasonable to conclude that moving objects occupy two locations at the same
moment from the above. Once more, since an instant in time is a fiction, it
isn't reasonable to conclude this.
Not even a mathematical limiting process could capture such ghostly 'entities'
in the physical world, whatever else it might appear to achieve in theory. But, even it could,
no camera (or radar device, or other piece of equipment) could record it. Hence, even
if an appeal to mathematical limiting processes was both viable and/or
available, it would be of no assistance. No experiment could conceivably
substantiate any of the conclusions Engels reached about moving bodies.
And
that explains why he and those who accept these ideas have to
force this view of motion onto nature.
Hence, this thesis about moving bodies has not emerged from the facts,
but 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." [Ibid.,
p.47. Bold emphasis alone
added.]
Of course,
as noted above, part of the problem here is what the word "instant" means.
[I am taking this word to mean the same as "moment in time", used by Engels.] So, it might be
thought that this 'problem' could be solved by means of a suitable definition.
However, even if this were possible, such an 'adjustment' would merely represent
the adoption of a new convention, and would have no bearing at all on the nature
of reality.5a
As
Trotsky argued:
"How should we really conceive the word 'moment'? If it is an
infinitesimal interval of time, then a pound of sugar is subjected during the
course of that 'moment' to inevitable changes. Or is the 'moment' a purely
mathematical abstraction, that is, a zero of time? But everything exists in
time; and existence itself is an uninterrupted process of transformation; time
is consequently a fundamental element of existence. Thus the axiom 'A' is equal
to 'A' signifies that a thing is equal to itself if it does not change, that is
if it does not exist." [Trotsky (1971), p.64.
Bold emphasis added.]
Unfortunately for Engels, if motion were to
take place in one of these "moments", that would mean that it couldn't
exist -– that is, not unless we are also prepared to reject the a priori
conclusion Trotsky expressed in the above passage.
But, if motion actually takes place -- as it surely does -- then what are we to make of
the claim that if something is moving it must be in at least two places in the
same instant, when the latter do not exist (according to Trotsky)? Does
this refute Trotsky, or Engels, or both? Is there even a straw-sized
contradiction here for dialecticians to "grasp"
to save their drowning theory?
Furthermore, an appeal to the abstract nature of some of the points
made above can't rescue Engels, either. His
analysis of motion is no less abstract itself! And, it can't have itself been derived
by abstraction from all (or any) of the forms of motion hitherto
experienced by either himself or humanity -- or even from a finite
sub-set observed by scientists and/or philosophers down the ages. That is because
Engels's thesis clearly appeals to things that, according to Trotsky, do not exist --
such as "moments" in time. And,
even if they
did exist,
we couldn't experience or observe them, and hence we couldn't use them to
confirm what Engels said. [Observations take place in time, and have a duration;
"instants" do not.]
Worse still, we can't abstract from such
instants in order to
agree with Engels, either.6
Whichever way we turn we hit yet another non-dialectical brick wall.
Motion
'Itself'
To be
sure, Engels promptly changed direction in the above passage, arguing that it is
motion itself that is contradictory, not just our thoughts about it that
are -- declaring that:
"Motion itself is a contradiction…."
[Engels (1976),
p.152. Emphasis added.]
In which case, it could be objected that Engels was actually arguing that our thoughts about motion are
contradictory because motion itself is. That is, our theories
depict the world more fully and truly when they reflect its contradictory nature, and
that substantive claims about the universe are justified if and when our ideas capture
reality more precisely (but, only if they have been tested in practice).
Unfortunately, if this response were correct, it would be inimical to DM,
anyway,
since that would mean DM-theory
itself contains contradictions, which would imply it is a contradictory
theory.7
[The disastrous implications that particular conclusion has for DM were outlined in Essay
Seven, and Essay
Eleven Part One.]
However, such a reply would give the game away, since it conforms
an earlier accusation that this view has been imposed on nature because there is
no way that Engels could know, or have known, that nature is contradictory in its entirety, and thus
that all motion in the entire universe, for all of time, is as he says it is. The very best that
Engels could claim is that our thoughts about motion are contradictory, and that this
suggests that motion in nature might be, too.
The problem with this fall-back position is that
(as will be apparent by the end of this Essay): our thoughts about motion
aren't the least bit contradictory, either.7a
Be this as it may, the above response fails
anyway to neutralise the fatal
consequences
outlined
earlier.
That is because Engels's philosophical thesis,
which was the result of an extrapolation from the meaning of a handful of words/'concepts' to
fundamental aspects of reality,
is openly Idealist
(on this see Essay
Two and Twelve
Part One).
Engels himself pointed this out:
"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.]
Compare
these comments with those of
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.]
Worse still,
and
for reasons given above, not only can
this
'theory' not be confirmed, its subject matter (i.e., the thesis that a
moving body occupies and does not occupy the same place in the same instant,
being in two places at once)
resists all attempts to make sense of it, as we
will see.
Substantive
philosophical 'truths' like this (about motion) are ambitiously universal in
intent,
but are thoroughly parochial in origin. Indeed,
their promulgators' epistemologically imperialist intentions (which stretch
across all regions of space and time) remain stubbornly unmatched
by any obvious capacity to satisfy such excessive philosophical ambitions with adequate
material support, or any at all.
So,
throughout history, traditional theorists (like Engels
-- but
more particularly, Hegel) have privileged speculation ahead even of a
perfunctory search for supporting evidence. Indeed, they assume that all of nature
must be as their 'surgically enhanced'
words
seem to them to depict it.
However, if this
approach to
Super-Truth
were valid, it would mean
that the universe
possessed
these features simply because of the idiosyncrasies
of Indo-European Grammar --
the language group in which most of this hyper-bold talk
has been concocted.
(5)
Explanation Or
Re-Description?
The Problem
Stated
Perhaps even worse still:
It isn't
easy to see how the 'contradictory' nature of motion could in any way explain it,
nor
is it easy to see how it could form part of a wider scientific account of anything
at all.
At best,
this way of characterising motion simply re-describes it.
More
specifically, it is difficult to see how one 'part' of a 'contradiction' is
capable of exercising
a causal
influence over any other 'part', or
indeed how one or both of these UOs (i.e., this
"here" and
that "not
here")
could make anything move.
[A more general objection to this way of seeing
change is presented
here.]
[UO =
Unity of Opposites.]
As Engels depicts things,
both 'parts' of this UO seem to appear together: a
body is "here" and "not here" all at once, as it were:
"Motion itself is a contradiction; even simple mechanical
change of place can only come about through a body being both in one place and
in another place at one and the same moment of time, being in one and the same
place and also not in it." [Engels (1976),
p.152.]
In that
case, it
looks like
questions concerning the proximate cause of motion (with the implied
temporal concomitants such questions often motivate)
can't be
answered by anyone who prefers this way of depicting movement. The mere fact that a moving
body is "here" does not appear to be capable of making it become "not here". Indeed, this alleged contradiction
seems to lack any causal powers whatsoever, any capacity to make
things happen. It isn't so much that the dialectical batteries have run down as
it is that there don't appear to have been any supplied
with the original item -- and it has no slot for them to fit into.
This probably explains why Engels didn't even
attempt to construct a causal account of motion based on the contradiction
he claims to have found there (and, as far as can be ascertained, no DM-theorist
since has filled in the gaps). But, even if a DM/causal account were to be
provided one day, it isn't easy to see how these alleged contradictions could explain motion; how does a
being "here" and "not here" (all at once) explain why
anything
actually moves? What work do such contradictions do --
even if you believe in them?
It could be objected here that this radically misconstrues DM, for the
counter-argument presented above misleadingly splits apart
the assumed 'sections' of a contradiction when DM itself requires
contradictions to be constituted by (or to be based upon) interpenetrated
opposites. A dialectical contradiction is a relation, not a thing.
Moreover, and contrary to the above, DM 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.
However, even if this reply
were acceptable, no attempt was made in Engels's work -- and, to my knowledge, none has
been made anywhere else -- to explain how contradictions can have
any effect on anything at all, anywhere, anyhow, and in whatever
preferred causal or mediational/dialectical language they are expressed -- that
is, other
than figuratively. [More on this in Essay Eight Parts
One and
Two.] And, this is quite apart
from the fact that this alleged contradiction (in motion) doesn't appear to be relational
at all. What precisely is being related to what? What "relation" is this
particular one meant to picture or reflect? Is a body related
to itself as it moves? But, how would that make it move?
[The best attempt that I have so far seen from a Marxist
Dialectician to explain the
rationale behind this view of motion and change has been taken apart
here.]
Of course, it could be argued that it is the relation among
bodies that makes them move; that response will be examined below, and in more
detail in Essay Eight Part Two.
Moreover, it is far from easy to see how a contradictions could exercise any sort
of effect on anything at all unless it was translated into, or expressed somehow
in,
physical/material terms (which will be attempted below). At some point, bits of
matter are going to have to be moved about the place. Now, this
physically inconsequential word ("contradiction") doesn't seem to have the
required physical presence -- the oomph, as it were -- to carry out menial tasks
like this.8
[HM = Historical
Materialism.]
Furthermore, if the volunteered
DM-response above were correct
(but see below),
contradictions wouldn't appear to be of much
help in explaining social change, let alone changes in nature. If no
causal role is assignable to contradictions in DM (with respect to motion,
or, indeed, with respect to anything at all), then they certainly can't serve in
such a
capacity in HM. The alleged contradictions in Capitalism, for example, wouldn't, therefore, make anything actually happen
(they would, at best, be the result of other things happening (for which
DM-theorists would no have no explanation, since these 'other things' wouldn't
themselves have been caused by contradictions), or they'd be the result of
certain specific social relations).
The cause or causes of social development would be totally
obscure (given this (assumed) rejection of any
causal role for such contradictions to play). 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 and society.
[Of course, that might be the real reason why they can't
do this --, but they certainly do not see things this way, to
state the obvious.]
Conversely, this could mean
that if the development of class society is still to be accounted for in terms
of the supposed contradiction between the forces and relations of production,
contradictions could be dispensed with at no loss to HM, since (given the above
response) contradictions would do no work in HM either, playing no causal
role. In that case, the sooner they are pensioned-off the better. Attention
could then be focussed on the genuinely causal nature of the above relations --
suitably phrased in historical and materialist terms. Naturally, this would involve a radical
re-write of HM, abandoning much of the traditional
Hermetically-inspired jargon,
which has up until now only managed to stifle Marxist theory.
If
so, this means that
dialecticians need to specify -- as a matter of some urgency -- what, if
anything, is so causal about the contradictions they seem to see everywhere, so
that the latter can at least do some genuine work in HM. At present they do not appear to
be part of the action; at best, they seem to be merely decorative.
On the other hand, the assignment of a causal role to contradictions in HM or DM
-- so that they cease to be merely ornamental -- would generate insuperable difficulties for
both theories, as we will soon see.
Are
Contradictions Causes?
As hinted at above, even if it were possible to assign some sort of causal role
to contradictions (albeit expressed in suitably acceptable dialectical
language), it would still not help DM-theorists account for motion. That is
because (according to Engels) motion allegedly involves a body being in one
place and not in it, all the while being in two places at one and the same
'instant'/'moment'. The problem is: How does this actually explain
motion causally -- or in any other sense? What exactly does it add to a
scientific account of the same phenomenon? All it appears to offer is a
paradoxically-worded re-description.
In order to make the last point clearer, it is worth pondering once again the answer to this question:
Do
contradictions cause motion (i.e., do they make it happen), or does motion merely
reveal the presence of contradictions as it unfolds? On one
reading of Engels's account, it looks like it is motion that causes (or
creates) contradictions. Hence, according to this way of reading his exact words, something must be in
motion first for it to bring about contradictory, simultaneous occupancy
and non-occupancy of successive locations. But, as we will soon see, this would
mean that one or both of the following hypotheticals would have to be true:
(1)
If contradictions didn't exist,
motion could still take place.
(2)
If motion ceased, contradictions would still
remain.
(1)
The relevance of the first of these is
underlined by the fact that unless motion was already underway, a contradiction could not
be inferred.
At the very least, this option prompts a further question: Which came first
-- movement or
contradiction? The answer to this might be why Engels spoke about contradictions being
"solved", and then "re-asserted", since, on that basis, it looks like motion causes
contradictions, not the other way round.
Of course, it could be argued that these two go hand-in-hand; so
it no more makes sense to ask which came first, movement or contradictions than
it would to ask: "Which came first, counting or numbers?"
But, as we will see later on in this Essay, there are (in fact) examples of
motion in the real world where no contradiction is implied, directly or
indirectly. So, perhaps this is the case here, too?8a
(2) The second option above follows from the simple observation that a stationary
body can occupy two places at once, and it can be in one place and not in
it at the same time. [Examples of both are given
below.]
In that case, (2) suggests that contradictions aren't a
sufficient
cause of motion, whereas (1) indicates they aren't even necessary.
Moreover, and with respect to (1), once more, Engels himself appears to
have
reasoned from his understanding of what motion is to its contradictory
implications. In that case, it looks as if there is no causal role
for contradictions to play with respect to motion itself, as far as Engels saw things -- that is, there seems to
be no way that they could make anything move. At best, they appear to be
conceptually derivative, not causative; they depend on motion, not the other
way round. Hence, as things now stand,
it looks like things first of all move, and only then
do contradictions emerge -- and even then this just applies to our depiction of motion.
If so, it
might be correct to say that contradictions operate solely at a conceptual
level -- they appear to have no part to play in the physical action, on
the ground, as it were.
Given this modified view, it would seem that
objects in the world just move, but they do not to do so because they become embroiled in
literal contradictions.
[So, for example, moving bodies do not argue among themselves about the
occupancy or non-occupancy of this or that 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 do this if
literal contradictions (as opposed to a figurative, DM-extension to
this word) were operative in such cases. (On this, see
Note 1, and Essay Eight Parts
One and
Three.)]
In fact, given Engels's account of
motion, it seems that it is we who derive these paradoxical conclusions in
our attempt to depict something that just takes place (without any such fuss) in nature.
In other words,
according to this interpretation of Engels's views, it looks like the 'fault'
lies in us, not in
things.
However, this
way of depicting motion is clearly unacceptable to DM-theorists; they insist
that we must begin with material reality not with a description of it.
From there, according to them, we must postulate only those contradictions that
really exist in nature or society -- based perhaps on their reflection in human
thought, confirmed in practice. Clearly, human beings study
motion and its attendant contradictions using the conceptual resources they have
to hand, which might not always be up to the job. Or so a counter-claim might
go.
But, even
this response 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 this is so occupies the latter three quarters of this
Essay. Also, see
here.]
In relation to Engels's account of motion, as will soon emerge, there is no clearly
specifiable set of possibilities -- or even actualities -- 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 nature is too complicated for us to
describe -- it is because his words fail to be a description in the first place.
Hence, Engels's 'description' of motion is not just empty, it isn't even a
description!
Again, it could be objected that the above analysis is misguided since it
compartmentalises reality, distorting the account of nature given in DM.
In response to this it is also worth pointing out that we do not have to divide
the 'parts' of a contradiction one from another (or from other relevant aspects
of reality) to make the above argument work.
If each and every contradiction postulated by dialecticians (whether derived
from "really existing material forces", or not) is given a sufficiently complex,
dialectical background (interconnected within the Totality, required by the
theory, verified in practice, etc., etc.), that still would not amount to an explanation of the
causal or "mediated" links that are required. A widening of the domain (to the
entire Totality if need be) cannot suddenly provide an explanation of how
the simultaneous presence and absence of an object in one and the same place
could possibly make it move -- or even how it could account for motion in
any way at all.
An appeal to forces here would be to no avail, either -- as will be
demonstrated in detail in Essay Eight
Part Two. Unless forces are anthropomorphised, they too cannot account for
movement and change in DM-terms. [That cryptic comment will also be explained in
Essay Eight Parts One and
Two.]
Furthermore, but the alleged reflection
of contradictions 'in the mind', which might be thought capable of providing the 'conceptual
connection' that supposedly exists between a cause and its effects (or between various mediated items in the Totality), cannot create a genuine
connection if there are none already there in reality for it to reflect.
Contradictions must have some sort of material basis if they are to be
reflected in thought; they cannot just be conceptual. And yet, what material
form do they take?
Unless sense can be given to the idea that contradictions are capable of connecting
things in the required way -- in reality and not just 'in the
mind' --, in order to provide some sort of grist for the DM-causal/mediational
mill to grind away at, a DM-style reflection would advance the explanation of motion
not one inch.
Even assuming it could be shown that contradictions do in
fact
represent a material relation between objects and/or processes -- which have been abstracted from
(or read into) the phenomena
(in an as yet
unspecified way!) -- they
still couldn't account for motion. That is because this would simply amount to a
re-description of the phenomena, once more. We still await the explanatory punch-line: how do
contradictions make things move? What is the material point to this Hegelian
myth?
If, though, it is now claimed that such a causal (mediational) link between events must to
be postulated (i.e., it is just assumed to exist to make the theory work), then that would merely provide a conceptual
link between the said events, once more -- and such it would remain until the
physical details were filled in. Without the latter, the contradictory nature
of motion would remain at best a conceptual, but not yet a material aspect of reality.
[That outcome should surprise no one given the Idealist origin of DM-use
of "contradiction".]
If, on the other hand, it is claimed that the mere presence of the said conceptual
connection indicates that such causal links must exist in reality -- that is, if
the complex reflection theory of knowledge is assumed to be true (wherein the
human mind acquires knowledge actively, in practice etc.) --,
then that would still not explain how contradictions could actually cause
motion. How do contradictions succeed in moving things about the place?
Here, the dialectical spade is not just turned, it snaps in two.
Clearly, the above difficulties will only be resolved at some point if a clear
explanation is given as to how contradictions can make things move -– or, at least,
until it is shown how and in what way the above objections are misguided.
However, as should now seem plain, the role that contradictions supposedly play
in motion is not helped by an account that depicts them (1) As the product,
not the cause of motion (making them derivative), or
(2) As the result of human reflection on the nature of motion (implying
they are merely conceptual, and are thus Ideal).
Hitherto,
DM-theorists have been content
merely to label certain states-of-affairs
"contradictory" without apparently giving any thought to the lack of explanatory
role this empty ceremony assumes in their theory. Why call anything "contradictory" (and claim
so much for the use of this term) if no account can be given of how this actually explains why anything changes or moves?
'Internal Contradictions' And Motion
At this point, it could be argued that the above objections are all irrelevant since
DM-theorists are committed to the thesis that motion and change are caused by
internal contradictions; the above account seems to be obsessed with
external causes.9
Unfortunately, in connection with motion, there do not appear to be any internal
contradictions capable of impelling objects 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
And
there do not seem to be any 'struggles' taking place within moving bodies
that impel them onward (perhaps in the way that a drunken brawl might make a train carriage
wobble from side to side, only worse) --, and this would be so even if it were true that all bodies
are in fact UOs. No matter how intense this
supposed internal battle becomes, a
'metaphysical boxing match' of this sort seems incapable of generating self-propulsion.
Lenin's "demand", therefore, looks rather empty:
"Dialectics requires an all-round
consideration of relationships in their concrete development…. Dialectical logic
demands that we go further…. [It] requires that an object should
be taken in development, in 'self-movement' (as Hegel sometimes puts it)…." [Lenin
(1921), p.93. Bold emphases added. This entire topic is examined in
great detail in Essay Eight Parts
One and Two.]
"
Furthermore, there do not appear to be any identifiable contradictions situated
at the leading edge of a moving body 'dragging' it along, just as there seem to
be none at the
back 'pushing'.
Worse still: both of these scenarios (even if they were remotely
plausible) would clearly involve the creation of kinetic energy out of thin
air.
In that case, with regard to individual bodies, motion can't be
an example of change through "internal contradictions".
It could be replied that since locomotion and development in a system
are the result of forces
acting on bodies/processes, the contradictory nature of motion can easily be accounted for on
the basis of a network of internal, systematically-opposed forces. This
would then make the unit within which contradictions (and thus motion) occur the whole,
not the part, which seems to be the assumption underlying the comments made in previous
few paragraphs.
Naturally,
that response would make a mockery of the
claim that all objects change through self-development, or that they barrel
along because they are self-motivated. Just as it would make a mockery of
Lenin's contrast between a mechanical, 'external' account of movement and
change, and a dialectical account. On this modified, 'theory', no object
would be self-motivated -- never mind what Lenin demanded. -- it
would be moved by forces internal to the system of which it is a part,
but external to each object 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)…." [Ibid., 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 to the conventions
adopted at this site.]
However, even if systematically-opposed
forces could somehow be interpreted as contradictions -- or if they could
at least be regarded as
constituting them -- that would still fail to show how internal contradictions
could explain motion (or, rather, a change in motion), or even how they could
initiate it. Nor would it account for
the contradictory nature of motion itself; at best, all this would do is
appeal to the allegedly contradictory nature of the system of forces that
supposedly produced or changed any motion 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 with whatever
now maintains it (if anything does) -- at least not obviously so. 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 this might be done.
Hence, whether or not it is true that movement is
caused/mediated by a disequilibrium within a system of incipient forces
('internal' or otherwise), that still wouldn't affect the alleged fact that once
moving, a body appears to do contradictory things. Even given the truth of such an
'internalist', or even 'externalist', account of contradictions and forces, the fact that a body is in
two places at once is a consequence of this setup. But, the "in two
places at once" (etc.) descriptor (or its physical correlate) doesn't also
cause motion in addition to the forces at work in the system. Indeed, while
forces might cause motion (or, rather,
cause a change in motion), the alleged contradictory nature of the movement that
results from this has no part to
play in the action.
So, even if the 'internalist'/'externalist' picture were correct,
Engels's analysis of motion would still amount to nothing more than a
re-description of it; it would still be the case that motion makes bodies do allegedly contradictory
things, not the other way round. Hence, the contradictions that Engels highlights are still derivative, and not at all explanatory.
It is worth
re-emphasising this point: even if opposing forces could explain
contradictory motion (which thesis is demolished in Essay
Eight Part Two, anyway), the nature of the connection between the paradoxical
states that moving bodies appear to display and forces has still to be established. All
that the addition of opposing forces has achieved is to account for the origin
of one
contradiction (motion) in terms of another (oppositional forces). The
contradictory nature of motion itself is still locked in the descriptive mode
-- it does no work. Whether or not forces can explain motion (or even changes in
motion) is not being questioned here, yet. Even supposing they could,
the contradictions Engels supposedly saw in moving bodies remain descriptive.
We are still owed an explanation as to why a moving body being "here and not
here at the same time" and "in two places at once", accounts for its motion as opposed to merely re-describing it.
Of course, on
this view, motion (or, indeed, change in motion) would be causally related to
forces, but this just divorces the latter from the contradictory behaviour of
moving bodies (a point Engels himself seems to have conceded -- on that, see
Note
10). So, even if it were the case that opposing forces caused motion
(or changed it),
this still would provide no useful role for the observation that motion is
itself contradictory. As far as DM is concerned (that is, on the basis one
particular interpretation
that appears to be inconsistent with what Engels himself said about forces
-- again, see
Note 10), what seems to be important is the alleged fact that
opposing forces are contradictory; the other notion (about the
contradictory nature of motion) still appears to be redundant; it serves no obvious
purpose, and plays no role in the action.10
[As will be argued at length in Essay Eight Part
Two, the appeal to oppositional forces to explain
contradictions (and/or contradictory totalities) is no less misguided. There, it
will be demonstrated in extensive detail that not only is there no conceivable interpretation of
opposing forces that could account for contradictions (in FL or DL), there is no
viable literal or figurative way of depicting contradictions as forces.]
[DL = Dialectical Logic; FL = Formal Logic.]
Of course,
even more revealing is the fact that in classical Physics forces are supposed to
change the motion of bodies; this means that the idea that something has
to maintain movement (whether it is contradictory or not) depends on an obsolete Aristotelian theory
of movement. If so, the fact
that contradictions can't supply a causal explanation of motion is
all to the good, for if the allegedly contradictory nature of motion caused
and maintained movement, much of post-Aristotelian (Newtonian) mechanics would
have to be binned.11
But, then again, if such 'contradictions' don't and can't explain motion
(i.e., they do not change or initiate it),
why make such a fuss about them?
Well, despite the above, it could be objected that this whole discussion seriously
misunderstands the nature and role of contradictions in dialectics. As John Rees
points out:
"[These] are not simply intellectual tools but
real material processes…. They are not…a substitute for the difficult empirical
task of tracing the development of real contradictions, not a suprahistorical
master key whose only advantage is to turn up when no real historical knowledge
is available." [Rees (1998), pp.8-9.]
Hence, it could be argued that the problem with the above criticisms is that
they substitute an abstract analysis for one that should be focus on real material forces.
This objection is considered in detail elsewhere at this site (here,
here,
here,
and here), where Rees's
and other dialecticians' epistemological
and methodological claims are examined at length, alongside a consideration of
the "real material contradictions" to which most DM-theorists appeal to illustrate
their theory -- as well as the spurious claim
that dialecticians do not use their theory as a "master key" to unlock
reality, when they clearly do. [On that, see Essay
Two.]
The claim will also be revived here
and here (but, more
specifically
here, here and
here) that material contradictions
cannot account
for change, since they are locked in the descriptive mode (and a
confused mode, at that).
An Indistinct
Note
However, one further possibility hasn't yet been examined: What if it is
entirely unclear what Engels was trying to say in the passage under
consideration? Indeed, what if it could be shown that he was in fact saying nothing
at all comprehensible?
In that case, it would be completely beside the point whether or not
there are any genuine examples of "material contradictions" in nature
(at least, not as Engels saw them). Well, no
more than there would be any point in Christians, for example, trying to
locate the actual Trinity somewhere in outer space. The problem here lies not so
much with the search itself (in that it might be too difficult, or would take too
long), but with the nature and description of something that could be looked for. If we
are given nothing comprehensible to search for, plainly no search can begin.
[As noted in Essay Six,
you can look, for example, for your keys if you do not know where they are, but not if
you do not know what they are.]
But, is there any substance to these claims?
The next few sections aim to show
that there is -- and plenty more than enough.
Is Engels's Account
Comprehensible?
A Minimum Requirement
Before an empirical investigation into the real material cause of motion can
begin, we need to be clear precisely what it is we are being asked to
examine. As things turns out, it isn't possible to determine what Engels was 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.]
In order to substantiate these
allegations, several further ambiguities in Engels's account will need to be addressed
first.
An
Initial Ambiguity
Engels tells us that a body must be:
"[B]oth in one place and in another place at
one and the same moment of time, being in one and the same place and also not in
it." [Ibid.,
p.152.]
Here, he appears to be claiming two separate things that
do not immediately look equivalent:
L1: Motion involves a body being in one place and in
another place at the same time.
L2: Motion involves a body being in one and the
same place and not in it.
L1 asserts that a moving body must be in
two places at once, whereas L2 says that it must both be in one place
and not in it, while leaving it unresolved whether it is in a second place
at the same or some later time -- or even whether it could be in more
than two places at once. To be sure, it could be argued that it is implicit in
what Engels said that this occurs in the "same moment of time"; however, I am
trying to cover every conceivable possibility, and it is certainly
possible that he did not. [The significance of these comments will emerge as the Essay
unfolds.]
It is also far from easy 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 M isn't located at X -- if it is "not in X"
--, then it can't also be located at X (contrary to what Engels
asserts). On the other hand, if M
is located at X, then it can't also not be at X!
Otherwise, Engels's can't mean by "not" what the rest of us mean by that word.
But, what did he mean?
Moreover, if M is in two places at once --
say in X and Y at the same time --, then it can't be in Y
but must be in Y and another place -- otherwise it will
be stationary at Y.
[We will return to these initial problems later
in order to see if there is any way around them.]
Be this as it may, it is
important to be clear what Engels means here because L1 is actually
compatible with the relevant body being at rest! This can be seen if we
consider a clear example: where an extended body is motionless
relative to an
inertial frame.
Such a body could be at rest and in at least
two places at once. Indeed, unless that body were itself a mathematical
point, or discontinuous in some way, it would occupy the entire space
between at least two distinct spatial locations (i.e., it would occupy a finite volume interval). But since all real bodies are
extended in this way, the mathematical point option seems irrelevant, here.
[Anyway, it will be considered below.]
A commonplace example of this sort of situation would be where, say, a train is at rest relative to a platform.
Here, the train would be in countless places at once, but still stationary
with respect to some inertial frame. [There are countless examples of this
everyday phenomenon.]
[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 a more rigorous form using
vector algebra and/or set theory. In the last case considered below, just such a
translation will be given to substantiate that particular claim.]
Unfortunately, even this ambiguous case could involve a further equivocation
regarding the meaning of the word "place" -- the import of which Engels clearly
took for granted. As seems plain, "place" could either mean the general location
of a body (roughly identical with that body's own topological shape, equal
in volume to that body --, or, on some views very slightly larger than its volume, so
that the body in question can fit
'inside' its containing volume interval). Alternatively, it could involve the
use of a system of precise spatial coordinates (which would, naturally, achieve something
similar), perhaps pinpointing its centre of
mass, and using that to locate the body, etc.
Of course, as noted above, Engels might have been referring to the motion
of mathematical points, or point masses. But, even if he were, it
would still leave unresolved the question of the allegedly contradictory nature
of the motion of gross material bodies, and how the former relates to the
latter.
It is Engels's depiction of motion that is unclear; because of
that, I
will concentrate on ordinary material bodies. Anyway, since DM-theorists hold that their theory can account for motion in the real world, the
motion of mathematical points -- even where literal
sense can be made of them and of the idea that they can move
(if such
points do not exist in physical space, they can hardly be said to move) will not in
general be entered into here.
L2 itself involves further ambiguities that similarly fail to
distinguish moving from motionless bodies. Thus, a body could be located within an extended region
of space and yet not be totally inside it. In 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 word "in". However, it could be
objected that "in" has been replaced here by with "totally inside".
Even so, it is worth
pointing out that Engels's actual words imply that this is a legitimate
interpretation of what he said:
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. So, a mundane example of this
ambiguity is where, say, a 15 cm long pencil is sitting in a pocket that is
only 10 cm deep. In that case, the pencil would be in, but not entirely
in, the pocket -- that is, it would be both in and not in the pocket at the same
time, but still at rest with respect to some inertial frame. L2 certainly
allows for such a situation. Engels's use of the word "in" and the
rest of what he said carries this ambiguity.
Hence, it
seems that Engels's words are compatible with a body being motionless
relative to some inertial frame. And this is still the case even when L1
and L2 are combined, as Engels intended they should:
L3: Motion involves a body being in one place and
in another place at the same time, and being in one and the same place and not
in it.
An example of L3-type
--
but apparently
contradictory -- 'lack of motion' would involve a situation where, say, a car is
parked half in, half out of a garage. Here the car is in one and the same place
and not in it (in and not in the garage), and it is in two places at once (in the garage
and in the grounds of the house),
even while it is at rest relative to a suitable inertial frame.
In which
case, the alleged contradiction Engels is interested in can't be the result of
motion; it is in fact a consequence of the vagueness or the ambiguity of his description.
This can be seen from the further fact that objects at rest relative to some inertial
frame can and do display the same apparent 'contradictions' as
those that are in motion with respect to the same inertial frame. Naturally, if things
at rest share the very same vague or ambiguous features (when they are expressed in language) as those
that are in motion, Engels's description clearly fails
to pick out what is unique to
moving bodies.
This is not a good start.
At
best,
L3 simply depicts the
necessary
but not the sufficient conditions for motion. In that case, the alleged
contradictory nature of L3 has nothing to do with
movement
actually occurring, since the same description could be true of bodies at rest,
which share the same necessary conditions. As already noted, alleged paradoxes
like this arise from the ambiguities implicit in the language Engels himself
used -- and, as it turns out, language he misused. [This will be discussed in greater
detail below.]
Nevertheless, in the next few sections several attempts will be
made to remove and/or resolve these
equivocations in order to ascertain what, if anything, Engels might have
meant by the things he tried to say about moving bodies.
First Attempt At Disambiguation
As will also be demonstrated in Essay Six
-- in relation to Trotsky's (and
indirectly
Hegel's) attempt to analyse the LOI --, Engels's account of motion is in fact
far too vague to be of much use.11a
[LOI = Law of Identity.]
I now propose the following disambiguation of Engels's comments about motion in
order to determine if there is any sense at all to be made of what he concluded
about moving bodies:
L5: A body B in
motion involves change of place such that:
L6: B is at
(X1, Y1, Z1) at
t1 and at
(X2, Y2, Z2) at
t1.
L7: (X1,
Y1, Z1) is not the same place as (X2, Y2,
Z2).
[Where,
(Xi, Yi, Zi)
etc., are coordinate triples, and t1 is a temporal variable.]
This opening set looks more promising.
However, it is worth noting that this clarity has only emerged because of the
introduction of the phrase "change of place", in L5. Unfortunately, if this
expression does
succeed in bringing out what Engels meant it would suggest that change
explains motion, not the other way round. Perhaps this minor difficulty can be
circumvented; I will leave that for others to decide.
[Still others, of course,
might wonder exactly how the word "change" could be explicated (given
this theory) 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 the latter
term would not alter the truth of L5, but it would make it eminently circular.]
However, even if this 'niggle' were resolvable, the initial promise the above
set of sentences seemed to offer soon evaporates when it is remembered that L5-L7
fail to rule
out cases where an extended body might move at a later time, say t2,
but not at t1. That is, B could still be
stationary at t1, and in two different places at once (because it is
an extended object), and at rest with respect to some inertial frame, with the subsequent motion taking place
at t2, not at
t1
-- as we saw above with that car.
The significance of this observation is 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 this object moved later, when we are
still owed a 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 of the
future predicted motion of this object will only attract the same criticisms --
that is, if
L5-L7 were merely replaced with propositions that just change the temporal
variable to t2,
while no other adjustments are made. This is because, 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
failed to do this originally.
L6-L8 below attempt to fix this glitch.
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 need to be made, it would seem:
L8: A body B in motion involves change of place
only at t1, such that:
L6: B is at
(X1, Y1, Z1) at
t1 and at
(X2, Y2, Z2) at
t1.
L7:
(X1, Y1, Z1) is not the same place as
(X2, Y2, Z2).
Of course, the same caveats could be applied to later
instants, so that such a description captures the movement of the body in question along its entire trajectory. That would merely entail the use of "ti"
in the place of "t1"
in L8 and L6. This complication will be ignored here, since it doesn't
seem to affect the points at issue.
Unfortunately, however, L6-L8 do not appear to imply a contradiction --, that
is, not unless it is clear that B is no
longer at
(X1, Y1, Z1) at
t1, since
it is possible for a body to be in two places at once. For example, few
would regard it as a contradictory feature of reality that a cake, say,
could be in a box and in a supermarket all at once, and stationary with
respect to some inertial frame all the while.
On the
other hand, if
a die-hard dialectician could be found who
thought
that that scenario was contradictory,
he/she
would need to explain to the rest of us exactly what this alleged contradiction amounted
to,
and
how, in virtue of its being in two such places at once, for example, the cake
involved
was
engaged in some sort of 'struggle', and against what it was 'struggling'! As we
will see in Essay
Seven,
the dialectical classicists
hold that objects turn into whatever their opposites are, that is, whatever
they turn into whatever they are contradicted by, or are 'struggling' with. In this example, that would seem to involve such cakes
'struggling' with and then turning into the buildings that housed them! Since no
one in their left mind could reasonably be expected to believe this, cakes in
supermarkets can't be
regarded as in anyway contradicting the bricks and mortar that surround them.
Anyone who still thinks this is advised to seek professional help.
So, in order to rectify this, we need to replace L6 with L9, as follows:
L8: A body B in motion involves change of place only
at t1, such that:
L9: B is at
(X1, Y1, Z1)
at t1 and not at
(X1, Y1, Z1)
at t1, and B is at
(X2, Y2, Z2)
at t1.
L7:
(X1, Y1, Z1) is
not the same place as
(X2, Y2, Z2).
Now, this set (henceforth called
ℒ)
certainly looks inconsistent. The question, though, is: Can all its constituent
sentences be false at once? Only if we can rule out that
eventuality is it possible to construct a contradiction from all and only
elements of ℒ.
[At this point it is worth
recalling that a set S of sentences is inconsistent just in case
not all of its elements can be true at once. But a "contradiction"
requires more than this. In the simplest case, the elements of a binary
sub-set of sentences formed from elements of S are contradictory just in
case (1) those elements are inconsistent and (2) they cannot also be false. In short, they cannot both be true
and they cannot both be false.
This salient fact
is invariably overlooked by DM-theorists, which, naturally, leads them into confusing
contradictions with inconsistencies and/or contraries -- and, in many cases, with a host of
other unrelated things, too. (Any who
object to the alleged 'pedantry' here should read
this first and
then think again.)]
The question is, therefore:
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.
[In fact L9
is an inconsistent sentence anyway, and hence it is 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 attends to).
But since DL is based on the claim that inconsistent sentences can be true,
I have ignored this
alleged
fact here because it would
beg the question.]
(2) L8 is linked to L9 by means of a "such that" phrase, so the truth or
falsehood of L8 is sensitive to the truth or falsehood of L9. Hence, when L9 is
false, L8 is, too.
(3) L7 could be false if
(X1, Y1, Z1)
was the same place as
(X2, Y2, Z2).
This would make L9 false, as well.
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 have noticed the illegitimate way in which the
schematic sentences of
ℒ (and others) have been interpreted here to derive this spurious
result. The reason for this ploy (and what its implications are) will be commented upon
presently.
Second Attempt At Disambiguation
From this point on it will be assumed that the difficulties with Engels's
account noted in the previous section (whether or not they are legitimate) can be resolved, and that there exists some way of reading his words that
implies a contradiction, and which succeeds in distinguishing moving from
motionless bodies.
Perhaps the following will suffice:
L10: For some body b, at some time t, and for
two places p and q, b is at p at t and not at
p at t, and b is at q at t, and p is
not the same place as q.
This looks pretty contradictory. With
suitable conventions about the use of variables we could abbreviate L10 a little
to yield this slightly neater version:
L11: For some b, for some t, for two places
p and q, b is at p at t and not at p at
t, and b is at q at t.
However, one point needs
underlining here: none of the strictures dialecticians impose on the LOI
must be allowed to stand if L11 is to work, otherwise we would lose the ability to talk about
"the same body", "the same time" or "the same place". This would also affect the
application of certain conventions governing the use of terms such as "same
variable", "same meaning" and "same reference". Hence, if we are to depict the
contradictory nature of motion successfully we are forced to accept as valid
the application of the LOI to the use of the same words
and the same variables ranging over temporal instants (but, as a rule of language,
not a
'logical truth' -- why this is so is explained in Essay Twelve
Part One). Since protracted
examples of motion take place over very long time periods, we can't appeal to the relative stability of
language to fix the reference of these variables (or that of
their ordinary language counterparts), if the LOI is not applicable in all cases.
[MFL = Modern Formal Logic; LOI = Law of
Identity.]
But, if the LOI is rejected then Engels's description would become irredeemably vague.
Many of the 'spurious' objections rehearsed
toward the end of the previous section (in relation
ℒ) depended on
ignoring some or all of these conventions; as a result those objections were
entirely illegitimate. Of course, that ploy itself was aimed at highlighting
this very point: the use of variables in FL is based on conventions that
DM-theorists must themselves observe (in ordinary discourse, and/or in logic) if
Engels's analysis of motion is to be rendered comprehensible, but which
conventions vitiate their own criticisms of the LOI! Naturally, it is a moot point which horn of this dilemma they will want
to "grasp": either accept the Hegelian criticisms of the LOI and sink Engels's
analysis of motion, or accept Engels's account and abandon Hegel's
criticism of the LOI.
It could be objected that the above comments represent a caricature of
the criticisms that dialecticians make of the LOI. The relative stability of
both material bodies and linguistic expressions permits them to talk
about such things as the "same body", the "same word", the "same variable", and so on.
Moreover, dialecticians do not flatly deny the LOI, they just claim that it is
true only within certain limits. In addition, they hold that objects and
processes in change possess "identity-in-difference".
These responses are considered in detail in
Essay Six
(the relative stability argument, for example, is neutralised
here); 'dialectical contradictions'
themselves are analysed in
Note 1 and
here.
Of course, hard-nosed dialecticians might choose to ignore MFL
altogether. That is, of course, their right. But they would then find it rather
difficult to say what Engels actually meant in the quoted passage above. [Anyway, that
bolt hole will be blocked later on in this Essay.]
Unfortunately however, even as it stands, and despite the foregoing (that is, if the contentious claims made
above about the LOI and MFL are indeed misconceived, and are thus withdrawn), L11
would still fail to be a logical contradiction, and that is because of several more annoying ambiguities.
In fact,
this new batch of vagaries turns out to be far more intractable than
the relatively minor ones considered so far.
A Fatal Ambiguity
This latest set of equivocations
revolves around the supposed reference of the "t" variable in L11:
L11: For some b, for some t, for two places
p and q, b is at p at t and not at p at
t, and b is at q at t.
It is always possible to argue
that L11 really amounts to the following:
L12: For some b, during interval T,
and for two 'instants' t1 and t2
[where both t1 and t2
belong to T, such that t2
> t1], and for two places p and q, b is
at p at t1, but not at p at t2,
and b is at q at t2.
[In the above, t1 and t2 are
themselves taken to be
sets of nested sub-intervals,
which can be put into an
isomorphism with suitably
chosen intervals of
real numbers; hence the
'scare' quotes around the word
"instant" in L12. (Incidentally,
t2
> t1
means that t2
is later than t1.)]
Clearly, the implication here is that the unanalysed variable "t" in L11
actually picks out a time
interval T (as opposed to an instant in time) -- brought out in L12
-- during which the
supposed movement takes place. This would licence a finer-grained discrimination
among T's sub-intervals (i.e., t1 and t2) during
which this occurs.12
Two possible translations of L12 in less formal
language might read as follows:
L12a: A body b, observed over the course of a second, is
located at point p in the first millisecond, and is located at q a
millisecond later.
L12b: A body b, observed over the course of a
millisecond, is located at point p in the first nanosecond, and is
located at q a nanosecond later.
And so on…
Indeed, this is how motion is normally
conceived: as change of place in time -- i.e., with time having advanced
while it occurs. If this weren't so (i.e., if L12 is rejected), then L11 would imply that the supposed change
of place must have occurred outside of time -- or, worse, that it happened
independently of the passage of time --, which is either incomprehensible (as
even Trotsky would have admitted), or it would imply that, for parts of
their trajectory, moving objects (no matter of how low their speed) moved with
an infinite velocity! [This was pointed out
earlier.]
And yet, how else are we to understand
Engels's claim that a moving body is actually in two places at once? On
that basis, a moving body would move from one place to the next outside of
time -- that is, with time having advanced not one instant. In that case, a
moving body would be in one place at one instant, and it would move to another
place with no lapse of time; such motion would thus take place outside
of time. But, according to Trotsky,
that sort of motion wouldn't exist, for
it would not have taken place in time.
Indeed, we would now have no right to say that such a 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.] By a
suitable induction clause, along the entire trajectory of a body's motion it
would not, therefore, be possible to say that a moving body was at the beginning of
a journey before
it was at the end!
[The reasons for saying this will be detailed
below, but the
latter conclusion depends on the argument presented
here, which should be read
first. Trotsky's worries about instants are
examined below, and in Essay Six. The
contrary idea that if a body is located at a point
at an instant, it must be stationary, is also examined below.]
Despite this it would seem that this latest difficulty can only
be neutralised by means of the adoption of an implausible
stipulation
to the effect that whereas time isn't composed of an infinite series of
embedded sub-intervals -- characterised by suitably defined
nested sets of real
numbers --, location is.
[Naturally, such a stipulation would have to reject Trotsky's strictures on
events taking place only in time.]
This would further mean that while we may
divide the position a body occupies as it moves along as finely as we wish -- so that no matter
to what extent we slice or magnify a body's location, we would always be able to
distinguish two contiguous (or proximate) points allowing us to say that a moving body was
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.
Clearly, this is an inconsistent approach to
the divisibility of time
and space -- wherein we are allowed to divide one of these (space) as
much as we like, while the same is disallowed of the other (time).
[It could even be
argued that this is where the alleged 'contradiction' originally arose -- it was
introduced into this 'problem' right at the start by this inconsistent
(implicit) assumption, so no wonder it emerged at a later point -- no puns
intended.]
This protocol
might at first sight seem to neutralise an earlier objection (i.e., that even though a moving body might be in two
places, we could always set up a one-one relation between the latter and two
separate instants in time, because time and space can be represented as equally fine-grained),
but, plainly, it
only achieves this by stipulating (without any justification) that the successful mapping of places onto
nested intervals of real
numbers (to give them the required
density and
continuity) is
denied of temporal intervals.
The Classical
Response
So, there seem to be three distinct possibilities with
these two separate variables (i.e., concerning location and time):
(1) Both time and
place are infinitely divisible.
(2) Infinite divisibility is true of location only.
(3) Infinite divisibility is true of either but not both (i.e., it is true of time but not place, or
it is true
of place but not time).
Naturally, these aren't the only alternatives, but they seem to be the only
ones that are relevant to matters in hand.
Of course,
one particular classical response to this dilemma ran along the lines that the infinite
divisibility of time and place implies that an allegedly moving body is in fact
at rest at some point. Hence, if we could specify a time at which an object
was located at some point, and only that point at that time, it must be at
rest at that point at that time. [This seems to be how Zeno at least argued.]
Nevertheless, it seemed
equally clear to others that
moving bodies can't be depicted in this way, and that motion must be an
'intrinsic' (or even an 'inherent' property)
of moving bodies (that is, we can't depict moving bodies
in a way that would imply they are stationary), so that at all times a moving body must be in
motion, allowing it to be in and not in any given location at one and the same
time. [This seems to be Hegel's view of the matter -- but good luck to anyone
trying to find anything that clear in anything he wrote about this topic!]
If so, one or more of the
above options must be rejected. To that end, it seems that for the latter set of individuals
1) and 3) must be dropped, leaving only 2):
(2) Infinite divisibility is true of location only.
However, it
is worth pointing out that the paradoxical conclusions classically
associated with these three alternatives only arise
if other,
less well appreciated (often implicit) assumptions are either left out of the picture
or are totally ignored
-- i.e., in addition to those alluded to above concerning the continuity
of space and the (assumed)
discrete nature of time. As it turns out, the precise form taken by
several of these suppressed and unacknowledged premisses depends on what view is taken of
the allegedly 'real' meaning of the words like "motion" and "place".
In Essay Three
Part One
and Essay Twelve Part One, it was
argued that philosophical 'problems' of this sort only arise when ordinary words are
twisted beyond recognition (which view, incidentally, was
endorsed by Marx), and
the
new conventions for the use of such
terms that emerge as a result are
then misinterpreted as super-empirical truths, not conventions at all.
In short,
the 'classical' approach only gets off the ground if linguistic
conventions/stipulations, and/or rules, are mistakenly viewed as
Super-Scientific, mega-empirical propositions, or
as matters of fact.
That is, this approach mistakes an implicit
decision to use words in a novel way as a fundamental truth about reality
itself. It misconstrues the medium for the content.
Indeed,
this is precisely how
theorists (in ancient Greece) began to misread
the products
of social relations (conventions/rules) as if they were the real relations
between things, or even as those things themselves (thus
fetishising
language). Because of this they imagined they could 'derive' Super-theses
like these from
the 'philosophical' jargon they had invented.
As a result of this 'wrong turn' (although there were clear
ideological motives for taking it -- on this, see below and
here), Traditional Philosophers
reasoned that the word "motion", for example, implied there was some sort
of 'problem' (or 'contradiction', or 'paradox'), which needed to be resolved. Few, if
any, questioned the original distortion/fetishisation that had been inflicted on ordinary words
(for
motion, place and change), which linguistic deformation had artificially created such 'difficulties'.
That is
because, of course, these thinkers came from those sections of society that
had
been divorced from
the world of
collective labour and communal life, and whose theories reflected the ideal view
of reality this privileged life-style encouraged. For the same reason it also
arose from an ideologically-motivated denigration of the vernacular.
[These allegations
will be fully-documented in Essay Twelve (summary
here).]
So, in their view, if the
world is ultimately Ideal, it would of course be quite 'safe' to infer
Super-Scientific truths about it from language
alone, as we saw George Novack point out
earlier.
The fact
that the classical 'paradox' of motion was based solely on a set of initial
(surreptitious and, as it turns out, illegitimate and unacknowledged)
false
linguistic
moves like this is confirmed by the further fact that the acceptance or rejection of one
or more of the three options listed above (repeated below)
can't be (and has never been) based
on evidence of any sort. Severally or collectively, each of these
alternatives is founded on a linguistic convention overtly or covertly
accepted by all parties to this metaphysical
con-trick,
one that uses what is supposed to be the 'real'
meaning of the word "motion" -- or, indeed, the 'real' meaning of any of the
other terms associated with it (such as "place", "same", "time"
and "instant").
Moreover,
the choice of one or more of options (1) to (3) (as a way motivating a favoured
'solution' to this artificially-induced 'problem') also depends on the idea that
even if the specification of the location of a body is in no way problematic (in that we can always declare that a moving body is in
two places at once), the specification of time is.
Thus
while the identification of point
instants in time was seen to be the 'problem',
the specification
of points in
space hardly raised a eyebrow. With respect to DM, this can be seen by the way
that Trotsky, for example,
failed to draw the same conclusions about locations
in space that he drew about points in time.12a
(1) Both time and
place are infinitely divisible.
(2) Infinite divisibility is true of location only.
(3) Infinite divisibility is true of either (i.e., of time but not place, or
of place but not time).
Nevertheless, these appear to be among the fundamental issues that have
exercised philosophers for millennia -- and now dialecticians. In their 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 implicitly opted for alternative (2):
(2) Infinite
divisibility is true of location only.
[With
the word "indefinite" perhaps replacing "infinite" here in some cases.]
As has
already been noted, this
choice was motivated by a surreptitious exclusion: the indefinite division of time was
ruled out, while that of position wasn't.13
Finally,
but more importantly, the traditional metaphysical 'solutions' that have been on offer
for centuries were
also based on the rejection of
at least
one implication of the ordinary understanding of motion, which
is that moving bodies occupy different places at different times. This is
such a mundane connotation of our every day grasp of certain kinds of motion 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.
However, as we shall soon see (and again in
several other
Essays
posted at this site), the protocols of ordinary language and common understanding are not so easily
ignored, dismissed,
or depreciated.
Back To The Drawing-Board
The Devil In The Detail
However,
there are (and can be) no (a priori) empirical constraints on the length of
time intervals. In fact,
as was also noted above, Engels's account of motion was not (and
could not have been) derived from observation, mediated via the naïve or
the sophisticated version of the RTK. Nor could his idea of 'motion in general'
--
nor, indeed, of 'abstract motion' -- have been materially-grounded, either.
[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 discrimination
sufficiently fine-grained enough to allow the study of
movement in the detail required, so that 'reflection' (or 'abstraction') could
be presented with anything useable to work with, or upon, in order to decide
what does or does not happen to moving bodies in an 'instant'.
And it is little use objecting that this or that
'must' be true of 'motion itself', for that would be to concede the fact that a 'must'
like this had been
derived from the meanings of a few words, which words, as we will soon see,
are far less straight-forward than traditional theorists would have us believe.
It could be objected that
the classical analysis of motion follows deductively from certain incontestable
premises. There are only a handful of possibilities that the world could
conceivably present to us; Engels's analysis, via Hegel, is based on one of these. So, what's the
problem?
Once more, the problem is
that the deducibility or
otherwise of these conclusions depends on the use of several artificially
modified/constrained words (such as "place", "move", "time", "moment", etc.), which have
either been idiosyncratically, or narrowly (re-)defined, or which have had their meanings
altered in other ways.
In that case, nothing reliable can follow from them (as I hope to show
later in this Essay). This was, of course, the point
Marx was trying to make.
Even worse, not only does
nothing follow from such distorted language (or abstract 'concepts'), it is impossible
to give a clear sense (or any sense) to the classical account (nor, indeed, to more modern versions
of it that depend upon
the same defective tradition). In fact, as will be demonstrated in
Essay Twelve Part One, all
such accounts are non-sensical
and
incoherent; they not only do not say anything comprehensible
about the world, they
can't.
In that
case, if humanity does in fact possess an
'abstract'
idea of motion (but this will be contested below,
and in other Essays posted at this site), it can't have been derived
from
'reflection', nor could it have been based on anything found in the material
world. And those observations become all the more
apposite
if this allegedly
'abstract'
idea of motion itself originated from (a) The inequitable
constraint mentioned above -- i.e., that which was arbitrarily imposed on the allowable length of temporal intervals, but excused
of point locations in space --,
for no good reason; and (b) A
ruling-class view of reality.
In
short, Engels's theory wasn't based on reflection (howsoever this 'process' is
understood), or on evidence, or even on 'abstraction', but only on 'concepts' that are
themselves the product of traditional/classical
stipulations (or covert conventions) -- which were then
imposed
on reality inequitably!
Space To Let
Returning now to consider several earlier options:
L11: For some b, for some t, for two places
p and q, b is at p at t and not at p at
t, and b is at q at t.
L12: For some b, during interval T,
and for two 'instants' t1 and t2
[where t1 and t2
belong to T, t2
> t1], and for two places p and q, b is
at p at t1, but not at p at t2,
and b is at q at t2.
(2) Infinite divisibility is true of location only.
[L12a: A body b, observed over the course of a second, is
located at point p in the first millisecond, and is located at q a
millisecond later.
L12b: A body b, observed over the course of a
millisecond, is located at point p in the first nanosecond, and is
located at q a nanosecond later. And so on…]
However,
if for some reason L12 were to be rejected as an alternative interpretation of L11 (that
is, if the idea that time is continuous and indefinitely divisible is flatly denied (while
this condition is asymmetrically allowed of space) -- i.e., if option (2)
above is
imposed on the phenomena)
--, then there seems to be no consistent way of ruling out the following as yet
another possible reading:
L13: For some b, for just one instant t, for
three places p1, p2 and p3,
b is at p1 at t, but not at p2
at t, and b is at p3 at t
(where p2
and p3 are proper parts of p1).
Here, a finer-grained discrimination of
position (but not of time) means that L13 is not contradictory at all, since a body can be
in two places at once whether it moves or not (as we have seen), with no
implication that it both is and is not in any one of them.14
Translated, L13 could be read
as follows:
L13a: A stationary body b, observed over the course of
an instant, is at
(X1, Y1, Z1) and
(X3, Y3, Z3), but not at
(X2, Y2, Z2), where
(X3, Y3, Z3)
and
(X2, Y2, Z2)
are both located inside
(X1, Y1, Z1).
L13b: A moving body b, observed over the course of an
instant, is at
(X1, Y1, Z1) and
(X3, Y3, Z3), but not at
(X2, Y2, Z2), where
(X3, Y3, Z3)
and
(X2, Y2, Z2) are both located inside
(X1, Y1, Z1).14a
[An obvious objection to the above is neutralised in Note 14a
(link above).]
An everyday example of L13 might involve a case where a ship, say, enters port:
here the ship could both be in the water and in the port at the same time (and hence simultaneously extended across several locations,
and thus be in at least two places at once), and be moving, but with no
implication that it is entirely in any one of these at one and the
same instant, or that it is fully occupying any specific part at any moment,
nor yet occupying every point in this finite region (so that it need not
be in other areas of that port, for example, at that time). In the latter case,
while it is still inside the said port it wouldn't be in,
say, the dry dock (which is also part of that port),
nor in the staff canteen, nor in a host of other places in that port, at that time.
Moreover, if the ship were stationary with respect to some inertial frame, the
same possibilities would still apply. Here, this ship
could be in one place and not in it (fully), and in two or more places at
once, and stationary (or moving), and yet imply no contradiction. That is
because this particular example employs a finer-grained division of place to compensate
for the arbitrary imposition of the opposite convention on time.
In that case, the alleged contradiction vanishes once again.
[I have given a more technical version of this scenario in Note 15.]15
As pointed
out above, L12 and/or L13 can only be rejected successfully by an ad hoc
stipulation to the effect that while spatial location
can be
divided indefinitely, time may not.
But,
even then we have just seen that Engels's claims still don't work!
In which
case, of course, the allegedly contradictory nature of motion
is at best an artefact of convention -- which
only
works by constraining the divisibility of time but not of place --;
hence it isn't
one based on any genuine features of reality.16
At worst,
it is the product of a
confused use of philosophical jargon.
Further Problems
Pick Your 'Contradiction'
It could be objected to all
this that while it might not be possible to express the contradictory
nature of motion in ordinary (or even technical) language,17 motion in
the real world must nevertheless be contradictory.18
This might involve the acceptance of one or more of the following (but so far
suppressed) assumptions:
L14: An object can't be in motion and at rest at one and the
same time (in the same inertial frame).18a
L15: If an object is located at a point it must be at rest at
that point.18b
L16: Hence, a moving body can't 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 argued that L14-L16 (or their 'dialectical' equivalent) capture the
rationale behind Engels's analysis of motion.
Indeed, if this weren't so, it would suggest that motion was either (a)
impossible or (b) illusory --, or even (c) that it was a sort of 'stop-go' affair.18c
As far as (c) is concerned, motion would be
analogous to the way movement is depicted by, say, the use of film. Here, motion only appears
to be continuous when it is in fact discontinuous, being composed of
rapidly sequenced 'freeze frames', as it were. When played at a certain speed,
this 'fools' the human eye into 'seeing' continuous movement. Given this
'quasi-static' view of motion, a 'moving' body (in the real world, not on film!)
would occupy a point and be stationary at that point, and then occupy another
point an instant later, and be stationary there too, and so on. Naturally, what
the said object gets up to in between such locations at such times would be, on
this view, somewhat mysterious. But, on its own, that wouldn't be enough to make this picture of motion false, no
more than quantum discontinuities now invalidate QM --
that is, given the way that motion is depicted in Traditional Philosophy.19
[QM = Quantum Mechanics.]
Options (a)
and (b) above are absurd and won't be considered in this Essay.
In order to
reject this 'quasi-static' view (i.e., option (c)), consideration might be given to
one or more of
the following
(each defined in relation to a suitable
inertial frame, as necessary):
L18: If a
body is located at a point it is at rest.
L19: If that body subsequently occupies another point, it
must be at rest there, too.
L20: Hence, on this view (i.e., according to (c)
above), motion is no more than successive point
occupancy. This means that locomotion must be composed of either: (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 moment of location/rest, followed by the
subsequent entry into existence of a new, but seemingly identical body at the
next moment, at the new point, giving only the impression of motion.
[Option (ii) would resemble the way that neon lights in a complex sign, say, can be turned on and off in sequence to create the illusion of motion.
It seems Leibniz held a version of this
theory.]
L21: L20(i) involves a body in discontinuous motion
separated by periods of instantaneous rest. L20(ii) involves 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 intervening locations.
[Of course, this depends on the further
assumption that there are an
infinite, or a potentially infinite, number of points between any two
points.]
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. In that case, that body can't be at rest at 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 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 will not be pursued further here:
L27a: Therefore, either motion is impossible
or illusory (which is absurd), or motion can't be discontinuous.]19a
However, it is worth noting that the
above argument begins with the rejection of an apparent contradiction --
that which is expressed in L14 (restated here for ease of reference, but
re-numbered
L28, and hence very slightly altered) 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 are genuine contradictories; I will
ignore that minor complication here. On the other hand, if they aren't even
propositions, then they cannot be contradictories to begin with.
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
Hence, if
these 'niggles' are ignored,
L29 is true if L28 is false, and vice versa.
As is well-known, an analogous series of assumptions motivated Zeno to
try to
'prove' that motion was either impossible or illusory. DM-theorists obviously
reject Zeno's conclusion, but it seems they can only do that by accepting L28
(or its equivalent), and by rejecting L29, 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 true) -- which would mean that a body could be moving and at rest at
the same time --,
L17 might not look quite so compelling.
At any rate, it is clear that dialecticians have to reject one 'contradiction' (expressed
in L29) in order to derive their own (in L17).
Now, when
L17 is conjoined with L28 we obtain the following:
L17a: Since a body 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
so, it is worth asking: Which one of the following 'contradictions' is it
legitimate to accept or reject: L17 or L29?
L17: A moving body must both occupy and not occupy a point at
one and the same instant.
L29: A body can be at rest and in motion at the same time
in the same inertial frame.
Which of these
'contradictions' is the
more absurd? If L29 is true, it looks like L17a cannot be derived in any
obvious way from the sorts of considerations advanced in
L14-L27. This would mean that Engels's analysis is defective
--
always assuming, of course, that his 'argument' depends on such considerations
and that some sense can be made of anything he said in this regard.
Nevertheless, it is clear
from the way that the above argument has been constructed that L17a itself
depends on the truth of L28 (repeated here again for ease of reference):
L28: A body 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.
That is because L14-L27 began
with the assumed truth of L14 -- or, its equivalent, L28. The reverse
implication doesn't appear to hold. This means that L28 does not seem to pre-suppose
the truth of the conclusion drawn in L17a, whereas the conclusion drawn in L17a looks like it depends on L28. This in turn suggests
that L28 might be the more fundamental of the two.
[L14: An object can't be in motion and at rest at one and the
same time (in the same inertial frame).]
Be that as it
may, L28 is itself false if L29 is 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
rule this out. In order to eliminate this new difficulty, therefore, L29 must be
modified; perhaps in the following manner:
L30: With respect to the same inertial frame and the
same instant in time, a body can be at rest and in motion.
[L30 'contradicts' L30a:
L30a: With respect to the same inertial frame and the
same instant in time, a body can't be at rest and in motion.]
L30 now certainly looks 'contradictory'
(especially if "at rest" is taken to mean "not in motion with respect to the
same inertial frame").
Nevertheless, it was the rejection of L30 (or its equivalent) that led to the
derivation of L17a. Hence, if L30 is always false (i.e., if L30a is always
true), it looks like L28 must always be true, too (given certain other assumptions, and if
worded appropriately).
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.
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! This 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 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 located wholly at any other point in the same reference frame at the same
time.
L33: But, a moving body must be located wholly at two points
at the same time, otherwise it would be at rest.
L34: Since L33 is impossible (by L32), motion
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 decide. But, L31-L34 demonstrate that L17a doesn't have
to follow from the rejection of L30, even if the alternative outcome proves
unpalatable.
It is now clear that the
refusal to accept the 'contradiction' contained in L30 can lead to two
distinct 'contradictory' conclusions. One of them is inconsistent with experience (i.e., the
latter half of L34, i.e., L34b), while the other is self-contradictory (i.e., L17a):
L17a: Since a body 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 these two
outcomes proves to be the least unacceptable will depend on other
priorities. If it is felt that experience is unreliable, L34b might be
preferable. On the other hand, if contradictions are regarded as fundamental
features of reality, and appearances are held to be deceptive, or unreliable,
L17a might well be chosen. It is also worth noting, however, that neither option is
empirically verifiable; in fact they both transcend any
conceivable body of evidence and all possible experience.21
Nevertheless, given the fact that dialecticians also believe that
appearances contradict underlying 'essences' they are the last ones who can
legitimately appeal to experience to refute Zeno-esque conclusions like L34b. In fact,
if the DM-thesis that underlying 'essences' 'contradict' appearances is itself
true, then, since
it appears to be the case that there are moving bodies, in 'essence' the opposite
must be the case! Hence, if appearances 'contradict' reality it seems that, essentially,
no bodies move, and Zeno was right after all!
Putting this annoying corollary to one side for now, it is worth
emphasising that both halves of these two 'derivations' rely on the sorts of
ambiguities encountered earlier with respect to L1-L13 (alongside several others analysed below).
Aprioristic 'arguments' like these only seem to work because they are shot-through with equivocation
and distortion; indeed,
this is partly why the above two conclusions finally descend into
absurdity and incoherence -- as we are about to discover.
Theatre Of The Absurd
The absurdity in L34b
is quite plain for all to see and needn't detain us any
longer. However, the ludicrous nature of L17a
isn't
perhaps quite so obvious. It
may nevertheless be made more explicit by means of the following argument:
L35: Motion implies that a body is in one place and not in it
at the same time; that it is in one place and in another at the same instant.
L36: Let A be in
motion and at
(X1, Y1, Z1), at
t1.
L37: L35 implies that A is also at some other
point -- say,
(X2, Y2, Z2), at
t1.
L38: But, L35 also implies that A is at
(X2, Y2, Z2) and at another place at
t1;
hence it is also at (X3, Y3, Z3),
at t1.
L39: Again, L35 implies that A is at
(X3, Y3, Z3) and at another place at
t1;
hence also at (X4, Y4, Z4), at
t1.
L40: Once more, L35 implies that A is at (X4, Y4, Z4) and at another place at
t1;
hence also at (X5, Y5, Z5), at
t1.
By n successive applications of L35 it is
possible to show that, as a result of the 'contradictory' nature of motion, A
must be everywhere in its trajectory if it is anywhere, and all at t1!22
But, that is even more absurd than L34b!
L34b: Despite appearances to the contrary, all bodies are
at rest.
The only way to avoid such an outlandish conclusion would be to maintain that L35
implies that a moving body is in no more than two places at once. But
even this wouldn't help, for if a body is moving and in the second of those two
places, it can't then be in motion at this second location -- unless,
that is, it were
in a third place at the very same time (by L15 and L35). Once again,
just as soon as a body is located in any one place it is at rest
there, given this way of viewing things. The proposed dialectical derivation outlined above required
that
very assumption, repeated here:
L15: If
an object is located at a point it must be at rest at that point.
L35: Motion implies that a body is in one place and not in it
at the same time; that it is in one place and in another at the same instant.
Without L15 (and hence L35), Engels's conclusions wouldn't follow; so on this 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 just what creates this latest
problem: if that body is located at that second point, it must be at rest there,
unless it is also located at a third point at the same time.
This itself follows from L17 (now encapsulated in L17b):
L17: A moving body must both occupy and not occupy a
point at one and the same instant.
L17b: A moving object must occupy at least two
places at once.
Of course, it could be argued that L17b is in fact true of the
scenario depicted in L35-L40 -- the said body does occupy at least two places at once namely
(X1, Y1, Z1)
and (X2, Y2, Z2).
In that case, the above objection is misconceived.
Or, so it might be maintained.
The above objection would
indeed be misconceived if Engels had managed to show that a body can only 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, and if the
body is in
(X1, Y1, Z1)
and (X2, Y2, Z2),
at t1 then
it must also be in any point between
(X1, Y1, Z1)
and (X2, Y2, Z2),
at t1
--,
say
(Xk, Yk, Zk).
But, as soon as that is admitted, there seems to be no way to avoid the
conclusion drawn above: if a moving body is anywhere it is everywhere, at the same time.
[And that is
why the question
was posed earlier about
the precise distance between the points at/in which Engels says a body performs
such 'contradictory' marvels.]
On the other hand, the combination here of an "at least two places at once"
with and an "at most two places at once" would amount to an "exactly two
places at once".
L17d: A moving object must occupy exactly two
places at once.
L15: If
an object is located at a point it must be at rest at that point.
Any attempt made by DM-theorists to restrict a moving body to
the occupancy of exactly two places at once would work only if that body came to rest at the second of
those two points! L15 says quite clearly that if a body is located at a
point (even if this is the second of these two points), it must
be at rest at that point. In that case, the above escape route will only work
if DM-theorists reject their own characterisation of motion, which was
partially captured by L15. [This option also falls foul of the
intermediate points
objection, above.]
In that case, if L15 still stands, then at the second of
these two proposed DM-points (say, (X2, Y2, Z2)),
a moving body must still be moving, and hence in and not in
that second point at the same instant, too.
It is worth
underling this conclusion: if a body is located at a second point (say, (X2, Y2, Z2)) at
t1,
it will be at rest there at t1, contrary to the assumption
that it is moving. Conversely, if it is still in motion at t1,
it must be elsewhere also at t1,
and so on. Otherwise, the condition that a moving body must be both in a place
and not in it at the very same instant will have to be abandoned. So,
DM-theorists can't afford to accept L17d.
Consequently, the unacceptable outcome --, which holds that as a result of the
'contradictory' nature of motion, a moving body must be everywhere along
its trajectory, if it
is anywhere, at the same instant -- still follows.
Again, it could be objected that when body A is in the second
place at the same instant, a new instant in time could begin. So, while
A
is in (X2, Y2, Z2)
at t1, a
new instant, say t2,
would start.
To be sure, this ad hoc amendment avoids the disastrous implications
recorded above. However, it only succeeds in doing so by introducing several new difficulties of its own, for this would mean that
A
would be in (X2, Y2, Z2) at
t1
and at t2,
which would plainly entail that A was located in the same place at two different times,
and that in turn would mean that it was stationary at that point!
It could be objected, once more, that A-like objects
occupy two places at once, namely
(X1, Y1, Z1)
and (X2, Y2, Z2),
so the above argument is defective. Indeed, this is why the above 'derivation'
-- i.e., the one that show that a moving body must be everywhere along
its trajectory, if it is anywhere, at the same instant -- can't work. We can perhaps clarify this objection by means of the following:
L38: L35 also implies that A is at
(X2, Y2, Z2) and at another place at
t1,
hence it is also at (X3, Y3, Z3)
at t1.
[L35: Motion implies that a body is in one place and not in it
at the same time; that it is in one place and in another at the same instant.]
The idea here is that if we select, pair-wise, any two
points that a body occupies in any order (either
(X1, Y1, Z1)
and (X2, Y2, Z2),
or
(X1, Y1, Z1)
and (X3, Y3, Z3),
or
(X1, Y1, Z1)
and (Xn, Yn, Zn),
and so on), then L17c will still be satisfied:
L17c: A moving object must occupy at most
two places at once.
Unfortunately, this seemingly promising escape route turns into yet another cul-de-sac.
Here is why:
It was maintained that Engels just needed a body to be in any two
places at once. But, the third place above -- (X3, Y3, Z3)
-- isn't implied by his description of the
'contradiction' involved. L38 only works by ignoring the fact that the
other place that A is in is precisely
(X1, Y1, Z1);
so, it can't be
in
(X3, Y3, Z3)
at that time --, or it doesn't have to be, which is all that is needed.
So, when A is both in
(X1, Y1, Z1)
and
(X2, Y2, Z2),
and
(X1, Y1, Z1)
and (X3, Y3, Z3),
and so on, it can't be in at most two places at once, since it is in this case in more than
two. So, the use of "and" scuppers this line of defence.
It could be objected that the above response only works because
an "and" has been substituted for an "or". The original response in fact argued
as follows:
R1: If we select pair-wise any two
points a body occupies in any order (either
(X1, Y1, Z1)
and (X2, Y2, Z2),
or
(X1, Y1, Z1)
and (X3, Y3, Z3),
or
(X1, Y1, Z1)
and (Xn, Yn, Zn),
or..., and so on), then L17c will be satisfied.
But not:
R2: If we select pair-wise any two
points a body occupies in any order (i.e.,
(X1, Y1, Z1)
and (X2, Y2, Z2),
and
(X1, Y1, Z1)
and (X3, Y3, Z3),
and
(X1, Y1, Z1)
and (Xn, Yn, Zn),
and...,
and so on), then L17c will be satisfied.
Unfortunately, once more, this reply just catapults us back to an
earlier untenable position, criticised above, as follows:
"This is because, between any two points there is a third point, and if the
body is in
(X1, Y1, Z1) and (X2, Y2, Z2),
at t1 then
it must also be in any point between
(X1, Y1, Z1) and (X2, Y2, Z2),
at t1 --, say
(Xk, Yk, Zk).
Once that is admitted there seems to be no way to forestall the conclusion drawn
above that if the body is anywhere it is everywhere at the same time."
In that case, the reply encapsulated in L38/R1 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, say,
(Xk, Yk, Zk),
also at t1.
In that case, R2 is still a valid objection.
In order to see this, a few of the subscripts in R2 need only be
altered, as follows:
R3: If we select pair-wise any two
points a body occupies in any order (i.e.,
(X1, Y1, Z1)
and (X2, Y2, Z2),
and
(X1, Y1, Z1)
and (Xk, Yk, Zk),
and
(X1, Y1, Z1)
and (Xi, Yi, Zi),
and so on), then L17c will not be satisfied.
It is surely philosophically irrelevant whether we label such
points with iterative letters (i.e., "k" or "i") or with
numerals ("1", "2" or "3"). [Recall, the points labelled with iterative letters
(i.e., "k" or "i") are intermediate points.]
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,
(Xk, Yk, Zk),
at the same moment.
R3 thus implies
that L17c is false.
L17c: A moving object must occupy at most
two places at once.
Since there is a
potentially infinite number of points
between any two points, there is no way that L17c can be true.
Moreover, it is also worth asking of L38: Is A at
(X2, Y2, Z2), at t1?
If it is, then it must be elsewhere at the same time, or it will be stationary,
once more.
So much is agreed upon. In that case, the only way to stop the absurd induction
(i.e., that which derived the conclusion that if a moving body is anywhere it
must be everywhere) would be to
argue as follows:
L38a: L35 also implies that A is at
(X2, Y2, Z2) and at another place at
t1,
hence it is also at (X1, Y1, Z1),
at t1,
but not at (X3, Y3, Z3),
at
t1.
[L38: L35 also implies that A is at
(X2, Y2, Z2) and at another place at
t1,
hence it is also at (X3, Y3, Z3),
at t1.]
However, this 'straw', once clutched, has unfortunate
consequences that desperate dialecticians might want to think about before they
claw at it too eagerly:
L38b: If A is at
(X2, Y2, Z2)
and (X1, Y1, Z1),
at t1,
but not at (X3, Y3, Z3),
at t1,
then it must be at (X3, Y3, Z3), at
t2.
L38c: If so, A will be at two places --
(X2, Y2, Z2)
and (X3, Y3, Z3)
-- at different times (i.e.,
(X2, Y2, Z2),
at t1,
and (X3, Y3, Z3),
at t2).
L38d: In that case, between these two locations
(i.e., (X2, Y2, Z2)
and (X3, Y3, Z3)), the motion
of A will cease to be contradictory -- since it will not now be in
these two places at the same time, but in these two places at different times.
Hence, dialecticians can only escape from
the absurd consequence that their theory implies that a moving object is
everywhere at the same time by abandoning their belief in the contradictory
nature of motion at an indefinite number of locations intermediate in its transit
-- for
example, right after it leaves the first two places it
occupied in its journey!
It now looks like DM-theorists can only counter the above criticisms, and
maintain their view that motion is 'contradictory', if they are prepared to
impose
several more ad hoc stipulations on nature (of the sort mentioned
above, none of which seem to work
anyway).
But, as we have seen
several times already, such a response would be fatal to DM since it would
undermine their belief that reality itself is contradictory (rather than
just the things we say about it that are), all the while confirming the
suspicion that it is only certain ways of representing nature that
appear to be contradictory --
which "ways of representing nature", incidentally, still await clarification.
This option would, of course, mean that this
part of DM (at least) is thoroughly conventional, and thus entirely
subjective -- and still defective!
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 'necessary truths' (i.e., a priori 'theses') about
reality. Such theses are based solely on an extrapolation from the supposed
meaning of a few specially-selected words to fundamental truths about the universe, valid for all of
space and time.
Clearly, with respect to Engels's analysis of motion, this predicament is
further compounded by an attempt to
circumvent several fundamental conventions found in our use of ordinary language --, such as those
expressed by the LOC and the LOI. [I will endeavour to substantiate these claims
below, and in detail in Essay Twelve
Part One.]
[LOC = Law of Non-contradiction; LOI = Law of
Identity; FL = Formal Logic; DL = Dialectical Logic.]
Finally, it could be argued that the above criticisms
beg the
question, since dialecticians do not doubt the application of principles drawn
from FL -- such as the LOC --, they merely point to their limitations when
confronted with change and motion. That rather odd claim is neutralised in Essay
Four and
Essay Eight Parts One and
Three.
Suffice it to say here that dialecticians themselves have yet to account for motion in
anything like a comprehensible form -- or even depict it accurately! So, whether
or not it is correct to say
that FL can account for motion and change, it is now quite clear that
DL
itself can't.
Even more annoying: in
Essay Four we saw that,
contrary to what dialecticians constantly tell us, FL can quite easily cope with
motion and change.
Yet Another Absurd Dialectical
Consequence
Another, perhaps less well appreciated consequence of this view
of motion and change -- which, if anything, is even more absurd than the one
outline above --, is the following:
If Engels were correct (in his characterisation of motion and
change), we would have no right to say that a moving body was in the first
of these 'Engelsian locations' before it was in the second.
L3: Motion involves a body being in one place and
in another place at the same time, and being in one and the same place and not
in it.
That is because such a body, according to Engels, is in both
places at once. Now, if the conclusions in the
previous section are valid
(that is, if dialectical objects are anywhere in their trajectories, they are
everywhere all at
once), then it follows that no moving body can be said to be anywhere
before it is anywhere else in its entire journey! That is because such
bodies are everywhere all at once. If so they can't be anywhere first and then
later somewhere else.
In the dialectical universe, therefore, when it come to motion
and change, there is no before and
no after!22a
In that case, according to this 'scientific theory', concerning
the entire trajectory of a body's motion, it would be impossible to say it was at the beginning of its journey
before
it was at the end! In fact, it would be at the end of its journey at the same
time as it sets off! So, while you might foolishly think, for example, that you
have to board an aeroplane (in order to go on your holidays) before you disembark at your
destination, this 'path-breaking' theory tells us you are sadly mistaken: you
must get on the plane at the very same time as you get off it at the 'end'!
And the same applies to the 'Big
Bang'. While we might think that this event took place billions of years
ago, we are surely mistaken if this 'super-scientific' theory is correct. That is because any two events in the entire history of the universe
must have taken place at the same instant, by the above argument. Naturally,
this means that while you are reading this, the 'Big Bang' is in fact still taking
place!22b
To be sure, this is absurd, but that's Diabolical Logic for
you!
No
Word Is An Island
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.
As we have seen, Engels asserted 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 doing so, he was clearly appealing to what he regarded as the
established, inter-subjective meaning 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. Ordinarily, that in itself
wouldn't be a problem, since we understand phrases like these perfectly well in
our day-to-day affairs without recourse to definitions and the like. But, in
specialised areas of study (especially those that seek to revise or correct the
way we see things), a sloppy approach to theory is unacceptable. Indeed, such cavalier
attitudes to ordinary language have a tendency to backfire on those foolish enough
to adopt them. Again, this is especially
true of those who attempt
to press the vernacular into service way beyond its remit.
The
ability to think one's way around such linguistic conundrums with ease 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' these 'serial graspers' to ignore the internal contradictions this
approach introduces into
their own theory. [More on that
here and
here.]
However, as we will see in Essay
Seven (and
here), DM-theorists are
highly selective over which 'contradictions' they choose to "grasp", and which
they blame on defective or on competitive theories. Hence, when dialecticians "grasp" the 'contradictions' they claim
to see in motion and change,
they attribute these to nature itself, and fail to blame this on Hegel's
logical incompetence,
or on Engels's lack of clarity, or both.
On the other hand, when contradictions appear in rival theories, these become a
handy excuse for rejecting them. In this way, they tell us that by rejecting or
'resolving' such contradictions science
can advance. But, if science advances by rejecting or 'resolving' contradictions in
and between theories, then, plainly, the science of kinematics can't advance unless this
'dialectical contradiction' is also resolved (as, indeed, it will be by the end of this Essay,
except this will be achieved by dissolving it).
However, just as soon as that has been done, dialecticians
will surely have to abandon their belief in the 'contradictory' nature of
motion, or risk holding up the progress of science.
This self-inflicted quandary I have called
"The
Dialecticians' Dilemma".
As seems obvious, 'dialectically' clutching at a 'contradiction'
doesn't make it disappear. As DM-theorists view things, motion is still
'contradictory', whether or not anyone else sees things this way. Hence, the
significance of
"grasping a contradiction" appears to be this: Anything that might
ordinarily seem puzzling or paradoxical suddenly stops bothering
dialecticians (that is, if it ever did). But, this move only works if it is accepted
as a fact that this is the way the world actually is. If so, and on this
basis, DM-theorists seem to think they can cease worrying about the
contradictions their approach introduces right 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 the world to be viewed in the right way (where
"viewed" in fact means "Ignore what you can't explain", and
then "Accuse critics of not understanding dialectics").
Despite the spin, this nevertheless implies that it is impossible to
explain what it could possibly mean 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 is of little use to
anyone, least of all to dialecticians, now that it is plain that not even they
can explain motion, merely re-describe it in perplexing ways. All that Engels's 'analysis'
seems to have achieved, therefore,
is stop dialecticians worrying about their defective theory, leaving
motion, as they see it, still a 'paradox'.
In that case, if there is a rational solution
to this 'paradox' (if we but knew what it was), it is no good asking dialecticians to
search for it. They gave up on that
score the moment they leafed through Hegel's 'Logic', and began "grasping"
'contradictions'.
Left to them, this branch of Physics would simply grind
to a halt.23
Ordinary Language And Paradox
However, Engels did at least make an attempt to use everyday terms in his
endeavour to show that they were not all they seemed to be. Or, rather, that
when considered 'dialectically', the vernacular reveals more about reality than
might otherwise have been apparent -- especially to those who
are mesmerised by
'commonsense', or perhaps those who have been bamboozled by that inner
fifth-columnist, the "abstract understanding".
Nevertheless, anyone who disagrees with the 'dialectical'
conclusion Engels drew would no doubt be reminded that these few words -- or the
'concepts' they supposedly represent -- clearly and unambiguously imply the
'contradictions' that Engels and Hegel said they did. In that case, defenders of
this view of things could claim that these two had simply made several implicit
'contradictions' explicit.
Intentionally or not, by arguing this way Engels
succeeded in situating his paradoxical theses in an ancient metaphysical tradition
stretching back as far as Zeno,
Parmenides and
Heraclitus -– a tradition which
ordinary working people had no hand in building, but which is (demonstrably) based on ruling-class
forms-of-thought and on a distortion of the
vernacular, the
only language that links humanity directly with the material world, as Marx
himself pointed out:
"The philosophers have only
to dissolve their language into the ordinary language, from which it is
abstracted, in order to recognise it, as the distorted language of the actual
world, and to realise that neither thoughts nor language in themselves form a
realm of their own, that they are only manifestations of actual life."
[Marx
and Engels (1970), p.118. Bold emphasis added.]
Indeed, Engels's approach began to falter
as soon as he attempted to squeeze some metaphysical juice out of such desiccated
philosophical raisins; that is,
when he tried to extract 'paradoxical' conclusions from a few rather innocent looking
words.
Naturally, only by those who have already
capitulated to the view that reality is fundamentally 'contradictory' will agree
with the conclusions Engels reached. Others,
however,
might be forgiven for remaining sceptical
--, particularly those who (not unreasonably) think that
Engels's 'solution' is far more puzzling
than the original 'problem'.
Indeed, if the nature of motion is
problematic, calling it "contradictory", while making no attempt to
explain how this actually accounts for
anything, is no help at all.
If these
alleged 'contradictions' do no work (as was argued
above), then their presence
here is, at best, unhelpful. That is because we can now see that these
'contradictions' are the direct product of an over-active imagination,
compounded by a naive acceptance of the Idealist gobbledygook Hegel inflicted on humanity.
In that
case, Engels's 'analysis' is an obstacle to understanding, which
will, of course, need removing if science is to advance.
Lack Of Imagination
In fact,
Engels failed to consider other far more likely possibilities; indeed, it looks
like it never occurred to him that his 'contradictory' conclusions might not
follow if he had instead given consideration to the full range of words/ and/or meanings
available to us in ordinary language. To be sure, these are easily accessed by those
determined to use the vernacular with far greater consistency, honesty and
sensitivity than Engels, Hegel or Zeno ever managed.24
Engels clearly wanted to make a specific point about the paradoxical implications of a
handful of seemingly innocent ordinary words. As we will see, he did this by unwittingly altering
their everyday use while imagining that the meanings of several
other ordinary terms that are normally
associated with them remained unaffected.
In doing this he wasn't, of course, alone. Semantic sleights-of-hand like
this have been practiced time and again throughout the
history of Traditional Philosophy; and they are still being played. Even careful
philosophers often fail to notice that their own work involves what can only be
called "piecemeal selectivity" in the use of certain words.
Indeed, they have invariably assumed it is possible to
tinker around with several specially chosen expressions while the meaning of any words
normally associated with them remain the same. Selectivity like this is, alas,
double-edged. In fact, these associated words -- whose meanings Engels
simply also took
for granted -- prove to be equally (if not more) problematic than those he
finally latched onto. As we are about to see, this unexpected turn of events will not
only vitiate Engels's 'analysis' of motion, it will fatally undermine every single
classic account, too.
If, for example, an ordinary word like "motion" possess 'contradictory'
implications -- according to Hegel and Engels --, then perhaps other terms they
failed to consider might have analogously paradoxical connotations, given this
perverse way of viewing language. What about the word "place", for
instance? What if it turns out to be just as 'problematic'? In such
circumstances, could we continue to accept the validity of Engels's conclusions
about "motion" if the interplay between these two intimately connected words is
more complex than he imagined, and an alteration to one changed the other?
More pointedly: What if certain
senses of the word "place" neutralise Engels's interpretation of the word "move"?
Clearly, Engels's argument relies on the meaning of "place" remaining fixed
while he tinkered around with "move". But, if "place" itself has no set
meaning, then any conclusions based on the
supposition that it has will automatically come under suspicion. Worse still,
any argument based on one aspect of the ordinary meaning of "place",
which undercuts the 'philosophical' sense of "motion", must be subject to
even greater doubt. That is because, if the sense of the latter is
compromised by the slippery nature of the former (or vice versa), the meaning of
neither can emerge unscathed, in view of their intimate connection.
In fact, as we are about to see, this in-built complexity has the salutary
effect of deflating the philosophically grandiose conclusions Engels (and
others) thought he (they) could derive from a handful of mundane-looking words when he (they) used a non-standard application
of "motion" with what he (they) took to be a standard use of "place", and vice versa.
Ordinary Objects Regularly Do The Impossible
Many of the ambiguities noted above (in relation to Engels's analysis of
"motion") actually depend on systematic vagueness in the meaning of the word
"place" and its cognates. Even when translated into the precise language of
coordinate algebra/geometry, the meaning of this particular word doesn't become much clearer.
[Of course, this is not to criticise the vernacular; imprecision is one of
its strengths. Nor is it to malign mathematics! However, when ordinary words are
imported into Philosophy, where it is almost invariably assumed they have a single unique
(or 'essential')
meaning, problems invariably arise.]
In fact, as it turns out, there is no such thing as
the meaning of the word "place" -- or of "move".
This lack of clarity carries over into our use of technical terms
associated with either word; the application of coordinate systems, for example,
requires the use of rules, none of which is self-interpreting. [The point of
that comment will be explained presently.]
Nevertheless, it is relatively easy to show (by means of the sort of
selective linguistic 'adjustment' beloved of metaphysicians, but applied in contexts they generally fail to consider)
that ordinary objects and people are quite capable of doing the metaphysically
impossible. The flexibility built into everyday language actually 'enables'
the mundane to do the magical, and on an alarmingly regular basis. Such
everyday 'prodigies' do not normally bother us -- well, not until some bright spark tries to do a little
'philosophising' with them.24a
If the
ordinary word "place" is now employed in one or more of its usual senses, it is
easy to show that much of what Engels had to say about motion becomes
either false or uninteresting. Otherwise, we should be forced to concede
that ordinary people and objects can behave in extraordinary -- if not
miraculous --
ways.
Consider,
therefore, the
following example:
L41: The strikers refused to leave their place of
work and busied themselves building another barricade.
Assuming that the reference of
"place" is
clear from the context (that it is, say, a factory), L41 depicts objects
moving while they remain in the same place -- contrary to what
Engels said (or implied) was possible. Indeed, if this sort of motion is
interpreted metaphysically, it would involve ordinary workers doing the
impossible -- moving while staying still!
Of course, it could be objected here that L41 is a highly contentious example,
and not at all the sort of thing that Engels (or
other metaphysicians) had in mind by their use of the word "place".
But, Engels didn't
tell us what he meant by this term; he simply assumed we'd understand his
use of it. If, however, it is now claimed that he didn't mean by "place"
a sort of vague "general location" (like the factory used in the above example), then that would confirm the point being made in this part of the
Essay: Engels didn't say what he
meant by "place" since there was nothing he could have said
that wouldn't have ruined his entire argument. Tinker around with the word
"place" and the meaning of "motion" can't fail to be compromised
(as noted above). This can
be seen by considering the following highly informal 'argument':
L42: Nothing that moves
can stay in the same place.
L43: If anything stays in the same place, it
can't move.
L44: A factory is one place in which workers
work.
L45: Workers move about
in factories.
L46: Any worker who moves can't stay in the same place
(by L42, contraposed).
L47: Hence, if workers move they can't do so in
factories (by L44 and L45).
L48: But, some workers stay in factories while
they work; hence, while there they can't move (by L43).
L49: Therefore, workers work and do not work in factories, or
they move and they do not move.
As soon as one meaning of
"place" is
altered (as it is in L44), one sense of "move" is automatically affected
(as in L45), and vice versa (in both L47 and L48). In one sense of
"place", things can't move (in another sense of "move") while staying in one
place (in yet another sense of "place"). But, in another sense of both they can,
and what is more, they can typically do both. Failure to notice this produces 'contradictions'
to order, everywhere (as in L49).
Even so, who believes that workers work and do not
work in factories? Or that they move and do not move while staying in the same place?
Perhaps only those who "understand" dialectics...?
Dialectical Objects Do The
Oddest Things
Do They Move Or Simply Expand?
Clearly, Engels's 'theory' of motion has to be able to take account of ordinary objects if it
is to apply to the real world and not just to abstractions, or to
physically meaningless mathematical 'points'. But, this is just what his
'theory' can't do, as we
are about to
see.
It could now be
objected to the comments made in previous few sections that if "place" is defined precisely (without
altering the meaning of "move") it would be possible to understand what Engels
and Hegel were trying to say. In that case, it could be argued that if "place"
is defined by the use of precise spatial coordinates (henceforth, SCs), Engels's
account of motion would become viable again.
Or, so some might think.
Of course, the problem here is that in the example
above (concerning those
contradictory mobile/stationary workers), if we try to refine the meaning of the
word "place" a little more precisely, it will come to mean something like "finite (but
imprecise) three-dimensional region of space large enough to contain the
required object". Well, plainly, in that sense things can and do move
about while they remain in the same region (i.e., "place") --
since, by default, any object occupies such a region as it moves -- that
is, it must always occupy a three-dimensional region of space large enough
to contain it as it moves; it certainly doesn't occupy a larger or a smaller space
(unless it expands/contracts)! Moreover, objects occupy finite
regions as they move in relation to each other (or they wouldn't be able to move).
Hence, if defined this way, moving objects always occupy the same space, and
hence they don't move! That is, if they always stay in the same space, they
can't move. As we have seen, objects always occupy the same space, even as they
move. So, they both move and don't move! Plainly we need to be more precise.
So, of the many options there are before us, the following seem
to be relevant to the
point at hand:
(1) If an object always occupies the same space
(which fits it like a glove, as it moves), then it can't actually move!
(2) If it occupies a larger space as it moves, it must expand.
(3) If it moves about in the same region of
space (such as a factory), it still can't move!
(4) If it
successively occupies spaces equal to its own volume as it moves, the
situation is even worse, as we will soon
see.
Now, if the
'regions' mentioned above are constrained too much, nothing would be able to move
-- this is Option (1).
Put
each worker in a tightly-fitting steel box that exactly fits him or her and
watch all locomotion grind to a halt.
Put that worker in a region of space, and he/she still won't be
able to move
-- this is Option (3). That is because if we define motion as successive occupancy of
regions of space, then this worker can't move since he/she is always in the same
region.
The difficulty here is plainly one of
relaxing the required region an object occupies sufficiently enough to allow it to move from
one place to another without stopping it moving altogether (that is,
preventing Option (3) from undermining Option (4)), all the while
providing an account that accommodates the movement of medium-sized objects in
the real world. But, once this has been done the above difficulties soon
re-appear, for it is quite clear that objects still move while staying in the
same place -- if the place allowed is big enough for them to do just
that!
Indeed, this fact probably accounts for most (if not all) of the
locomotion in the entire universe. Clearly, and in the limit, if anything moves in nature it must remain in the same
place, i.e., in the universe! Of course, that would be to relax the definition
of "same place" far too much. But, how can we tighten the definition so that objects aren't
put in straight-jackets once more? (i.e., Option (1),
again).
At first sight, the above objection (concerning a
precise enough definition of
"place") seems reasonable enough. Engels clearly meant something a little more
precise than a vague or general sort of location (like a factory). But, what?
It might seem that Engels's argument can be rescued if tighter protocols for
"place" are prescribed --, perhaps those involving a reference to "a
(zero volume mathematical) point, in three-dimensional space, located by the use of precise
SCs". But, this option would embroil Engels's account in far more intractable
problems. That is because such an account would plainly relate to
mathematical point locations, or the movement of mathematical points
themselves -- and we saw earlier that that was a non-starter.
Clearly, things cannot
move about in such points -- but this has nothing to do with the supposed nature of reality.
These 'entities' do not (and could not) exist in nature for them
to contain anything. That is because such points aren't containers. They have no volume and are made
of nothing. If this weren't the case, they'd not be mathematical points, they'd be regions.
As noted above, if Engels meant something like this in his use of "place", his account would
fail to explain or accommodate
the movement of gross material bodies in nature, for the latter do not
occupy mathematical points.
Moreover, it is no use appealing to larger numbers/sets of such points located by SCs;
no material body can occupy an arbitrary number of points, since points
aren't
containers.
Perhaps we could define a region (or a finite volume
interval) by the use of SCs? Maybe so, but this would merely introduces another
classical conundrum (which is a variation on several of
Zeno's
other paradoxes): how a region (or a volume interval) can be composed of
points that have no volume. Even an infinite number of zero volume
mathematical points adds up to zero. Now, there are those who think this
conundrum has a solution (just as there are those who think it doesn't), but it
would seem reasonably clear that the difficulties surrounding Engels's 'theory'
are not likely to be helped by importing several more from another set of
Paradoxes.
Be this as it may, it is far more likely that Engels's use of the word "place" implies an
implicit reference to
a finite three-dimensional volume interval (whose limits
could be defined by the use of well-understood rules in
Real
and
Complex Analysis,
Vector
Calculus, Coordinate Algebra and
Differential Geometry,
etc.).
Clearly, such volume intervals must be large enough to hold (even temporarily) a
given
material object. If so, this use of the phrase "volume interval" would in principle
be no different from the earlier use of "place" to depict the movement of those workers!
If
they can move about in
locations big enough to contain them, and who remain in the same place while doing so,
Engels's moving objects can do so, too -- except they would now have a more precise "place"/region
in which to do it.
However, and alas, this sense of "place" is no use at all, for when
such workers move, they will, by definition, stay in the same place! [Option
(3), again!]
Naturally, the only way to avoid this latest difficulty would be to argue that the location
of any object must be a region of space (i.e., volume interval) equal
to that object's
own volume.
This is in effect
one
of the classical definitions. In that case, as the said object moves, its
own exact volume interval would move with it, too; the latter would follow each moving object around more
faithfully than its own shadow, and more doggedly than a world-champion bloodhound. But,
plainly, if that were the case, it would mean that objects would still move while
staying in the same place -- since, plainly, any object always occupies a
space equal to its own volume, which would, on this view, travel everywhere with it, like a sort
of metaphysical glove. [Option (1),
again!]
As seems plain: if that is so, we now have two problems where once
there was just one, for we should have to explain
not only how bodies move, but how it is also possible for volume intervals to move so that they can
faithfully shadow the objects
they contain!
However, and far worse: in that case, not only would we have to explain how locations
(i.e., volume intervals) are themselves capable of moving, we would also
have to explain what on earth they could possibly move into!
What
sort of
ghostly regions of space could we appeal to, to allow regions of space
themselves to move into them?
Even worse still: these 'moving volume intervals'
must also occupy volumes equal to their own
volume, if they are to move (given this 'tighter' way of characterising
motion). And, if they do
that, then these new 'extra' locations containing the volume intervals themselves must
now act
as secondary
'metaphysical mittens', as it were, to the original 'ontological gloves'. Metaphorically speaking, this
theory, if it took such a turn, would be moving backwards, since an
infinite regress would soon confront us, as spatial mittens inside containing
gloves, inside holding gauntlets, piled
up alarmingly to account for each successive spatial container, and how it could
possibly move. As seems reasonably clear, we would only
be able to account for locomotion this way if each moving object were situated
at the centre of some sort of 'metaphysical onion', each with a potentially infinite
number of 'skins'! [Iterated Option (1)!]
It could be countered that even though objects occupy spaces equal
to their own volumes, as they move along they then proceed to occupy successive
spaces of this sort (located in the surrounding region, for example), all of
which are of precisely the right volume to contain the moving object that now
occupies them, and which can be located/defined precisely. On
this revised scenario, moving objects will leave their old locations behind as they barrelled along.
This now brings us to a consideration of Option (2) and/or Option (4) -- now
modified to (4a) --, from earlier:
(2) If (an object) occupies a larger space as it moves, it must
expand.
(4a) An object
successively occupies spaces (or volume intervals) equal to its own volume as
it moves.
I will reject (2) as absurd. If anyone wants to defend it, they
are welcome to all the headaches it will bring them its train.
Considering, now, Option (4a):
Even if (4a) were a correct interpretation of what Engels meant,
and it was a viable option
(and sense could be made of these new, and accommodating locations without re-duplicating
the very same problem, noted in the previous few paragraphs), no DM-theorist could afford to appeal to such
successive volume intervals. That is because dialecticians claim that moving
bodies occupy at least two such "places" at the same time,
being in one
of them and not in it at the same moment. Clearly, if motion were defined in such
terms (that is, if it were characterised as involving objects successively occupying spaces
equal to their own volumes), then moving objects would occupy at least two of
these
volume intervals at once.
In that case, 'dialectical objects' would not so much move as stretch or
expand!
[Modified Option (2)!]
To see this more clearly, it might be useful to examine the above
argument more
closely.
If the centre of mass (COM) of a 'dialectically moving' object, D, were located at, say,
(Xk, Yk, Zk)
and (Xk+1, Yk+1, Zk+1), at the same time (to satisfy the requirement that moving bodies occupy at least two such "places" at the same time,
being in one of them and not in it), it would have to occupy a space larger than its own volume
while doing so.
Let us call
such a space "S", and let the volume interval containing
(Xk, Yk, Zk)
and (Xk+1, Yk+1, Zk+1) be
"δV1", leaving it open for the time being
whether S and δV1 are the
same or are different. Thus, if the COM of D is in two
such spaces (i.e.,
(Xk, Yk, Zk)
and (Xk+1, Yk+1, Zk+1)) at once,
D would plainly be in S, and would occupy δV1. But, once again, that would
mean that D would move while remaining in the same space -- i.e., it
would remain inside S, or inside δV1 (whichever is preferred), as its COM moved from
(Xk, Yk, Zk)
to (Xk+1, Yk+1, Zk+1),
in the same instant. [Option (3), again!]
[Except, we can't speak of a 'dialectal object' moving from
one point to the next since that would imply it was in the first
before it was in the second, and that it was in the second after it
was in the first. But, as we have seen, if such an object is in both
places at the same time, there can be no "before" or no "after", here.]
Now, the only way to avoid the conclusion that D moves
while occupying the same space S and/or δV1
--, and hence that it appears to stay still while it moves, just like the 'mobile/stationary' workers we encountered earlier --
would be to argue that
such spaces remain where they are while D moves into successively new
locations, or new spaces. This seems to be the import of
Option (4a).
But, as D moves it still occupies δV1,
only we would now have to argue that as it does so it also moves into a new δV
each time, say, δV2
-- except that δV2 must
also contain (Xk+1, Yk+1, Zk+1)
and (Xk+2, Yk+2, Zk+2)
-- otherwise it would not be a new
containing volume interval that satisfied the requirement
that moving bodies occupy at least two such "places" at the same time,
being in one of them and not in it.
Plainly, all objects have to occupy some volume interval or other
at all times (or they would 'disappear'). However, in D's case it has to do this
while also occupying new volume intervals at the same time as it moves
along (otherwise, as we
saw, it would move while being in the same place, and thus that it didn't move!).
So, if D
occupies only one S or only one
δV at once, it would be at rest in either. [Options (1)
and (3).] Hence, it must occupy at least two
of these at the same time (if, that is, we accept the 'dialectical' view of motion).
If so, the only apparent way of avoiding the conclusion that D-like
objects move while staying still is to argue that they occupy two successive
Ss, or two successive δVs (perhaps these are partially 'overlapping',
perhaps not), at once. Unfortunately, this would now mean that D-like
objects would have to occupy a volume/volume interval bigger than either of S
or δV at once, and hence: they must expand or stretch.
It could be objected that two successive
δVs would
contain
(Xk, Yk, Zk)
and
(Xk+1, Yk+1, Zk+1)
--
that is, δV1
would contain
(Xk, Yk, Zk)
and
δV2
would
contains (Xk+1, Yk+1, Zk+1)
--, so the above objection is misguided. Maybe so, but the point is that dialectical
objects must occupy two δVs
at once, and if that is so, both
δVs must
contain
(Xk, Yk, Zk)
and (Xk+1, Yk+1, Zk+1),
jointly or severally, otherwise such objects couldn't occupy two spaces (two
δVs) at
the same time.
But, if that is so, and D isn't stationary while it
occupies δV2,
and as we saw
above in an analogous context, it must also occupy δV3
at the same time, and so on.
Successive applications of this
argument would have D occupying bigger and bigger volume intervals (i.e.,
δV1
+ δV2
+ δV3
+ δV4
+...,+ δVn),
all at the same time. In
the limit, D could fill the entire universe (or, at least, the entire
volume interval encompassing its own trajectory), all at the same time -- if it moves and
if Hegel is to be believed!
There thus seems to be no way to depict the
motion of D-like objects that prevents them from either moving while staying
still, or, from expanding alarmingly like some sort of metaphysical
Puffer Fish.24b
![](/web/20140524014506im_/http://anti-dialectics.co.uk/Puffer-12.jpg)
Figure One: At Last! An Organism That
'Understands' Dialectics
Either way, Engels's theory finds itself in
yet another
Hermetic Hole.
The reader should now be able to see for
herself what mystical mayhem is introduced into our reasoning by this cavalier
use of (contradictory) metaphysical language. When one sense of "move" is
altered, one sense of "place" can't remain the same, nor vice versa.
Of course, no one believes the above
ridiculous conclusions, but there appears to be no way to avoid them using the
radically defective and hopelessly meagre conceptual and/or logical resources DL supplies its
unfortunate victims.
[DL = Dialectical Logic; SC = Spatial
Coordinate.]
Or Do They Concertina?
On the other hand, it seems that 'Dialectical objects' must
concertina as they move.
Consider a simple body B made of 3 connected parts: P1,
P2 and P3,
all arranged in the same line, so that there are no gaps between them.
Let B move such that at t1,
the centre of the leading edge of P1
is at (X1, Y1, Z1),
the centre of the leading edge of
P2
is at (X2, Y2, Z2),
and centre of the leading edge of P3
is at (X3, Y3, Z3).
Let us also assume that the centre of the leading edge of
P3
now moves to (X4, Y4, Z4).
Finally, let us assume that the distances between each of (X1, Y1, Z1),
(X2, Y2, Z2), (X3, Y3, Z3)
and (X4, Y4, Z4)
are all the same.
Now, if all moving objects occupy two places at once, and if B
moves in a line parallel to the line joining the centre of the leading edge of
P1 to the
centre of the leading edge of P3,
then the centre of the leading edge of P1
must occupy (X1, Y1, Z1)
and (X2, Y2, Z2),
the centre of the leading edge of P2
must occupy (X2, Y2, Z2)
and (X3, Y3, Z3),
and the centre of the leading edge of P3
must occupy (X3, Y3, Z3)
and (X4, Y4, Z4),
at the same time. In effect, B would concertina as it moved, with the
front end of, say, P1
crushing or penetrating the back end of P2,
and overlapping it right up to its own leading edge -- in effect, wiping
P2
out!
[This result, of course, depends on the answer to an
earlier question: How far apart are
the two places a moving body occupies that Engels referred to? If this is left indeterminate, then any
length will do. Even then, if a specific length is decided upon, we could make
the distance between the above parts equal to that length, and the same result will still
follow. (That is done below, anyway.)]
It can't be the case that the trailing edge of
P2
will leave (X2, Y2, Z2)
just before the leading edge of P1
reaches it, since, as
we have already seen, there is no before and now after here, since all
such motion must take place at the same time for it to constitute a 'dialectical
contradiction'.
Now, it could be objected that P1
and P2 for
example will occupy the space between (X1, Y1, Z1)
and (X2, Y2, Z2)
and (X2, Y2, Z2)
and (X3, Y3, Z3), respectively, as B moves, but this isn't possible. That is
because there are no gaps between any of the three parts of this object for any
of those parts to move into. So, if B were, say, a single carriage train,
then P1
would comprise the rear section of that carriage, P2
the middle third, and P3
the front end. This view of motion would therefore have these parts of this
single carriage crushing the one in front. [I have considered the
option that there is such a gap, below.]
[At a later date, I will add diagrams to make
this and the other examples considered here a little clearer to the reader.]
Again, it might be argued that the structural properties of B
(intermolecular forces, etc.) will prevent this from happening. That is
undeniable, but this response also has the unfortunate consequence that while B
may be in two places at once as it moves, none of its parts could be! And
that in turn would imply that while B was racing along, none of its
parts would be moving -- since they are not allowed to be in two places at once!
Similar, if not worse problems afflict a 'dialectical object'
undergoing circular or more complex forms of movement, such as helical or spiral motion.
So, consider a rotating disc, D, of negligible thickness
divided by a diameter line, T, into two equal semi-circular sectors, S1
and S2. If
we set the centre of this disc as the origin, then we can set the leading edge of S1
so that it
lies along T. In addition, let there
be a point p1
on T, r units from the centre, with co-ordinates (r, θ1).
Let the leading edge of S2
also
lie along T, and let there
be a point p2,
r units from the centre, with co-ordinates (r, θ2).
Plainly, this means that p1
and p2 lie
on the same trajectory, a circular path r units from D. [I have used
polar co-ordinates in two-dimensions here to simplify this
example.]
Now, if all moving objects occupy two places at once, and if B
rotates clockwise, then the leading edge of S1
must pass through both p1
and p2,
and the leading edge of S2
must pass through both p2
and p1,
at the same time. But this is even worse than the 'dialectically linear
movement' considered above, since, in this case, either (1) D will
totally disappear -- as both of its sectors occupy the same semi-circle that the
other one occupied -- or, (2) Both of these sectors must stretch to cover the
entire disc, ramming into the back of one another as they did so, compressing
each into a region with zero area!
Now it might be possible to defend this picture of dialectal
objects as they smash into one another by arguing that the above scenarios are
heavily biased. For example, in the linear case above, while the centre of the
leading edge of P3
might move to (X4, Y4, Z4),
the distance between (X3, Y3, Z3)
and (X4, Y4, Z4)
need not be equal to that between (X1, Y1, Z1)
and (X2, Y2, Z2)
and (X2, Y2, Z2)
and (X3, Y3, Z3).
Let us say, therefore, that the distance between (X3, Y3, Z3)
and (X4, Y4, Z4)
is δL.
In this case, therefore, B will move forward
δL units, as
will each of its parts.
This would have the effect on S1
such that it would no longer move to (X2, Y2, Z2),
but to some intermediate point (X1+δx, Y1+δy, Z1+δz),
with the same sort of thing happening to the other leading edges. The same would
also happen to the trailing edge of S2,
which, let us say was at (Xi, Yi, Zi),
at t1.
Now, the trailing edge of S2
and the leading edge of S1
can't occupy the same space, as should seem obvious; so let us say that
the distance between (X1, Y1, Z1)
and (Xi, Yi, Zi)
can be made as small as we like -- let us stipulate that this is
δS (where it
is left open whether or not δS
> δL).
In that case, there would be a gap, δS,
between at least two of the parts.
Hence, the trailing edge of S2
would move to (Xi+δx, Yi+δy, Zi+δz)
while the leading edge of S1
moves to (X1+δx, Y1+δy, Z1+δz).
Plainly, these are not the same points. If so, S1
won't smash into the back of S2
as imagined above. And, the same sort of conclusion can be drawn in connection
with the rotating disc, too.
Unfortunately, this reply fails, too. That is because the centre
of the leading edge of S1
has to occupy two places at once, if Engels and Hegel are to be believed.
So, the centre of the leading edge of S1
has to occupy (X1, Y1, Z1)
and (X1+δx, Y1+δy, Z1+δz),
and the centre of the trailing edge of S2
has to occupy (Xi, Yi, Zi)
and (Xi+δx, Yi+δy, Zi+δz),
at the same time. Now, if δS
is zero, then (X1+δx, Y1+δy, Z1+δz)
will lie beyond (Xi, Yi, Zi),
which means that the leading edge of S1
will smash into the back of S2.
The same will happen if δS
<
δL. On the other hand, if
δS
> δL
then a larger and larger gap will open up between S1
and S2,
which will widen all the more as B continues to move. So,
B will either (1) Begin to fragment, or it will (2) Concertina, as
it moves. The same will happen to the disc.24b1
So, this 'theory' is still stuck in a Deep Dialectical Ditch.
Coordinates To The Rescue?
Despite this,
it could be argued that if the ordinary word "place" is so vague then it should
be replaced with more precise concepts; those defined in terms of SCs,
once more. But, as the following argument shows, that would be another backward
move (no pun intended!):
L50: A place can be defined by the use of SCs.
L51: SCs are composed of ordered
real number
3-tuples (i.e., number triples, defined precisely -- see L52)
in R3.24c
L52: However, when written correctly, the elements in such
3-tuples
must occupy their assigned places (by the ordering rules). Consider then the
following ordered triplet: <x1, y1,
z1>.
Each element in such an SC must be written precisely this way, with xi,
yi and
zi
(etc.) all in their correct places.
L53: But, the situating of such elements can't itself be
defined by exact SCs, otherwise an infinite regress will ensue.
L54: Consequently, this latter sense of "place"
(i.e., that which underlies the ordering rules for SCs) can't be defined (without circularity)
by means of SCs.
This means that the definition of "place" by means of SCs is itself
dependent on a perfectly ordinary meaning of "place", and, further,
that the latter sense of "place" must already be understood if a co-ordinate system is
to be set-up correctly.
Therefore, the ordinary word "place" can't be defined without circularity by means of a coordinate
system.
In short, the precision introduced by means of SCs is bought at the expense of
presupposing mundane linguistic facts like these.
Of course, this is not to malign coordinate geometry, but it
reminds us that any branch of human knowledge (even one as technical and
precise as modern
mathematics) has to mesh with ordinary language and everyday practice (at
some point), if it is to be set-up to begin with. Everyday facts like these are
soon forgotten (in the course of one's education), since, as Wittgenstein
pointed out, we are taught to squash such simple questions very early on. As a
result we inherit the mythological structures that previous generations have
built on top of unexamined foundations like this.
If, on the other hand, a typographically identical word (viz.: "place") were to
be defined in this way, and then used in mathematics or physics, it wouldn't be the same
word as the ordinary word "place" upon which the definition itself is
predicated. And, if this new term, "place", is used to define the movement of objects in
DM, then the motion of gross bodies in the material world would still be unaccounted for.
It
could be objected here that it is surely possible to disambiguate the
ordinary word so that it could be employed in a
DM-analysis of motion --, meaning that it was no longer confused with the less precise phrase
"general location".
Since this has yet to be done
(even by DM-advocates, who, up until now, have in fact shown that they
aren't even aware of
this problem!) it remains to be seen whether this promissory note is
redeemable. However, even if it were, it would still be of little
help. As we have seen, and will see again, the word "place" (even as
it is used in mathematics) is
itself ambiguous, and necessarily so. [There is more on this in Note 25.]
Moreover, Engels's account requires motion to be depicted by a
continuous variable, while one or both of time or place is/are held to be
discrete, otherwise a contradiction wouldn't emerge (which is, of course,
something even Hegel recognised).24d This trick is accomplished
either by (1) the simple expedient of ignoring examples of
discrete forms of motion (several of which are given below), and/or
by (2) failing to consider
instances where both time and place are continuous -- all the while
imagining that the relevant ordinary words use to depict both have been employed
with their usual senses, and have not been altered by these new contexts.25
Even assuming a stricter
sense of "place" could be cobbled-together somehow, that would still be
of little help. This is because it would either make motion itself impossible --
or, if possible, incomprehensible -- since, given Engels's account, a moving
object would have to be everywhere if it is anywhere, and, it would not
so much move as expand or stretch, as noted earlier.
Everyday Miracles?
This means that in a
perfectly ordinary sense, things can both move and stay in the same place
while they do so. Indeed, they are quite capable of remaining stationary
while they undergo a change of place, moving and not moving all at once!
The first of these was depicted above with respect to those
stationary/mobile workers; the second
(where something can both move and not move all at once -- and, in
this case,
involving a discrete sense of "move" into the bargain), is illustrated
in the next
example:
L55: NN was second in line when MM, who had been first in the queue, suddenly dropped out. Hence, NN
moved to the front of the queue even though he remained rooted to the spot.26
In L55, we have a perfectly ordinary example where a fellow human being manages to do the
'metaphysically impossible' (without even breaking into a dialectical sweat), moving while staying
still (relative to some inertial frame). Clearly, it is possible to move to
the front of a queue (in one sense) even without moving at all (in another sense), relative to some inertial frame.
Indeed, it'
is
also possible to think of cases of discontinuous (i.e., discrete) motion whereby, even
though something once moved, nothing need now be moving -- and yet in one
sense something still moves. This would also involve whatever it was that
did all this 'moving and not moving at the same time' doing so in a different
sense from that which is illustrated in L55. In fact, it is possible to show that some things
can move (again in a discrete sense) while they occupy none of the
intervening places between successive locations. All of these
possibilities are illustrated below:
L56: The footprints moved across the snow-covered yard,
indicating where the scabs were hiding.
L57: Easter moves to a new date each year.
L58: "See, the page numbers in this book you sold
me move about erratically. The book has been printed and bound all
wrong!"
L59: The Ground Staff moved the cricket pitch to the other side
of the square.
L60: The organisers of the rally moved the meeting to seven
o'clock.
L61: The strobe light moved across the floor picking out each
dancer.
In L56, we have stationary 'objects' (i.e., the footprints created by
individuals who had earlier moved across the said yard), which still move (across
the yard) even while each item (each footprint) is stationary.
In L57, nothing
actually moves even while it still does! In L58, nothing moves once again, but yet
something actually moves (namely the faulty numbering), and it does so discretely
while not occupying any of the intervening spaces, which spaces do not
exist either for anything to move into! [Of course, in such circumstances, we'd
probably use "jump" instead of "move"; but to jump is also to move.]
A similar picture emerges in L59,
where a discrete object moves a reasonable distance, but which object
doesn't exist while it moves, nor does it occupy any of the intervening spaces
on its 'journey', but which intervening spaces do exist! Similar
situations are illustrated in L60 and L61.
Not only that, but continuous and yet stationary things can move while remaining still:
L62: As I look down on the scene, the immobile line of
pickets moves out of sight, curling right round the block; each striker holding
her ground, rooted to the spot.
L63: The wire moves in a spiral around this tree.
It's been in the same spot so long that the tree has partially grown around it.27
Finally, some things can move -- but to
nowhere in particular -- and they can stay quite still while they are doing it:
L64: This road is going nowhere.28
Such mundane examples (there are countless others), using
perfectly ordinary words in situations we
all readily comprehend, demonstrate that the seemingly 'obvious'
metaphysical principles that thinkers like Engels dreamt-up actually depend on
non-standard applications (i.e., distortions) of the vernacular (as
Marx pointed out).
Of course, it could be objected that these examples of 'motion'
are not at all what Engels meant by "motion"; indeed, he was quite careful to
emphasise that he was only interested in one sort of motion: continuous change of
place with respect to time:
"[A]s soon as we consider things in their motion, their change,
their life, their reciprocal influence…[t]hen we immediately become involved in
contradictions. Motion itself is a contradiction; even simple mechanical
change of place can only come about through a body being both in one place and
in another place at one and the same moment of time, being in one and the same
place and also not in it. And the continual assertion and simultaneous
solution of this contradiction is precisely what motion is." [Engels (1976),
p.152. Italicised emphases added.]
In this passage, Engels is perfectly clear that he meant "simple mechanical
change of place", which is different from the non-standard senses of the word paraded above.
Or, so it could be
argued.
Unfortunately, however, as we have seen, it isn't easy to ascertain what (if anything) Engels actually did
have in
mind by "simple mechanical change of place". Indeed, much of what
he said is compatible with no movement having occurred, so that the supposedly
'contradictory' aspects of an object's trajectory have
nothing to do with whether that object is moving or not.
Moreover, as we have also seen, Engels's use of language implies that 'dialectical' objects threaten
to expand
alarmingly, concertina destructively,
or spread out to occupy an
entire region, whenever they try to move.
Furthermore, dialecticians can't appeal to what we 'all know' about the meaning
of the word "motion", nor should they suppose we 'all know' perfectly well what
Engels meant when he referred to it. As the above examples indicate, there is no one thing we all mean by this
word (and its associated terms), even though we all do know what we mean
by each of them individually when they feature in ordinary contexts
(like those depicted above).
And, as far as
Engels's own use is concerned, we may only agree with the claim that
DM-theorists know what Engels meant by "motion" when they succeed in
explaining to the rest of us precisely what that is.
Unfortunately, to date, there have been no significant moves in
that direction (irony intended).
In addition, the above examples were deliberately drawn from everyday situations
-- those that are readily understood. It is Engels's use of the word
"move" that turns out to be non-standard and incomprehensible.
Finally, it
might be felt that the above emphasis on the ordinary sense of words is
inappropriate in a scientific/philosophical analysis of motion and change. This objection is
considered in detail elsewhere
at this site. Anyway, Engels himself
used ordinary words to make his point -- which was that every example
of motion in reality involves a contradiction, including those parts that can be depicted by our use of the
vernacular.29
Inferences From Language To The World
Thought
Experiment In Place Of Scientific Experiment
Once again, it could be argued that any account of motion would have to involve contradictions
because of what must be the case if objects in reality -- independent
of thought -- actually move, which they clearly do. Hence, despite what
we might say, the real world contains countless examples of
motion and change, each of which is contradictory.
Now, the
use of modal terms here is quite revealing for it confirms something that has
been implicit all along (hinted at earlier): this type of argument depends on
inferences being made from the alleged meaning of a few specially selected words
-– which have been given an idiosyncratic re-interpretation in isolation from other associated terms, divorced from their ordinary contexts of use -- to necessary truths about the world.
'Deductions' like these invariably precede a perfunctory empirical 'investigation' -- if, that is, the latter is
even so much as attempted by dialecticians. The results that these inferences appear to warrant
are then regarded as absolute certainties, which their inventors find it impossible
to question. This is, of course, because such
Super-truths are based on language alone,
and not on evidence. [On this in general, see Essay Twelve
Part One.]
As pointed out earlier, Engels performed no controlled experiments before or after he drew
the above conclusions about motion. In fact, it is impossible even to describe
a single observation or experiment -- other than a
thought experiment,
which would itself depend on the sorts of ambiguities highlighted above -- that
could conceivably confirm Engels's claims about motion. This is partly
because 'contradictions' themselves can't be observed,
and partly because of the modal, universal and omni-temporal character of the
conclusions themselves.30
This means that the only substantiation Engels could have
offered to support his claims would have been
language-based; he would have to refer
anyone sceptical of his conclusions to what certain words really meant.
It would be no good advising non-believers to look harder at the phenomena,
refine their search or redo their experiments --, which is, of course, why one finds no
evidence in books on dialectics that confirm or even so much as vaguely support
a belief in the
contradictory nature of motion. All we find in its place are dogmatic assertions
-- perhaps linked in with a very brief thought experiment --, both
based on a brief consideration of a few of the words/concepts involved. [Readers are invited to check!]
Thus, Engels's only 'evidence' was an appeal to the
philosophical use of language -- and to Hegel and Zeno's use, too --, not how such words feature in everyday
life. This
predicament (which he shares with all other metaphysicians) invariably
passes unnoticed because (1) It is so
widespread Traditional Thought, (2) It has been going on now for well over
two thousand years ('East' and 'West'), and (3) It is imagined that by
looking at certain words (or their 'real' meanings) the Armchair
Philosopher is actually examining the world itself, and not simply a few
specially-selected, jargonised expressions that are in fact divorced from
reality.
The idealist implications of this traditional approach to
'knowledge' were
well summarised by 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.]
[The reason for the traditional confusion of talk about talk with
talk about things is examined in Essay Twelve
Part One (and in other Parts of
that Essay -- summary
here).]
Nevertheless, the
denotation of
the words used in this specialised vocabulary is
simply taken for granted; indeed, the question whether such words actually have a denotation is seldom ever raised.
This critical view of philosophical word-magic gains
support from the fact that 'philosophical problems' like this can't be solved by an appeal to evidence. That is why they depend solely on a
distorted use of language,
and it is also why this
is all Engels ever offered his readers, and why it is all he could
ever have offered
his readers, in this respect.
Nevertheless, Engels
restricted his comments neither to examples of motion he had personally
investigated, nor to the entire set of examples experienced by humanity
up until his day.
Still, he felt quite confident that he could extrapolate from his own understanding of a
few ordinary-looking words to conclusions that were applicable to every conceivable
example of motion anywhere in the universe, for all of time:
"Never anywhere has there been matter
without motion, nor can there be…. Matter without motion is just as
inconceivable as motion without matter. Motion is therefore as uncreatable
and indestructible as matter itself…." [Engels (1976), p.74. Bold emphases
added.]
"[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, p.152.
Bold emphasis added.]
If fact, what Engels actually did -- and this was the extent of the 'careful' scientific
research he carried out in this area -- was to copy the analysis of
motion he found in Hegel's Logic!
And Hegel hasn't gone down in history as a great experimental
scientist.
As we shall see (in Essays Nine Part
One and
Two, and Twelve (summary
here)),
these easily missed facts possess revealing ideological implications of their
own.
Metaphysical Con-Trick
Engels's
feeling of confidence in the results he so effortlessly obtained no doubt arose from his
consideration of one particular interpretation of "motion" (but no others).
Hence, we find him claiming that:
"[E]ven simple mechanical change of place can only come
about through a body being both in one place and in another place at one and the
same moment of time, being in one and the same place and also not in it."
[Ibid.,
p.152.]
But, how could Engels possibly
have known
this? How could he have been so sure that every single example of motion
throughout the
entire universe, for all of time, could only occur in the
way he alleged? If we rule out the absurd idea that Engels was some sort of
deity, there are in fact only two possible answers to that
question:
(1) Engels's certainty was based on his grasp of the 'concept'
of motion itself. But, as seems obvious from his comments,
Engels actually based his conclusions on his own understanding of a handful of words
about motion, and on the ideas he lifted from Hegel, but not on the 'concept' of motion itself (if there is
such a thing). Neither he nor anyone else has access to such a concept
independently of the words that supposedly allude to it.
And yet, divorced from the wide variety of ways we ordinarily
talk about motion (illustrated by the many examples given in this Essay), who is
to say what is the correct way to understand such words in novel contexts like
these?
Or, whether the meaning of any technical terms that have been used are the same as
the meaning of the ordinary words
they supposedly replace/supersede? Or, that there is only one way to interpret them?
Or, that Engels and Lenin hit upon the correct way to comprehend them
(and then only after reading Hegel -- as opposed to sifting through the
relevant scientific data)? Or even whether
the
language
they used means anything at all?
However, and more to the point: precisely who decided
that such off-the-cuff conclusions (about substantive features
of the world, true for all of space and time) can be read from the alleged meaning of a few words?
Did the rest of us miss a meeting?
(2) The second possible answer revolves around a likely response that might have
occurred to several readers: Surely a rejection of Engels's understanding of
motion would be paradoxical, if not contradictory itself. That is because
it would
represent a repudiation of what the concept of motion actually implies. Consequently, on
this view, anyone who fails to interpret motion along these lines (involving a body being
in two places at once (etc., etc.)) only succeeds in revealing that they have misunderstood what
motion is in-itself. Indeed, it would flatly contradict what we all
ordinarily understand motion to be.
Or, so it could be claimed.
However, Engels's analysis of motion is
itself
paradoxical and (openly) contradictory; so even by his own lights, there
appear to be equally good reasons for rejecting his interpretation of motion as
there are for accepting it. If it is paradoxical to reject his version, it is equally
paradoxical to accept it.
Moreover, an appeal to experience to decide between these two
alternatives is of little help, and for this is so for at least four reasons:
(i) As has already been pointed out, Engels drew his conclusions
about motion without
referring to any evidence at all. His views were clearly not based on
experience; they were aimed at interpreting reality beyond any and all
conceivable experience.
(ii) Our experience of motion is as ambiguous as the words we use
to depict it are. The examples given above (and in the Notes below) indicate
that our ordinary ways of speaking about motion are far more complex than Engels, Zeno, Hegel or
even Lenin ever imagined. [Of course, in their everyday speech they will have
shown they knew this; it was only when they began to 'philosophise' that they
were led astray.] Anyway, not even an
indefinitely large finite number of observations of cats moving about on or off assorted mats
(and the like), could confirm whether motion is or is not continuous,
discontinuous, or if it is composed of countless discrete, concatenated 'sub-movements' -- or, indeed, whether it
is
something else we have as yet no words to describe. Even with advanced technological assistance, we
still wouldn't be
able to tell if motion was the one or the other.
[Indeed, as we have seen, there is no one thing that is
motion. Our use of this word, and its associated terms, is far too complex to
constrain in this way. (See the next two points.)]
(iii) Ordinary language, and thus everyday experience -- as a
matter of fact -- allows for both sorts of motion:
discrete and
continuous. This was demonstrated in the above examples. It is only a metaphysical
prejudice (itself based on other priorities that will be exposed in Essay
Twelve (summary here)) that (a)
Consigns certain depictions of motion to the realm of "appearance", or
"commonsense", while others are said to refer to "reality itself";
and that (b)
Regards one type of motion as
primary, the rest secondary.
(iv) The notion that there are such entities as
"things-in-themselves" (or that there is something called "motion-in-itself",
or "motion itself") is
hopelessly confused, and this isn't just because it represents a thinly disguised form
of "absolute" motion -- as will be argued elsewhere at this site
(until then, see Note 10). As we will see,
reference to "motion-in-itself" is unintelligible; small wonder then that it has
yet to be explained by anyone.31
Nevertheless, and once more, a repeated use of the word "must" in response to
the above -- as, for example, in a retort that might well have occurred to
some readers: "That's all very well,
but motion must involve a body being in two places at once…(etc., etc.)" --
could itself only have been based on a conceptual or linguistic analysis of a
limited range of uses of words associated with movement. Again, that would
amply confirm the view maintained here that dialecticians are happy to draw
universally true inferences from
a handful of specially-selected words,
and then foist the results on reality -- the use of "must" here would reveal yet again
this propensity to impose favoured a priori theses on nature.
When pressed to
provide evidence to substantiate their claim to be in possession of Super-scientific knowledge
like this of motion --
applicable to every region of space and time -- all that
DM-theorists would be able to offer in support would be the supposed meaning of a few words!
Once again, apart from an absurd alternative explanation for their possession of superior
knowledge (i.e., that those making such claims are
deities of some sort, who have access to a profound, semi-mystical
fountainhead
of knowledge (concerning
the nature of
"reality-in-itself")), 'conceptual/linguistic analysis' is the only conceivable source of
hyper-bold 'dialectical' claims like these.
And that explains why Engels omitted the data supporting his 'theory' -- and no one
since has bothered to supply any.32
Exclusively Linguistic?
It might be felt that the
above discussion completely misses the point: DM deals with real material
contradictions in the actual world, verified by careful empirical
investigation and tested in practice. Not only that, it is based on the thesis that reality
is contradictory (and that is itself founded on the scientifically confirmed belief in universal change).
It goes way beyond the idea that this is only true of the
language we use to depict nature. If contradictions in
nature are difficult to capture in ordinary language that is because ordinary
language is inadequate to the task (as, indeed,
TAR itself maintains; cf., Rees
(1998), pp.45-52). It certainly does not show that reality is free from contradictions.
Or
so it could be argued.33
However, this response won't do. Admittedly, the world is the way it
is independent of language and human knowledge, but unless we are capable of
expressing ideas about the world in a clear and determinate manner we are surely
in no position to make any definite claims about it. This is all the more so
with respect to DM where every attempt to render it perspicuous has failed -- as we
have just seen in relation to Engels's account of motion (and as we will see
with respect to other core DM-theses in other Essays posted at this site).
Engels certainly thought he could derive what he took to be a contradiction from
a consideration of ordinary words depicting movement and change. But, if his
'derivation' (and Hegel's) is shot-through with error and ambiguity, the
motivation to claim that reality is contradictory weakens considerably (and it
fades even more when it is recalled
that this idea itself is based on a series of
egregious logical blunders that
Hegel himself
committed). And in that state it will remain until
DM-theorists produce the evidence that motion everywhere in existence (past,
present and future) is as they say it is -- or until they succeed in
demonstrating that they have alternative ways of 'intuiting' the 'deeper aspects
of reality'
that are mysteriously unavailable to the rest of us.
Objects and events in nature do not confront humanity already sorted,
labelled and categorised. We do not literally see contradictions in
reality; they require considerable argumentative stage-setting even before
dialecticians can themselves assert that they exist. Hence, the question whether
there are 'objective' contradictions in nature -- based as it is (in this case at
least) on a quirky misuse of language (somewhat akin to the bogus question
whether the King in chess ever did marry the Queen, or, indeed, whether they
received planning permission to build those two Castles in the corner) -- is itself irredeemably
confused. And, of course, to such non-questions there are no answers.34
Plainly, it is the non-standard interpretation that dialecticians put on ordinary words
that conjures-up the
paradoxes they label "contradictions" -- that is, even where they
manage to get the
latter
word right.
In that case, far from reality being 'contradictory', it is the
DM-use of language
that is incoherent and paradoxical.
Conclusion
In this Essay, we have seen that Engels's account of motion is
not only shot-through with ambiguity and equivocation, it is irredeemably unclear.
Even if we
knew what he was banging on about, his 'analysis' depends on an asymmetric convention
that places no limit on the divisibility of location while it places just such a
limit on that of time.
Even if this asymmetry is waved to one side, his 'theory' would
imply that dialectical objects, when they move, if they are anywhere, they are
everywhere all at once, and that they don't so much move as expand (or contract) alarmingly.
Finally, we have also seen that his conclusions (even if we
knew what they were) only seem to follow if we ignore the many changes in
meaning that words like "place" and "move" undergo in different surroundings. In
fact, as it turned out, no sense at all could be made of what Engels was trying
to tell us.
But, what of the so-called 'Law of Identity'? Doesn't this 'Law' mean
that change and movement are impossible? It is to this pseudo-problem that I
now turn.
Notes
1.
Dialectical 'Contradictions'
[This forms part of Note 1.]
It isn't easy to form a clear idea of the DM-thesis that
reality is fundamentally contradictory:
"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.]
"Motion is a contradiction, a unity of contradictions."
[Ibid.,
p.256.]
[See also Note 2, below.]
With respect to DM, at least, this is
largely because the whole topic has been discussed (by dialecticians) with the utmost lack of clarity -– the work of
Graham
Priest
excepted, of course.
In Essays Four,
Six, Eight Parts
One,
Two, and
Three and Eleven
Part One, I
hope to demonstrate that while DM-theorists frequently use the term
"contradiction" in their attempt to expose the alleged limitations of FL, the
vast majority display little or no comprehension of either or both. Nevertheless,
this hasn't prevented them from
claiming that their understanding of "contradiction" is superior to that of
Formal Logicians.
According to dialecticians, the wider application of this term
(in DM) allows them to account for motion and change, while those who confine
themselves to the use of FL are unable to do so. However, as we will see in
the present Essay, this allegation is grossly inaccurate, at least with respect to
motion. Indeed, the rest of the Essays published at this site will show that not only can
DL not
account for change itself, dialectical logicians struggle to account for something as
mundane as a bag of sugar!
[DL = Dialectical Logic; LOC = Law of
Non-Contradiction; FL = Formal Logic.]
Clearly, the term "contradiction" is employed in FL in a
technical sense, and one that is widely misunderstood by DL-aficionados. [More on
this in Essay Four, Eight Parts
One,
Two and
Three, and Essay Eleven
Part One.]
As far as ordinary language is concerned, one of the ways in which we
can speak
about change involves employing a rule (that many also misconstrue as a logical truth
(i.e., the LOC)), which enables us to draw certain inferences (should we choose to do so) from
what might appear to be contradictory propositions. If two putatively
contradictory sentences are held true at different times, then (given certain
other constraints) speakers of that language would normally conclude that the subject of
those sentences had changed. For instance, consider the following:
C1: NN isn't a member of
Respect,
at t1.
C2: NN is a member of Respect, at t2
(t2
> t1).
A change like this would usually be recorded more directly,
either by the use of a tensed verb or by the employment of some form of paraphrase, as in: "NN has joined Respect", or "NN wasn't in
Respect last year, but now she is", etc. This means that such apparently
contradictory sentences -- coupled with wider uses of negation -- 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 the opposite of the truth (irony intended).
[Of course, the above was written before
Respect
self-destructed back in 2007! It is now called the
Respect Coalition.]
That being so, the idea that ordinary language and FL can't account for change is, quite frankly, bizarre. In fact, without the
resources available in the vernacular, human beings wouldn't have been able to
conceptualise change at all.
[And that comment applies equally well to scientists
and dialecticians. Again, as demonstrated
here, ordinary language can handle change far
better than the obscure and wooden terminology invented by metaphysicians. (That observation is especially
true of the impenetrable jargon Hegel concocted.)]
In that case, if, by their use of language, dialecticians actually
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 the DM-'analysis' of motion).
Now, as far as FL is concerned, two propositions are
contradictory just in case they cannot both be true and cannot both be
false at once. [The latter condition is almost invariably ignored by DM-critics
of FL. (Some deny there is a distinction here, even after it has been pointed out to
them! In fact, they tend to call such fine distinctions and careful attention
to detail "pedantic".
The dialectical confusion that results if such distinctions are ignored can be witnessed in
all its glory,
here.)
Its importance will emerge later.]
Naturally, when conjoined (as in ¬(p
& ¬p)), this characterisation of contradictory propositions represents the
simplest form of FL-contradiction.
[The difference between "contradictory" and "contradiction", also
ignored by DM-fans, is explained
here.]
Examples
of more complex FL-contradictions would include
either or both of the following:
C1: ¬[(P → Q) v (P → R)
↔ (P → (Q v R))].
C2: ¬[¬(Ex)(Fx & ¬Gx)
↔ (x)(Fx → Gx)].
[In the above, "(E...)" is
the existential
quantifier; "↔" is a biconditional
sign (and stands for "if and only if"); "(x)" is the universal quantifier; "&"
stands for "and"; "v" is the inclusive "or"; "¬"
stands for the negation operator; "→"
is the conditional
sign ("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 predicate-binding variable.
(More details
here, and
here.)
C1 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)]."
C2 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)]."
Some might wonder when sentences like these would ever be used.
However,
Mathematical Logic and the
Foundations of Mathematics are full of propositions like this,
and many others far, far worse. (This links to a PDF.)]
These, of course, are just two of the potentially infinite number of logical
contradictions which can be generated in MFL. DM-theorists would be hard-pressed
to find space -- even in their quirky universe -- for
contradictions 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 particularly the LOC with one another,
and all of them with opposites,
inconsistencies, absurdities, contraries, paradoxes, puzzles, quandaries, oddities, irrationalities,
oppositional processes, antagonism, forces, events that go contrary to expectations, and a
host of other idiosyncratic ideas. In
fact, they are so eager to see contradictions everywhere, they find they have to alter the
meaning of this word so that (for them) it becomes synonymous with "struggle",
"conflict" and "opposition". [More details on these and other dialectical confusions
and convolutions are given
in Essays Four,
Six, Eight Parts
One,
Two and
Three, and Eleven
Part One.]
A typical example of this genre appeared 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.]
So, tensions within the communist hierarchy are
'contradictions', are they? But, no one ever explains why such things should be
called "contradictions" when they are obviously far better described as "tensions" or
"conflicts".
Some might
conclude that this is just another example of Ms Lichtenstein's pedantry,
but that isn't so. [On 'pedantry', see
here.] There are
important political reasons for rejecting the use of "contradiction" in
the way it is employed by Dialectical Marxists. [On that, see Essay Nine
Part Two.]
Specifically:
(1) Its use allows dialecticians to argue for anything they like
and its opposite
(often by the same individual, on the same page or in the same speech!), no matter how
anti-Marxist or counter-revolutionary this "anything" happens to be.
The latter are often 'justified' on the basis that since everything is 'contradictory'
and a 'unity of opposites', Marxist theory and practice should be contradictory,
too!
(2) It is used to
rationalise a whole range of
substitutionist tactics, strategies and manoeuvrings, on the grounds that although Marx,
for example, insisted on the self-emancipation of the working class, we can
substitute for them (a) The Party, (b) The Red Army, (c) 'Third World'
guerrillas, (d) 'Progressive' nationalists, (e) Students, (f)
Sympathetic/left-wing politicians, (g) any number of other social forces/groups,
no matter how contradictory this might seem. Any who object..., well they just do not 'understand' dialectics
or the 'contradictory' nature of Marxism, the class war, the former USSR..., etc., etc.
(3) Its use 'allows' DM-fans to look at the
long-term failure of Dialectical Marxism and fail to see it for what this is: a
long-term and profound refutation
of their core theory, 'Materialist Dialectics'. In fact, it also
'allows' them to see
this abysmal record as the
opposite of what it is -- on the grounds that
appearances 'contradict' underlying 'essence'. So, if Dialectical Marxism looks
hopelessly unsuccessful and a catastrophic failure, the opposite is in fact the case. This
then encourages dialecticians to stick their heads in the sand, while our
movement slowly runs into those very same sands.
(4) Because of
(3), its use provides them with a
source of
consolation for the ineffectiveness of their entire movement,
its perennial divisiveness and its
ever present internecine warfare ("Well, what else can one expect in a contradictory
universe?").
So, this isn't just pedantic point-scoring; the use of this
word has had very real and
disastrous political consequences.
[I present many more examples of the odd things DM-fans say about
their 'contradictions' in Essay Eight Part Two --
here and
here, for instance.]
Be this as it may, DM-theorists themselves would be the
first to point out
that their interest
lies not so much with contradictory propositions as it does with real material forces,
which express, or even constitute, conflicts in nature and society
(but only if they have been confirmed in practice). Furthermore, since the
vast majority of classical DM-theorists believe that reality itself is fundamentally
contradictory, propositions which accurately describe the world ought to be
contradictory -- i.e., they should reflect
the contradictions that exist in nature and society.
But, because (contradictory) propositions are plainly linguistic expressions they are
plainly not material forces as such. This must mean that such propositions
aren't oppositional per se -- even though they
supposedly
reflect, or can be used to reflect at some level the dynamic nature of certain processes in reality
--
according to dialecticians.
On
the other hand, even if such propositions were oppositional, they
would only be so in a
derivative sense. In any case, the idea appears to be
that while objects and processes in nature are contradictory and subject to
change, any use of language aimed at depicting reality must reflect this adequately if it is to be
objective.
Or, so the case for the defence might go.
However, 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 claim that two
supposedly contradictory propositions are both true at once (or are both
false at once -- as noted above, dialecticians do not appear to be aware of this particular caveat) would automatically be regarded as mistaken
or confused in some way.
Indeed, that
fact alone
could provide sufficient grounds for questioning whether one or both of any
allegedly true 'contradictory' propositions on offer were in fact propositions
to begin with. If it is unclear what is being proposed (in the sense of "putting
something determinate up for consideration"), then anyone attempting to do
so can't be
proposing anything determinate -- that is, this side of their words being disambiguated. [Examples of
this are given
below, and later in the main body of this Essay. See also
here.]
Several factors might contribute to this state of affairs: (1) The
said 'propositions' could contain typographically similar words that have
different
denotations; (2)
They could harbour ambiguous, vague, or figurative
expressions; (3) They might be drawn from different areas of discourse, and
so on.
From such a perspective, the presumption would always be that both 'halves' of an alleged
contradiction could only be held true by someone in the grip of some sort of
linguistic or interpretative confusion. 'Contradictions' that have been
generated in this way wouldn't normally be regarded as capable of revealing
fundamental truths about reality; they would perhaps convey more
about the linguistic naivety of anyone so easily taken in.
In that case, the disambiguation or clarification of these alleged 'contradictions'
should
eliminate this 'problem'. Only an exceedingly naive person (or worse, a Mad Dog
Idealist -- like Hegel) would conclude that just
because certain words and/or sentences appear to be contradictory, nature
and society must be contradictory,
too.
Indeed,
this austere approach should recommend itself to materialists; not only was the
alternative view (that there are 'contradictions' in reality)
invented by card-carrying mystics, it 'implies' that the natural world possesses properties
that are only rightly attributable to human beings
-- i.e., the ability to converse and to disagree (i.e.,
to
contradict one another).
In addition, and to its credit, this austere approach
helps undermine the influence of the traditional doctrine that fundamental aspects of reality may
be inferred solely from the logical properties of language -- or, rather, in this particular case,
that
they can be derived
from a series of
sophomoric errors concerning the nature of contradictions
(outlined a few paragraphs
back and in much more detail,
here).
Naturally, DM-apologists will view claims like these with some suspicion;
indeed, these opinions might even appear to be dogmatic and aprioristic. It
could be argued that this obsession with the fine detail of linguistic usage must itself collapse into LIE, since it presumes to offer a
linguistic solution to what is in fact a philosophical,
scientific or practical problem.
[LIE =
Linguistic Idealism.]
However, the opposite of this is in fact the case; the approach adopted here
seeks to undermine the traditional metaphysical belief (which
dialecticians
themselves have bought into) that
fundamental truths about reality may be inferred from
language and/or 'concepts' alone. But, it is the world 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.
That approach, is of course, associated with Idealism:
"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 shows, DM-contradictions can't be
confirmed by experience, nor can they be
verified in any other way. (The allegation that this attitude to confirmation smacks of 'positivism', or
even 'empiricism', has been batted out of the park,
here.) In Essay Twelve, the ideological motivation
underlying the
contrary view will be exposed for what it is: a form of LIE (summary
here).]
Nevertheless, it is important to be able to recognise when the descriptive
capacities of language begin to break down. This is highly relevant with respect
to DM-theses since they break down alarmingly easily; indeed, when examined
closely, they invariably turn out to be confused, ambiguous,
non-sensical and
incoherent -- as
several Essays posted at this site demonstrate.
Moreover, it is equally important to be able to distinguish
spurious pictures (or, indeed, non-pictures) of reality from the genuine article. DM-theorists
themselves do this when they highlight the confused and/or self-contradictory
nature of rival accounts of nature and society, and advocate their rejection on that basis. [This
allegation is substantiated in Essay Eleven
Part One.]
On the other hand, DM-theorists believe that their analysis begins
with reality (albeit mediated by the conceptual/practical resources available to human beings
at any given time);
they then require that our linguistic resources are adapted accordingly. On this
view, if nature is contradictory, and if ordinary language and FL can't accommodate that
fact, then both must be judged limited and/or defective in some way and
thus in need
of supplementation with concepts drawn from 'Materialist Dialectics' -- or even
from Hegel.
It isn't easy for a response to this to appear un-dogmatic.
Language has been moulded throughout history by an evolving set of social
norms and conventions, which have themselves been refined by countless factors
at work across several Modes of Production. Because of this, it might seem possible to
argue
that when faced
with situations that appeared to be 'contradictory', human beings not only could,
they actually did develop dialectical categories. [However, the 'factual basis' for this
supposition will be undermined in Essay Fourteen Part One (summary
here).]
Even so, given other conventions that were in
fact adopted -- in practice; no one supposes that overt decisions were
taken, here --, this supposition is far more than highly unlikely.
As the word itself suggests,
to contradict someone is to gain-say or deny what they say is true (or
false, as the case may be). So, if someone says it is raining, and someone else
says it isn't, they are contradicting one another, and that fact is not altered
by either of these cases: (1) It is indeed pouring down with rain, or (2) The weather 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. All that is required is that
if one of them is true, the other is false, and vice versa. We'd not be able to understand anyone who
claimed both of these
characters were in error. Fanciful circumstances to one side, how is it possible for it to be
false that it is
and false that it isn't raining at the same time and in the same
location?
Some might point to the vagueness of
sentences like "It is raining". This would mean that both of the above could in
fact be false, since it might be indeterminate whether it is raining or not
(i.e., when 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). To be
sure, sentences like these are vague, but just as soon as it had been decided
that it is actually raining, then 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. In circumstances like these,
we'd not be able to make sense of anyone who said both were false, or
both were true.
But, what if we can't decide if it is or it isn't raining?
In that case, these sentences would be neither true nor false until a
decision had been made either way. In such circumstances, these sentences would fail to
be
propositions until this had been resolved. If we can't decide when it is raining or when it isn't 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 is raining.]
However, in everyday life (i.e., outside the use of aesthetic,
ethical, political and/or religious
vocabulary (etc.), where the meaning of words is often "essentially
contestable"), these sorts of conundrums do not normally arise. When in
doubt, we say things like "It is trying to rain...", "It is spitting, I
think...", or "I reckon it is clearing up...". Only a hardcore
contrarian
would say things 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 this approach to all such sentences,
they would either have very few friends or they'd enjoy a severely limited social life
-- either that, or they would be diagnosed with a
Personality Disorder of some sort. And, if we all adopted such an
attitude, inter-communication would grind to a halt. [On this, see also
here.]
Moreover, contradicting someone could be aimed at
challenging a truth, and not always confronting falsehood, as many
seem to think.
It could be objected that it was earlier claimed that:
...if someone says
it is raining, and someone else
says it isn't, they are contradicting one another, and that fact is not altered
by either of these cases: (1) It is indeed pouring down with rain, or (2) The weather 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 decide if it is or it isn't raining?
In that case, these sentences would be neither true nor false until a
decision had been made either way. In such circumstances, these sentences would fail to
be
propositions until this had been resolved. If we can't decide when it is raining or when it isn't 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 is raining.]
Which is it to be? If we can't say whether sentences like
these are true or whether they are false, then how can they be contradictory?
The objector forgot to quote this caveat:
All that is required is that if one of these is true, the other is false,
and vice versa.
And we can decide this well in advance of knowing whether one of
them is in fact true, or whether one of them is in fact false. As noted below,
this capacity is based on rules we have for the use of the negative particle,
and, as with any rule, we can decide how that rule would/could be applied in
advance of actually applying it. For instance, we can decide what would, and
what would not count as offside in football (soccer) even if there is no game
actually being played when we so decide, or if no more games will ever be played
--, or, even if, during a game, we lose sight of the pitch and the alleged
offence itself. Plainly, this is because rules aren't capable of being true or
false, just practical or impractical, applied or mis-applied, etc. Hence, this
particular rule is independent of any alleged truth or falsehood.
This topic is, of course, connected with the so-called 'Law of
Excluded Middle' [LEM], as it is supposed to feature in ordinary discourse. In
that case, we
might be tempted to agree with 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." [Hegel
(1975), p.174;
Essence as Ground of Existence, §119.
Bold emphasis added.]
To which Engels added the following (oft quoted) gloss:
"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 to the
conventions adopted at this site.]
However, as I have argued in Essay Nine Part One:
Nevertheless, it is difficult to
see what Hegel was trying to say here. That is because any attempt to
interpret him requires the 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 wrote. If an author always
means both (or even neither) then interpretation is impossible, and any attempt to unravel
his/her meaning becomes self-defeating (as we are about to see).
So, if Hegel were right, if absolutely
"everything is opposite" and there is no "either-or", 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: "Both P and Q", "either
P or Q", "neither P nor Q",
or
"either P or Q, but not both".
But, if P and Q are
inconsistent (that is, if,
for example, Q implies not P, and/or vice versa), and we interpreted his words one way (perhaps
that he believed both P and Q),
then we should still have to admit he accepted
both as part of the "unfolding of truth" (as he might have put it), which would
mean by his own lights, of course, that we would be unfolding error
instead!
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 this assumption it would become
impossible either to comprehend or defend him. If Hegel genuinely
cast doubt on the "either-or of understanding" (and he wasn't being
enigmatic, disingenuous, mendacious
or merely playful), and assuming he was correct to do so, then any attempt to
interpret him as asserting P or asserting Q would have to
conclude that he asserted both. [I give a clear example of this, below.]
In that case, any
determinate interpretation of
Hegel would have to ignore his own advice, and reluctantly accept
the deliverances of the "either-or" of ordinary language (along with its
corollaries), and acknowledge that, of either P or Q, he believed only one, not
both.
Here, truth would advance -- by yet another
dialectical
inversion --, but, only if we learnt (once again) 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'."
Now, either Hegel accepted P or he accepted
Q -- indicating that there is at least one 'either-or' "in heaven or
in earth" -- i.e., right here!
On the other hand, if
he took his own advice and accepted
both P and Q, 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 (or any
technical meaning his epigones might want to attribute to them), but solely concerns
how we are to understand him now, in this world, by the perusal of
the very material words (in print, or on a screen) found in his books,
employing common understanding in order to do so.
Hence, it is beside the point whether
the rationale for his own (dialectical, then speculative criticism) of the use of these terms by the "abstract understanding" is legitimate or not (irony intended). Since Hegel's writings
appear before us now as phenomenal objects, and given that they are not
self-interpreting (and Hegel is no longer with us to explain himself --
but, even then we'd have to accept he meant either P or Q, not both), they face the ordinary cannons we employ elsewhere to
understand anyone's words. In order to read and perhaps interpret Hegel as
believing this or that, but not both, nor neither (etc.), 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'
cons some of us into thinking it can.
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., that we view 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, §119.]
In that case, if "everything is opposite",
and Hegel's works were written somewhere on this planet, and copies of them still take
on physical form, in this universe(!), then anything he committed to paper must be its own opposite,
too -- or, he was wrong.
[Irony intended again.]
In
either case, it would be
foolish to believe Hegel was serious (or even that he had thought things through with
due care) when he wrote the above words, while also accepting what he said about
the LEM -- the
dread "either-or".
Hence, and following Hegel's advice,
the above passage should be re-written along the following 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 and opposition, in itself, and in other things, too. The finitude of things will and will not
then lie in the want of correspondence, and actual correspondence, between their immediate being, and what
they essentially are, or are not, and both. Thus, both 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, as well: 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 noisily, 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."
Everyday, non-abstract understanding will,
I think, readily see what arrant nonsense results from Hegel's 'genius' when we apply
it to his own words (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 on real paper, but was written on Ideal paper, neither in heaven nor on earth
-- and that they themselves
do not exist anywhere, either (or both, or neither), in order to do that (or not).
[On the acid and base
fiasco, see here.]
In a recent book [Stewart
(1996)] a number of misinterpretations and misrepresentations of Hegel's work
were corrected by a handful of Hegel scholars. However, there would seem to be
no point to this exercise if Hegel's ideas about "either-or" were
correct. If he is right in what he says -- that in the entire universe there
is no either-or -- then there would be some truth even in the wildest allegations about
his work.
For instance, these: that Hegel fully
accepted without question the unlimited applicability of the LOI in every
conceivable circumstance without any qualifications whatsoever (and this includes
its use in dialectical
and speculative thought as well as in relation to change), and he did not; that he flatly denied that reality/thought is contradictory
in any sense at all, and he did not; that he doubted the
truth of every single one of his own ideas all the time, and he did not; that he wrote nothing at all in German in his entire life,
and
he did not; that everything he wrote was actually written
by
Schelling
-- in fact it was published
only yesterday, and it
wasn't --; that he was a Martian, and he was not...
[Any attempt to reject any of the above
alternatives on the grounds that Hegel must have accepted one of them, but not both
-- or, indeed, that we must do likewise -- will have to use the dread LEM in
order to do so, vitiating Hegel's challenge, and theirs.]
It could be objected that this line of attack
completely misunderstands the nature of
DL as Hegel
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 correct, a quick
reference to DL will indicate it is both.
This means that until DL-fans commit
themselves to one or other view (but not both) we can't even begin to
evaluate anything they say -- and neither can they!
Unfortunately, just as soon as they actually manage to specify what they mean
(e.g., that they intend this but not that), we must cease to take
them seriously -- since they would then have employed the dread LEM,
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 criticisms, or not (or
both).
Once more, these 'ridiculous conclusions'
either do, or they do not follow from what Hegel wrote. If the above
response is right, and they do not follow, then there is at least one either-or at work here, namely this one (since both options wouldn't be
correct in this case -- only one option would be). And if that is so, then the
'ridiculous conclusions' do indeed follow, since Hegel would in that case be
wrong to assert there is no either-or anywhere in existence.
Hence, taking each 'ridiculous conclusion',
one at a time, if we maintain it doesn't follow, then we will have applied the
LEM once more -- in that we would thereby have denied that that particular 'ridiculous
conclusion' both does and does not follow, and thus that one of these either-or
options must obtain --, and we obtain the same result.
On the other hand, if they do follow,
then they do anyway.
Either way, they follow...
QED
The problem with sweeping claims like the one
above about "either-or" -- that is, concerning the supposed limitations of certain principles of
FL (and especially
those that express patterns found 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.
It is of course possible to 'adapt' Engel's comments in like
manner to take account of his own advice (but to save the reader's/readers' sanity, this
has only been inflicted on half of one of his paragraphs):
"At first sight and not at first sight this mode of
thinking and of not thinking seems, and it does not 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 whether he doesn't...."
So, not even Engels could have taken his own advice and hope to
have made sense.
[His argument concerning the status of living organisms is
destructively analysed
here and
here.]
So, the facility we have in language (which apparently goes back as far as records last,
and as far back as human beings have been able to argue -- indeed, without
it, we would not be able to comprehend indicative sentences before we
knew whether they were true or whether they were false (why that is so is
explained in detail 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 the linguistic practices we now have
(and the social relations from which they have arisen), it is 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 -- that is,
without (retrospectively) altering what the word "contradiction" itself means). 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 the account presented here sliding into some
form of
Psychologism, it should be read in conjunction with the careful
distinctions set out in Shanker (1998), particularly Chapter Three, and
especially pp.97-120. Of course, there is nothing wrong with using the word
"contradiction" is a new way, but that having been done, this new use can't
affect its ordinary employment, nor relate to it, let alone its role in
FL.]
In cases where disputants might appear to be doing this
(i.e., where both parties to an argument are gain-saying one another but where
both also seem to be speaking the literal truth), the most
likely response we'd make 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). Not only that,
but, these
conventions prevent
us from understanding anyone who might think otherwise. Worse still, they also
prevent us from understanding how humanity could ever have developed
alternative conventions, or how we could make sense of anyone who supposed that they
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: (1) The way that negation works
in language, and (2) The capacity language has of allowing us to understand an empirical
proposition (i.e., a fact-stating sentence) before we know whether it is true or
whether it is false. [More on that 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",
since most logicians (particularly mathematical logicians) regard contradictions
as false, whereas if 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), not a logical truth,
a contradiction in language can't be true or false. If 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, is explained here.)
Of course, this creates problems for the
Truth Tables,
but that can be overcome by a stipulation to the effect that in FL, a
contradiction is always given the value "F".]
These claims are as bold as they are controversial, so I shall
defend each in turn.
Take the first -- which was that we should fail to understand
anyone who believed a contradiction could be true (or, rather, how two
contradictory propositions could both be true or both be false), and that we would seek to
disambiguate it (or them) in order to make sense of what it or (they) said. Consider the following example:
B1:
John Rees wrote and did not write The Algebra of
Revolution.
B1a: John Rees wrote The Algebra of
Revolution.
B1b: John Rees did not write The Algebra of
Revolution.
Let us suppose someone asserted that B1 was true -- or that both B1a and B1b
were true. Faced with this, we would find it difficult to take this person, or what
they said, either literally or seriously; that is because both halves of
B1 couldn't be true,
nor could they both be false.
[Some might think that these are not the type of contradictions
that are of interest to dialecticians; that objection will be fielded
later on in
this Note.]
However, if
both B1a and B1b were still held true, then, trivial cases aside (such as
the names "John Rees" and/or "The
Algebra of Revolution"
refers to two separate individuals/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 could imply that John Rees was the author of the
said work; in another quite ordinary sense it might suggest that the book was
not hand-written, but was perhaps word-processed. [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 did not hand-write
it (or hand-write it himself). It would then be clear that B1 only
appeared to be contradictory because of this elementary equivocation. We
wouldn't automatically think that there were real
material forces at work behind the struggle to produce this book, no matter
how well-confirmed each half of B1 happened to be.
[This shows that an
empirical check in such cases isn't relevant to what is in fact a logical
or conceptual issue.]
Again, someone might object, arguing that the above line of
attack reveals the LIE implicit in the logical caveats this Essay
advances, for
it seems to restrict the options available to reality by appealing to controversial logical/linguistic pre-conditions.
But, that would be to mistake the approach adopted here for its opposite. The
strategy employed at this site seeks to undermine the idea that substantive truths about
reality can be derived
from logical, conceptual or contingent features of language. It does this
by basing itself on what
we would now try to do (prior to, and independently of any theory) to
interpret/understand what appear to be contradictions as and when they
might arise. In that case, these Essays appeal to rules (i.e., normative social practices) we already use or with which we
comply, not to a series of truths
that can be inferred from a misconception of the nature of such rules.
Hence, no truths are being inferred (by me) from the above
observations, merely a denial that anyone can derive any truths at
all from a misconstrued
set of puzzling words.
Indeed, it is the opposite (dialectical) view that collapses into LIE, for it confuses
linguistic/logical rules with empirical -- or Super-empirical -- truths. In DM, this
takes place when, for example, dialecticians
treat the LOC as a truth
which they think could be (and often is) false. This leads them to argue that
contradictions themselves can be true. But, if, as noted earlier, the LOC is in fact a rule (or if it
expresses a rule we ordinarily use in relation to negation), it can't be either true or
false -- any more than orders or questions can be true or false.
[Further ruminations on this theme will be resumed in Essay
Twelve Part One, where it will be
demonstrated in detail why the aforementioned confusion of
rules with substantive truths about the world is a characteristic feature of
Traditional Thought. That is because it implies there is a hidden world --
anterior to experience --, accessible to thought alone, thus undermining and
devaluing communally constituted aspects of the ordinary use of language, and
thus the experience of working people. It is from such
ideologically-motivated confusion that Metaphysics (and now dialectics) originally
arose.]
Admittedly, the example above
(i.e., B1) is glaringly trite, but it was deliberately chosen so that the
strategy of disambiguation would be clear to all.
Nevertheless, and
against this, it could be objected that DM-theorists are more
concerned with the analysis of real material forces operating inside
Capitalism in order to assist in its demise. In that case,
simplistic examples like B1 are not even remotely relevant. Nor are they
dialectical contradictions.
Or, so it could be argued.
In order to counter this response, the sort of
contradictions DM-theorists are interested in will be analysed elsewhere
at this site (and in unprecedented
detail -- for example, here,
here and
here). There, it will be shown
that these "real material contradictions" turn out not
to be contradictions to begin with (in any sense of that word; more specifically
here,
here and
here) -- and they can't be turned into them howsoever they are interpreted,
or 'surgically enhanced'.
With respect to the other assertion made above -- that we would
fail to understand alternative conventions, given the ones we already have --,
the key point is that as social beings we may only succeed in understanding
something when, plainly, it is presented to us in a language and a form with which we are
familiar --, and typically, but not exclusively, this takes place in ordinary
language. And that, too, can be asserted with some confidence since the word
"understand" is (patently) in ordinary language already. [The
significance of that point will emerge in Essay Thirteen
Part Three.] But, discourse is not a
free-floating phenomenon; its invention and evolution are both a function of
our social and material development. In
addition, our use of language is subject to constraints we have inherited
from previous generations, which we clearly
had no hand in shaping.
Indeed, all of us had to be socialised (by parents, siblings, carers, teachers and
peers) into using language within, and in compliance with these constraints. As
individuals, we manifestly did not socialise ourselves.
Moreover, we demonstrate our mastery of this complex
socio-linguistic medium when we begin to communicate and interact with others.
While we can form thoughts as we please, we can't do so under logico-linguistic/social conditions of our own choosing
(to paraphrase Marx).
Now, it is tempting to think that such limitations are physical -- or at
least that they represent merely contingent constraints on the use of language --, but that
would be a serious mistake. There are physical and contingent constraints
on language (for example, no one could utter or understand a trillion word
sentence), but these aren't the limitations alluded to above.
[A clue to the nature of these limitations can ascertained by
anyone who reads the Essays posted at this site, especially where it has been
demonstrated time and again how quickly DM-theses fall apart, and how they can't be repaired no matter what is done to them. That
sort of limitation isn't physical; it is conceptual. Another example can be found
here.]
B1:
John Rees wrote and did not write The Algebra of
Revolution.
Fortunately, however, the negative points made (against DM) in this Essay 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 these points will become a little clearer.
In relation to understanding others who speak different
languages, or individuals from the past, we can translate
what they have to say (ancient or modern)
into our own language, but we may do so only if we act within the constraints currently
operating on us -- unless we want to restrict ourselves merely to simple transliteration.
This means that because we can't make sense of
contradictory speech now, we can't comprehend the
supposition that contradictions could ever have been held true by anyone in
the past, either.
Of course, there have been mystics who professed all manner of odd
and contradictory ideas. Other than Hegel, this includes, for instance,
Buddhist logicians and 'teachers' (this links to a PDF), but it is a moot
point whether anyone has ever understood the strange things they say. Indeed,
mystics themselves tell us they don't understand the conundrums they come
out with. [More on this in Essay Fourteen Part
One (summary here).]
Even so, we are equally incapable of
translating (not transliterating) any language, ancient or modern, into our own in comprehensible
terms while attempting to depict its users employing contradictory speech,
all the while holding these contradictions true. This doesn't imply that we
have to reject the idea that such individuals actually believed these contradictions
were true, but we certainly can't hold them true. We may acknowledge the
fact that some individuals (in the past (or whenever)) speak, or have spoken, in
paradoxical ways, but given what we now mean by the words we use, it is now impossible to make
sense of what possibilities these ancient/mystical sayings could have presented to
those who produced them -- nor, indeed, determine whether or not they
presented anything at all. Moreover, since these odd individuals invariably fail
to explain themselves, it is quite clear they
couldn't make sense of them either.
[DM-fans certainly can't explain their 'contradictions', and
complain regularly that critics just do not "understand" dialectics.]
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 sophisticated 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 should consult Berto (2007), Goldstein (1992, 2004), Field (2008), and Slater (2002, 2007a), as well as
this review.
[Incidentally, the aforementioned
"limitations" are not those that words exercise upon us, but
how we collectively -- through our socialisation -- understand and thus
use the words
we already have. To suppose otherwise would be to
fetishise language.]
Some may take exception to the above assertions, claiming that they
can imagine speakers holding certain contradictions true (which
contradictions represent real material forces), namely themselves! Dialecticians, it seems,
are living disproof of the sweeping allegations made in this Essay.
Or, so it could be argued.
However, this Essay aims to show that Hegel's and Engels's claims
(that motion is 'contradictory') are far too confused for them to be assessed for
their
truth or their falsehood (and hence that the 'contradiction' they claim to see
in moving bodies isn't one to
begin with). 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-thesis that reality is suffused with UOs will be destructively
criticised in Essay Seven
Part One.
[UOs = Unity of Opposites.]
In which case, because it isn't possible to make sense of any of
the examples of 'dialectical contradictions' presented to us by DM-theorists, the above
"sweeping allegations" have everything going for them. Since
dialecticians have shown they themselves are incapable of explaining these mysterious
'contradictions' to anyone, this can serve as further
confirmation. [On that, see here.]
Indeed, on Internet discussion boards, when academic Marxists and revolutionary activists
alike have been asked
(repeatedly) to explain what 'dialectical contradictions' are, they have signally
failed to do so. [Links to many of these discussions can be found
here.]
To be sure, as noted earlier, there have been, and still are, religious believers who
assent to all manner of apparently contradictory ideas, but this doesn't refute
the above allegations. Their talk is often non-propositional, and wall-to-wall
non-sense, as will be
demonstrated in a later Essay. The same comment applies to
Buddhists
(this links to a PDF) -- or, more
pointedly, to Zen
Buddhists --, who seem to glory in paradox.
However, in relation to the claim that we wouldn't be able to
make sense 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.
This isn't because it would be especially 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 die-hard dialecticians 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
attempting to disambiguate it).
As noted earlier, trite
examples like B2 have been deliberately chosen to illustrate a point that is
all too easily missed: when faced with the paradoxical things people sometimes
say, we automatically try to disambiguate their words, or their actions;
we adopt what
Donald Davidson once called
the "principle of charity" when
attempting
to grasp their meaning. [Davidson (2001).]
[Of course, in doing so, we have to distinguish between
speakers' meaning (i.e., what they hope to convey or achieve by their words) and
word meaning (i.e., what those words mean). The failure to do this will only lead
us into the sort of confusion that undermines
Voloshinov's work, for example, and that of his
epigones. (I have gone into this in considerable detail in Essay Thirteen
Part Three.)]
Hence, when confronted with someone who
asserted an apparent contradiction we would normally employ this policy (trivial examples
excepted, of course).
[Indeed, this is the approach I have adopted (in a
modified, but less sympathetic form) in relation to the odd things Zeno, Hegel and
Engels had to say about motion, in this Essay.]
This doesn't mean that this will necessarily distort what was
said; 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 DM-rejectionists out there, they would be hard-pressed to explain to anyone else
what they themselves took the sense of a true contradiction to be (that is, not
without using yet another Nixon
card), as the rest
of this site aims to show.
[And
that comment applies to any 'dialectically-motivated' responses elicited from those who
might think to question the above
assertions.]
Clearly, this doesn't mean that we shouldn't exercise some degree
of sensitivity toward other belief systems (past or present), but we may only do
so in terms of current linguistic protocols. If confronted with what appears to be weird and/or
paradoxical beliefs held by others, we wouldn't be able to translate or interpret them
literally and claim we understood them. And, if anyone claimed that
they could do this, it would automatically throw into doubt the validity of
their translation (unless the meaning of the word "translate" itself
had
changed) -- always supposing, of course, that they hadn't merely
transliterated
the relevant inscriptions/writings
instead.
However, if what had been 'translated' were held to be literally
true, and was still paradoxical, then whatever else we could make of it, we would have to abandon all talk of its literal truth.
Either that, or, once again, we would have to understand the words "literal"
and/or "truth" non-literally!
[This topic is still under intense debate; on his see Creary and Read
(2000), especially Chapter 12: Cerbone (2000). See also
Conant (1991), and Forster (1998).]
So, until and unless DM-theorists explain themselves, we are
forced to conclude that 'dialectical contradictions' do not depict anything in reality in
any meaningful sense.
Nevertheless, this is not
being asserted because I personally think that reality contains no contradictions, or because I have
concluded that the world either is or is
not as these allegedly 'true contradictions' might to depict it -- or
even because
contradictions are always false (which is the classical view). To argue along
these lines
would be to fall into the same trap that ensnares DM-theorists, and would amount
to the derivation of the opposite a priori thesis -- about reality to
that adopted by DM-theorists -- from an
alternative linguistic convention, which I might have found more acceptable.
On the contrary, contradictions fail to depict
the world not because they are false, but because they aren't depictions to
begin with. They represent the disintegration of description, since
they violate materially-grounded linguistic rules we already have for the use of
the negative particle. [On this, see Essay Twelve
Part One.]
Finally, it could be argued that the above comments are misguided since dialecticians do not question
the general application of principles drawn from FL, such as the
LOC; they merely point to their
limitations when it comes to accounting for change.
That particular claim will be put under considerable pressure
throughout this and other Essays at this site, where it will be shown that it is
dialecticians who can't account
for motion or change.
Added 12/02/10: A story on the BBC website
("Do
speedy elephants walk or run?") illustrates how an "either-or" question is
answered by scientists without them having to agree with 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 is that elephants do both, they run
and walk. Is this a contradiction? Does this refute the claims made above? Can this be
'resolved', DM-style, by means of a series of a priori, dogmatic assertions? Or
by disambiguation?
Well, here is how the website article explains 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 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 cant 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 concatenated to save space.]
So, this apparent
contradiction was resolved by detailed observations (and clear definitions),
which
led to a new discovery: that elephants run with their front legs, but walk with
their back legs. Had these researchers been dialecticians, it is unlikely that
this advance would have been made; we would merely have been told to "grasp"
this 'contradiction' and move on (no pun intended).
[More on that in Essay Seven
Part One.
Compare this with the
Mickey Mouse Science one finds in books on DM. General logical
issues are discussed in Essay Four, and other related topics (such as the
"interpenetration of opposites" and change through "internal contradiction") are
reviewed in Essays
Seven and Eight
Parts One,
Two and
Three. Those who feel that the
above comments do not in fact address 'dialectical contradictions' should read
this,
this,
this, and
this, and then think
again.]
2.
Engels was, of course, openly borrowing from Hegel:
"If, now, the first
determinations of reflection, namely, identity, difference and opposition, have
been put in the form of a law, still more should the determination into which
they pass as their truth, namely, contradiction, be grasped and enunciated as a
law: everything is inherently contradictory, and in the sense that
this law in contrast to the others expresses rather the truth and the
essential nature of things. The contradiction which makes its appearance in
opposition, is only the developed nothing that is contained in identity and that
appears in the expression that the law of identity says nothing. This
negation further determines itself into difference and opposition, which now is
the posited contradiction.
"But it is one of the
fundamental prejudices of logic as hitherto understood and of ordinary thinking
that contradiction is not so characteristically essential and immanent a
determination as identity; but in fact, if it were a question of grading the two
determinations and they had to be kept separate, then contradiction would have
to be taken as the profounder determination and more characteristic of essence.
For as against contradiction, identity is merely the determination of the simple
immediate, of dead being; but contradiction is the root of all movement and
vitality; it is only in so far as something has a contradiction within it
that it moves, has an urge and activity.
"In the first place,
contradiction is usually kept aloof from things, from the sphere of being and of
truth generally; it is asserted that there is nothing that is contradictory.
Secondly, it is shifted into subjective reflection by which it is first posited
in the process of relating and comparing. But even in this reflection, it does
not really exist, for it is said that the contradictory cannot be
imagined or thought. Whether it occurs in actual things or in
reflective thinking, it ranks in general as a contingency, a kind of abnormality
and a passing paroxysm or sickness....
"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 a
particular DM-theorist, James Lawler) were made here, and
several
more will be posted in Essay Twelve, at a later date.
3.
An alternative translation -- which appears in Volume 25 of Marx and Engels
Collected Works
(MECW) -- renders the last sentence as follows:
"And the continuous origination and simultaneous
solution of this contradiction is precisely what motion is." [MECW, Volume 25,
p.111. This can be found
here.]
The above version manages to defuse some of the criticisms
outlined in the main body of this Essay, but not all. Who, for instance,
"solves" these contradictions, and how do they do it? More pointedly, how do
they manage to do this quite so quickly (i.e., simultaneously
with the "origination" of each new contradiction)?
Moreover, this passage introduces several difficulties of its
own, for it leaves it entirely mysterious from where these contradictions originated. Indeed, it
appears to promote contradictions above motion; they cause it, not it them.
Naturally, in a system derived from AIDS, where reality is just
the development of Mind, the ability of contradictions to cause change, or to
make things move, seems to make
some sort of crazy sense. Apart from
that, it doesn't.
[AIDS =
Absolute Idealism; LIE =
Linguistic
Idealism.]
4.
On this, see Note 3, above.
However, as we have seen in other Essays posted at this site,
dialecticians regularly make this mistake, imagining that they are talking about the
world when in fact they are indirectly drawing attention to their own idiosyncratic use of
language. This
is, of course, part of the reason why DM is classified here as a form of LIE. [For more on that, see Essays
Three Part One
and Twelve
Part One.]
The fact that DM falls apart so easily when these linguistic
confusions are exposed merely confirms the accuracy of the above observation.
5.
To be sure, as usual, the picture is far more complicated than this opening salvo
might suggest. Later on in this Essay, examples will be given where both
stationary and moving objects occupy two places at once. However, it is reasonably
clear that Engels didn't have these in mind when he spoke so boldly about the
contradictory nature of motion. On the other hand, if he had taken them
into account, his whole 'analysis' would have been completely undermined.
Quantum phenomena
that supposedly violate this caveat (i.e., the claim there is no evidence that
moving objects occupy two places at once, etc.) don't affect this negative conclusion. No one supposes that in
experiments which suggest an electron, for example, can be in two places at once
that this particle moves from one of these places to the other. What is supposed
to happen is that when one electron is aimed at a double slit and focused on a
screen, it appears to have taken two separate paths at the same time.
So, it hasn't moved between the latter two locations at the same time; it has, it seems,
merely followed two paths.
There are of course those who
question the standard interpretation of such experiments.
[This topic is
connected with
wave-particle duality. More about that,
here.]
5a.
However, and independently of the comments made in the main body of this Essay, if
instants have no duration then -- according to
Trotsky -- they can't exist,
since they are merely 'abstractions'.
But,
what they are 'abstracted' from Trotsky forgot to say. How does one abstract an instant?
Insubstantial spectres like these can't be what all time intervals have in
common -- non-existent duration-less 'points'? [On this, see Note 6.]
6.
'Abstraction' is dealt with in Essay Three
Parts One and
Two.
Instants in time share nothing with our experience of time, and
so they can't be derived from it by a 'process of abstraction'.
Of course, it could be argued that scientists and philosophers
extrapolate from finite moments in time (i.e., from time intervals) to such
instants. Hence, as such, these instants are mental/Ideal constructs, capable of
being mapped onto the
Real Numbers.
This line of argument has been neutralised
here (and in general in
the two Essays mentioned above).
7.
The idea here might run as follows: If
knowledge results from the reflection in the mind of complexities
found in reality (mediated by practical activity) -- and which is correct only "within certain
limits" -- then, even a provisionally correct theory must faithfully
represent the contradictory nature of the world. In this limited sense,
human/social categories would then be relatively adequate to the world (again, if they
are correct, and have been tested in practice), but they will not have been projected onto it. This
interpretation might then allow DM-theorists to draw substantive conclusions
about the world from a consideration, or application of the concepts and
categories found in
thought (howsoever they got there). Even so, these theories would still only approach absolute truth asymptotically.
Indeed, some might want to call such concepts and categories "presuppositions".
[If, on the other hand, the Kantian/Hegelian route is taken by dialecticians, whereby
the concepts and categories of thought are what they are because of the nature
of cognition/'dialectical reason' itself, then they should admit that they
have imposed
their ideas on nature, contrary to what they
swear they never do. To
date, only certain
HCDs seem prepared to take this 'Kantian/Hegelian' detour.]
Of course, this flies in the face of what Novack said:
"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.]
Be this as it may, such claims are examined in greater detail in
here and
here. However, in addition
to th above, it is worth highlighting several serious problems this approach to
knowledge faces:
(1) Elsewhere, it will be argued that this way of looking at language forms part
of what I have called the RRT. This is a theory that in fact projects 'knowledge'
onto nature
under the pretence that language/'cognition' merely
reflects what is already there.
[RRT = Reverse Reflection Theory; this will be
explained in Essay Twelve Part Four.]
Because of their implicit acceptance of the RRT dialecticians assume that they are in a position to state in advance of experience what the
world must be like before anyone knows what it is like.
This
involves them in
specifying what certain
'concepts'/words
correspond with in reality predicated
solely on the basis of the supposed logico-linguistic features of the expression of
such thoughts.
[They certainly wouldn't wish to put things this way, nor would
they even recognise that this is what they actually do. However, numerous examples were given in Essay
Two that reveal the propensity all
dialecticians have for asserting dogmatic and a priori theses about
fundamental aspects of reality, true for all of space and time, from the
meaning of a handful of expressions/'concepts' borrowed from Hegel and
Traditional Thought. A detailed analysis of the a priori origin of core DM-theses can also be found
here.]
Of course, this thesis itself (i.e., that language reflects the
world) can't have been derived from the world. [Or, if it can,
we have yet to see the proof.] In that case this theory -- which claims that knowledge is a
complex reflection of reality -- must itself have been imposed on nature
(once more, contrary to the claim that
this is never done).
Nevertheless, an additional idea operating behind the scenes here seems to be that
reference to
experience, observation or practice is necessary if we are to weed items out
that aren't actually found in nature, or
which do not reflect 'objective' reality. [Otherwise, of course, an
appeal to empirical checks
to test which linguistic expressions are genuinely represented in nature by real
material processes and/or relations would be an empty gesture.] In fact, because
it is impossible to specify ahead of time which parts of this (now
supposedly
legitimate) a
priori picture of the world might never be eliminated after testing
in this manner, all knowledge
is provisional. Or so it could be, and has been, argued.
Despite
this, DM-theorists still aim to tell their readers what the fundamental aspects of
reality are, valid for all of space and time. They inform us that
everything in reality is contradictory and constantly changing, that
all objects and processes are powered by the interplay between 'interpenetrated, internal opposites',
and that the world is a single interconnected
'Totality'
composed of 'mediated' parts/wholes,
governed by the laws of dialectics, and which is susceptible to 'rational' explanation. In
addition, we are informed
that each part is dependent on every other part, and that the nature of the
whole is determined by the complex interconnections between the parts, etc., etc.
But, the only evidence for such universal
theses is a series of inappropriate extrapolations from a few highly
tortured linguistic expressions -- justified by an appeal to some rather shaky
but nonetheless
seriously garbled Stone Age Logic --,
substantiated by a few highly clichéd,
specially selected, constantly recycled and
contentious examples. [Labelled
Mickey Mouse Science
in Essay Seven Part One.]
Unfortunately, this means that if an inventory were drawn up of theories that are, or could be viable candidates for explaining
nature, DM would struggle to make the bottom of the reserve
list.
However, if nature were reflected in thought, so that
aspects of reality were embodied in language, and if it were then claimed that this justified inferences
from language to the world, it would be impossible
to account for falsehood. If thought is a
reflection of the world, then it could never be
incorrect -- in the same way that a mirror image is never wrong.
Of course, it could be argued that a sophisticated application of
the RTK [not to be confused with the RRT], with its emphasis on the 'partial' or
'relative' status of truth, on practice and the "one-sided" nature of
abstractions (etc., etc.), is able to neutralise these difficulties. After
all, mirrors can and do distort reality (at least with
respect to left-right symmetry, and human/object morphology (in, say, a
hall of
mirrors), etc.), but few are
taken in by this. Moreover, it could be maintained that when other criteria are
incorporated into the mix (such as increased consistency and greater explanatory
power), defective theories could be weeded out as part of the search for an ever more accurate
account of the world and how to change it.
[RTK = Reflection Theory of Knowledge.]
Maybe so, but mirrors can't reflect what is not there.
Hence, if language and thought were mirrors (or even lenses, to vary the
metaphor) -- distorting or not -- we
would have to conclude that everything expressible in language must exist
in reality. Even though they might distort things, mirrors can't conjure into existence objects and processes that
aren't there. But, followers of
Meinong
excepted, who in their left mind is prepared to admit that whatever language contains must exist/subsist
somewhere in nature?
Who wants to allow for the existence of, say,
Harpies and
Gorgons -- even in a
distorted form -- simply because we have words for them? On the
other hand, if such 'entities' are so easily admitted into 'Being' (by the
expedient of simply naming
them), why bother looking for evidence in support? Indeed, if this approach to
knowledge were viable, any search that went
beyond leafing through every Dictionary,
Thesaurus,
Encyclopaedia of Mythology, and Textbook of Grammar would be superfluous. In that
case, Science would become a sub-branch of lexicography or of
hermeneutics.
Naturally, it could be argued that even mythical beasts and
fictional characters are composed of 'images' that have been derived from
experience. Where human judgment goes wrong is in knitting some of these
together in incorrect or fanciful ways. For example, a Harpy is formed from a combination
of human and animal 'images'. However, experience tells us that these beasts do
not exist. Hence, we can imagine all sorts of 'possible beasts', only some of
which actually inhabit this universe (as far as we know).
This particular
response will be
tackled in Essay Three Part Five, and Essay Thirteen Part One (here).
Suffice it to say that the idea under review here is that it is words, not 'images', that reflect reality. In that
case, this metaphor is committed to the view that if we have words for
something, it must exist. ['Images' will be examined in the above Essay. See
also, Essay Thirteen
Part One.]
Of course, anyone committed to such a theory would have problems
pointing out the ontological equivalent of prepositions, conjunctions, adverbs,
definite or indefinite articles, and the like.
Putting this worry to one side, it might be
difficult, too, for anyone who accepts this view of language to explain how
words for non-existent beings (such as Harpies and Gorgons), even if these are based on
images stored in separate dialectical heads, can be harmonised with a social
interpretation of language.
[This topic will be
addressed in detail Essay Thirteen Part Three. There is a variant of this theme, but based on
the 'images' focussed on by Lenin in MEC. Lenin's argument (if such it may be
called) is demolished in Essay Thirteen
Part One.]
[MEC = Materialism and Empirio-Criticism,
i.e., Lenin (1972).]
However, the specific point under consideration here was in fact
the following claim:
[That the aforementioned]
interpretation might then allow DM-theorists to draw substantive conclusions
about the world from a consideration, or application of the concepts and
categories found in thought (howsoever they got there).
Even so, these theories would still only approach absolute truth asymptotically.
Now, we have already established that DM-theorists go way beyond
such seemingly modest disavowals, claiming to know what the fundamental features of
reality are -- valid for all of space and time --, and derived solely from the alleged meanings of certain words.
Some might think to bring in ideology here, but that can't
affect the above. Ideology supposedly 'inverts' things. However, even if this were
an apt metaphor, ideology cannot
create (by inversion or reflection) what isn't there. [I will say more about this in Essay Three Parts Four
and Five.
Until then, see here.]
Moreover, an earlier reference to the
hermeneutic gyrations required to make this
theory work was deliberate. This word was in fact derived from
Hermes, the interpreter of
the Gods. So, the phrase was used because of the many accusations advanced in these Essays that DM is
just a modern-day form of
Hermeticism.
This allegation is also linked to another ancient
idea: that Philosophy and Theology were invented by the Greek 'god',
Hermes (or, in Egypt, by
'his' equivalent,
Thoth -- on
this see Boylan (1999), Faivre (1995), and Fowden (1993)). Of course,
Philosophy as a discipline was invented by ruling-class theorists, but it was part of
an
ideological package aimed at tracing its roots to the thoughts of the 'gods'. [Why this is so will be
explored in Essay Twelve Parts Two and Three (summary
here),
where the phrase "ruling-class theorist" will be explained more fully. Until
then, see here,
here
and here.]
This isn't as wild an accusation as it might first seem. In fact,
Marx himself advanced it:
"Feuerbach's
great achievement is.... The proof that philosophy 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. I have used the on-line version, here. Bold emphasis
and link added.]
[Indeed, it is arguable that this is why Marx abandoned
philosophy in the mid-, to late-1840s; on that, see
here.]
This approach to
knowledge -- which has, in one form or another, dominated much of 'Western' (and
'Eastern') thought
ever since -- sought to connect
arcane philosophical jargon with the divine, or a priori, structure of reality
(i.e., with 'Being' itself).
It is this
observation that partially motivates the claim advanced in these Essays that Traditional
Thought
represents,
not the material world, but an ancient ruling-class
view of
an ideal world, anterior to experience, which is more real that the universe we
see around us. Hence, we are told by boss-class theorists that this hidden world
-- which is accessible to thought alone -- underlies appearances,
and
lends to reality its 'essence'. That world is thus thoroughly immaterial.
Given this
approach to knowledge, it is solely the language that is used that tells us what this hidden world must be like (for we have no
other access to it). In that case, this hidden world is a reflection of
certain forms of thought/language --, not the other way round. [As noted earlier, I
call this the RRT. More about this in Essay
Twelve Part Four.]
In each Mode of Production, and in diverse class societies, different
versions of the same general belief (in the divine/a priori structure of
reality) have been used by Traditional Thinkers to rationalise the power and
authority of contemporaneous forms of the state, and thus the different
relations of production that humanity has experienced. It is here,
precisely where dialecticians have accept/appropriated significant parts of this ancient world-view, that ruling ideas succeed in ruling militant
minds.
Some might object that philosophical ideas can't remain the
same for thousands of years and across different modes of production; this runs
counter to core ideas in Historical Materialism.
But, we don't argue the same
for 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.
"The abolition of religion as the illusory
happiness of the people is the demand for their real happiness. To call
on them to give up their illusions about their condition is to call on them to
give up a condition that requires illusions. The criticism of religion
is, therefore, in embryo, the criticism of that vale of tears of which
religion is the halo." [Marx
(1975c),
p.244.
Italic emphases in the original.]
The above remarks applied back in Ancient Babylon and Egypt,
just as they did in China and India, in Greece and Rome, in the Middle Ages and
they have done so right across the planet ever since.
The same is true of the core thought-forms found throughout Traditional
Philosophy -- that there was indeed this invisible world, accessible to thought
alone --, especially since Marx also believed that:
"...philosophy 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.]
This, of course, helps explain why Marx thought this
entire discipline 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.
[This topic is spelt out in more detail in Essay Fourteen Part
One (summary here);
its affect on Dialectical Marxism is
spelt-out here.]
Naturally, the (postulated!) DM-account of the origin of mythical beings is
more sophisticated than previous paragraphs might appear to suggest. But, a
distorted view of reality, howsoever it is produced (be this from alienation,
a "one-sided" theory, ideology, or indeed from the process of abstraction itself) --
whether it results in an upside down image, a blurred one, or even one wearing a
pink tutu -- it matters not; it is still a view of reality (given
the applicability of the reflection metaphor, sophisticated version
or not), and in that case it is an Ideal view. A mirror can't invent.
Hence, this metaphor implies that things like
dragons, fairies, ghosts and hobgoblins -- not to mention
Atlantis,
heaven, hell and Nowhere -- must exist somewhere, in some form, just because we have the words for them!
On the other hand, if these 'entities' do not exist,
then the mirror metaphor is defective and should be abandoned.
[DL = Dialectical Logic.]
Of course, it could be objected that raising superficial
objections like these based on contingent features of reality entirely misses the
point: dialecticians are interested in the essential nature of reality, and
these are reflected in (or by) DL.
Nevertheless, more-or-less the same objections can also be directed at the principles
supposedly encapsulated by DL.
But worse: as
we have seen (here,
here,
here,
here and
here), DL is far too confused to
have 'captured' anything in thought, distorted or otherwise.
Or, to put the same point in reverse: if the essential
nature of reality is reflected in (or by) DL, then reality would be a madhouse.
![](/web/20140524014506im_/http://anti-dialectics.co.uk/pollock.stenographic.jpg-for-web-NORMAL.jpg)
Figure Two: What The World Might Look Like If
DL Were True
Furthermore, since these
general/'essential' features of reality are often
highly abstract (or they are
expressed in suitably abstract language), the
contention advanced here (that these are all
misconstrued rules of grammar, and are
not truths at all) has more than just a little prima facie plausibility
going for it.
[Incidentally, the above comments also answer the objection that the a
priori concepts and categories of DL capture the form but not the content of
reality. Again, since this topic is examined in more detail in Essay Three
Part One and Essay Twelve, no more will be
said about it here.]
(2) The phrases "relative adequacy" and "relative truth" are
themselves hopelessly unclear. Expressions like these are obviously linked to the DM-thesis that
human knowledge "asymptotically" approaches 'absolute
truth' over time. However, when examined more closely, these ideas are in fact
inimical to DM. This is because they imply that humanity is and always will be infinitely ignorant
of everything, no matter how "relatively" complete our knowledge of anything
might happen to be at any given point in history.
On this basis, far from being "relatively adequate", or even "relatively true",
knowledge will always remain infinitely incorrect. That in turn is because the difference between a
finite and an infinite body of knowledge is itself infinite.
A relevant passage from Engels comes to mind again (which was
commented on in Essay Two):
"The identity of thinking and being, to use
Hegelian language, everywhere coincides with your example of the circle and the
polygon. Or the two of them, the concept of a thing and its reality, run side by
side like two asymptotes, always approaching each other but never meeting. This
difference between the two is the very difference which prevents the concept
from being directly and immediately reality and reality from being immediately
its own concept. Because a concept has the essential nature of the concept and
does not therefore prima facie directly coincide with reality, from which
it had to be abstracted in the first place, it is nevertheless more than a
fiction, unless you declare that all the results of thought are fictions because
reality corresponds to them only very circuitously, and even then approaching it
only asymptotically…. In other words, the unity of concept and phenomenon
manifests itself as an essentially infinite process, and that is what it is, in
this case as in all others." [Engels to Schmidt (12/03/1895), in Marx and Engels
(1975), pp.457-58.]
First
of all Engels failed to say how he knew it was true that knowledge is
convergent. Of course, if what Engels said were true, it would be
infinitely wrong. That is because, when asserted, that claim must itself be
infinitely far from the 'truth', if we are to believe what Engels says. And, manifestly, the fact that
knowledge is an infinitary process can't be confirmed in practice (or in
any other way).
Secondly,
the idea of an
asymptotic approach in mathematics is
connected with the concept of a
limit -- if the limit concerned can be shown
to exist. Alas, Engels failed to
prove that there is such a limit for knowledge to approach in the
required manner (in fact, he didn't even so much as attempt such
a proof; and, as far as can be ascertained, no dialectician since has bothered to do
so). In that case,
Engels's 'mathematical metaphor' is doubly inappropriate: if there is no limit,
human knowledge must be
divergent. And if that
is so, then, at any point in human history, our knowledge must be infinitely far
from
'Epistemological Valhalla'
-- which, it is worth recalling, still hasn't been shown to exist. On
this view, given Engels's inapt metaphor, humanity will always be infinitely
ignorant of anything and everything.
Kant's
Noumenon
by any other name?
[On convergence, see
here.]
Of course, it could be argued that although certain
iterative functions in
mathematics yield infinite sequences that doesn't mean that the
distance between any intermediate value given by a
partial sum of that
function and the point toward which it is converging is itself infinite. For
example, the sequence: 1 +
1/2 + 1/4 + 1/8 +...+ 1/2n
converges on 2 (as n
→ +∞), but none of the
rational
numbers (formed from the partial sums of this series)
is infinitely far from 2.
This is not strictly so, but even if it were, the above would
have been an effective response had
Engels bothered to prove that the limit he claims exists (implied by the asymptote
metaphor) actually does exist; but since he didn't, it isn't.
The only way this sceptical conclusion can be avoided
would be to deny that 'absolute knowledge' is in any
way infinitary. Clearly, that would place a condition on the object of
knowledge before we knew what it was! Of course, it would also mean that several
passages from the DM-classics (quoted
elsewhere at this site) would need to
be revised -- or ignored --, along with the above 'asymptote' metaphor, since they
manifestly imply such an infinitary task. Indeed, they go further -- they say
it is infinite, and even call this a "demand".
7a. That is to say, our
everyday -- and even our scientific -- thoughts about motion aren't
contradictory, whereas those concocted by Idealist Philosophers might be (that
is, if
any
sense can be made of what they said).
8.
As noted above, in Hegel's system, the existence of 'real contradictions' made
some sort of crazy sense. Hence, if reality is just "thought" writ large, then linguistic categories may be projected ("foisted") onto
reality quite 'legitimately', since nature is 'self-developing Mind' anyway, or,
at least, an aspect of it. But, as we will see in Essay Twelve, this doctrine is itself a throwback to
Ancient Greek (and
earlier) ideas, where conflicts in nature and society were initially depicted in
mythical and theological terms
(i.e.,
where it was thought that the universe was the playground of evil and/or
benevolent agents/'gods'), then later in an ethical, political, conceptual or purely
abstract linguistic form.
[The
reason why this view of the world was conducive to wider ruling-class interests
will also be outlined in Essay
Twelve (summary
here) -- but it was hinted at in
Note 7. See also
here
and here.]
8a. Of course, it could
be argued that since everything in the universe is in motion, the question,
"Which came first, motion or contradictions?" doesn't arise. However, as we
will see later, things are not
quite so straight-forward.
9.
Quotations from Lenin (and others) concerning 'internal contradictions', and
self-development (etc.) were given in Essay Two; cf., Rees (1998), p.7. This topic is
examined in much more detail in Essay Eight Parts
One and
Two.
9a. Although Woods and
Grant came very close to asserting this:
"So fundamental is this idea to dialectics that
Marx and Engels considered motion to be the most basic characteristic of
matter.... [Referring to a quote from Aristotle:] [T]his is not the
mechanical conception of motion as something imparted to an inert mass by an
external 'force' but an entirely different notion of matter as self-moving....
"The essential point of dialectical thought is not that it is based on the idea
of change and motion but that it views motion and change as phenomena based on
contradiction.... Contradiction is an essential feature of all being. It lies at
the heart of matter itself. It is the source of all motion, change, life and
development. The dialectical law which expresses this idea is the unity and
interpenetration of opposites....
"The universal phenomena of the unity of opposites is, in reality, the
motor-force of all motion and development in nature. It is the reason why it is
not necessary to introduce the concept of external impulse to explain movement
and change -- the fundamental weakness of all mechanistic theories. Movement,
which itself involves a contradiction, is only possible as a result of the
conflicting tendencies and inner tensions which lie at the heart of all forms of
matter....
"...Matter is self-moving and self-organising." [Woods and Grant (1995),
pp.43-45, 47, 68, 72. Bold emphases added.]
The long quotation from Hegel, given
above, shows where these two
'discovered'
these odd ideas -- they certainly didn't obtain them from scientists. [On this, see Essay Eight Part
One.]
10.
In
fact, Engels himself torpedoed the idea that forces can be viewed as
contradictions when he claimed that:
"All motion is bound up with some change of place…. The whole of
nature accessible to us forms a system, an interconnected totality of bodies….
[These] react one on another, and it is precisely this mutual reaction that
constitutes motion…. When two bodies act on each other…they either attract each
other or they repel each other…in short, the old polar opposites of
attraction and repulsion…. It is expressly to be noted that
attraction and repulsion are not regarded here as so-called 'forces', but
as simple forms of motion." [Engels (1954),
pp.70-71. Bold emphasis added.]
As will be
argued in detail in Essay Eight Part
Two, this observation pulls the rug from under anyone
who wants to maintain that forces can be used to model contradictions.
Anyway, and despite the above, this entire account of motion does no real work; the
explanation of movement isn't advanced one nanometre by re-describing
it as "contradictory". The supposed 'contradiction' (that is, the one relating to
where a body is and is not, and when it is supposedly there -- but, not that which relates to the
allegedly contradictory nature of forces) neither initiates nor sustains movement. Worse still,
an appeal to 'contradictions' obscures the much clearer picture
we already have in Physics and Applied Mathematics.
Furthermore, if Absolute Space is left out of the picture, the
precise nature of motion clearly depends on the
inertial frame
chosen. It doesn't
depend on the simultaneous non-occupancy and occupancy of point locations. This
can be seen from the fact that given a particular frame of reference, a body
could be at rest relative to that frame, but with respect to another such frame
it could be in motion. Hence, motion is inertial-frame sensitive, not
'vaguely-located-point-occupancy-and-non-occupancy' sensitive.
It would seem, therefore, that unless
DM-theorists believe in Absolute Space, their insistence that motion is
contradictory (because of their quirky view of point-occupancy) is unsustainable.
Relative notions of space imply that the contradictory behaviour of moving
bodies (if such it be) is a consequence of change of reference frame: in that
case, bodies would be in motion -- or they would be stationary -- depending on
which inertial frame was selected; but they would not be either
motionless or moving because of the alleged contradictions inherent in
motion itself. In which case, the 'contradictory' nature of motion can't be an
'objective' feature of reality if it promptly disappears as soon
as a different inertial frame was selected.
It could be objected here that just because motion apparently
stops and starts according to the choice of reference frame doesn't mean that
its contradictory nature isn't objective. No more would we conclude that, say, the
boiling point of water was not really 100ºC if it was then measured in
degrees Fahrenheit or in degrees
Kelvin.
To be sure; but unfortunately, if that constitutes an effective reply to the points made
above, it would at the same time prove fatal
to the DM-view of motion. That is because it openly concedes that scientific
knowledge is conventional.
Again, exception could be taken to that response. It could
be argued that the fact that the temperature of a body can be read on two
or more different conventionalised scales does not imply that temperature itself (or whatever it
supervenes upon)
isn't an objective feature of
reality. The same goes for the
depiction of motion in different reference frames.
However, these two cases are
not at all the same; no matter what system we use, a body has some temperature or
other (with the latter defined perhaps in terms of
energetics). This is not so with choice of inertial frame (unless,
of course, we count a zero
velocity as a velocity by default -- but, even then, the alleged 'contradiction'
would still vanish).
In one particular frame, a body
could be in motion and (assuming DM is correct) appear to be 'objectively' contradictory. In
another frame, and at the same time, that body could be stationary and
objectively non-'contradictory' (in Engels's sense), too. Hence, at the
same time, a body could be moving and not moving, 'contradictory' and 'not
contradictory'. Which of these options is finally settled upon will be a
consequence, not of the nature 'motion itself' (whatever that is), but of the choice of reference frame. Since reference
frames aren't 'objective' features of the world (they are human inventions!),
and since the 'contradictory' nature of motion is sensitive to choice of frame,
the conclusion seems inescapable: the 'contradictory' nature of motion (if
such it be) isn't an
'objective' feature of reality, either.
Alert dialecticians at this point might want to argue that this
sentence is eminently contradictory:
"Hence, at the
same time, a body could be moving and not moving, 'contradictory' and 'not
contradictory'."
But, this is just another ambiguous sentence, and its allegedly
contradictory nature will disappear upon disambiguation, as we saw
here.
It could be argued that the above would mean that motion
itself isn't an objective feature of reality if it disappears in the
above fashion when a different reference frame is chosen. That is not so, for if an object is
moving with reference to one frame, but is stationary with respect to a second
frame, then other objects will be moving in a different way
with respect to that frame. So, while the alleged contradiction would disappear,
motion in the wider system would not. For example, if the first reference frame
is a volume interval containing only the Moon, and is stationary, the Earth will be in motion
relative to that frame while the
Moon isn't. Swap the reference frame to a volume interval that contains
only the Earth,
mutatis
mutandis, and the Moon will now be moving relative to a stationary
Earth.
[Sure, the Earth will still be rotating, but all we have to do is
make the reference frame a finite region on the Earth's surface, and the Earth
would stop rotating relative to this new frame. For example, from where you are
now sat, or stood, the earth appears not to be rotating, which used to be one of
the strongest arguments that it isn't. On whether or not the earth is
'objectively' in motion, see
here.]
This means that motion (at least as it is viewed in modern Physics) is a
conventionalised bi-product of the choice of inertial frame. Therefore, if
DM-theorists are to rescue the 'objectivity' of their theory from the trashcan
of 'subjectivity', it looks like they will have to postulate the existence of Absolute Space. Otherwise, they would have
to concede that the 'contradictions' they attribute to motion are in fact
artefacts of the choice of reference frame, and not something inherent
in moving bodies.
It isn't easy to see a way out of
this DM-cul-de-sac, or at least one that makes no further
concessions to conventionalism -- or, alternatively, one that makes unwelcome concessions
to
Space/Time Absolutism.
This partly explains why (a few generations
ago) in Stalinist Russia, philosophers and scientists found it difficult to
square Einstein's theory with DM, and why some rejected it. If revolutionaries are still unaware of these problems,
STDs certainly weren't. Cf., Graham
(1971), pp.111-38; see also Joravsky (1961), Krementsov (1997), Vucinich (1980,
2001), and Wetter (1958).
[STD = Stalinist Dialectician.]
Once more, it could be objected that even if the above were
correct,
once moving (in a suitable inertial frame), an object must be doing something
contradictory.
The reply to that objection occupies the rest of
this Essay.
11.
This isn't meant to single Engels out here for special attention; it is equally
impossible to determine what, if anything,
Zeno, Hegel
or Lenin were trying to tell us about motion, either.
However, if it is maintained that systems of supposedly contradictory
forces are responsible for the contradictory nature of motion, then it would be difficult to account for un-accelerated
motion. Clearly, this sort of (constant) change takes place where no net forces are
operating. That being so, the exact source of the alleged contradictions here
would be
even more obscure.
Of course, one consequence of DM seems to be that there might
be no un-accelerated motion in nature (in that (1) The opposite supposition would involve a body
possessing identically the same velocity from moment to moment -- which
would, of course, amount to a fatal concession to the LOI -- or that (2) It
wouldn't be moving in a gravitational field, which, in this universe, is
impossible). Nevertheless,
DM-induced conundrums like this will not, I take it, worry genuine scientists
too much, or for too long.
[LOI = Law of Identity.]
And all this
is, of course, quite apart from the fact that such a DM-view of velocity will
have to be imposed on nature.
As far as (2) is concerned, given the fact that
gravitational forces have been
edited out
of the picture in Relativity (on that, see
here), even
if this were so, an appeal to such forces to account for acceleration would be
to no avail, since there are none!
Nevertheless, if a suitable frame of reference is chosen, any
body can be said to have zero velocity and be undergoing acceleration for about as long as it takes hard-core DM-fans to
abandon their criticisms of the LOI.
Hence, for any body b moving at v
kmph relative to the centre of mass of the Galaxy, say, let a reference frame for it
also move at v kmph with respect to that centre of mass. In that
case, b will have zero velocity with respect to that frame. The only
response a DM-acolyte could make to this would it seems have to involve a
reference to 'abstractions' (i.e., in that it involves the use of
"abstract identity"). That last ditch DM-defence is also examined, and demolished, in Essay
Six.
11a. Hegel's
'analysis' of Identity is partially covered
here, and indirectly throughout Essay Six; but will be
examined more fully in Essay Twelve (summary
here).
11b. This is because,
if it is unclear what is being proposed (as is the case with L9, given the
convention introduced in L7) then nothing has yet been proposed.
L9: B is at
(X1, Y1, Z1),
at t1 and not at
(X1, Y1, Z1),
at t1, and B is at
(X2, Y2, Z2),
at t1.
L7:
(X1, Y1, Z1) is
not the same place as
(X2, Y2, Z2).
Of course, if L9 depicts one of the ambiguous cases mentioned
already (that is, if B is in fact stationary -- like that car half in,
half out of the garage), then it will be clear what is being proposed. But, in
that case, L9 won't provide us with the required necessary and sufficient
conditions for movement, and we'd be back to square one again. Anyway, in order to
see if some sense can be made of what Engels is trying to tell us, I have
ignored this serious difficulty for now. However, I will return to it later since it will soon become
apparent that Engels's theory can only be made to work if we ignore our ordinary
use of language and substitute for it distorted 'philosophical' jargon --, as both Marx and Engels
pointed out:
"The philosophers have only
to dissolve their language into the ordinary language, from which it is
abstracted, in order to recognise it, as the distorted language of the actual
world, and to realise that neither thoughts nor language in themselves form a
realm of their own, that they are only manifestations of actual life."
[Marx
and Engels (1970), p.118. Bold emphases added.]
Engels clearly forgot about his earlier warning!
This isn't a minor, or trifling point; it is in fact central to understanding
why traditional philosophers and dialecticians find they have to impose
their theories on the world, and thus why their ideas invariably collapse into
LIE. [On this, see
Essay Twelve Part One and Essay
Two.]
12.
A detailed discussion of these aspects of Zeno's analysis of motion can be found in Angel (2002). Also,
see Note 19a and Note 24,
below.
[Incidentally, this way of looking at the
Reals is outlined in Newton-Smith (1980).
On whether time is composed of 'instants', see Read (2007), pp.79-115.]
12a. But
Trotsky
wasn't, of course, the only one to do this. Engels also failed to
consider the possibility that an object could be in two times for the same
place -- i.e., in and not in one instant, at that place. But, if time
advances while bodies move (or indeed stay still), and everything is contradictory, then this must surely be
possible.
And if that is so, what is to stop us saying that a moving body occupies
the first place in one of these odd instants, and the next place in the second
overlapping instant -- locating the alleged contradiction in time, and not in
space/motion (or, perhaps, even eliminating both)?
Of course, it could be pointed out that if a body
is
in two times for the same
place then it must be stationary.
In
order to neutralise that objection it might be wise to examine the subtle
differences that exist between these two sentences (always assuming there are any):
B1: Body b is in two different times for
the same place.
B2: Body b is in the same place at two
different times.
I do not propose to do that here, but it is worth noting that
neither of these imply that the said object is stationary, since that object
could still be moving and could return to the original location at a later time --,
hence it could be in the same place at two different times.
Moreover, it is also worth recalling that evidence
can't distinguish between these two a priori
'possibilities' (i.e., between B1 and B2).
13. This
is taken to be an important DM-assumption since it is the only way that Engels's
claims about the contradictory nature of motion can be defended, as is argued at
length in the main body of this Essay.
14.
It is worth pointing out that L13 doesn't say that b is both at p1 and
not at p1 at t. What it
does say is this:
L13: For some b, for just one instant t, for
three places p1, p2 and p3,
b is at p1 at t, but not at p2
at t, and b is at p3 at t, where p2
and p3 are proper parts of p1.
Hence, a finer-grained analysis of position allows for the
fact that while at the macro-level, an object might be locatable in one
place (say, p1) at one
'instant', at the micro-level it could still be in that same place (i.e.,
still in p1)
while also being in one or more other sub-spaces of p1 (say, p3)
at the same time. In other words, b could be in p1, and
while not in all of p1 (i.e., not in,
say, p2,
which is a proper part of p1),
it would still be in p1
(in this case, in, say, p3,
which is also a proper part of p1).
Hence, b could be in, but not in every part of p1 at t
-- and either be in motion or be stationary at that time --, meaning that b
would be in two places at once: p1 and p3.
So, if the location of bodies can be given in finer-grained detail -- even if
this manoeuvre is inconsistently disallowed of time -- a body could still be in one place and not in
it, and in two places at once, while being stationary, with no contradiction
implied.
[This is the simplest of these cases; the reader is left to
determine more complicated ones for herself. The
complex nature of ordinary and/or
technical language allows for the depiction of motion and location in ways undreamt of by
Zeno, Heraclitus,
and Hegel -- or even Engels -- that is, in their 'philosophical'
deliberations. On this, see below and in the main body
of this Essay.]
Some might think this ignores what Engels actually says:
"[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.
Bold emphasis added.]
However, as we saw earlier, it is far from clear what Engels
meant by this:
"...even simple mechanical change of place can only come
about through a body being both in one place and in another place at one and the
same moment of time, being in one and the same
place and also not in it." [Ibid.]
Here Engels says that a moving object is "in one and the same
place and not in it." He is clearly using "in" in a very odd way, and it isn't too
clear whether he (or any other dialectician) is capable of explaining how this
can be literally true -- save they just label it a 'contradiction',
take their bat and ball home, and refuse to
say any more. But, this just highlights the problem, it doesn't make it any
easier to determine what Engels is proposing, or if he is proposing anything
determinate at
all.
In that case, it is worth pointing out that in L13:
L13: For some b, for just one instant t, for
three places p1, p2 and p3,
b is at p1 at t, but not at p2
at t, and b is at p3 at t, where p2
and p3 are proper parts of p1,
b is in
p1
and not in it in this sense: it is in
p1
and not in all of p1.
This is just as legitimate an interpretation of Engels's words as the traditional
(but hopelessly unclear) version is.
This analysis might be contested on the grounds that it removes the
contradiction from Engels's words.
But, and despite what he himself says, it isn't too clear that Engels's
words were contradictory to begin with, since little sense can be made of them
as they stand.
If we can form no clear idea what Engels is saying, then what he is saying can't
be said to be contradictory.
"Motion itself is a contradiction; even simple mechanical
change of place can only come about through a body being both in one place
and in another place at one and the same moment of time, being in one and the same
place and also not in it." [Ibid. Bold emphasis added.]
We have already seen that extended bodies can be in two places at
the same time -- while stationary -- with no contradiction implied, so the allegedly
contradictory aspect of motion must arise from this clause:
"...being in one and the same
place and also not in it [at the same moment in time -- RL]."
Well, is this the contradiction we have been led to
all along to believe?
If so, imagine these scenarios:
[1] NN is queuing for tickets, and finds herself at the front of
the queue at 12 noon (before the box office opens), but she needs to go for some
food. So, she asks MM to act as her proxy in the queue while she leaves to buy
sandwiches, which she does at 12.05pm. Here NN is both in and not in the queue
at 12.05. She is still in the queue since MM is guarding her place, but she is
not in the queue since she has left to get food. So, here we have a moving
body, NN, who is both in the queue and not in it at the same time, with no
contradiction implied. This only appears contradictory because of the equivocal
meaning of "in".
[2] NM is selected by his coach to play for the first team squad.
The team leaves for a match at 1500 hours, but NM misses the plane. So, NM is in
the team (the coach hasn't dropped him), but not in the team (he isn't
accompanying them), all at the same time, and this could be true
whether or not NM is moving. [Some might want to point out that a team is not a
place, but quite apart from the fact that Engels was unclear what he meant by
"place", we often speak about a player securing or gaining his/her place in the
team.] Here, once again, the equivocation centres on "in".
[3] Consider the
Klein Bottle:
![](/web/20140524014506im_/http://anti-dialectics.co.uk/kleinBottleNormalShowStill_med.jpg-for-web-NORMAL.jpg)
Figure Three: The Non-Dialectical Klein Bottle
Let an object slide down the central tube that runs through this
bottle. Because the inside of this bottle is the same as the outside, then
that object will be inside and not inside this bottle at the same moment; it would
be in and not in the same place at once. And this would be so whether or not the said
object was moving. [Here, the equivocation centres on "same place", i.e.,
whether "insides" can be the same as "outside" in certain circumstances. A
similar ambiguity also appears in example [5], below.]
[An analogous 'contradiction' can be manufactured for a stationary
object situated on a
Möbius Strip,
or even worse, on
Möbius
Gears:
![](/web/20140524014506im_/http://anti-dialectics.co.uk/MobiusStrip.jpg)
Figure Four: A Möbius Strip -- Concocted By
The CIA?
![](/web/20140524014506im_/http://anti-dialectics.co.uk/moebgear.jpg)
Figure Five: Möbius Gears -- An
MI5 Invention?
A stationary object
on these gears would be on and not on one surface all at once. Here we can see
that equivocations like this are not confined to the preposition "in".]
[4] MN has had her amputated hand replaced by a
prosthetic.
At 02.20pm she inserts this artificial hand into a glove. Hence, her hand is
both in and not in that glove. Her hand is in the glove in the sense that this is her hand now.
But, it isn't in the glove in
the sense that it isn't a real hand, or the hand she was born with. [Here the equivocation is over "same object".]
[5] NN is in the corridor of a hotel outside her room at 1730
hours (on a Friday), but at the same time she is inside the hotel. So, she is
outside and inside (or outside and not outside), all at once. There are
countless examples of this use of prepositions and adjectives. For example, a
book on a shelf may be above the floor but below the roof. So, it is at one and
the same time above and not above. A box might be stored near a wall but far
from the door; so, at one and the same time, it is both near and not near. [Ancient Greek
Philosophers made much of these equivocations.]
It might be objected that not only are these examples somewhat
artificial and forced; they are not at all what Engels meant. But, it isn't at all clear
what Engels meant. Anyway, only [3] is arguably artificial.
And, as we will discover, in the abstract, while Engels's 'theory'
might seem to some to be eminently sound, when we look at concrete examples (like
those above, or others below), it can be seen for what it is: artificial and
forced itself.
For more examples like this, and worse, see Note 15,
Note 16 and the main body of this
Essay.
14a. It could be
objected that
(X1, Y1, Z1)
in this example is a mathematical point. If so, it can't have other
points located inside of it -- so it can't be the case that: "(X3, Y3, Z3)
and
(X2, Y2, Z2) are both located inside
(X1, Y1, Z1)."
This is easily rectified:
L13c: A stationary body b, observed over the course of
an instant, is located in a finite region ℛ and
at (X3, Y3, Z3), but not at
(X2, Y2, Z2), where
(X3, Y3, Z3)
and
(X2, Y2, Z2)
are both located inside ℛ.
L13d: A moving body b, observed over the course of
an instant, is located in a finite region ℛ and
at (X3, Y3, Z3), but not at
(X2, Y2, Z2), where
(X3, Y3, Z3)
and
(X2, Y2, Z2)
are both located inside ℛ.
15. The following is an example of this type of motion partially expressed in vector
algebra:
V1: Let B be a body moving in
ℝ3
(or some Vector Space) with
respect to a given reference frame.
V2: Let B be at/in both
(X1, Y1, Z1)
and
(X2, Y2, Z2)
at t1.
V3: Let B be a complex composed of n segments, b1
to bn, arranged in an ordered n-tuple <b1,..., bn>.
V4: Let the position vectors of the centre of
mass of b1
and bn be u and v, respectively.
V5: Let v – u = w.
V6: Let the distance between
(X1, Y1, Z1)
and
(X2, Y2, Z2)
be mod d, (where d is the vector joining
(X1, Y1, Z1)
to
(X2, Y2, Z2)).
V7: Let mod w > mod
d.
V8: Let the direction vector parallel to d be lw (where
l is a Real Number).
V9: Let B be moving at time t1 with
velocity vector s, such that s =
mw (where
m is a Real Number).
V10: In that case, part of B is at
(X1, Y1, Z1),
and another part of B is at
(X2, Y2, Z2), but other
parts of B are at neither of these two points, all at t1.
V11: So, B is moving parallel (in either
sense) to the line
joining these two points, also at t1.
V12: Or, alternatively, B is
stationary (with respect to some inertial frame); i.e., if s =
0 (or even if
m = 0), and all the above considerations would still apply.
Here, we have a more technical version of the ambiguous case
mentioned in the main body of this Essay (concerning a boat entering port, etc.). Translated, the
above could apply to the following scenario:
Ports are generally
bigger than boats, and are composed of countless 'parts' (land, water,
buildings, shorelines, etc.). A boat can, therefore, be in port and be located at several
points within that port, and yet not be located at every point in that
port (with no
implication that it is both in and not in 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), all at the same
time. And these could all be true independently of whether that boat is
moving or not with respect to a suitable inertial frame (that is, if we set s
at zero).
16. This
observation would remain true even if such 'spatial location sentences' employed
co-ordinates (expressed as real number triples). As we shall see, technical
specifications aren't free from their own ambiguities.
An example of
just such an equivocation would be the
following: in <x1, y1, z1> and <x1, y1, z1>, each variable letter is in the
"same place"
(i.e., each is situated in its respective ordered triple, first, second or
third) while also being in a different place (on the page/screen).
Indeed, not only are they in the same place,
they are also in
different places while they are in the same place (i.e., they
are on your screen and mine -- and, clearly, they are all in the solar system), all at
the same time!
Consider, too, this variation on the same theme: <x1, y1, z1> and <
y1, z1,
x1>.
Here, each letter is in the same place (they are on the same page/screen -- or
even geographical location -- as each other), and yet each letter is in a
different place (in the ordered set). So, each letter is and is not in
the same place. Do you see any of them moving?
Now, try saying any of that in Hegel-speak!
And these are very simple examples! I won't do so here, but it
would be
possible to construct examples that are difficult to follow -- since they would
involve much more detail and the use of complex equivocations --, but with
sufficient application, it would be possible to ascertain their content, all of
which would make the same point: it is easy to manufacture
'contradictions' using equivocal language -- ordinary or technical --
almost at will.
[Of course, with technical languages, the equivocations emerge
only when translated into ordinary language. No one using ordered n-tuples, for
example, would regard them as 'inherently contradictory'.]
[I have in fact done something rather similar with words for identity and
difference in Essay Six, here.]
To paraphrase Wittgenstein: the conventions of ordinary language are exceedingly complex.
Dialecticians ignore them at their
non-dialectical peril.
17. Some might
conclude that this is because ordinary language is defective (in certain
respects); cf., TAR pp.45-50.
It is important to note that the view that ordinary language is defective
isn't shared by the present author;
the opposite is in fact the case. This topic will be addressed in detail
in Essay Twelve Part Seven. [On this, see
the lengthy discussion here.]
18. Although, at this point, because we have reached linguistic bedrock (i.e., in
order to proceed further we should have to revise fundamental linguistic
conventions -- in this case, for instance, promulgating non-symmetrical stipulations about space and time),
this latest "must" is in effect the argumentative equivalent of thumping the
table, and nothing more.
18a.
This
'assumption' sometimes masquerades as part of the claim that motion is an
'inherent' property of bodies in motion –- that certainly appears to be Graham
Priest's interpretation of Hegel's views in this regard. [Priest (2006), pp.175ff.]
The most obvious problem with this view is that a body can be moving in one
reference frame while stationary in another. Hence, the idea that there is
something 'inherent' (or 'intrinsic') to moving bodies seems to rely on space
being
Absolute!
Priest's analysis will
be considered here at a later date, as will that of
Marquit (1978, 1982), and the views of other dialecticians.
18b. L15 is taken to
mean:
L15a: If an object is wholly located at a point it must be at rest at
that point.
18b1.
Lenin had the following to say about this option:
"Movement is
the presence of a body in a definite place at a given moment and in another
place at another, subsequent moment -- such is the objection which
Chernov repeats (see his
Philosophical Studies) in the wake of all the 'metaphysical'
opponents of Hegel. This objection is incorrect: (1) it describes the
result of motion, but not motion itself; (2) it does not show,
it does not contain in itself the possibility of motion; (3) it depicts
motion as a sum, as a concatenation of states of rest, that is to say,
the (dialectical contradiction is not removed by it, but only concealed,
shifted, screened, covered over." [Lenin (1961),
p.257. Quotation marks altered to conform to the conventions adopted at this
site.]
Lenin here speaks about "motion itself". How he
knew what "motion itself" amounted to he unfortunately kept to himself. As we
will see, there are examples of motion that indeed do what this character, Chernov,
had said of them. [On that, see Note 18c.]
Anyway, the point is that Lenin rejects this
possibility, so we can see that this assumption (i.e., the truth of L16)
underpins at least his understanding of 'dialectical motion':
L16: Hence, a moving body can't be located
at a point, otherwise it wouldn't be moving, it would be at rest.
Indeed, Lenin quotes approvingly Hegel on this (I have
reproduced
the whole passage; Lenin only quoted part of it):
"If we
wish to make motion clear to
ourselves, we say that the body is in one place and then it goes to another;
because it moves, it is no longer in the first, but yet not in the second; were
it in either it would be at rest. Where then is it? If we say that it is between
both, this is to convey nothing at all, for were it between both, it would be in
a place, and this presents the same difficulty. But movement means to be in this
place and not to be in it, and thus to be in both alike; this is the continuity
of space and time which first makes motion possible. Zeno, in the deduction made
by him, brought both these points into forcible opposition. The discretion of
space and time we also uphold, but there must also be granted to them the
over-stepping of limits, i.e. the exhibition of limits as not being, or as being
divided periods of time, which are also not divided. In our ordinary ideas we
find the same determinations as those on which the dialectic of Zeno rests; we
arrive at saying, though unwillingly, that in one period two distances of space
are traversed, but we do not say that the quicker comprehends two moments of
time in one; for that we fix a definite space. But in order that the slower may
lose its precedence, it must be said that it loses its advantage of a moment of
time, and indirectly the moment of space." [Hegel (1995),
pp.273-74; partially
quoted in Lenin (1961),
p.257. The editors of
Lenin's text have clearly used a slightly different translation.]
I have attempted to clarify certain aspects of
Hegel's argument in L18-L27, in the main body
of this Essay.
Lenin had much else to say about Zeno and the
dialectical nature of motion in the surrounding pages.
I will consider these comments, and those
advanced by Hegel, in a later re-write of this Essay.
18c. In fact, there
have been important theorists who have argued that motion is discontinuous, and a
'stop-go' sort of affair. For example,
Gassendi and the early
Leibniz.
[Although, as with anything one asserts about Leibniz's
philosophical theories,
this needs to be heavily qualified. On Leibniz's arguments for the
discontinuity of motion, and his debt to Gassendi, see Leibniz (2001),
pp.xxvii-xxix, lxxix, 77-83, 93-99, 159-63, 169-73, 187-203. See also Wilson
(1989), pp.77, 169-70, 205. On the general background to this aspect of
Leibniz's work, see
Mcdonough (2007). For everyday examples of discontinuous motion, see
here.]
So, Leibniz argued that if motion was continuous, it
would be impossible to explain faster and slower speeds. If speed is the number
of points a body traverses along its trajectory in a given time, an increase in
speed would involve that body traversing more points in the same time interval.
But, the number of points in a body's trajectory is infinite; if so, it can't
traverse more points in the same time interval, since all such infinities
are equal (i.e.,
in modern parlance,
they
have the same cardinality). The only way to account for different speeds,
on this view of trajectories and infinities, is to argue that at a lower
speed, a body rests at each point a bit longer -- and vice versa for
those that move faster. [Leibniz coupled these observations with the conclusion that motion is
illusory!] To be sure, we now think we know more about the
nature
of infinity than they did in Leibniz's day (following on
Cantor's
work), but I suspect that Leibniz would have seen through this spurious area of
modern mathematics reasonably quickly (but not necessarily along the lines set
out here).
[On this, incidentally, see
Gefter (2013).]
Moreover, there are versions of the
Block Theory (involving the so-called
B-Theory
of Time and
Perdurantism)
that imply motion is illusory, and only appears continuous because of our
'subjective' perception of the passage of time. [On this, see Hawley (2004,
2010);
although I am not suggesting that Hawley has adopted this particular interpretation of this
family of theories. For a different take on this, see Gallois (2003). On the
complexities underlying our perception of fast and slow motion, and the
complexities of 'zoëtrope
motion', see Phillips (2011).]
For some idea how I would respond to metaphysical theories of time
like these (that is, if this were the main topic of these Essays!), see
here, and
here -- but, in general,
here.
19.
On this, see Note 18c above.
In fact, the analogy with moving pictures creates its own problems for
dialecticians since
even freeze-frames (or 'still' pictures) contain some blurring of the
depicted motion (no matter how fast the shutter speed). This is because
pictures actually capture motion in a temporal interval, not in an instant in time.
[Of course, that
minor niggle can be overcome somewhat by considering
flip cards and cartoons. On this, check out the moving horse
here.]
If anything, this analogy is more closely in tune with a view of
change pictured by certain uses of ordinary language: that motion takes
place in time and has nothing to do with the sorts of abstract
metaphysical 'instants'/'moments' that Engels, Trotsky and other
dialecticians seem fixated upon. In that case, what little evidence there is
(from this source -- i.e., ordinary experience), is
consistent with the picture adopted here. [Although, 'the picture' presented by
our use of ordinary language is highly complex, so there is no such thing as
the 'picture' here. There are many 'pictures', as we will see as this Essay
proceeds. Anyway, I am not advocating my own
theory in this Essay -- and not 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.]
To be sure, this 'stop-go' view of motion would present problems
for certain fundamental physical laws (namely the conservation of momentum); but if
this is indeed how nature behaves, these laws will need revising, anyway. Other
significant advances in science have certainly been predicated on overturning what at one time seemed
to be 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 Idealists.
19a. Of course, spelt
out in all their glory, these and other premisses, assumptions, proofs and
conclusions are far more complex than might be suggested in this Essay. [Hegel's
actual arguments can be found in Note
18b1.] However, since this isn't meant to be an academic exercise,
those I take to be the most relevant have been stripped down to their
'bare essentials'. [Any readers who want to study this topic in more detail might
want to start with Mazur (2007), Angel (2002), Blay (1998), and
Huggett (2010). Also see Note 12
and Note 24.]
On the various infinites and paradoxes of the Reals, and much
more besides, see Hunter (1996), Lavine (1998), and Moore (2001).
20.
The status of these
indicative sentences will be left somewhat vague for the time being.
[This has
something to do with the sorts of ambiguities discussed in later sections of
this Essay.]
Nevertheless, in the
main body of this Essay, the following are taken to be contradictories:
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.
Strictly
speaking these should be:
L28: A body can't be at rest and in motion at the same time
in the same inertial frame.
L29a: It is not the case that a body can't be at rest and
in motion at the same time in the same inertial frame.
However the more
colloquial L29 has been adopted here for obvious reasons.
21. It
might be thought that L34b is both testable and false. But L34b said the following:
L34b: Despite appearances to the contrary, all bodies are
at rest.
But, it isn't possible to test something "despite appearances
to the contrary", for obvious reasons.
[That is because, plainly, any test has to depend on the
appearances delivered by instruments, computers, recording devices, etc. More
on this in Essay Three
Part Two.]
This isn't to suggest that there are no theoretical problems
bedevilling either option, but there is no way of experimentally testing them.
If moving bodies occupied points in space (and were thus stationary) during
intervals of the order of, say, 10-1000000
seconds (or less), we would never be able to tell (without recourse to yet more
of those pesky appearances).
On the other hand, if they occupy at most two such places in the
same interval (in accord with Engels's analysis), we still wouldn't be able to
tell. This shouldn't surprise us; both options are metaphysical and aren't
therefore based on processes in this world, having been
conjured into 'existence' by a distortion of the only language that secures our
knowledge of nature --
the vernacular,
and the practices that surround it -- and then imposed on reality.
Of course, certain aspects of modern Physics postulate minimum
times and
distances:
Planck mass: 2.17645(16) 10-8
kg;
Planck temperature: 1.41679(11) 1032
K;
Planck length: 1.61624(12) 10-35
m;
Planck time: 5.39121(40) 10-44
s
But these are
conventions -- they are required by
theory.
Even if all but the first of the above are never actually measured, or measurable, there is no way
any of them can be shown to be
universally/eternally valid
minima.
22.
Naturally, a full derivation here would involve a potentially infinite number of
steps, but that doesn't prevent the implications of the theory being clear if
they are expressed by a rule. [This instance would require small changes in direction,
too. Anyone familiar with "space filling curves"
will know what I mean.]
22a. Any conclusion to
the contrary is plainly motivated by the illusion that appearances do not
contradict underlying 'essences'. [Irony intended.] This 'prize' theory clearly penetrates to the heart of 'Being', and ends up concluding that in
'essence' the universe is in fact the opposite of the way it appears --
and is thus
Parmenidean, not
Heraclitean!
22b. If, indeed, these
are genuine implications of
DL, then there is no "while", since, as we have
seen, this 'path-breaking' theory means that there is no such thing as 'before'
and 'after' when it comes to motion. If there is no "before" or "after", there can't be a "while",
either.
In fact, these two absurdities seem to me to be in effect physical
correlates of the Medieval
Ex
Falso Quodlibet argument -- that is, from a
contradiction anything follows. In this case, we can see that from the allegedly
contradictory motion of a body it follows that it is everywhere all at once, and
that it is in every point along in its trajectory (no matter how far apart they
might be) at the same time. On this, see
Note 24b, below.
Other absurd consequences of this 'theory of motion' are examined
below.
23.
This isn't, of course, a quandary confined to the musings of DM-theorists; Traditional
Philosophers (i.e., metaphysicians) still can't explain motion, and neither
can modern science -- if by "explain motion" we mean "provide
a metaphysical and/or necessary account of motion itself". Vectors, tensors,
geodesics and scalar energy gradients can't physically move things about the
place. Motion isn't produced by some sort of Inverse Square Law of Abstraction.
This isn't to denigrate or undermine the work of scientists; all that is being denied here is the
capacity of anyone to provide a metaphysical explanation of motion
-- as
opposed to a scientific account of it.
[Exactly why metaphysicians can't explain anything, let alone
motion, will be left for Essay Twelve
Part One to settle.]
24. For a much more illuminating analysis of these terms, cf., Black (1954).
Also see Grünbaum (1967), Salmon (1970), and
Note 12 and
Note 19a, above.
Having said this, and as far as I am aware, there is as yet no
satisfactory dissolution of this spurious problem. In that case, the present
Essay is completely original in this regard, even if far more work needs
devoting to it. But, as I have already said, this isn't meant to be an academic
exercise.
24a.
Needless to say, the alleged fact "that ordinary objects and people are
quite capable of doing the metaphysically
impossible" is meant to be taken ironically, here! These 'prodigies' are only
'possible' if we insist on reading the vernacular in the same crass way
as metaphysicians.
24b. Once more, this might look like a
topological
version of the infamous 'Quodlibet'
argument (that is, from a contradiction, everything follows). I have not used
this hackneyed objection to Hegelian 'logic' in these Essays, since, applied
unrestrictedly, it is not a principle with which I would agree. However, applied
here, restrictedly, it seems to imply that a moving 'Hegelian object' must
fill the entire universe (or, at
least, the entire volume interval encompassing its own trajectory), all at once.
A simple derivation of Ex Falso Quodlibet can be found
here.
24b1.
Indeed, this applies to every atom in a 'dialectically moving
body', too; each atom will also have to be in two places at once as it moves, which
means the entire body will either concertina or collapse into a point mass.
24c. Or, in
spherical polar co-ordinates: <r, θ, φ>; in
cylindrical polar co-ordinates: <ρ, φ, z>. I have confined this argument to
three-dimensional space, or R3,
to minimise its complexity.
24d. There is an
interesting, if overly metaphysical discussion of this topic in Adamson (2002),
pp.5-58. Nevertheless, Adamson's solution (drawn from the confused writings of
Bergson)
seems far worse than the disease it was intended to cure. [It is worth adding
that Adamson's characterisation of
Analytic Philosophy is,
unfortunately, misleading. However, I do not propose to defend that contentious allegation
here.]
25.
"Context" in this instance is meant to be interpreted linguistically, not situationally. The
latter form of contextualism is examined in more detail in Essay Thirteen
Part Three, and refers to the
intentional, social and/or interactive circumstances of an utterance. Linguistic
contextualism relates to the sentential role a word, phrase or clause might
occupy; i.e., whether or not a certain word, for example, is functioning as a
noun, adjective, verb, adverb, etc., and what sort of a noun, adjective, verb,
adverb, etc., it is. It thus refers to the logical and/or grammatical role that
expressions occupy.
However, in addition to cases where ordinary objects seem to be able to move
while remaining in the same place, there are numerous examples that illustrate the
fact that two or more objects (howsoever these are interpreted) can be in the same place at the same time,
further illustrating the 'miraculous' properties of the word "place":
(1) Consider the following 4-tuples: <x1,
x2, x3, t1> and <x4, x2,
x3, t1>.
In this case, at least two variables (i.e., x1 and x4)
occupy the same place at the same time -- namely the first place in
their respective 4-tuples (by the ordering rules).
However, we don't have to rely on 'abstract' examples like this to make the
same point:
(2) Consider, say, two waves travelling across the surface of a
body of water, but orthogonal to one another (or, indeed, at any angle greater
than zero but less than 360 degrees). At some point, these two waves will cross,
and the moment they (or parts of them) do, they will both be in the same place at the same time.
This would still be the case whether or not it is true to say that motion is
contradictory, or that time is made of instants or intervals.
In fact, ordinary examples of this 'impossibility' are even easier to find:
(3) Imagine two workers in the same canteen at
work at precisely 10 am on the same day. Here we have two 'objects' in the same
place at the same time -- namely, these two workers in the canteen at 10 am.
(4) Part of a mother and her unborn baby occupy the same space at
the same time. So do any of her/your internal organs.
(5) Ten workers complete an application form.
Each puts his/her name in the same box at the top of the page. In this case,
there will
be 10 names
occupying the same place (namely, the top of each form) at the same time.
Alternatively, a
teacher tells a class of thirty, six-year olds to write their names in the same
place, namely at the top of the page. Here, once more, there would be thirty 'objects' in the same place (namely at the top of each page,
again), even
though they are also in different places (i.e., on different pages, in different
parts of the classroom).
(6) This sentence ends in the same place as the
next. This sentence ends in the same place as the next. This sentence ends in
the same place as the next. This sentence ends in the same place as the next…
In relation to the above examples, it won't do to suggest
that the exact same place isn't meant every time. For instance, there is
no way that 30 children will all write their names in the exact same spot, even
if they all managed to write their names at the top of each page. Indeed, but
the whole point of these examples is to show that not every use of "same place"
implies "exactly the same place". But, even if it did, as we have seen,
there is no way that "exactly the same place" can be defined without the use of
the much looser, ordinary sense of "place".
Indeed, it is possible to imagine cases where moving
objects somehow manage to remain stationary while they are moving -- revealing yet another
amazing 'contradiction':
(7) Consider an object located at (x1,
x2, x3, t1) with respect to some inertial frame. Let that
frame itself move with respect to another inertial frame. In that case, the
object in question could remain stationary with respect to the first frame,
while it moves with respect to the second.
Again, an ordinary example will suffice to illustrate this 'contradiction':
(8) A child is ascending a descending escalator
in such a way that she remains stationary (even momentarily) with respect to an
arbitrary point not on that
escalator.
Of course, in all such cases, the alleged 'paradoxes' and 'contradictions' they
reveal are easily resolved by clarifying the many equivocations and ambiguities
they contain. Unfortunately, this eminently reasonable strategy isn't available
to DM-enthusiasts -- that is, not without it undermining what few examples of
'real contradictions' they have managed to scrape together over the last two
hundred years
in support their ramshackle 'theory'.
26.
To compound the problem, a queue doesn't have to be composed of a line
of people actually standing anywhere, or of cars waiting to board a ferry; for example, it could consist of a list
of the names of patients due for an operation, or of a group of people waiting
for a call-centre operator to answer their calls. Clearly, in cases like these we
would have instances of movement (in one sense) even where no movement
(in another sense) had taken place, if one or more in each queue dropped out, and others
were moved up
the list, while not moving anywhere.
In such circumstances, 'queue jumping' could
also occur when the proposed interloper was neither on the list nor located anywhere near
any others on the list (there being no list in this case, just an electronic
queue, perhaps). Here, those in the queue would move while remaining stationary, as would
any queue jumpers.
This illustrates how, when the circumstances surrounding the use
of certain words are altered sufficiently, the sense of those words (and of
those associated with them) changes
accordingly (and indeed vice versa) -- something Engels and the vast
majority of philosophers appear not to have
noticed.
[This change of meaning refers to what we would say, and how we
would interpret any words used, in such circumstances. (I merely add this to
forestall complaints that this contradicts (no pun intended) what was said about
'contextualism' in Essay Thirteen Part
Three.)]
However, in their everyday use of language DM-theorists and traditional
philosophers are not quite this semantically-challenged; they only become 'Linguistic
Philistines' when they
attempt
to do some a priori Superscience (i.e., Metaphysics), employing words as if
they were complete novices or were using a foreign language for the first time.
Linguistic naivety is the price one has to pay, it seems, for the
low grade skill involved in discovering 'philosophical truths' by thought alone. In fact, this is
the first hurdle adepts have to negotiate: becoming a
Linguistic
Philistine.
Update 16/05/2011: The other night I watched a
film called
Poodle
Springs. Among other things, this film was about a mythical town on the
California/Nevada
border, in the USA. Near the end of the film one of the characters revealed a
sinister plot to have the Nevada border moved a few miles west so that Poodle
Springs would then be in Nevada, not California. So, if that border had been
relocated (apparently it wasn't in the end), Poodle Springs would have moved
from California to Nevada while not having moved at all.
This is yet another perfectly ordinary sense of "move" that
traditional metaphysicians ignored. Indeed, for centuries, whenever borders
between countries were moved (often after a war) many hundreds, and possibly
thousands of square miles of territory moved from one country to another --
while remaining perfectly motionless in the process.
[Lists of border changes since WW1 can be found
here.]
Another example springs to mind (no pun
intended): In 1974,
the UK Government re-organised the County Boundaries. Overnight, millions of
residents found they had moved counties -- while not having moved an inch!
Are any of these significant 'movements' of land and real estate
"both in one place and in another place at
one and the same moment of time,...in one and the same place and also not in
it"? How could they be if they moved and did not move? All that happened in
many cases was that new lines were drawn on a map somewhere, and a few
signposts, fences or border checkpoints were changed/relocated. They
certainly moved, but nothing else did, even while it did!
Update 09/03/2014: We now read this from the BBC:
"Kiruna:
How to move a town two miles east
"By Tabby Kinder
"This
spring work will begin to move Sweden's northernmost town two miles to the east.
Over the next 20 years, 20,000 people will move into new homes, built around a
new town centre, as a mine gradually swallows the old community. It's a vast and
hugely complicated undertaking.
"'When people hear
that we're designing, creating and building
a whole new city from scratch they think
we're doing a utopian experiment,' says
architect Mikael Stenqvist. But there's too
much at stake to think of it as an
experiment, he says....
"More than 3,000
apartment blocks and houses, several hotels
and 2.2m sq ft (0.2m sq m) of office, school
and hospital space will be emptied over the
next two decades -- while alternatives are
built on the new site. The old church voted
Sweden's most beautiful building in 2001
will be taken apart, piece by piece, and
rebuilt.
"'We want to have as
much of the existing character from the old
city as possible, but costs and market
mechanics mean we can't move everything,'
says Stenqvist.
"The move has been
dictated by the local iron mine - one of the
most valuable iron ore deposits in the whole
of Sweden, and Kiruna's largest employer.
"The story began in
2004, when the state-owned mining company,
Luossavaara-Kiirunavaara AB (LKAB), sent a
letter to the local government explaining
that it needed to dig deeper into a hill
just outside the town, which could cause the
ground beneath thousands of apartments and
public buildings to crack or give way. A
decade later, sure enough, huge fissures are
appearing across the city, creeping towards
the centre.
"'Everyone that lives
in Kiruna has known that the city will
eventually be relocated -- everyone can see
the mines eating up the city,' says Viktoria
Walldin, one of the social anthropologists
hired to work on the relocation. 'The
question has always been when.'...
"Before anyone can
move, LKAB has to buy their existing
property, so that they can buy a new one in
the new town. But the sums are nightmarish.
"'The general idea is
for LKAB to purchase people's homes from
them at market value plus 25%, and then sell
them a property in the new city,' says
Stenqvist. 'But how do you work out what the
market value is for a house in a city that
doesn't even exist?'...
"'It's a
new situation and no-one really knows how to handle it," says Yvel Sievertsson,
urban transformation officer at LKAB. 'We have hundreds of people working on the
issue alone, including researchers at the University of Stockholm. The goal is
to have the new city centre ready before we start to move everyone over, and
then to move everyone at once in one or two stages, to impact people's
businesses as little as possible.'
"'We have been around
the world looking at how other countries
like Germany and parts of Africa have
handled similar projects, but they are just
moving small villages and houses, not huge
city centres,' says Sievertsson. 'We're
using all the expertise we can to help us,
but it's a completely unknown
situation.'..." [Quoted from
here. Accessed 09/03/2014. Quotation
marks altered to conform to the conventions
adopted at this site. Several paragraphs
merged to save space. Link added.]
Hence, this town is and isn't being moved. It is being
moved in the sense that it will appear in a new location two miles to the east
of where it is now, but it isn't being moved in the sense that the vast majority
of the buildings are remaining where they are (or they will probably be
demolished). What is being moved is the population, and even that
is being moved in a piecemeal fashion. This means that the population will be in
countless places at once, in and not in any of them, since it is an extended
aggregate, even when it isn't being moved, let alone when it is being
moved.
The population will be in Kiruna, but not in any one place
in Kiruna -- that is, not unless all 20,000 are squeezed into someone's house!
But even then, unless they are all squeezed into the same geometric point,
they still won't be in the same place. So, they will and won't be in Kiruna,
even if they are all rooted to the spot, or are all moving! Which means that
this is yet another 'contradiction' that has nothing to do with motion.
So, will this town going to be in two places at once, in one and
not in it at the same time? Hardly, since the town will be in two places for a
year or so (while the residents are being moved out), but it won't be both in
one place and not in it at the same time. And yet, when the move has been
completed, the town will still have been moved.
However, during the move, there will in fact be two towns,
both called by the same name, so Kiruna won't in fact be in two places at
once. There will be two towns in two places!
Moreover, the old church mentioned above will be taken apart and
moved to the new site. However, while the parts of that church will certainly
move, the church itself will cease to exist in between locations (if by "church"
we mean the assembled object, not its disassembled parts). So, while this church
moves, it won't occupy two places at once, and be in one of them and not in it,
since there will be no church in existence between locations for it to do that.
Of course, this 'non-existence problem' applies to countless
things that are disassembled and then moved, or which are transmitted in another
form while they are being moved. For example, consider someone moving home; let
us suppose they disassemble several items of furniture (for instance, beds,
bookcases, tables, etc.), move them across the city and re-assemble them at
their new location. Since each of these items ceases to exist in the move (even
though their parts still exist), they will still have moved even though they
haven't been in two places at once, in one and not in the other.
Suppose further, you are reading a book on an
e-reader.
This book will have been transmitted/transferred to that reader in a form that
is different from the form in which it was originally written (especially if the
book in question was committed to paper over thirty years ago). But, while it
was being transmitted/transferred to that e-reader, it was no longer a book, but
a series of electronic signals/pulses. Now, while that book has certainly been
moved, it wasn't in two places at once, in one of them and not in it at the same
time, since between locations it ceased to exist as a book. Of course, this also
applies to countless examples of movement like this -- for instance, the
transmission of TV programmes, text messages, phone conversations (or, indeed,
any conversation, since they are all transmitted through the air, or some other
medium), coded messages, and e-mails.
Naturally, it could be argued that these latest examples have
been deliberately mis-described (or their description has been intentionally
slanted) so that they seem to violate Engels's description of motion. For
instance, while it is true that a text message is transmitted in a different
form, it still exists in an electronic form between locations. In fact, it
always is, and remains in, an electronic form, even as it is being written. And
the electronic signals/pulses certainly conform to Engels's description of
motion.
The first part of this might be correct (the fact that a text
will exist in an electronic form between locations), but the message on the
sender's screen -- the actual letters and/or pixels -- doesn't/don't exist while
it is being transmitted, so the above points still stand.
Of course, the second part, about Engels's description of motion
being correct, has been disputed throughout this Essay.
Notice, once again, that as soon as we
understand the surrounding circumstances,
the apparent 'contradictions' vanish.
27. I have
had to use slightly stilted language in some of these examples so that the use
of the word
"move" is quite clear. Normally, one would employ other, more appropriate terms;
but that having been done, the danger might then be that more than one dialectician
is likely to
miss the point. For example, L63 would more normally be:
L63a: The wire winds around this tree in a
spiral. It's been in the same spot so long that the tree has partially grown
around it.
[L63: The wire moves in a spiral around this tree.
It's been in the same spot so long that the tree has partially grown around it.]
In this
example, it is irrelevant whether the wire has
actually shifted position over the years, because that particular sense of "move" is not the same as the one
expressed in this instance. Wires
can move around trees (with no change of place implied) just as gaps can run through
crowds and holes through
Polo Mints. Here, the wire moves around the tree
(i.e., it winds through the same 360 degrees of turn, perhaps several times)
while not itself rotating around the tree's geometric centre (in one sense of
"rotate"), whether or not the radius of each turn alters over the years. Winding
around a tree is a different sort of movement from, say, gripping it more
or less tightly over time -- or, indeed, from slipping down the trunk.
28.
Several other examples of motion that are not easy to squeeze into the
traditional
'dialectical straightjacket' include the following:
(1) Imagine a situation where the sun is shining intermittently
through the clouds,
sometimes casting shadows, sometimes not. In such circumstances, someone could
say:
M1: "An hour ago, the shadow of that telegraph pole was over
there, now it's moved over here."
In this instance, although it would be correct to say that the shadow had
moved, in the circumstances depicted, its episodic existence (as the
Sun disappeared behind the clouds, only to reappear minutes later) means
that there would be no continuity between each successive location. Here, we
would have something that moved, which had been in two (possibly) widely
separated locations, but which had not been in any of the intermediate points
between them, and which had ceased to exist during in that interval. In this case, therefore, we would have something that moved
that did not move!
Moreover, while moving, the shadow isn't
in the two places mentioned at once, nor in any in between.
It could be objected here that since a shadow is not a
moving object, it isn't a counter-example to Engels's claims about
motion. Perhaps so, but according to Lenin a shadow only has to be
objectively external
to the mind for it to be material.
"[T]he sole 'property' of matter with
whose recognition philosophical materialism is bound up is the property of
being an objective reality, of existing outside our mind." [Lenin (1972),
p.311. Italic emphasis in the original.]
"Thus…the concept of matter…epistemologically
implies nothing but objective reality existing independently of the human
mind and reflected by it." [Ibid.,
p.312. Italic
emphasis in the original.]
If so, shadows would be moving material objects (in Lenin's sense).
In that case, we may rescue Engels only by
contradicting Lenin -- or vice versa. [Of course, if shadows aren't
counted as
material, but they can move, then motion and matter are not linked in the way
Lenin and Engels imagined they
were -- on this see Essay Thirteen
Part One -- or even Point
(2) below.]
But then again, maybe not, since what Engels actually said was
this:
"[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.]
So, it is "motion itself", not so much moving bodies, that
interested him, and shadows certainly move.
(2) Consider a case where, say, a woman is consulting the plans
for her new house, but who, upon being shown the latest drawings, exclaims:
M2: "Wait a minute, you've moved the front door.
We agreed it should go here next to the window, but you've put it to over there
near the sink!"
Here, we would have an
intentional object
that had been 'moved' to a new location, one represented perhaps by pencil or
ink marks on a plan. Not only that, but since the original 'intentional object'
doesn't yet exist (after all, in this instance there is as yet no house and so no door, merely marks on
a page!), this would be a clear case of movement not involving a material object
--,
but which
'object' cannot have occupied two places at once (in one sense of "place",
etc.), nor any in between.
Naturally, this means that motion is not the sole property of matter;
again,
contrary to what Engels and Lenin believed:
"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…." [Engels (1976),
p.74. Bold
emphasis alone added. For Lenin's comments, see Essay Twelve
Part One.]
If intentional objects can move --
and if mind is not matter -- then not all that moves is material.
Be this as it may, even if an actual drawing of a door had been moved (as
opposed to an intentional object having done so), it still need not have
occupied two places at one and the same time, since there might not even be
two places for it to occupy.
There are a host of possibilities here: The door could now be in the 'same place' (i.e., right by the window), but in a
different room (hence, it would be in one and the same place, but which place
had now moved (while the object itself had not, in one sense of "move"), if the same 'intentional window' had also been re-located
in a new room. So the door would still be next to the window in a new room -- and
hence in the same place relative to another intentional object (the door), but
in a different place relative to a third (the new room), or in the 'same place'
in a different building, or in the 'same place' with new surroundings (e.g., the
walls could have been altered), and so on.
Try saying any of that in Hegel-speak!
There are many other possibilities. Readers are invited to
imagine a few of their own. Ordinary language and our common understanding allow for
a host of
alternatives undreamt of in the philosophical ramblings of Idealist
bumblers like Hegel and Zeno.
Moreover, even if the drawing of the original door had been
rubbed out and re-drawn elsewhere, while it would still be true to say that
something had moved, it would not be true to say that whatever it was that had
moved had been in these two places at the same time, nor that it had occupied
any intervening locations, either. Of course, no one imagines that in such cases
a drawing of a door slides across the page, even though in some cases
it could do just that -- if, say, it were part of a computer-aided design. But even then, this would be an example of simulated movement
(that is, it would be represented by sets of pixels successively lit up on the screen), as
was the case with
the strobe example mentioned in the main body of this Essay.
(3) Another familiar example concerns the different aspects a
shape can assume while it is being observed -- even though nothing actually 'changes
places':
M3: "The front of that Necker Cube moves to
the back when I look at it for a few seconds."
![](/web/20140524014506im_/http://anti-dialectics.co.uk/neckercube.jpg)
Figure Six: Motion With No Movement?
Here, in Figure 1, it would be odd to say that the front and back
of the said cube both occupied and did not occupy the two places which they had
moved into
(the back or the front) at the same time, and that both were in two places at
once (i.e., front or back again), even though it would be perfectly normal to
say that the front and the back had moved (i.e., "changed places"), as indicated.
Other examples
of 'gestalt' switches (in Figures 3-6) could be described
equally well in the same uncontroversial manner. [Here shapes move, or change, but it
isn't easy to say how they do this, or where they move to, or what 'places'
they occupy while they are doing it!] In such cases, we would have at
least two intentional/perceptual objects occupying no places at all, even while
they moved!
![](/web/20140524014506im_/http://anti-dialectics.co.uk/image5.jpg)
Figures Seven To Ten: Four More
Dialectically-Annoying, But No Less
'Reactionary', Objects
(4) Furthermore, some things can move, and not change place
even while they are doing just that! Consider a line of soldiers marching along a road
in strict order, or the numbers on the face of a watch on someone's wrist on a
moving train, or the words in a book on that same train, or the numbers on the
screen of a calculator (or letters on a computer screen) as they are typed in,
etc. In each case, several things remain in the same place (i.e., they stay in
the same order relative to one another: first, second or third (etc.)
in
line) even while they move (i.e., they change location relative to something else).
Hence,
in the first example above, soldier NN could be second in line (and stay second)
as the squad marches down the road -- and
he could remain second, even if the distance between each soldier alters. In that case,
NN would remain in the same place (i.e., second) even as he moved.
The same is true of numbers typed
into a calculator (or letters on a computer screen), on a train. So,
π =
3.1415926535..., but as the calculator screen hurtles along at 100
mph on that train, the "3" at the front still remains in the same place, at the
front, as does the "3" in tenth place! [It is also worth recalling that numerals
are eminently material objects, so this isn't an 'abstract' example.]
Again, the words in a book certainly remain where they are while
travelling at 100 mph -- train journeys do not scramble the printed page! -–; so they too can stay in the same location and the same order
while they hurtle along.
Of course, several of the above examples depend on the use of
figurative (or in some cases slightly stilted) English, but Engels's own use
of language in this respect is even more non-standard, and hardly less
figurative (that is, where any sense can be made of it).
Anyway, the rather odd sentence constructions I have employed in
several of the examples in the main body of this Essay (and in those above) were a direct consequence of the
fact that I had to limit myself to using the word "move" (and its cognates) to
make each point seem relevant. Less stilted versions could easily have been
devised if a wider selection (of the many words we have available to us in
ordinary language for depicting change) had been chosen. They would then allow
the same points to be made, but in less
stylistically-challenged ways. Indeed, the last example listed in the main body
of this Essay (L64)
did precisely that.
L64: This road is going nowhere.
If a more intelligent use were
made of the countless
words we have in English that enable us to speak about motion
and change, the number of
'contradictions' language appears to sanction (but only to those who
insist on understanding the vernacular in a crude manner) would multiply
alarmingly. Consider the following:
(5) Coal seams run through mountains (and they remain
stationary while they do so), just as roads run through tunnels, mountains and cliff
faces. Messages can run through sticks of rock, just as they can also travel
down a line of stationary messengers who pass them along by word of mouth (and a
stationary message can run along a line of bill boards, with one word on each
board); paths can climb hills (without moving) just as easily as tracks can
ascend mountains, and stairs/steps can connect floors in hotels, offices,
theatres and sports stadia.
Moreover, perfectly still wiring can wind effortlessly about inside TV sets, radios and
computers; fences cemented into the ground can descend into valleys, surround
farmsteads, disappear over
the horizon and encircle fields; string can coil round a parcel, and perfectly
motionless moats can encircle castles; buildings can rise above one another just
as cliffs can tower over climbers. Bandages can cover heads just as
towels can wrap around bodies; stories can switch to new locations even as
they reside in books that have remained on the same shelves for many years. Tram
lines can cut through the city centre just as Panics can sweep through crowds, just as behaviour patterns
can propagate through animal and human populations --, or, indeed, just as
feelings of resentment can spread through a workforce sat motionless in a
meeting as management reveals its latest 'fair offer'.
And lists like this are extendable...
Once again, try saying any of this in Hegel-speak.
[But, lists do not
apparently occupy at least two places at once -- or maybe they can if
they are found in two separate copies of this Essay, say: on your computer
screen and on mine. Nor do the other things mentioned in the above list
occupy two places at once, being in one place and not in it at the same time --
but they still move in the way suggested each time.]
Ordinary language is an
amazing
resource.
29. Engels's theory must account for the motion of gross bodies in
the material world otherwise it would be of no use to DM-theorists trying to
explain, say, the motion of a cat on a mat -- let alone the economic and social
changes we see in Capitalism. If his theory can't account for the sort of mundane things that are
all too easily
depicted in ordinary language, it stands little chance of being employed
successfully to help us make sense of the complex movement of, say, electrons
and/or
social classes.
30.
This is argued in detail in Essay Seven.
More importantly, Engels's conclusions are uncheckable in
this world, as we have seen. That is because they do not depend on anything
in this world for their validity, having been divorced from it by a crass misuse
of words in order to fiddle a quirky, Ideal result.
In doing this, dialecticians and Traditional Philosophers not
only ignore the most important resource the human race has available to it for
understanding anything which is capable of being comprehended -- i.e., ordinary language (which
has been tested and refined in social practice for thousands of years) --, they
distort it into the bargain. Small wonder then that it
isn't possible to make
sense of anything they say.
Those who think ordinary language is defective, or of limited
use, are encouraged to shelve that worry until Essay
Twelve has been posted (preliminary summary
here), and then
think again. [In the meantime,
check this out.]
Of course, some like Graham Priest think we
can observe contradictions. His ideas will be examined in a later Essay; in
the meantime readers are directed here
for further details. However, not even Priest thinks that contradictory
motion can be observed.
31.
Hyphenated, metaphysical terms like these (i.e., "Things-in-themselves",
"Being-for-itself", etc.)
litter much of post-Kantian
Continental Philosophy (and, alas, DM-texts), where
they only succeed in clouding thoughts that are already hopelessly vague.
Working in tandem with the 'magical power' of
innocent-looking quotation marks (as they feature in, for example,
"Thing-in-itself", and "Being-for-us", etc.), this neat typographical combination
'allows' those enamoured of them to penetrate right to the heart of reality while sat at a
keyboard, or in an armchair.
Hence, any riposte offered here (by me to any objections raised
against the claims advanced at this site), which is similarly be-decked in such
talismanic finery, should work like magic, too. In that case, I could reply to
anyone who objects to the points I have made in this Essay in a like manner;
hence, all metaphysical/dialectical terms are
"Intrinsically Incomprehensible" since they are thoroughly "Obscure-in-themselves",
having been invented by "Mystics-R-Us".
That should put an end to Traditional Philosophy/DM -- just
as it removes any need by me to justify their "Long-overdue-termination".
Those still unconvinced by the above ploy are clearly not "Thinking-as-such"; they should stop
"Being-picky-in-themselves" over which "Quotation-marks-and-hyphens-they-heed", and which they find "Still-unconvincing-to-them".
Clearly, a "Quotation-mark-hyphenated-response" wins every time.
"End-of-story".
The Supernatural Power possessed by hyphens and quotation marks will be
examined in more detail in Essay Twelve.
32.
Or even looked for any!
Again, it could be argued that this entire analysis of motion is completely
misguided since DM-theorists are really only interested in the movement of
material bodies in objective reality. The examples considered in this Essay hardly address this issue at all.
Or, so it could be maintained.
In reply, it is worth noting that with respect to Leninist dialecticians at
least, if we define matter as
objective existence external to the mind, then few of the examples given
here would fail to be genuine instances of movement in the real world. Hence, this
objection is itself wide of the mark.
Until DM-theorists themselves tell us what they take
matter to be (having prevaricated on this issue for over a hundred and
forty years
-- as will be demonstrated in Essay Thirteen
Part One), they are in no position to find
fault with the counter-examples presented in this Essay.
33. These
objections are examined throughout this Essay,
and in others posted at this site. On the dubious belief in universal change,
for example, see here. On
whether DM can account for it, see
here.
34. This argument is worked out in considerable detail in Essay Twelve
Part One.
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