Moreover it would seem absurd even to speak in this way, to speak,
that is to say, of a man or house or anything else that has come
into existence as having been altered. Though it may be true that
every such becoming is necessarily the result of something's being
altered, the result, e.g. of the material's being condensed or
rarefied or heated or cooled, nevertheless it is not the things that
are coming into existence that are altered, and their becoming is
not an alteration.
Again, acquired states, whether of the body or of the soul, are
not alterations. For some are excellences and others are defects,
and neither excellence nor defect is an alteration: excellence is a
perfection (for when anything acquires its proper excellence we call
it perfect, since it is then if ever that we have a thing in its
natural state: e.g. we have a perfect circle when we have one as
good as possible), while defect is a perishing of or departure from
this condition. So as when speaking of a house we do not call its
arrival at perfection an alteration (for it would be absurd to suppose
that the coping or the tiling is an alteration or that in receiving
its coping or its tiling a house is altered and not perfected), the
same also holds good in the case of excellences and defects and of the
persons or things that possess or acquire them: for excellences are
perfections of a thing's nature and defects are departures from it:
consequently they are not alterations.
Further, we say that all excellences depend upon particular
relations. Thus bodily excellences such as health and a good state
of body we regard as consisting in a blending of hot and cold elements
within the body in due proportion, in relation either to one another
or to the surrounding atmosphere: and in like manner we regard beauty,
strength, and all the other bodily excellences and defects. Each of
them exists in virtue of a particular relation and puts that which
possesses it in a good or bad condition with regard to its proper
affections, where by 'proper' affections I mean those influences
that from the natural constitution of a thing tend to promote or
destroy its existence. Since then, relatives are neither themselves
alterations nor the subjects of alteration or of becoming or in fact
of any change whatever, it is evident that neither states nor the
processes of losing and acquiring states are alterations, though it
may be true that their becoming or perishing is necessarily, like
the becoming or perishing of a specific character or form, the
result of the alteration of certain other things, e.g. hot and cold or
dry and wet elements or the elements, whatever they may be, on which
the states primarily depend. For each several bodily defect or
excellence involves a relation with those things from which the
possessor of the defect or excellence is naturally subject to
alteration: thus excellence disposes its possessor to be unaffected by
these influences or to be affected by those of them that ought to be
admitted, while defect disposes its possessor to be affected by them
or to be unaffected by those of them that ought to be admitted.
And the case is similar in regard to the states of the soul, all
of which (like those of body) exist in virtue of particular relations,
the excellences being perfections of nature and the defects departures
from it: moreover, excellence puts its possessor in good condition,
while defect puts its possessor in a bad condition, to meet his proper
affections. Consequently these cannot any more than the bodily
states be alterations, nor can the processes of losing and acquiring
them be so, though their becoming is necessarily the result of an
alteration of the sensitive part of the soul, and this is altered by
sensible objects: for all moral excellence is concerned with bodily
pleasures and pains, which again depend either upon acting or upon
remembering or upon anticipating. Now those that depend upon action
are determined by sense-perception, i.e. they are stimulated by
something sensible: and those that depend upon memory or
anticipation are likewise to be traced to sense-perception, for in
these cases pleasure is felt either in remembering what one has
experienced or in anticipating what one is going to experience. Thus
all pleasure of this kind must be produced by sensible things: and
since the presence in any one of moral defect or excellence involves
the presence in him of pleasure or pain (with which moral excellence
and defect are always concerned), and these pleasures and pains are
alterations of the sensitive part, it is evident that the loss and
acquisition of these states no less than the loss and acquisition of
the states of the body must be the result of the alteration of
something else. Consequently, though their becoming is accompanied
by an alteration, they are not themselves alterations.
Again, the states of the intellectual part of the soul are not
alterations, nor is there any becoming of them. In the first place
it is much more true of the possession of knowledge that it depends
upon a particular relation. And further, it is evident that there is
no becoming of these states. For that which is potentially possessed
of knowledge becomes actually possessed of it not by being set in
motion at all itself but by reason of the presence of something
else: i.e. it is when it meets with the particular object that it
knows in a manner the particular through its knowledge of the
universal. (Again, there is no becoming of the actual use and activity
of these states, unless it is thought that there is a becoming of
vision and touching and that the activity in question is similar to
these.) And the original acquisition of knowledge is not a becoming or
an alteration: for the terms 'knowing' and 'understanding' imply
that the intellect has reached a state of rest and come to a
standstill, and there is no becoming that leads to a state of rest,
since, as we have said above, change at all can have a becoming.
Moreover, just as to say, when any one has passed from a state of
intoxication or sleep or disease to the contrary state, that he has
become possessed of knowledge again is incorrect in spite of the
fact that he was previously incapable of using his knowledge, so, too,
when any one originally acquires the state, it is incorrect to say
that he becomes possessed of knowledge: for the possession of
understanding and knowledge is produced by the soul's settling down
out of the restlessness natural to it. Hence, too, in learning and
in forming judgements on matters relating to their sense-perceptions
children are inferior to adults owing to the great amount of
restlessness and motion in their souls. Nature itself causes the
soul to settle down and come to a state of rest for the performance of
some of its functions, while for the performance of others other
things do so: but in either case the result is brought about through
the alteration of something in the body, as we see in
the case of
the use and activity of the intellect arising from a man's becoming
sober or being awakened. It is evident, then, from the preceding
argument that alteration and being altered occur in sensible things
and in the sensitive part of the soul, and, except accidentally, in
nothing else.
4
A difficulty may be raised as to whether every motion is
commensurable with every other or not. Now if they are all
commensurable and if two things to have the same velocity must
accomplish an equal motion in an equal time, then we may have a
circumference equal to a straight line, or, of course, the one may
be greater or less than the other. Further, if one thing alters and
another accomplishes a locomotion in an equal time, we may have an
alteration and a locomotion equal to one another: thus an affection
will be equal to a length, which is impossible. But is it not only
when an equal motion is accomplished by two things in an equal time
that the velocities of the two are equal? Now an affection cannot be
equal to a length. Therefore there cannot be an alteration equal to or
less than a locomotion: and consequently it is not the case that every
motion is commensurable with every other.
But how will our conclusion work out in the case of the circle and
the straight line? It would be absurd to suppose that the motion of
one in a circle and of another in a straight line cannot be similar,
but that the one must inevitably move more quickly or more slowly than
the other, just as if the course of one were downhill and of the other
uphill. Moreover it does not as a matter of fact make any difference
to the argument to say that the one motion must inevitably be
quicker or slower than the other: for then the circumference can be
greater or less than the straight line; and if so it is possible for
the two to be equal. For if in the time A the quicker (B) passes
over the distance B' and the slower (G) passes over the distance G',
B' will be greater than G': for this is what we took 'quicker' to
mean: and so quicker motion also implies that one thing traverses an
equal distance in less time than another: consequently there will be a
part of A in which B will pass over a part of the circle equal to
G', while G will occupy the whole of A in passing over G'. None the
less, if the two motions are commensurable, we are confronted with the
consequence stated above, viz. that there may be a straight line equal
to a circle. But these are not commensurable: and so the corresponding
motions are not commensurable either.
But may we say that things are always commensurable if the same
terms are applied to them without equivocation? e.g. a pen, a wine,
and the highest note in a scale are not commensurable: we cannot say
whether any one of them is sharper than any other: and why is this?
they are incommensurable because it is only equivocally that the
same term 'sharp' is applied to them: whereas the highest note in a
scale is commensurable with the leading-note, because the term 'sharp'
has the same meaning as applied to both. Can it be, then, that the
term 'quick' has not the same meaning as applied to straight motion
and to circular motion respectively? If so, far less will it have
the same meaning as applied to alteration and to locomotion.
Or shall we in the first place deny that things are always
commensurable if the same terms are applied to them without
equivocation? For the term 'much' has the same meaning whether applied
to water or to air, yet water and air are not commensurable in respect
of it: or, if this illustration is not considered satisfactory,
'double' at any rate would seem to have the same meaning as applied to
each (denoting in each case the proportion of two to one), yet water
and air are not commensurable in respect of it. But here again may
we not take up the same position and say that the term 'much' is
equivocal? In fact there are some terms of which even the
definitions are equivocal; e.g. if 'much' were defined as 'so much and
more','so much' would mean something different in different cases:
'equal' is similarly equivocal; and 'one' again is perhaps
inevitably an equivocal term; and if 'one' is equivocal, so is
'two'. Otherwise why is it that some things are commensurable while
others are not, if the nature of the attribute in the two cases is
really one and the same?
Can it be that the incommensurability of two things in respect of
any attribute is due to a difference in that which is primarily
capable of carrying the attribute? Thus horse and dog are so
commensurable that we may say which is the whiter, since that which
primarily contains the whiteness is the same in both, viz. the
surface: and similarly they are commensurable in respect of size.
But water and speech are not commensurable in respect of clearness,
since that which primarily contains the attribute is different in
the two cases. It would seem, however that we must reject this
solution, since clearly we could thus make all equivocal attributes
univocal and say merely that that contains each of them is different
in different cases: thus 'equality', 'sweetness', and 'whiteness' will
severally always be the same, though that which contains them is
that is capable of carrying any attribute: each single attribute can
be carried primarily only by one single thing.
Must we then say that, if two things are to be commensurable in
respect of any attribute, not only must the attribute in question be
applicable to both without equivocation, but there must also be no
specific differences either in the attribute itself or in that which
contains the attribute-that these, I mean, must not be divisible in
the way in which colour is divided into kinds? Thus in this respect
one thing will not be commensurable with another, i.e. we cannot say
that one is more coloured than the other where only colour in
general and not any particular colour is meant; but they are
commensurable in respect of whiteness.
Similarly in the case of motion: two things are of the same velocity
if they occupy an equal time in accomplishing a certain equal amount
of motion. Suppose, then, that in a certain time an alteration is
undergone by one half of a body's length and a locomotion is
accomplished the other half: can be say that in this case the
alteration is equal to the locomotion and of the same velocity? That
would be absurd, and the reason is that there are different species of
motion. And if in consequence of this we must say that two things
are of equal velocity if they accomplish locomotion over an equal
distance in an equal time, we have to admit the equality of a straight
line and a circumference. What, then, is the reason of this? Is it
that locomotion is a genus or that line is a genus? (We may leave
the time out of account, since that is one and the same.) If the lines
are specifically different, the locomotions also d
iffer specifically
from one another: for locomotion is specifically differentiated
according to the specific differentiation of that over which it
takes place. (It is also similarly differentiated, it would seem,
accordingly as the instrument of the locomotion is different: thus
if feet are the instrument, it is walking, if wings it is flying;
but perhaps we should rather say that this is not so, and that in this
case the differences in the locomotion are merely differences of
posture in that which is in motion.) We may say, therefore, that
things are of equal velocity in an equal time they traverse the same
magnitude: and when I call it 'the same' I mean that it contains no
specific difference and therefore no difference in the motion that
takes place over it. So we have now to consider how motion is
differentiated: and this discussion serves to show that the genus is
not a unity but contains a plurality latent in it and distinct from
it, and that in the case of equivocal terms sometimes the different
senses in which they are used are far removed from one another,
while sometimes there is a certain likeness between them, and
sometimes again they are nearly related either generically or
analogically, with the result that they seem not to be equivocal
though they really are.
When, then, is there a difference of species? Is an attribute
specifically different if the subject is different while the attribute
is the same, or must the attribute itself be different as well? And
how are we to define the limits of a species? What will enable us to
decide that particular instances of whiteness or sweetness are the
same or different? Is it enough that it appears different in one
subject from what appears in another? Or must there be no sameness
at all? And further, where alteration is in question, how is one
alteration to be of equal velocity with another? One person may be
cured quickly and another slowly, and cures may also be
simultaneous: so that, recovery of health being an alteration, we have
here alterations of equal velocity, since each alteration occupies
an equal time. But what alteration? We cannot here speak of an 'equal'