Ethan asked:

If Zeno's paradox attempts to show existence is static and that motion and change are impossible,
why hasn't anyone postulated the opposite — i.e. that nothing is at rest and change is happening all
the time? This seems to me the obvious way of solving the problem. And sorry I think all the
mathematical solutions just don't cut it (no pun intended).

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Two points. The first about your opening 'If', and the second about your central 'why?'

(1)To begin with, it is not clear that "Zeno's paradox attempts to show existence is static and that
motion and change are impossible".

The alternative possibility which we should consider is that Zeno is attempting to give what is called a
"reductio" of a view he rejects, by showing that motion would beimpossible if one assumed what his
opponent assumes about space and time. A "reductio ad absurdum" where one shows that a set of
claims is contradictory. The moral of a "reductio" here might be that some people have an incoherent
picture about motion, rather than that there is no motion on any picture of motion whatsoever.

There is room for controversy about exactly what the objectionable set of assumptions is for Zeno. All
of our evidence about Zeno is second or third hand, the principal sources being critics of Zeno,
namely Plato and Aristotle. But there are grounds, in this evidence, for thinking that Zeno is
presenting a reductio ('there is no motion if we assume what you assume') rather than a positive
thesis ('there is no motion').

Without going through the whole thing, I'll point to two suggestive texts. See (i) the passage in
Aristotle's Physicswhere he reports that absurd conclusion that the arrow is stationary in flight
"follows if it is assumed that time is composed of nows". Is this Zeno's assumption, or an assumption
made by someone that Zeno is attacking? Aristotle isn't clear about this. But what Plato says about
Zeno's motivations may be relevant. See (ii) the opening section of Plato's dialogue Parmenides,
where Zeno is presented as advancing no positive thesis about anything at all. In that dialogue, Zeno
protests that he has been misunderstood as advancing some thesis of his own, whereas what he
meant to do was to show that what the pluralists believe leads to just as many absurdities as the
position of Zeno's teacher, the monist Parmenides. If one considers that Parmenides' monism
amounted to the thesis that there is just one thing, and is tempted by the definition of movement as
the change of one things position relative to another thing, one can see that Parmenides' monism
might have been attacked as denying an apparent fact, namely, that things move. If Zeno's aims were
throughout exactly those destructive ones attributed to him by Plato, then it would not make sense for
Zeno to assume that "time is composed of nows". The point of a reductio is to compare your
opponents assumptions, not to add assumptions of your own.

If interested, you are welcome to consider my MPhil thesis treatment of Zeno at
http://www.plato.plus.com/c1.htmland http://www.plato.plus.com/c2.html. In some respects I was
over harsh about Aristotle there, but I stand by the thought that Zeno was presenting a reductio, and I
stand by the account of that reductio and it's target.

(2) You then ask "why hasn't anyone postulated... that nothing is at rest and change is happening all
the time?". They have, a chorus will announce. Usually, the central historical proponents of this kind
of view are supposed to be either Heraclitus or Cratylus or both according to your reading and your
translation. A complication about these usual supposings, one complication amongst many, is that the
thesis that "nothing is at rest" is notequivalent to the thesis that "change is happening all the time".
To see this, note that changes happen to things. Therefore, the thesis that "change is happening all
the time" commits one to the existence of particular things in a way that "nothing is at rest" does not
(and in my opinion the latter idea is more central to the Heraclitean notion of flux than the former idea
is). This distinction matters because there are a large collection of reasons why, of late, philosophers
have been averse to that formulation of your thought which speaks of change.

You want to say that far from the universe being stable all the time in every respect, it's just "the
opposite". So, what you are attracted by is the idea that everything is changing all the time in every
respect. In brief, there are three kinds of reason for objecting to this idea: (a) that motion is relative,
(b) that the meaning of 'change' requires a contrast, and (c) that talk of change requires a context in
which things are to some degree stable.

(a) Something or other, perhaps a station, has to be assumed to be stationary if the talk of a change
of position is to have any sense. This consideration about the relativity of position change excludes
the possibility that one can talk of everything changing position. 'Changing position relative to what?',
would be the question. And in answering it one cannot but assume that something or other counts as
the station for the purpose of discerning a change of position. One drawback of this line of argument
is that it invites the curious debate (popular with Kantians) about absolute and relative space. In short,
does one actually need a thingrelative to which one is moving, or only something called an 'absolute'
location?

(b) If "Everything is changing all the time in every respect" there would be nothing which we could
pick out as not changing. The philosophically interesting move then is that 'this is changing' can only
mean something if the contrasting negative claim 'this is not changing' could also be meaningfully
applied somewhere or to something. Something about this point looks to be right. On the other hand,
this contrast-constraint on meaning is undeveloped here, and every development of it seems to take
us off in philosophically difficult directions. For instance, should we say that the contrast upon which a
word's meaning depends must be possible for each thing to which the word is to be applied? Why?
Or should we say that the contrast upon which a word's meaning depends must be possible within all
the things there are? What things are there then? Or is it just some of the things that there are that
matter here? Which then, and why? What is to be contrasted with what? For instance, might it be
allowed to give a contrast-meaning to 'change' to say that while everything on earth is changing all
the time in every respect God does not change? Or that there are contrastingly unchanging things 'in
the intelligible realm'? Maybe not, but the difficulty is that giving reasons for this will involve
developing a large body of thought about meaning and metaphysics and so on.

(c) If we can see that change happens to things, then there will be limits on how this idea of 'change'
can reasonably be used. In order for us to talk of a change, we must be able to talk of a thing. And
here comes the decisive move: it is some stability in a thing's qualities that permits us to refer to that
thing, to identify it. In order for us to able to talk of a thing, there must be some stability in the qualities
by which we are able to pick that thing out as being that thing. Some stability is essential to talk of
things, and talk of things is essential to talk of change. Therefore, the idea that the universe is
changing so much that it is "the opposite" of stable can't be made sense of.

Reason (c) is usually thought to be the most decisive against your proposal. But as I said at the
outset, it matters for these purposes whether you talk of everything changing all the time, or, which is
a different thesis with different implications, that nothing rests.

David Robjant

If you know something about Zeno, how come you missed out on Heraclitus? His philosophy was
"panta rhei", i.e. "nothing ever stops still". Will this satisfy you?

Jürgen Lawrenz

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