LECTURE 3 (225 b 5-226 a 22)

THERE IS NO MOTION PER SE IN THE CATEGORIES OTHER THAN QUANTITY, QUALITY, AND WHERE

             660. After the Philosopher has divided mutation into generation, corruption, and motion, he here subdivides motion into its parts.

             And since opposites are treated by the same science, he first establishes the species of motion, and secondly he shows how many kinds of immobility there are, where he says, 'The term "immovable" . . .' (226 b 10).

             Concerning the first part he makes two points. First he gives a conditional argument through which the division of motion into its parts is established. Secondly, where he says, 'In respect of Substance . . .' (225 b 10), he explains the given conditional argument.

             661. He concludes, therefore, from the above that since motion is from subject to subject, and since subjects are in some genus of the categories, then it is necessary that the species of motion be distinguished according to the genera of the categories. For motion takes its denomination and species from its terminus, as was said above. Hence, if the categories are divided into ten genera of things, namely, substance, quality, etc., as is said in the Categories and in Metaphysics, V; and if motion is found in three of them; then there must be three species of motion--namely, motion in the genus of quantity, motion in the genus of quality, and motion in the genus of where, which is called motion in respect to place.

             It was explained in Book III how there is motion in these genera and how motion pertains to the categories of action and passion.

             Hence it is sufficient here to say briefly that any motion is in the same genus as its terminus, not indeed in the sense that motion to quality is a species of quality, but by reduction. For just as potency is reduced to the genus of act because every genus is divided by potency and act, likewise motion, which is an imperfect act, must be reduced to the genus of perfect act. But insofar as motion is considered as to this from another, or from this to another, it pertains to the category of action and passion.

             662. Next where he says, 'In respect of Substance . . .' (225 b 10), he explains the given conditional argument.

             First he shows that there cannot be motion in the genera other than the three mentioned above. Secondly, where he says, 'Since, then, motion can belong . . .' (226 a 23), he shows how there is motion in these three genera.

             Concerning the first part he makes three points. First he shows that there is no motion in the genus of substance. Secondly, where he says, 'Nor is there motion . . .' (225 b 11), he shows that there is no motion in the genus of relation. Thirdly, where he says, 'Nor is there motion . . .' (225 b 14), he shows that there is no motion in the genera of action and passion.

             He omits three categories; namely, when, site, and state. For 'when' signifies being in time. But time is a measure of motion. Hence there is no motion in 'when' for the same reason [ratio] that there is no motion in action and passion, which pertain to motion. Site indicates a certain order of parts. But order is a relation. Likewise state refers to a certain relation of a body to that which is joined to it. Hence there cannot be motion in these two categories just as there is no motion in relation.

             He proves as follows that there is no motion in the genus of substance. Every motion is between contraries, as was said above. But there is no contrary of substance. Therefore there is no motion in respect to substance.

             663. But a difficulty arises here because the Philosopher himself says in De Generatione et Corruptione that fire is contrary to water. And in De Caelo he says that the heavens are neither generable nor corruptible because they do not have a contrary. Hence it seems to follow that things which are corrupted either are contraries or are composed of contraries.

             Regarding this some say that one substance can be the contrary of another, as fire is contrary to water, in regard to its form but not in regard to its subject. But according to this Aristotle's proof is not valid, because there would be motion in substance if substantial forms were contraries. There is motion from form to form because in alteration subject is not contrary to subject, but form is contrary to form.

             And therefore it must be said that fire is contrary to water in regard to the active and passive qualities, which are hot and cold, wet and dry, and not in regard to substantial forms. For it cannot be said that heat is the substantial form of fire since in other bodies it is an accident of the genus of quality.. And that which belongs to the genus of substance cannot be an accident of something.

             But even this answer presents a difficulty. It is clear that proper passions are caused by the principles of the subject, which are matter and form. If, therefore, the proper passions of fire and water are contraries, it seems that their substantial forms are contraries, because the causes of contraries are contraries. Moreover in Metaphysics, X, it is proven that every genus is divided by contrary differentiae. But differentiae are taken from forms, as is said in Metaphysics, VIII. It seems, therefore, that there is contrariety in substantial forms.

             664. Therefore, it must be said that the contrariety of differentiae, which is in every genus, is taken according to the common root of contrariety, which is excess and defect. All contraries are reduced to this opposition, as was said in Book I. For all differentiae which divide a genus are related such that one of them is in excess and the other in defect in respect to each other. Because of this Aristotle says in Metaphysics, VIII, that the definitions of things are like numbers, the species of which vary by the addition and subtraction of unity. But nevertheless it is not necessary that in every genus there be contrariety in respect to the nature [ratio] of this and that species, but only in respect to the common nature [ratio] of excess and defect. Since contraries differ to the greatest degree, it is necessary that contrariety be found in any genus when there are found two termini which differ to the greatest degree. And everything else of that genus falls between these two termini.

             But there would not be motion in that genus unless there happens to be a continuous passage from one extreme to the other. Therefore, in some genera these two conditions are absent, as is clear in numbers. For although all species of number differ in respect to excess and defect, nevertheless in this genus there are not two extremes which differ to the greatest degree. There is a minimum number--two--but not a maximum. Likewise there is no continuity between species of number, because each species of number is formally completed by unity, which is indivisible, and is not continuous with another unity. The genus of substance is the same. For the forms of diverse species differ from each other in respect to excess and defect insofar as one form is more noble than another. And because of this diverse forms can cause diverse passions, as was objected. Nevertheless one form of a species is not contrary to another in respect to its own proper nature [ratio].

             The first reason for this is that there is no maximum difference between two substantial forms such that there is passage from one form to another in order only through intermediaries. Rather when matter puts off one form, it can indifferently receive diverse forms without order. Hence Aristotle says in De Generatione et Corruptione that when fire is generated from earth, it is not necessary that there be a transition through the intermediate elements.

             The second reason is that, since the substantial existence of each thing is in something indivisible, there cannot be a continuity in substantial forms such that there might be a continuous motion from one form to another by the remission of one form and the incoming of another.

             Hence Aristotle's proof that there is no motion in substance because there is no contrariety in substance is demonstrative, and not just a probable argument, as the Commentator seems to indicate. Moreover, that there is no motion in substance can also be proven by means of another argument which he gave above; namely, the subject of substantial form is being in potency only.

             665. In qualities of the third species there clearly is contrariety in both senses [ratio]. For qualities can be extended and remitted such that there can be continuous motion from quality to quality. Moreover a maximum difference between two determinate extremes is found in the same genus, as in colours between black and white, and in taste between bitter and sweet.

             But in quantity and in place one of these, that is, continuity, is clearly found. But the other, that is, a maximum difference of determinate extremes, is not found in them if they are taken according to the common nature [ratio] of quantity and place, but only according as they are taken in some determinate thing. Thus in a species of animal or plant there is some minimum quantity, from which augmentation begins, and a maximum quantity, at which it ends. Likewise in place there are found two termini at a maximum distance in comparison to some motion. The motion begins from one of these and ends at the other, whether it be natural or violent motion.

             666. Next where he says, 'Nor is there motion . . .' (225 b 11), he shows that there is no motion in the genus of relation.

             For in whatever genus there is per se motion, nothing new of that genus is found in anything unless it changes. Thus a new colour is not found in any coloured thing, unless it be altered. But something new truly happens to that which is relative to another when that other changes, while it itself does not change. Therefore, in relation there is no motion per se, but only per accidens, insofar as a new relation results from some change. Thus equality or inequality results from change of quantity, and similarity or dissimilarity results from change of quality.

             667. In some cases that which is said here does not seem to present a difficulty. But in other cases it does.

             For there are certain relations which are not anything real in that of which they are predicated.

             This can occur in regard to both extremes of the relation, as when it is said that the self is the same as the self. This relation of identity would be multiplied to infinity if anything were the same as itself by means of an added relation. For it is clear that anything is the same as itself. Therefore this is a relation in respect to reason [ratio] only insofar as reason [ratio] takes one and the same thing as the two extremes of a relation. This also occurs in many other cases.

             Further there are certain relations of which one is real in the one extreme, and the other is in the other extreme only according to reason [ratio], for example, knowledge and the knowable. For the knowable is relative, not because it itself is referred to by some relation existing in it, but because something else is referred to it, as is made clear by the Philosopher in Metaphysics, V. Another example is when a column is said to be to the right of an animal. Right and left are real relations in the animal because the determinate powers on which these relations are based are found in animals. But in the column these relations are not present in respect to the thing but only in respect to reason [ratio]. For the column does not have those powers which are the foundations of these relations.

             Further there are certain relations in which a real relation is found to exist in respect to both extremes: for example, equality and similitude. For quantity and quality, which are the roots of these relations, are found in both extremes. This also occurs in many other relations.

             Hence, regarding those relations which posit something in only one extreme, it does not seem difficult to understand how, when that extreme in which the relation really exists is changed, something new is said relative to the other without that other changing. For nothing really happened to it. But in those cases in which a real relation is found in both extremes, it seems difficult to understand how something is said relatively of one, which does not change, because of a change of the other. For nothing new comes to something without a change of that to which it comes.

             Hence it must be said that if someone by changing becomes equal to me, and I did not change, then that equality was first in me in some way, as in a root from which it has real being. For since I have a certain quantity, it happens that I am equal to all those who have the same quantity. When, therefore, someone newly takes on this quantity, this common root of equality is determined in regard to him. Therefore nothing new happens to me because of the fact that I begin to be equal to another because of his change.

             668. Next where he says, 'Nor is there motion . . .' (225 b 14), he proves that there is no motion in the genera of action and passion.

             Action and passion do not differ from motion in subject. Rather they add an intelligibility [ratio], as was said in Book III. Hence to say that there is motion in action and passion is the same as to say that there is motion in motion.

             Therefore concerning this he makes three points. First he states his intention. Secondly, where he says, 'For in the first place . . .' (225 b 17), he proves his position. Thirdly, where he says, 'To sum up, then . . .' (226 a 19), he makes a certain distinction in order to clarify his position.

             He says, therefore, first that just as there is no motion of that which is relative, likewise there is no motion of agent and patient, nor, to speak absolutely, of mover and moved. For there cannot be motion of motion, or generation of generation, which are the species of mutation. Nor can there be mutation of mutation, which is their genus. Nor can there be corruption of corruption.

             669. Next where he says, 'For in the first place . . .' (225 b 17), he proves with six arguments that there cannot be mutation of mutation.

             The first is as follows. If there is mutation of mutation, this can be understood in two ways. First there might be a mutation of a mutation as a subject which is moved; just as there is a mutation of a man because the man is changed from white to black. Thus motion of motion as subject or mutation of mutation as subject can be understood as though the motion or mutation were moved; for example, that it becomes warm, or becomes cold, or is moved in place, or increases or decreases. But this is impossible since mutation is not a subject for it is not a per se subsisting substance. Therefore there cannot be a mutation of mutation as subject.

             670. Secondly mutation of mutation can be understood as of a terminus, as, for example, when a subject is moved from one species of mutation to another, as from becoming warm to becoming cold or becoming healthy. Thus two mutations are understood as the two termini of one mutation. For example, sickness and health are understood as two termini when a man is changed from sickness to health. But it is impossible for a subject to be moved per se from mutation to mutation. This happens only per accidens.

             He proves in two ways that this is not possible per se.

             The first proof is as follows. Every motion is a mutation from one determinate species to another determinate species. Likewise generation and corruption, which are divided against motion, have determinate termini. The difference is that generation and corruption occur between termini opposed as contradictories, while motion occurs between termini opposed as contraries.

             Therefore, if a subject be changed from mutation to mutation, for example, from becoming sick to becoming white, then at the same time that the subject changes from health to sickness, it will be changed from this mutation to another. For while the subject is still partly at the terminus from which, it is moved toward the terminus to which; just as while someone has some health, he is moved to sickness.

             Therefore, if motion from sickness to health be the terminus from which of another motion, then while this very mutation from sickness to health is still going on, the subject will simultaneously be changed from this mutation to another which succeeds it in the subject. But it is clear that when the first mutation has been terminated, that is, when the man is already changed from sickness to health, then any other mutation can thereafter succeed it. This is not surprising. For when the first mutation is terminated, the subject is at rest and is not being changed by any mutation. And for the same reason [ratio] it can be changed by any other mutation.

             If, therefore, there is a motion from one mutation to a second which succeeds it in the subject, it follows that this is a motion from the first mutation to some other indeterminate mutation. And this is contrary to the nature [ratio] of per se motion. For every motion is from a determinate terminus to a determinate terminus. For a body is not moved per se from white to just anything, but to black or an intermediate colour.

             It is clear, therefore, that two mutations are not the per se termini of any mutation.

             671. Secondly he proves the same thing with another argument.

             If there is mutation per se from a preceding mutation to a subsequent mutation, it is not necessary that the mutation always be to an occurring mutation, that is, to one which occurs simultaneously with the preceding mutation. Thus becoming white can be simultaneous with becoming sick, but becoming healthy cannot be simultaneous with becoming sick, because these are contrary mutations. Nevertheless it happens that becoming white and becoming healthy succeed becoming sick in the same subject. And this is what he means when he says that mutation from one mutation to another will not always be to an occurring mutation, for when it succeeds it is not occurring. Also the non-occurring mutation is between two other termini. For this reason the non-occurring mutation, to which one is changed from becoming sick, will be becoming healthy, which is opposed to becoming sick.

             That this is inconsistent is clear from the proposition established above: namely, that while the first mutation is going on, it will be simultaneously changed to a second mutation. Therefore while one is becoming sick, he will simultaneously be becoming healthy. For the terminus of becoming healthy is health--for it is from something to something else, as was said. Hence it follows that while something is being moved to sickness, it is also simultaneously being moved to health. But this is to be moved simultaneously to two contraries, and to tend toward them simultaneously. This is impossible. Thus it is clear that there is no per se mutation from one mutation to another.

             But it is clear that this might happen per accidens, as was said above, for he adds that it does happen per accidens, as when a subject is changed now by one mutation and later by another. For example, it might be said that something is changed per accidens from memory to forgetfulness or to any other mutation. For the subject of the mutation at one time is changed to knowledge, and at another time to something else, for example, to health.

             672. He gives the second argument where he says, 'In the second place . . .' (225 b 33). He sets forth two conditional arguments.

             The first is that if there be mutation of mutation or generation of generation, then it would somehow be necessary to proceed to infinity. For by the same reason [ratio] the second generation will have another generation, and so forth to infinity.

             The second conditional argument is that, if generations and mutations be so ordered that there is a mutation of mutation and a generation of generation, then if there will be a last mutation or generation, there must be a first. He proves this second conditional statement as follows. Let there be something which is generated simply, for example, fire. Now if there is generation of generation, then one must say that at some time this simple generation itself was also generated, and this becoming itself became. But when this generation itself was being generated, that which is generated simply, that is, fire, as yet was not. For a thing does not exist while it becomes. Rather when it is already made, then it exists primarily. Therefore while the generation of fire was being generated, fire was not yet made, and therefore it did not yet exist. And again the very generation of its generation for the same reason [ratio] at some time was generated. And thus, just as when fire did not yet exist when the generation of fire was being generated, likewise it follows that the generation of fire did not yet exist when the generation of the generation of fire was being generated.

             From this it is clear there cannot be a generation of fire if the prior generation is not completed. And for the same reason [ratio] the prior generation cannot occur unless the next prior generation is completed, and so forth back to the first generation. Hence if there were no first generation, there will not be the last, which is the generation of fire. But if one proceeds in generations to infinity, there is no first generation or mutation, because in infinity there is no first. Hence it follows that there is no generation or mutation. And if there is no generation or mutation, then nothing is generated or is moved. Thus if there is generation of generation and mutation of mutation, then nothing is generated or is moved.

             But it must be understood that this argument does not deny that mutation can follow mutation per accidens to infinity. It is necessary to say this according to the opinion of Aristotle who held eternal motion. He intends to show, as was said above, that there is no mutation of mutation per se to infinity. For the last would depend on an infinity of predecessors, and would never be completed.

             673. He gives the third argument where he says, 'Thirdly, if a thing . . .' (226 a 6). The argument is as follows.

             Both motion and rest are contrary to the same motion. For example, descent and rest in a lower place are contrary to ascent, and likewise generation and corruption are contrary. For contraries naturally occur in regard to the same thing. Therefore whatever is generated can be corrupted. But if there is generation of generation, it is necessary that generation be generated. Therefore generation is corrupted. But that which is corrupted must exist. For just as that which is not is generated, likewise that which is is corrupted. Therefore it is necessary that when something is generated and generation exists, then this same generation is corrupted: not indeed immediately after the generation ends, nor at a later time, but simultaneously. But this seems impossible.

             However it must be realized that generation is the terminus of that which is generated as substance. For generation is a transmutation to substance. But the subject of generation is not that which is generated; rather it is its matter. Hence Aristotle does not abandon his own position, by which he intends to show that there is no mutation of mutation as terminus.

             674. He gives the fourth argument where he says, 'Fourthly, there must be . . .' (226 a 10). The argument is as follows.

             In every generation there must be some matter from which that which is generated comes. Also in every mutation there must be some matter or subject. Thus in alteration the subject in respect to corporeal alterations is the body, and in respect to animal alterations it is the soul. Therefore, if generation is generated, there must be some matter for this generation. This matter is changed to the species of generation, just as the matter of generated fire was changed to the species of fire. But such matter cannot be found.

             Under this same argument he gives another approach. In any generation or mutation there must be some terminus to which something is moved. This terminus must be a definite and determinate 'this'. But neither generation nor motion is such a 'this'. Therefore it is not possible for there to be a generation of generation or of motion.

             675. He gives the fifth argument where he says, 'But in what sense . . .' (226 a 14). The argument is as follows.

             Species is related to species in the same way that genus is related to genus. Therefore, if there is generation of generation, then the generation of learning must be learning. But this is clearly false. For learning is the generation of knowledge and not the generation of learning. Therefore there cannot be generation of generation.

             676. He gives the sixth argument where he says, 'Finally, since there are . . .' (226 a 17). The argument is as follows.

             If there is mutation of mutation either as subject or as terminus, then, since there are three species of motion, as was said, that is, motion in 'where', in quantity, and in quality, it follows that one of these species must be the subject and terminus of another as well as of itself. It follows, therefore, that change of place is either altered or is moved in respect to place. This is more evidently impossible in a special case than in general. Therefore, it must not be said that there is mutation of mutation or generation of generation.

             677. Next where he says, 'To sum up, then . . .' (226 a 19), he shows how there can be mutation of mutation.

             He says that since a thing is moved in three ways, as was said above, that is, either per accidens, per se, or in respect to a part, mutation can be changed only per accidens, insofar as the subject of mutation is changed. For example, if someone runs or learns while he becomes healthy, then becoming healthy runs or learns per accidens, like a musician who builds. But we do not intend here to treat that which is moved per accidens. This we have already dismissed above.