Various Works

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