by Aristotle
offers no difficulty at all: accept one ridiculous proposition and the
rest follows-a simple enough proceeding.
We physicists, on the other hand, must take for granted that the
things that exist by nature are, either all or some of them, in motion
which is indeed made plain by induction. Moreover, no man of science
is bound to solve every kind of difficulty that may be raised, but
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 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
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
of the physicists that nothing comes into being from not-being. For
this is the reason why they use the phrase 'all things were
together' and the coming into being of such and such a kind of thing
is reduced to change of quality, while some spoke of combination and
separation. Moreover, the fact that the contraries proceed from each
other led them to the conclusion. The one, they reasoned, must have
already existed in the other; for since everything that comes into
being must arise either from what is or from what is not, and it is
impossible for it to arise from what is not (on this point all the
physicists agree), they thought that the truth of the alternative
necessarily followed, namely that things come into being out of
existent things, i.e. out of things already present, but imperceptible
to our senses because of the smallness of their bulk. So they assert
that everything has been mixed in every. thing, because they saw
everything arising out of everything. But things, as they say,
appear different from one another and receive different names
according to the nature of the particles which are numerically
predominant among the innumerable constituents of the mixture. For
nothing, they say, is purely and entirely white or black or sweet,
bone or flesh, but the nature of a thing is held to be that of which
it contains the most.
Now (1) the infinite qua infinite is unknowable, so that what is
infinite in multitude or size is unknowable in quantity, and what is
infinite in variety of kind is unknowable in quality. But the
principles in question are infinite both in multitude and in kind.
Therefore it is impossible to know things which are composed of
them; for it is when we know the nature and quantity of its components
that we suppose we know a complex.
Further (2) if the parts of a whole may be of any size in the
direction either of greatness or of smallness (by 'parts' I mean
components into which a whole can be divided and which are actually
present in it), it is necessary that the whole thing itself may be
of any size. Clearly, therefore, since it is impossible for an
animal or plant to be indefinitely big or small, neither can its parts
be such, or the whole will be the same. But flesh, bone, and the
like are the parts of animals, and the fruits are the parts of plants.
Hence it is obvious that neither flesh, bone, nor any such thing can
be of indefinite size in the direction either of the greater or of the
less.
Again (3) according to the theory all such things are already
present in one another and do not come into being but are constituents
which are separated out, and a thing receives its designation from its
chief constituent. Further, anything may come out of anything-water by
segregation from flesh and flesh from water. Hence, since every finite
body is exhausted by the repeated abstraction of a finite body, it
seems obviously to follow that everything cannot subsist in everything
else. For let flesh be extracted from water and again more flesh be
produced from the remainder by repeating the process of separation:
then, even though the quantity separated out will continually
decrease, still it will not fall below a certain magnitude. If,
therefore, the process comes to an end, everything will not be in