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  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

  different in different cases. Moreover, it is not any casual thing

  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'