Nor again is there anything intermediate between that which undergoes and that which causes alteration: this can be shown by induction; for in every case we find that the respective extremities of that which causes and that which undergoes alteration are together. For our assumption is that things that are undergoing [5] alteration are altered in virtue of their being affected in respect of their so-called affective qualities; for every body differs from another in possessing a greater or lesser number of sensible characteristics or in possessing the same sensible characteristics in a greater or lesser degree. But the alteration of that which undergoes alteration is also caused by the above-mentioned characteristics, which are affections of some underlying quality. Thus we say that a thing is altered by becoming hot or sweet or thick or dry or white; and we make these assertions alike of what is inanimate and of what is animate, and further, where animate things are in question, we make them both of the parts that have no power of sense-perception and of the senses themselves. For in a way even the senses undergo alteration, since [10] actual perception is a motion through the body in the course of which the sense is affected in a certain way. Thus the animate is capable of every kind of alteration of which the inanimate is capable; but the inanimate is not capable of every kind of alteration of which the animate is capable, since it is not capable of alteration in respect of the senses: moreover the inanimate is unconscious of being affected, whereas the animate is conscious of it, though there is nothing to prevent the [245a1] animate also being unconscious of it when the alteration does not concern the senses. Since, then, the alteration of that which undergoes alteration is caused by sensible things, in every case of such alteration it is evident that the extremities of that which causes and that which undergoes alteration are together. For the air is continuous with the one and the body with the air. Again, the colour is continuous [5] with the light and the light with the sight. And the same is true of hearing and smelling; for the primary mover in respect to the moved is the air. Similarly, in the case of tasting, the flavour is together with the sense of taste. And it is just the same in the case of things that are inanimate and incapable of sense-perception. Thus [10] there can be nothing between that which undergoes and that which causes alteration.
Nor, again, can there be anything between that which suffers and that which causes increase; for that which starts the increase does so by becoming attached in such a way that the whole becomes one. Again, the decrease of that which suffers decrease is caused by a part of the thing becoming detached. So both that which causes increase and that which causes decrease must be continuous; and if two [15] things are continuous there can be nothing between them.
[245b1] It is evident, therefore, that between the moved and the mover—the first and the last—in reference to the moved there is nothing intermediate.
3 · That everything which undergoes alteration is altered by sensible causes, and that there is alteration only in things that are said to be affected in their own [5] right by sensible things, can be seen from the following considerations. Of all other things it would be most natural to suppose that there is alteration in figures and shapes, and in states and in the processes of acquiring and losing these; but as a matter of fact in neither of these two cases is there alteration.
For when anything has been completely shaped or structured, we do not call it [10] by the name of its material: e.g. we do not call the statue bronze or the candle wax or the bed wood, but we use a paronymous expression and call them brazen, waxen, and wooden respectively. But when a thing has been affected and altered in any way we still call it by the original name: thus we speak of the bronze or the wax being [15] fluid or hard or hot (not only that—we also call the fluid and the hot stuff bronze), giving the matter the same name as the affection.
[246a1] Since, therefore, having regard to the figure or shape of a thing we no longer call that which has become of a certain figure by the name of the material that exhibits the figure, whereas having regard to a thing’s affections or alterations we do, it is evident that becomings of the former kind46 cannot be alterations.
Moreover it would seem absurd actually to speak in this way, to speak, that is [5] 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 matter’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.
[10] Again, 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 really in its natural state: e.g. a circle is [15] perfect when it becomes really a circle and when it is best), while defect is a perishing of or departure from this condition. So just 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 [246b1] of excellences and defects and of the things that possess or acquire them; for excellences are perfections and defects are departures: consequently they are not alterations.
Further, we say that all excellences depend upon particular relations. Thus bodily excellences such as health and fitness we regard as consisting in a blending of [5] hot and cold elements in due proportion, in relation either to one another within the body or to the surrounding; and in like manner we regard beauty, strength, and all the other 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 by which the thing is naturally produced or destroyed. Since, then, relatives are neither themselves [10] alterations nor the subjects of alterations 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, like that of form and shape, necessarily involves the alteration of certain other things, [15] 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 defect or excellence involves a relation with those things from which the possessor is naturally subject to alteration: thus excellence disposes its possessor to be unaffected or to be affected thus and so, while defect disposes its possessor to be affected or to be unaffected in a contrary way.
And the case is similar in regard to the states of the soul, all of which too exist [247a1] in virtue of particular relations, the excellences being perfections and the defects departures. Moreover, excellence puts its possessor in good condition, while defect puts its possessor in a bad condition, with regard to its proper affections. Consequently these cannot be alterations either, nor can the processes of losing and [5] 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, and are moved by [10] 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 of defect or excellence involves the presence of pleasure or pain (with which excellence and defect are always concerned), and pleasures and pains [15] are alterations of the sensitive part, it is evident that the loss and acquisition of these states
too must be the result of the alteration of something. 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 [247b1] there any becoming of them. For the possession of knowledge most especially 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 possessed of knowledge not by being moved itself but by reason of the presence of something else; for when it meets with the particular object, it knows in a [5] manner the universal through the particular. 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 use and activity in question is similar to these. And [10] the original acquisition of knowledge is not a becoming or an alteration; for we are said to know and to understand when our 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, no change at all can have a becoming. Moreover, just as when anyone has passed from a state of intoxication or sleep or disease to the contrary [15] state, we do not say that he has become possessed of knowledge again, in spite of the fact that he was previously incapable of using his knowledge, so, too, when anyone originally acquires the state, we do not 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 [248a1] adults owing to the great amount of restlessness and motion in their souls. Nature itself in some cases causes the soul to settle down and come to a state of rest, while in 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 [5] 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.
[10] 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 things that move an equal distance in an equal time have an equal speed, 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: [15] thus an affection will be equal to a length, which is impossible. But is it not only when an equal distance is moved in an equal time that the velocities are equal? But an affection cannot be equal to a length. Therefore there cannot be an alteration equal to or less than a locomotion; and consequently not every motion is commensurable.
But how will our conclusion work out in the case of the circle and the straight [20] line? It would be absurd to suppose that the motion of one thing 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 make any difference to the argument to say that the one motion must 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 one passes over the distance B [248b1] and the other C, B will be greater than C; for this is what we took ‘quicker’ to mean; and so it is also quicker if it traverses an equal distance in less time; consequently there will be a part of A in which B will pass over a part of the circle equal to the distance which C will traverse in the whole of A. None the less, if the two are commensurable, we are confronted with the consequence stated above, viz. that [5] there may be a straight line equal to a circle. But these are not commensurable; and so the corresponding motions are not commensurable either, and things not synonymous are all incommensurable. 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 they are homonymous. But 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, [10] then, that the term ‘quick’ has not the same meaning in the two cases? 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 they are not homonymous? For the term ‘much’ has the same meaning whether applied to water or to air, yet water and air are not commensurable; or, if this is not so, ‘double’ at any rate would seem to have the same meaning (denoting in each case the proportion of two to one), yet they are not commensurable. But here again may [15] we not use the same argument and say that the term ‘much’ is homonymous? In fact there are some terms of which even the definitions are homonymous; e.g. if ‘much’ were defined as ‘so much and more’, ‘so much’ would mean something different in different cases; ‘equal’ is similarly homonymous; and ‘one’ again is perhaps inevitably homonymous; and if ‘one’ is, so is ‘two’. Otherwise why is it that some [20] things are commensurable while others are not, if the nature is one?
Is it because they are in different primary recipients? 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 not47 since the primary recipients are different. But clearly we could thus make all things one and say that each is in a different recipient; thus equality, sweetness, and whiteness will be the [249a1] same, though that which contains them is different in different cases. Moreover, it is not any casual thing that is receptive of any attribute: each single thing is primarily receptive of a single attribute.
Must we then say that, if things are to be commensurable, not only must they be non-homonymous, but there must also be specific differences either in the attribute itself or in that which contains the attribute—that these, I mean, must not [5] 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 in an equal time they perform 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 by the other half: can we say that in this case the alteration is equal to the locomotion and of the same velocity? That would be [10] absurd, and the reason is that there are different species of motion. And if two things are of equal velocity if they move 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 for this? Is it that locomotion is a genus or that line is a genus? (For the time [15] is the same.) If the lines are specifically different, the locomotions also differ specifically from one another; for locomotion is specifically differentiated according to the specific differentiation of that over which it takes place. (And also accordingly as the instrument of the locomotion is different: thus if feet are the instrument, it is walking, if wings it is flying. Or is that not so? Is locomotion different only according to the shape of the path?) Thus things are of equal velocity if in an equal time they traverse the same magnitude; and when I call it ‘the same’ I [20] 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 some homonymies are far removed from one another, some have a certain likeness, and some are nearly related either generically or analogically, with the result that they seem not to be [25] homonymies though they really are.
When, then, is there a difference of species? If the same thing is in different recipients? or if different things are in different recipients? 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 it 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 [249b1] 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 such alteration occupies an equal time. But what alteration? We cannot here speak of equality here: what is equality in the category of quantity is similarity here. However, let us say that there is equal velocity where the same change is accomplished in an equal time. Are we, then, to find the commensurability in the recipient of the affection or [5] in the affection itself? In the case that we have just been considering it is the fact that health is one and the same that enables us to arrive at the conclusion that the one alteration is neither more nor less than the other, but that both are alike. If on the other hand the affection is different in the two cases, e.g. when the alterations take the form of becoming white and becoming healthy respectively, here there is no sameness or equality or similarity inasmuch as the difference in the affections at [10] once makes the alterations specifically different, and there is no unity of alteration any more than there would be unity of locomotion under like conditions. So we must find out how many species there are of alteration and of locomotion respectively. Now if the things that are in motion—that is to say, the things to which the motions belong in their own right and not accidentally—differ specifically, then their motions will also differ specifically; and if they differ generically or numerically, the motions also will differ generically or numerically. But there still remains the question whether, supposing that two alterations are of equal velocity, we ought to look for this equality in the sameness or similarity of the affections, or in the things [15] altered, to see e.g. whether a certain quantity of each has become white. Or ought we not rather to look for it in both? That is to say, the alterations are the same or different according as the affections are the same or different, while they are equal or unequal according as the things altered are equal or unequal.
The Complete Works of Aristotle Page 73