Book X
1
We have said
previously, in our distinction of the various meanings of words, that
'one' has several meanings; the things that are directly and of their
own nature and not accidentally called one may be summarized under four
heads, though the word is used in more senses. (1) There is the
continuous, either in general, or especially that which is continuous by
nature and not by contact nor by being together; and of these, that has
more unity and is prior, whose movement is more indivisible and simpler.
(2) That which is a whole and has a certain shape and form is one in a
still higher degree; and especially if a thing is of this sort by
nature, and not by force like the things which are unified by glue or
nails or by being tied together, i.e. if it has in itself the cause of
its continuity. A thing is of this sort because its movement is one and
indivisible in place and time; so that evidently if a thing has by
nature a principle of movement that is of the first kind (i.e. local
movement) and the first in that kind (i.e. circular movement), this is
in the primary sense one extended thing. Some things, then, are one in
this way, qua continuous or whole, and the other things that are one are
those whose definition is one. Of this sort are the things the thought
of which is one, i.e. those the thought of which is indivisible; and it
is indivisible if the thing is indivisible in kind or in number. (3) In
number, then, the individual is indivisible, and (4) in kind, that which
in intelligibility and in knowledge is indivisible, so that that which
causes substances to be one must be one in the primary sense. 'One',
then, has all these meanings-the naturally continuous and the whole, and
the individual and the universal. And all these are one because in some
cases the movement, in others the thought or the definition is
indivisible.
But it must be observed that the questions, what sort
of things are said to be one, and what it is to be one and what is the
definition of it, should not be assumed to be the same. 'One' has all
these meanings, and each of the things to which one of these kinds of
unity belongs will be one; but 'to be one' will sometimes mean being one
of these things, and sometimes being something else which is even nearer
to the meaning of the word 'one' while these other things approximate to
its application. This is also true of 'element' or 'cause', if one had
both to specify the things of which it is predicable and to render the
definition of the word. For in a sense fire is an element (and doubtless
also 'the indefinite' or something else of the sort is by its own nature
the element), but in a sense it is not; for it is not the same thing to
be fire and to be an element, but while as a particular thing with a
nature of its own fire is an element, the name 'element' means that it
has this attribute, that there is something which is made of it as a
primary constituent. And so with 'cause' and 'one' and all such terms.
For this reason, too, 'to be one' means 'to be indivisible, being
essentially one means a "this" and capable of being isolated
either in place, or in form or thought'; or perhaps 'to be whole and
indivisible'; but it means especially 'to be the first measure of a
kind', and most strictly of quantity; for it is from this that it has
been extended to the other categories.
For measure is that by which quantity is known; and quantity qua
quantity is known either by a 'one' or by a number, and all number is
known by a 'one'. Therefore all quantity qua quantity is known by the
one, and that by which quantities are primarily known is the one itself;
and so the one is the starting-point of number qua number. And hence in
the other classes too 'measure' means that by which each is first known,
and the measure of each is a unit-in length, in breadth, in depth, in
weight, in speed.
(The words 'weight' and 'speed' are common to both contraries; for each
of them has two meanings-'weight' means both that which has any amount
of gravity and that which has an excess of gravity, and 'speed' both
that which has any amount of movement and that which has an excess of
movement; for even the slow has a certain speed and the comparatively
light a certain weight.)
In all these, then, the measure and starting-point is
something one and indivisible, since even in lines we treat as
indivisible the line a foot long. For everywhere we seek as the measure
something one and indivisible; and this is that which is simple either
in quality or in quantity. Now where it is thought impossible to take
away or to add, there the measure is exact (hence that of number is most
exact; for we posit the unit as indivisible in every respect); but in
all other cases we imitate this sort of measure. For in the case of a
furlong or a talent or of anything comparatively large any addition or
subtraction might more easily escape our notice than in the case of
something smaller; so that the first thing from which, as far as our
perception goes, nothing can be subtracted, all men make the measure,
whether of liquids or of solids, whether of weight or of size; and they
think they know the quantity when they know it by means of this measure.
And indeed they know movement too by the simple movement and the
quickest; for this occupies least time. And so in astronomy a 'one' of
this sort is the starting-point and measure (for they assume the
movement of the heavens to be uniform and the quickest, and judge the
others by reference to it), and in music the quarter-tone (because it is
the least interval), and in speech the letter. And all these are ones in
this sense--not that 'one' is something predicable in the same sense of
all of these, but in the
sense we have mentioned.
But the measure is not always one in
number--sometimes there are several; e.g. the quarter-tones (not to the
ear, but as determined by the ratios) are two, and the articulate sounds
by which we measure are more than one, and the diagonal of the square
and its side are measured by two quantities, and all spatial magnitudes
reveal similar varieties of unit. Thus, then, the one is the measure of
all things, because we come to know the elements in the substance by
dividing the things either in respect of quantity or in respect of kind.
And the one is indivisible just because the first of each class of
things is indivisible. But it is not in the same way that every 'one' is
indivisible e.g. a foot and a unit; the latter is indivisible in every
respect, while the former must be placed among things which are
undivided to perception, as has been said already-only to perception,
for doubtless every continuous thing is divisible.
The measure is always homogeneous with the thing
measured; the 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 figures, and the one would
have been the triangle. And the same argument applies to all other
classes. Since, therefore, while there are numbers and a one both in
affections and in qualities and in quantities and in movement, in all
cases the number is a number of particular things and the one is one
something, and its substance is not just to be one, the same must be
true of substances also; for it is true of all cases alike.
That the one, then, in every class is a definite
thing, and in no case is its nature just this, unity, is evident; but as
in
colours the one-itself which we must seek is one colour, so too in
substance the one-itself is one substance.
That in a sense unity means the same as being is clear from the facts
that its meanings correspond to the categories one to one, and it is not
comprised within any category (e.g. it is comprised neither in 'what a
thing is' nor in quality, but is related to them just as being is); that
in 'one man' nothing more is predicated than in 'man' (just as being is
nothing apart from substance or quality or quantity); and that to be one
is just to be a particular thing.
3
The one and the many
are opposed in several ways, of which one is the opposition of the one
and plurality as indivisible and divisible; for that which is either
divided or divisible is called a plurality, and that which is
indivisible or not divided is called one. Now since opposition is of
four kinds, and one of these two terms is privative in meaning, they
must be contraries, and neither contradictory nor correlative in
meaning. And the one derives its name and its explanation from its
contrary, the indivisible from the divisible, because plurality and the
divisible is more perceptible than the indivisible, so that in
definition plurality is prior to the indivisible, because of the
conditions of perception.
To the one belong, as we indicated graphically in our
distinction of the contraries, the same and the like and the equal,
and to plurality belong the other and the unlike and the unequal. 'The
same' has several meanings; (1) we sometimes mean 'the same
numerically'; again, (2) we call a thing the same if it is one both in
definition and in number, e.g. you are one with yourself both in form
and in matter; and again, (3) if the definition of its primary essence
is one; e.g. equal straight lines are the same, and so are equal and
equal-angled quadrilaterals; there are many such, but in these equality
constitutes unity.
Things are like if, not being absolutely the same,
nor without difference in respect of their concrete substance, they are
the same in form; e.g. the larger square is like the smaller, and
unequal straight lines are like; they are like, but not absolutely the
same. Other things are like, if, having the same form, and being things
in which difference of degree is possible, they have no difference of
degree. Other things, if they have a quality that is in form one and
same-e.g. whiteness-in a greater or less degree, are called like because
their form is one. Other things are called like if the qualities they
have in common are more numerous than those in which they differ-either
the qualities in general or the prominent qualities; e.g. tin is like
silver, qua white, and gold is like fire, qua yellow and red.
Evidently, then, 'other' and 'unlike' also have
several meanings. And the other in one sense is the opposite of the same
(so
that everything is either the same as or other than everything else). In
another sense things are other unless both their matter and their
definition are one (so that you are other than your neighbour). The
other in the third sense is exemplified in the objects of mathematics.
'Other or the same' can therefore be predicated of everything with
regard to everything else-but only if the things are one and existent,
for 'other' is not the contradictory of 'the same'; which is why it is
not predicated of non-existent things (while 'not the same' is so
predicated). It is predicated of all existing things; for everything
that is existent and one is by its very nature either one or not one
with anything else.
The other, then, and the same are thus opposed. But
difference is not the same as otherness. For the other and that which it
is other than need not be other in some definite respect (for everything
that is existent is either other or the same), but that which is
different is different from some particular thing in some particular
respect, so that there must be something identical whereby they differ.
And this identical thing is genus or species; for everything that
differs differs either in genus or in species, in genus if the things
have not their matter in common and are not generated out of each other
(i.e. if they belong to different figures of predication), and in
species if they have the same genus ('genus' meaning that identical
thing which is essentially predicated of both the different things).
Contraries are different, and contrariety is a kind
of difference. That we are right in this supposition is shown by
induction. For all of these too are seen to be different; they are not
merely other, but some are other in genus, and others are in the same
line of predication, and therefore in the same genus, and the same in
genus.
We have distinguished elsewhere what sort of things are the same or
other in genus.
4
Since things which
differ may differ from one another more or less, there is also a
greatest difference, and this I call
contrariety. That contrariety is the greatest difference is made clear
by induction. For things which differ in genus have no way to one
another, but are too far distant and are not comparable; and for things
that differ in species the extremes from which generation takes place
are the contraries, and the distance between extremes-and therefore that
between the contraries-is the greatest.
But surely that which is greatest in each class is
complete. For that is greatest which cannot be exceeded, and that is
complete beyond which nothing can be found. For the complete difference
marks the end of a series (just as the other things which are called
complete are so called because they have attained an end), and beyond
the end there is nothing; for in everything it is the extreme and
includes all else, and therefore there is nothing beyond the end, and
the complete needs nothing further. From this, then, it is clear that
contrariety is complete difference; and as contraries are so called in
several senses, their modes of completeness will answer to the various
modes of contrariety which attach to the contraries.
This being so, it is clear that one thing have more
than one contrary (for neither can there be anything more extreme than
the extreme, nor can there be more than two extremes for the one
interval), and, to put the matter generally, this is clear if
contrariety is a difference, and if difference, and therefore also the
complete difference, must be between two things.
And the other commonly accepted definitions of
contraries are also necessarily true. For not only is (1) the complete
difference the greatest difference (for we can get no difference beyond
it of things differing either in genus or in species; for it has been
shown that there is no 'difference' between anything and the things
outside its genus, and among the things which differ in species the
complete difference is the greatest); but also (2) the things in the
same genus which differ most are contrary (for the complete difference
is the greatest difference between species of the same genus); and (3)
the things in the same receptive material which differ most are contrary
(for the matter is the same for contraries); and (4) of the things which
fall under the same faculty the most different are contrary (for one
science deals with one class of things, and in these the complete
difference is the greatest).
The primary contrariety is that between positive
state and privation-not every privation, however (for 'privation' has
several
meanings), but that which is complete. And the other contraries must be
called so with reference to these, some because they possess these,
others because they produce or tend to produce them, others because they
are acquisitions or losses of these or of other contraries. Now if the
kinds of opposition are contradiction and privation and contrariety and
relation, and of these the first is contradiction, and contradiction
admits of no intermediate, while contraries admit of one, clearly
contradiction and contrariety are not the same. But privation is a kind
of contradiction; for what suffers privation, either in general or in
some determinate way, either that which is quite incapable of having
some attribute or that which, being of such a nature as to have it, has
it not; here we have already a variety of meanings, which have been
distinguished elsewhere.
Privation, therefore, is a contradiction or incapacity which is
determinate or taken along with the receptive material. This is the
reason why, while contradiction does not admit of an intermediate,
privation sometimes does; for everything is equal or not equal, but not
everything is equal or unequal, or if it is, it is only within the
sphere of that which is receptive of equality. If, then, the
comings-to-be which happen to the matter start from the contraries, and
proceed either from the form and the possession of the form or from a
privation of the form or shape, clearly all contrariety must be
privation, but presumably not all privation is contrariety (the reason
being that that has suffered privation may have suffered it in several
ways); for it is only the extremes from which changes proceed that are
contraries.
And this is obvious also by induction. For every
contrariety involves, as one of its terms, a privation, but not all
cases are
alike; inequality is the privation of equality and unlikeness of
likeness, and on the other hand vice is the privation of virtue. But the
cases differ in a way already described; in one case we mean simply that
the thing has suffered privation, in another case that it has done so
either at a certain time or in a certain part (e.g. at a certain age or
in the dominant part), or throughout. This is why in some cases there is
a mean (there are men who are neither good nor bad), and in others there
is not (a number must be either odd or even). Further, some contraries
have their subject defined, others have not. Therefore it is evident
that one of the contraries is always privative; but it is enough if this
is true of the first-i.e. the generic-contraries, e.g. the one and the
many; for the others can be reduced to these.
5
Since one thing has
one contrary, we might raise the question how the one is opposed to the
many, and the equal to the great and the small. For if we used the word
'whether' only in an antithesis such as 'whether it is white or black',
or 'whether it is white or not white' (we do not ask 'whether it is a
man or white'), unless we are proceeding on a prior assumption and
asking something such as 'whether it was Cleon or Socrates that came' as
this is not a necessary disjunction in any class of things; yet even
this is an extension from the case of opposites; for opposites alone
cannot be present together; and we assume this incompatibility here too
in asking which of the two came; for if they might both have come, the
question would have been absurd; but if they might, even so this falls
just as much into an antithesis, that of the 'one or many', i.e.
'whether both came or one of the two':-if, then, the question 'whether'
is always concerned with opposites, and we can ask 'whether it is
greater or less or equal', what is the opposition of the equal to the
other two? It is not contrary either to one alone or to both; for why
should it be contrary to the greater rather than to the less? Further,
the equal is contrary to the unequal. Therefore if it is contrary to the
greater and the less, it will be contrary to more things than one. But
if the unequal means the same as both the greater and the less together,
the equal will be opposite to both (and the difficulty supports those
who say the unequal is a 'two'), but it follows that one thing is
contrary to two others, which is impossible. Again, the equal is
evidently intermediate between the great and the small, but no
contrariety is either observed to be intermediate, or, from its
definition, can be so; for it would not be complete if it were
intermediate between any two things, but rather it always has
something intermediate between its own terms.
It remains, then, that it is opposed either as
negation or as privation. It cannot be the negation or privation of one
of the two; for why of the great rather than of the small? It is, then,
the privative negation of both. This is why 'whether' is said with
reference to both, not to one of the two (e.g. 'whether it is greater or
equal' or 'whether it is equal or less'); there are
always three cases. But it is not a necessary privation; for not
everything which is not greater or less is equal, but only the
things which are of such a nature as to have these attributes.
The equal, then, is that which is neither great nor
small but is naturally fitted to be either great or small; and it is
opposed to both as a privative negation (and therefore is also
intermediate). And that which is neither good nor bad is opposed to
both, but has no name; for each of these has several meanings and the
recipient subject is not one; but that which is neither white nor black
has more claim to unity. Yet even this has not one name, though the
colours of which this negation is privatively predicated are in a way
limited; for they must be either grey or yellow or something else of the
kind. Therefore it is an incorrect criticism that is passed by those who
think that all such phrases are used in the same way, so that that which
is neither a shoe nor a hand would be intermediate between a shoe and a
hand, since that which is neither good nor bad is
intermediate between the good and the bad-as if there must be an
intermediate in all cases. But this does not necessarily follow. For the
one phrase is a joint denial of opposites between which there is an
intermediate and a certain natural interval; but between the other two
there is no 'difference'; for the things, the denials of which are
combined, belong to different classes, so that the substratum is not
one.
6
We might raise similar
questions about the one and the many. For if the many are absolutely
opposed to the one, certain impossible results follow. One will then be
few, whether few be treated here as singular or plural; for the many are
opposed also to the few. Further, two will be many, since the double is
multiple and 'double' derives its meaning from 'two'; therefore one will
be few; for what is that in comparison with which two are many, except
one, which must therefore be few? For there is nothing fewer. Further,
if the much and the little are in plurality what the long and the short
are in length, and whatever is much is also many, and the many are much
(unless, indeed, there is a difference in the case of an easily-bounded
continuum), the little (or few) will be a plurality. Therefore one is a
plurality if it is few; and this it must be, if two are many. But
perhaps, while the 'many' are in a sense said to be also 'much', it is
with a difference; e.g. water is much but not many. But 'many' is
applied to the things that are divisible; in the one sense it means a
plurality which is excessive either absolutely or relatively (while
'few' is similarly a plurality which is deficient), and in another sense
it means number, in which sense alone it is opposed to the one. For we
say 'one or many', just as if one were to say 'one and ones' or 'white
thing and white things', or to compare the things that have been
measured with the measure.
It is in this sense also that multiples are so called. For each number
is said to be many because it consists of ones and because each number
is measurable by one; and it is 'many' as that which is opposed to one,
not to the few. In this sense, then, even two is many-not, however, in
the sense of a plurality which is excessive either relatively or
absolutely; it is the first plurality. But without qualification two is
few; for it is first plurality which is deficient (for this reason
Anaxagoras was not right in leaving the subject with the statement that
'all things were together, boundless both in plurality and in
smallness'-where for 'and in smallness' he should have said 'and in
fewness'; for they could not have been boundless in fewness), since it
is not one, as some say, but two, that make a few.
The one is opposed then to the many in numbers as
measure to thing measurable; and these are opposed as are the relatives
which are not from their very nature relatives. We have distinguished
elsewhere the two senses in which relatives are so called:-(1) as
contraries; (2) as knowledge to thing known, a term being called
relative because another is relative to it. There is nothing to prevent
one from being fewer than something, e.g. than two; for if one is fewer,
it is not therefore few. Plurality is as it were the class to which
number belongs; for number is plurality measurable by one, and one and
number are in a sense opposed, not as contrary, but as we have said some
relative terms are opposed; for inasmuch as one is measure and the other
measurable, they are opposed.
This is why not everything that is one is a number; i.e. if the thing is
indivisible it is not a number. But though knowledge is similarly spoken
of as relative to the knowable, the relation does not work out
similarly; for while knowledge might be thought to be the measure, and
the knowable the thing measured, the fact that all knowledge is
knowable, but not all that is knowable is knowledge, because in a sense
knowledge is measured by the knowable. -Plurality is contrary neither to
the few (the many being contrary to this as excessive plurality to
plurality exceeded), nor to the one in every sense; but in the one sense
these are contrary, as has been said, because the former is divisible
and the latter indivisible, while in another sense they are relative as
knowledge is to knowable, if plurality is number and the one is a
measure.
7
Since contraries admit
of an intermediate and in some cases have it, intermediates must be
composed of the contraries. For (1) all intermediates are in the same
genus as the things between which they stand. For we call those things
intermediates, into which that which changes must change first; e.g. if
we were to pass from the highest string to the lowest by the smallest
intervals, we should come sooner to the intermediate notes, and in
colours if we were to pass from white to black, we should come sooner to
crimson and grey than to black; and similarly in all other cases. But to
change from one
genus to another genus is not possible except in an incidental way, as
from colour to figure. Intermediates, then, must be in the same genus
both as one another and as the things they stand between.
But (2) all intermediates stand between opposites of
some kind; for only between these can change take place in virtue of
their own nature (so that an intermediate is impossible between things
which are not opposite; for then there would be change which was not
from one opposite towards the other). Of opposites, contradictories
admit of no middle term; for this is what contradiction is-an
opposition, one or other side of which must attach to anything whatever,
i.e. which has no intermediate. Of other opposites, some are relative,
others privative, others contrary. Of relative terms, those which are
not
contrary have no intermediate; the reason is that they are not in the
same genus. For what intermediate could there be between knowledge and
knowable? But between great and small there is one.
(3) If intermediates are in the same genus, as has
been shown, and stand between contraries, they must be composed of these
contraries. For either there will be a genus including the contraries or
there will be none. And if (a) there is to be a genus in such a way that
it is something prior to the contraries, the differentiae which
constituted the contrary species-of-a-genus will be contraries prior to
the species; for species are composed of the genus and the differentiae.
(E.g. if white and black are contraries, and one is a piercing colour
and the other a compressing colour, these differentiae-'piercing' and
'compressing'-are prior; so that these are prior contraries of one
another.)
But, again, the species which differ contrariwise are the more truly
contrary species. And the other species, i.e. the intermediates, must be
composed of their genus and their differentiae. (E.g. all colours which
are between white and black must be said to be composed of the genus,
i.e. colour, and certain differentiae. But these differentiae will not
be the primary contraries; otherwise every colour would be either white
or black. They are different, then, from the primary contraries; and
therefore they will be between the primary contraries; the primary
differentiae are 'piercing' and 'compressing'.)
Therefore it is (b) with regard to these contraries
which do not fall within a genus that we must first ask of what their
intermediates are composed. (For things which are in the same genus must
be composed of terms in which the genus is not an element, or else be
themselves incomposite.) Now contraries do not involve one another in
their composition, and are therefore first principles; but the
intermediates are either all incomposite, or none of them. But there is
something compounded out of the contraries, so that there can be a
change from a contrary to it sooner than to the other contrary; for it
will have less of the quality in question than the one contrary and more
than the other. This also, then, will come between the contraries. All
the other intermediates also, therefore, are composite; for that which
has more of a quality than one thing and less than another is compounded
somehow out of the things than which it is said to have more and less
respectively of the quality. And since there are no other things prior
to the contraries and homogeneous with the intermediates, all
intermediates must be compounded out of the contraries. Therefore also
all the inferior classes, both the contraries and their intermediates,
will be compounded out of the primary contraries. Clearly, then,
intermediates are (1) all in the same genus and (2) intermediate between
contraries, and (3) all compounded out of the contraries.
8
That which is other in
species is other than something in something, and this must belong to
both; e.g. if it is an animal other in species, both are animals. The
things, then, which are other in species must be in the same genus. For
by genus I mean that one identical thing which is predicated of both and
is differentiated in no merely accidental way, whether conceived as
matter or otherwise. For not only must the common nature attach to the
different things, e.g. not only must both be animals, but this very
animality must also be different for each (e.g. in the one case equinity,
in the other humanity), and so this common nature is specifically
different for each from what it is for the other. One, then, will be in
virtue of its own nature one sort of animal, and the other another, e.g.
one a horse and the other a man. This difference, then, must be an
otherness of the genus. For I give the name of 'difference in the genus'
an otherness which makes the genus itself other.
This, then, will be a contrariety (as can be shown
also by induction). For all things are divided by opposites, and it has
been proved that contraries are in the same genus.
For contrariety was seen to be complete difference; and all difference
in species is a difference from something in something; so that this is
the same for both and is their genus. (Hence also all contraries which
are different in species and not in genus are in the same line of
predication, and other than one another in the highest degree-for the
difference is complete-, and cannot be present along with one another.)
The difference, then, is a contrariety.
This, then, is what it is to be 'other in species'-to
have a contrariety, being in the same genus and being indivisible (and
those things are the same in species which have no contrariety, being
indivisible); we say 'being indivisible', for in the process of division
contrarieties arise in the intermediate stages before we come to the
indivisibles. Evidently, therefore, with reference to that which is
called the genus, none of the species-of-a-genus is either the same as
it or other than it in species (and this is fitting; for the matter is
indicated by negation, and the genus is the matter of that of which it
is called the genus, not in the sense in which we speak of the genus or
family of the Heraclidae, but in that in which the genus is an element
in a thing's nature), nor is it so with reference to things which are
not in the same genus, but it will differ in genus from them, and in
species from things in the same genus. For a thing's difference from
that from which it differs in species must be a contrariety; and this
belongs only to things in the same genus.
9
One might raise the
question, why woman does not differ from man in species, when female and
male are contrary and their difference is a contrariety; and why a
female and a male animal are not different in species, though this
difference belongs to animal in virtue of its own nature, and not as
paleness or darkness does; both 'female' and 'male' belong to it qua
animal. This question is almost the same as the other, why one
contrariety makes things different in species and another does not, e.g.
'with feet' and 'with wings' do, but paleness and darkness do not.
Perhaps it is because the former are modifications peculiar to the
genus, and the latter are less so. And since one element is definition
and one is matter, contrarieties which are in the definition make a
difference in species, but those which are in the thing taken as
including its matter do not make one. And so paleness in a man, or
darkness, does not make one, nor is there a difference in species
between the pale man and the dark man, not even if each of them be
denoted by one word. For man is here being considered on his material
side, and matter does not create a difference; for it does not make
individual men species of man, though the flesh and the bones of which
this man and that man consist are other. The concrete thing is other,
but not other in species, because in the definition there is no
contrariety. This is the ultimate indivisible kind. Callias is
definition + matter, the pale man, then, is so also, because it is the
individual Callias that is pale; man, then, is pale only incidentally.
Neither do a brazen and a wooden circle, then, differ in species; and if
a brazen triangle and a wooden circle differ in species, it is not
because of the matter, but because there is a contrariety in the
definition. But does the matter not make things other in species, when
it is other in a certain way, or is there a sense in which it does? For
why is this horse other than this man in species, although their matter
is included with their definitions? Doubtless because there is a
contrariety in the definition. For while there is a contrariety also
between pale man and dark horse, and it is a contrariety in species, it
does not depend
on the paleness of the one and the darkness of the other, since even if
both had been pale, yet they would have been other in species. But male
and female, while they are modifications peculiar to 'animal', are so
not in virtue of its essence but in the matter, ie. the body. This is
why the same seed becomes female or male by being acted on in a certain
way. We have stated, then, what it is to be other in species, and why
some things differ in species and others do not.
10
Since contraries are
other in form, and the perishable and the imperishable are contraries
(for privation is a determinate
in capacity), the perishable and the imperishable must be different in
kind.
Now so far we have spoken of the general terms
themselves, so that it might be thought not to be necessary that every
imperishable thing should be different from every perishable thing in
form, just as not every pale thing is different in form from every dark
thing. For the same thing can be both, and even at the same time if it
is a universal (e.g. man can be both pale and dark), and if it is an
individual it can still be both; for the same man can be, though not at
the same time, pale and dark. Yet pale is contrary to dark.
But while some contraries belong to
certain things by accident (e.g. both those now mentioned and many
others), others cannot, and among these are 'perishable' and
'imperishable'. For nothing is by accident perishable. For what is
accidental is capable of not being present, but perishableness is one of
the attributes that belong of necessity to the things to which they
belong; or else one and the same thing may be perishable and
imperishable, if perishableness is capable of not belonging to it.
Perishableness then must either be the essence or be present in the
essence of each perishable thing. The same account holds good for
imperishableness also; for both are attributes which are present of
necessity. The characteristics, then, in respect of which and in direct
consequence of which one thing is perishable and another imperishable,
are opposite, so that the things must be different in kind.
Evidently, then, there cannot be Forms such as some
maintain, for then one man would be perishable and another imperishable.
Yet the Forms are said to be the same in form with the individuals and
not merely to have the same name; but things which differ in kind are
farther apart than those which differ in form.
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