LECTURE 8 (249 a 8-b 25)

FROM THE PRINCIPLES ESTABLISHED IN THE PRECEDING LECTURE HE SHOWS WHICH MOTIONS ARE COMPARABLE TO EACH OTHER

             940. After the Philosopher has shown in general what is required for things to be comparable, he here applies this discovered truth to the comparison of motions.

             He does this first in general, and secondly by comparing the motions of diverse genera, where he says, 'Suppose, then, that in a certain time . . .' (249 a 9), and thirdly by comparing the motions of one genus to each other, where he says, 'And if in consequence . . .' (249 a 12).

             He says, therefore, first that just as it is required in order for other things to be comparable that they be not equivocal and that there be the same primary receiver and the same species, likewise equal velocity of motion is said of that which is moved in an equal time through as much of another equal distance by a mutation of the same species.

             941. Next where he says, 'Suppose, then, that in a certain time . . .' (249 a 9), he treats the comparison of motions of diverse genera.

             He says according to the foregoing that if one mobile object is altered and another is moved with respect to place, can it not be said that the velocity of the alteration and the change of place is equal? But to say this is inconsistent. The reason for this is that motion has diverse species, and it was said before that things which are not of one species are not comparable. Since, therefore, change of place is not the same species as alteration, the velocities of local motion and alteration are not comparable.

             942. Next where he says, 'And if in consequence . . .' (249 a 12), he treats the comparison of motions of one genus in one genus.

             He does this first in respect to local motion, secondly in respect to alteration, where he says, 'And further, where alteration . . .' (249 a 29), and thirdly in respect to generation and corruption, where he says, 'And now we must consider . . .' (249 b 19).

             He does not mention increase and decrease because the same reasoning [ratio] applies here as in local motion since they occur in respect to some magnitude.

             Concerning the first part he makes three points. First he shows what is required for two local motions to be comparable to each other. Secondly, where he says, 'It is also similarly . . .' (249 a 17), he rejects a certain thing which seems to be required here. Thirdly, where he says, 'We may say, therefore . . .' (249 a 20), he concludes to his main point.

             Concerning the first part he makes two points. First he concludes that an inconsistency follows if it is said that all local motions are comparable. Secondly, where he says, 'What, then, is the reason . . .' (249 a 14), he explains why they are not all comparable.

             943. He says, therefore, first that if all things which are moved locally through an equal magnitude in an equal time have equal velocity, and if every local motion has equal velocity, it follows that the straight and the circular are equal. This may be understood in two ways: first in regard to straight and circular motion; secondly in regard to a straight and a circular line. The latter is better, for this follows from what he has stated. For if every straight and circular motion have equal velocity, and if motions are equally fast when they cross equal magnitudes in an equal time, then it follows that a straight and a circular magnitude are equal. And this latter is absurd.

             944. Next where he says, 'What, then, is the reason . . .' (249 a 14), he inquires into the cause of the non-comparability of straight and circular motions.

             He has concluded that if motions have equal velocity, then it follows that the magnitudes are equal, which seems absurd. Therefore, one might ask whether the cause of this non-comparability is due to the motion or the magnitudes. He asks whether the reason why a straight motion and a circular motion do not have equal velocity is that local motion is a genus containing beneath it diverse species (it was said above that things of diverse species are not comparable), or whether the reason is that a line is a genus containing beneath it the straight and the circular as diverse species. The time cannot be the cause of this incomparability, for all time is indivisible with respect to species.

             To this question, therefore, he answers that both are joined together. For in both cases there is found a difference of species, such that the difference of species in local motion is caused by the difference of species in the magnitude over which there is motion. He says that if that over which a thing is moved has species, it follows that local motion has species.

             945. Next where he says, 'It is also similarly . . .' (249 a 17), he rejects something which may seem to be required for the identity of species and the comparability of local motions.

             He says that sometimes local motions are differentiated in respect to that through which the local motion occurs as through an instrument. For example, if feet are that by which a thing is moved, the motion is called walking, and if wings are used, the motion is called flying.

             But this does not cause a difference of species in local motions but a difference in the figures of local motion, that is, this difference of mutations is not according to species but only according to some figure of motion, as the Commentator explains.

             But it may be better to say that he intends here to say that local motion is not differentiated in species through the instruments of motion but through the figures of the magnitude over which the motion passes. For thus the straight and the circular differ. The reason for this is that motions do not receive their species from mobile objects but rather from the things in regard to which mobile objects are moved. And the instruments are due to the mobile objects while the figures are due to that in which the motion occurs.

             946. Next where he says, 'We may say, therefore . . .' (249 a 20), he concludes to his position.

             Concerning this he makes three points. First he concludes to his main point. Secondly, where he says, '. . . and this discussion serves . . .' (249 a 22), he develops from the above conclusion a point which is worthy of consideration. Thirdly, where he says, 'When, then, is there a difference . . .' (249 a 25), he investigates the diversity of species.

             He concludes, therefore, first that since motions are not comparable unless they are of one species, and since local motions are not of one species unless there is the same magnitude in respect to species, it follows that those things are of equal velocity which are moved in an equal time with respect to the same magnitude. 'Same' is understood here to mean 'not different in species'. For in the same way motion also is not different in species. Therefore, in the comparison of motions one must consider what difference of motion there may be. If there is a difference in genus or species, they are not comparable. But if there is an accidental difference, they are comparable.

             947. Next where he says, '. . . and this discussion serves . . .' (249 a 22), he develops from the foregoing something which is worthy of consideration, namely a genus is not simply one, but a species is simply one. This is indicated in the preceding argument in which it was shown that things which are of one genus are not comparable, while things which are of one species are comparable. Since it was said above that the nature of comparables is the same, it seems that a genus is not one nature, but a species is one nature.

             The reason for this is that species is taken from the ultimate form, which in the nature of things is simply one. Genus, however, is not taken from a form which is one in the nature of things, but only from reason [ratio]. For man is not an animal through a form other than that by which man is man. Therefore all men, who are of one species, agree in the form which constitutes the species, because each of them has a rational soul. But there is not in man, or a horse, or an ass some common soul which constitutes animal beyond that soul which constitutes man, or horse, or ass (for if there were, then genus would be one and comparable, as is species). Rather the form of a genus is received only in the understanding by the abstraction of the intellect from differences.

             Therefore, a species is a unity which derives from one form existing in the nature of things. But a genus is not a unity because the diverse species of a genus receive predication according to the diverse forms existing in the nature of things. Thus a genus is one logically, but not physically.

             Therefore, a genus is in some way one, but not simply. Rather genera hide many joined things, that is, because of the similarity and nearness to unity of a genus, the equivocation of many things is latent in it.

             There are some equivocal terms so disparate that only the name is common. For example, a dog is said to be a celestial constellation and a barking animal.

             There are others which have some similarity. For example, the name 'man' is said of a real man and a picture of a man insofar as the latter has some similarity to a real man.

             Other equivocal terms are very close because of a conformity in genus (for example, when 'body' is said of a celestial body and a corruptible body, the term is used equivocally, speaking naturally, because their matter is not one. Nevertheless, they agree in logical genus, and because of this agreement in genus they seem to be not completely equivocal.) Or else they are very close in respect to some similarity, for example, he who teaches school is called a master, and likewise he who heads a house is called the master of the house, but equivocally. But this is a very close equivocation because of the similarity. For each is a director, one of learning, the other of a house. Because of this closeness either of genus or of similarity, they do not seem to be equivocal, but they are.

             948. Next where he says, 'When, then, is there a difference . . .' (249 a 25), since he has said that consideration must be given to the difference of motions to determine whether motions differ in species, he here asks how difference of species may be understood in regard both to motions and to other things. And since a definition signifies the essence of a species, he asks two questions: one about the species and the other about the definition.

             In regard to species he asks first whether we must judge that there is a different species only because the same nature is in different receivers, as the Platonists held. According to the above this is impossible. It was said that a genus is not simply one. Therefore, the diversity of species is not the result of the same thing being in different things, except according to the Platonists, who held that a genus is simply one. And because of this, as if answering the question, he adds, '. . . or must the attribute itself be different as well?' (249 a 26), as if he were to say that there is not a different species because the same thing is in another but because a different nature is in a different receiver.

             He asks a second question about definition. The question is, 'What is its terminus?' In other words, what is the definition which defines a species. Since things which are the same in definition are the same simply, he adds, as if answering, that the proper definition of a thing is that by which we are able to discern whether it is the same or different, for example, white or sweet. The term 'different' can be understood in two ways, even as before. First white is said to be different than sweet because in whiteness there is found a different natural subject than in sweetness. Secondly they are different because they differ not only with respect to the natural subject, but because they are totally not the same. These two are the same as those proposed above: namely, 'if the same is in another or if another is in another'. For it is clear that there is the same meaning [ratio] of identity and diversity in both species and definition.

             949. Next where he says, 'And further, where alteration . . .' (249 a 29), he treats the comparison of alterations.

             Concerning this he makes two points. First he shows that one alteration has a velocity equal to another. Secondly, where he says, 'But what alteration?' (249 b 1), he inquires how equality of velocity is present in alteration.

             He asks, therefore, first how one alteration is equal in velocity to another. And he proves that two alterations are equal in velocity. To be cured is to be altered. And it happens that one cure is quick and another slow, and some cures are simultaneous. Therefore, one alteration is equal in velocity to another. For that is said to be moved with equal velocity which is moved in an equal time.

             950. Next where he says, 'But what alteration?' (249 b 1), he points out that for local motion to be equal in velocity, there is required not only equality of time but also equality of the magnitude which is crossed. Granting that in alteration equality of time is required for equal velocity, he asks what else is required. This is what he means when he says, 'But what alteration?', that is, what can be said to be of equal velocity when an alteration occurs in equal time?

             The reason for this difficulty is that equality is not found in quality, in respect to which alteration occurs, such that we could say that an alteration has equal velocity when it arrives at an equal quantity in an equal time, which was said of local motion and which can be said of increase and decrease. Rather just as equality is found in quantity, so similarity is found in quality.

             He answers this difficulty where he adds, 'However, let us say . . .' (249 b 4).

             First he gives his answer to the difficulty. He says that an alteration ought to be said to have equal velocity if the same thing, that is, the thing which is altered, is changed in an equal time.

             951. Secondly, where he says, 'Are we, then, to find . . .' (249 b 5), he raises a question in regard to this answer. The question which he asks first is as follows. It was said that an alteration has equal velocity if the same thing is altered in an equal time. But that which is altered can be understood in two ways, namely, the passion with respect to which the alteration occurs and the subject of the passion. Therefore, the question is whether this comparison should be taken with respect to the identity of the passion or with respect to the identity of the subject of the passion.

             952. Secondly, where he says, 'In the case that . . .' (249 b 6), he answers one part of the question. He says that in alteration a double identity should be present in respect to the passion so that the alteration may have equal velocity. First, there should be the same quality in respect to species. For example, the same health is present in the eyes or some such thing. Secondly, the same received quality should be present in the same way, and neither more nor less. But if the passion, that is, the passive quality, is different in respect to species, for example, if one thing becomes white and another healthy, then in these two passions nothing is the same, or equal, or similar. And so because of the diversity of these passions there are diverse species of alteration and not one alteration just as it was said above that straight and circular motion are not one local motion. Therefore in comparing both local motions and alterations, one must consider whether the species of alteration or of local motion are the same or many. And this can be understood from the things in which there is motion. For if the things which are moved, that is, if the things in respect to which there is motion per se and not per accidens, differ in species or genus, then the motions also differ in species or genus. And if they differ in number, the motions also differ in number, as was said in Book V.

             953. Thirdly, where he says, 'But there still remains . . .' (249 b 15), having answered one part of the question which he asked, he seeks an answer for the other part. The question is whether the judgment that alterations are similar or have equal velocity ought to relate only to the passion, as to whether it is the same, or whether it should relate to the subject which is altered. For example, if a certain part of this body became white in this time, and if another equal part of the body became white in the same or an equal time, may the alteration be said to have equal velocity?

             His answer is that one should consider both, namely, the passion and the subject, but in different ways. For we judge that an alteration is the same or different because the passion is either the same or different. But we judge that an alteration is equal or unequal insofar as part of the altered subject is equal or unequal. For if a large part of this body becomes white and if another small part becomes white, the alteration will be the same in species but not equal.

             954. Next where he says, 'And now we must consider . . .' (249 b 19), he shows how comparison should be made with respect to generation and corruption.

             He does this first in respect to the proper opinion, and secondly in respect to Plato's opinion, where he says, 'If we adopt the theory . . .' (249 b 23).

             He says, therefore, first in regard to generation and corruption that in order that generation have equal velocity, we must consider if in an equal time the very thing which is generated is also indivisible in respect to species. For example, if in each generation a man is generated in an equal time, the generation has equal velocity. But generation does not have equal velocity only because an animal is generated in an equal time. For certain animals, because of their own perfection, require a longer time for generation. But a generation is said to be faster if the other is generated in an equal time. For example, if a horse is generated in the same amount of time in which a dog is generated, then the generation of the horse is faster.

             In regard to alteration he said that two things must be considered relative to the passion, namely, if there is the same health, and if it exists in the same way, neither more nor less. But in regard to generation, he says that only one thing must be considered, namely, if there is the same thing which is generated. He gives the reason for this by saying, '. . . because we have no pair of terms that will convey this "difference" in the way in which unlikeness is conveyed' (249 b 23). It is as if he were to say that in generation the only consideration is whether there is the same thing which is generated because in generation we do not have something which can be varied in two ways so that some difference arises, as in alteration there occurs a difference in that one and the same quality is varied in respect to more and less. For the substance of that which is generated does not receive more and less.

             955. Next where he says, 'If we adopt the theory . . .' (249 b 23), he treats the comparison of generation according to Plato's opinion. Plato held that number is the substance of a thing because he thought that the one which is the principle of number is the same as the one which is convertible with being and which signifies the substance of a thing. Moreover, oneness is totally of one nature and species. Therefore, if number, which is nothing other than an aggregation of units, is the substance of things according to the Platonists, it will follow that greater and smaller number will be predicated with respect to the diverse species of quantity, however, with respect to substance it will be similar in species. Thus Plato posited the species of oneness. But the contraries, the great and the small, by which things are diversified, are due to matter. And so it follows that just as one and the same health is two insofar as it receives more and less, so also substance, which is number, although it is of one species in respect to unity, will have duality insofar as it is a larger or smaller number. But in substance there is no common name which signifies either one, that is, the diversity which arises from the largeness or smallness of number. When a passion is present to a greater extent or excels in any way whatsoever, it is called 'more', for example, more white or more healthy. And when a quantity excels, it is called 'greater', as a greater body or greater surface. But we do not have a name which signifies in common the excelling of substance, which arises from the largeness of number according to the Platonists.