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Metaphysics   


measure of spatial magnitudes is a spatial magnitude, and in
particular that of length is a length, that of breadth a breadth, that
of articulate sound an articulate sound, that of weight a weight, that
of units a unit. (For we must state the matter so, and not say that
the measure of numbers is a number; we ought indeed to say this if
we were to use the corresponding form of words, but the claim does not
really correspond-it is as if one claimed that the measure of units is
units and not a unit; number is a plurality of units.)
Knowledge, also, and perception, we call the measure of things for
the same reason, because we come to know something by them-while as
a matter of fact they are measured rather than measure other things.
But it is with us as if some one else measured us and we came to
know how big we are by seeing that he applied the cubit-measure to
such and such a fraction of us. But Protagoras says 'man is the
measure of all things', as if he had said 'the man who knows' or
'the man who perceives'; and these because they have respectively
knowledge and perception, which we say are the measures of objects.
Such thinkers are saying nothing, then, while they appear to be saying
something remarkable.
Evidently, then, unity in the strictest sense, if we define it
according to the meaning of the word, is a measure, and most
properly of quantity, and secondly of quality. And some things will be
one if they are indivisible in quantity, and others if they are
indivisible in quality; and so that which is one is indivisible,
either absolutely or qua one.
2

With regard to the substance and nature of the one we must ask
in which of two ways it exists. This is the very question that we
reviewed in our discussion of problems, viz. what the one is and how
we must conceive of it, whether we must take the one itself as being a
substance (as both the Pythagoreans say in earlier and Plato in
later times), or there is, rather, an underlying nature and the one
should be described more intelligibly and more in the manner of the
physical philosophers, of whom one says the one is love, another
says it is air, and another the indefinite.
If, then, no universal can be a substance, as has been said our
discussion of substance and being, and if being itself cannot be a
substance in the sense of a one apart from the many (for it is
common to the many), but is only a predicate, clearly unity also
cannot be a substance; for being and unity are the most universal of
all predicates. Therefore, on the one hand, genera are not certain
entities and substances separable from other things; and on the
other hand the one cannot be a genus, for the same reasons for which
being and substance cannot be genera.
Further, the position must be similar in all the kinds of unity.
Now 'unity' has just as many meanings as 'being'; so that since in the
sphere of qualities the one is something definite-some particular kind
of thing-and similarly in the sphere of quantities, clearly we must in
every category ask what the one is, as we must ask what the existent
is, since it is not enough to say that its nature is just to be one or
existent. But in colours the one is a colour, e.g. white, and then the
other colours are observed to be produced out of this and black, and
black is the privation of white, as darkness of light. Therefore if
all existent things were colours, existent things would have been a
number, indeed, but of what? Clearly of colours; and the 'one' would
have been a particular 'one', i.e. white. And similarly if all
existing things were tunes, they would have been a number, but a
number of quarter-tones, and their essence would not have been number;
and the one would have been something whose substance was not to be
one but to be the quarter-tone. And similarly if all existent things
had been articulate sounds, they would have been a number of
letters, and the one would have been a vowel. And if all existent
things were rectilinear figures, they would have been a number of

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