is anything that can exist separately, over and above what is white.
For 'whiteness' and 'that which is white' differ in definition, not in
the sense that they are things which can exist apart from each
other. But Parmenides had not come in sight of this distinction.

  It is necessary for him, then, to assume not only that 'being' has
the same meaning, of whatever it is predicated, but further that it
means (1) what just is and (2) what is just one.

  It must be so, for (1) an attribute is predicated of some subject,
so that the subject to which 'being' is attributed will not be, as
it is something different from 'being'. Something, therefore, which is
not will be. Hence 'substance' will not be a predicate of anything
else. For the subject cannot be a being, unless 'being' means
several things, in such a way that each is something. But ex hypothesi
'being' means only one thing.

  If, then, 'substance' is not attributed to anything, but other
things are attributed to it, how does 'substance' mean what is
rather than what is not? For suppose that 'substance' is also 'white'.
Since the definition of the latter is different (for being cannot even
be attributed to white, as nothing is which is not 'substance'), it
follows that 'white' is not-being--and that not in the sense of a
particular not-being, but in the sense that it is not at all. Hence
'substance' is not; for it is true to say that it is white, which we
found to mean not-being. If to avoid this we say that even 'white'
means substance, it follows that 'being' has more than one meaning.

  In particular, then, Being will not have magnitude, if it is
substance. For each of the two parts must he in a different sense.

  (2) Substance is plainly divisible into other substances, if we
consider the mere nature of a definition. For instance, if 'man' is
a substance, 'animal' and 'biped' must also be substances. For if
not substances, they must be attributes-and if attributes,
attributes either of (a) man or of (b) some other subject. But neither
is possible.

  (a) An attribute is either that which may or may not belong to the
subject or that in whose definition the subject of which it is an
attribute is involved. Thus 'sitting' is an example of a separable
attribute, while 'snubness' contains the definition of 'nose', to
which we attribute snubness. Further, the definition of the whole is
not contained in the definitions of the contents or elements of the
definitory formula; that of 'man' for instance in 'biped', or that
of 'white man' in 'white'. If then this is so, and if 'biped' is
supposed to be an attribute of 'man', it must be either separable,
so that 'man' might possibly not be 'biped', or the definition of
'man' must come into the definition of 'biped'-which is impossible, as
the converse is the case.

  (b) If, on the other hand, we suppose that 'biped' and 'animal'
are attributes not of man but of something else, and are not each of
them a substance, then 'man' too will be an attribute of something
else. But we must assume that substance is not the attribute of
anything, that the subject of which both 'biped' and 'animal' and each
separately are predicated is the subject also of the complex 'biped
animal'.

  Are we then to say that the All is composed of indivisible
substances? Some thinkers did, in point of fact, give way to both
arguments. To the argument that all things are one if being means
one thing, they conceded that not-being is; to that from bisection,
they yielded by positing atomic magnitudes. But obviously it is not
true that if being means one thing, and cannot at the same time mean
the contradictory of this, there will be nothing which is not, for
even if what is not cannot be without qualification, there is no
reason why it should not be a particular not-being. To say that all
things will be one, if there is nothing besides Being itself, is
absurd. For who understands 'being itself' to be anything but a
particular substance? But if this is so, there is nothing to prevent
there being many beings, as has been said.

  It is, then, clearly impossible for Being to be one in this sense.

                                 4

  The physicists on the other hand have two modes of explanation.

  The first set make the underlying body one either one of the three
or something else which is denser than fire and rarer than air then
generate everything else from this, and obtain multiplicity by
condensation and rarefaction. Now these are contraries, which may be
generalized into 'excess and defect'. (Compare Plato's 'Great and
Small'-except that he make these his matter, the one his form, while
the others treat the one which underlies as matter and the
contraries as differentiae, i.e. forms).

  The second set assert that the contrarieties are contained in the
one and emerge from it by segregation, for example Anaximander and
also all those who assert that 'what is' is one and many, like
Empedocles and Anaxagoras; for they too produce other things from
their mixture by segregation. These differ, however, from each other
in that the former imagines a cycle of such changes, the latter a
single series. Anaxagoras again made both his 'homceomerous'
substances and his contraries infinite in multitude, whereas
Empedocles posits only the so-called elements.

  The theory of Anaxagoras that the principles are infinite in
multitude was probably due to his acceptance of the common opinion