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 word 'is' they should be making the one to be many-as if
'one' and 'being' were always used in one and the same sense. What
'is' may be many either in definition (for example 'to be white' is
one thing, 'to be musical' another, yet the same thing be both, so the
one is many) or by division, as the whole and its parts. On this
point, indeed, they were already getting into difficulties and
admitted that the one was many-as if there was any difficulty about
the same thing being both one and many, provided that these are not
opposites; for 'one' may mean either 'potentially one' or 'actually
one'.

                                 3

  If, then, we approach the thesis in this way it seems impossible for
all things to be one. Further, the arguments they use to prove their
position are not difficult to expose. For both of them reason
contentiously-I mean both Melissus and Parmenides. [Their premisses
are false and their conclusions do not follow. Or rather the
argument of Melissus is gross and palpable and offers no difficulty at
all: admit one ridiculous proposition and the rest follows-a simple
enough proceeding.] The fallacy of Melissus is obvious. For he
supposes that the assumption 'what has come into being always has a
beginning' justifies the assumption 'what has not come into being
has no beginning'. Then this also is absurd, that in every case
there should be a beginning of the thing-not of the time and not
only in the case of coming to be in the full sense but also in the
case of coming to have a quality-as if change never took place
suddenly. Again, does it follow that Being, if one, is motionless? Why
should it not move, the whole of it within itself, as parts of it do
which are unities, e.g. this water? Again, why is qualitative change
impossible? But, further, Being cannot be one in form, though it may
be in what it is made of. (Even some of the physicists hold it to be
one in the latter way, though not in the former.) Man obviously
differs from horse in form, and contraries from each other.

  The same kind of argument holds good against Parmenides also,
besides any that may apply specially to his view: the answer to him
being that 'this is not true' and 'that does not follow'. His
assumption that one is used in a single sense only is false, because
it is used in several. His conclusion does not follow, because if we
take only white things, and if 'white' has a single meaning, none
the less what is white will be many and not one. For what is white
will not be one either in the sense that it is continuous or in the
sense that it must be defined in only one way. 'Whiteness' will be
different from 'what has whiteness'. Nor does this mean that there