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
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.