Physics   

only as many as are drawn falsely from the principles of the science:
it is not our business to refute those that do not arise in this way:
just as it is the duty of the geometer to refute the squaring of the
circle by means of segments, but it is not his duty to refute
Antiphon's proof. At the same time the holders of the theory of which
we are speaking do incidentally raise physical questions, though
Nature is not their subject: so it will perhaps be as well to spend a
few words on them, especially as the inquiry is not without scientific
interest.
The most pertinent question with which to begin will be this: In what
sense is it asserted that all things are one? For 'is' is used in many
senses. Do they mean that all things 'are' substance or quantities or
qualities? And, further, are all things one substance-one man, one
horse, or one soul-or quality and that one and the same-white or hot
or something of the kind? These are all very different doctrines and
all impossible to maintain.
For if both substance and quantity and quality are, then, whether
these exist independently of each other or not, Being will be many.
If on the other hand it is asserted that all things are quality or
quantity, then, whether substance exists or not, an absurdity results,
if the impossible can properly be called absurd. For none of the
others can exist independently: substance alone is independent: for
everything is predicated of substance as subject. Now Melissus says
that Being is infinite. It is then a quantity. For the infinite is in
the category of quantity, whereas substance or quality or affection
cannot be infinite except through a concomitant attribute, that is, if
at the same time they are also quantities. For to define the infinite
you must use quantity in your formula, but not substance or quality.
If then Being is both substance and quantity, it is two, not one: if
only substance, it is not infinite and has no magnitude; for to have
that it will have to be a quantity.
Again, 'one' itself, no less than 'being', is used in many senses, so
we must consider in what sense the word is used when it is said that
the All is one.
Now we say that (a) the continuous is one or that (b) the indivisible
is one, or (c) things are said to be 'one', when their essence is one
and the same, as 'liquor' and 'drink'.
If (a) their One is one in the sense of continuous, it is many, for
the continuous is divisible ad infinitum.
There is, indeed, a difficulty about part and whole, perhaps not
relevant to the present argument, yet deserving consideration on its
own account-namely, whether the part and the whole are one or more
than one, and how they can be one or many, and, if they are more than
one, in what sense they are more than one. (Similarly with the parts
of wholes which are not continuous.) Further, if each of the two parts
is indivisibly one with the whole, the difficulty arises that they
will be indivisibly one with each other also.
But to proceed: If (b) their One is one as indivisible, nothing will
have quantity or quality, and so the one will not be infinite, as
Melissus says-nor, indeed, limited, as Parmenides says, for though the
limit is indivisible, the limited is not.
But if (c) all things are one in the sense of having the same
definition, like 'raiment' and 'dress', then it turns out that they
are maintaining the Heraclitean doctrine, for it will be the same
thing 'to be good' and 'to be bad', and 'to be good' and 'to be not
good', and so the same thing will be 'good' and 'not good', and man
and horse; in fact, their view will be, not that all things are one,
but that they are nothing; and that 'to be of such-and-such a quality'
is the same as 'to be of such-and-such a size'.
Even the more recent of the ancient thinkers were in a pother lest the
same thing should turn out in their hands both one and many. So some,
like Lycophron, were led to omit 'is', others to change the mode of
expression and say 'the man has been whitened' instead of 'is white',
and 'walks' instead of 'is walking', for fear that if they added the