Aristotle: The Complete Works. Aristotle
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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’.
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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