LECTURE 23 (223 a 16-224 a 16)

DIFFICULTIES CONCERNING THE EXISTENCE AND UNITY OF TIME ARE ANSWERED

             625. After the Philosopher has treated time, he here answers certain difficulties concerning time, first in regard to the existence of time, and secondly in regard to the unity of time, where he says, 'One might also raise . . .' (223 a 29).

             Concerning the first part he makes two points. First he raises two difficulties, and secondly he answers them, where he says, 'Is it because it is . . .' (223 a 18).

             He says, therefore, first that the following difficulties are worthy of careful consideration: how is time related to the soul, and why does time seem to be everywhere, that is, on the earth, on the sea, and in the heavens.

             626. Next where he says, 'Is it because it is . . .' (223 a 18), he answers the above questions. First he answers the second one, which is easier, and then the first one, where he says, 'Whether if soul . . .' (223 a 22).

             He says, therefore, that time is a certain accident of motion, because it is the number of motion. (An accident is usually called a passion or a state.) Hence, wherever there is motion, there must be time. But all bodies are mobile, at least in respect to local motion, if not the other kinds of motion, for all bodies are in place. Someone might object that, although all bodies are mobile, nevertheless they are not all moved. Rather some are at rest. Thus it does not seem that time is in all things. To refute this he adds that time is together with motion, whether the motion be actual or potential. For everything that can be moved, but is not actually moved, is at rest. And time not only measures motion, but also rest, as was said above. Hence it follows that there is time wherever there is motion, either actual or potential.

             627. Next where he says, 'Whether if soul . . .' (223 a 22), he answers the first question.

             Concerning this he makes three points. First he asks the question. Secondly, where he says, '. . . for if there cannot be . . .' (223 a 23), he raises an objection regarding the question. Thirdly, where he says, '. . . but only that of which . . .' (223 a 26), he answers the question.

             The question, therefore, is whether or not there is time if soul does not exist.

             628. Secondly, where he says, '. . . for if there cannot be . . .' (223 a 23), he raises an objection to show that there would be no time. If it is impossible for there to be something which can number, then it is impossible for there to be something numerable, that is, able to be numbered. But if the numerable is not, number is not. For number exists only in that which is actually numbered or in that which is potentially numerable. Therefore it follows that, if something which is able to number does not exist, then number does not exist. But nothing can number except the soul, and among the parts of the soul nothing except the intellect. For to number is to relate numbered things to one first measure, and this is done by reason [ratio]. Therefore, if no intellective soul exists, there is no number. But time is a number, as was said. Therefore, if no intellective soul exists, there is no time.

             629. Next where he says, '. . . but only that of which . . .' (223 a 26), he answers the question.

             He says that, if there is no soul, one must say either that time does not exist, or, more correctly, that without soul time is some kind of a being--if, for example, it happens that there is motion but no soul. For if there is motion, it is necessary that there also is time. For before and after are in motion, and the before and after of motion, insofar as they are numerable, are time.

             To understand this answer it must be realized that, if there are numbered things, then there must be number. Hence, both numbered things and their number depend on one who numbers. Now the existence of numbered things does not depend on an intellect unless there is some intellect which is the cause of things, as is the divine intellect. However, their existence does not depend on the intellect of the soul. Only numeration itself, which is an act of the soul, depends on the intellect of the soul. Therefore, just as there can be sensible things when no sense power exists, and intelligible things when no intellect exists, likewise there can be number and numerable things when no one who numbers exists.

             But perhaps the conditional proposition which he gave first is true; that is, if it is impossible for there to be someone who numbers, then it is impossible for there to be anything numerable. This is similar to the following true proposition: if it is impossible for there to be someone who senses, then it is impossible for there to be something sensible. For if there is something sensible, it can be sensed. And if it can be sensed, then there can be something which senses. Nevertheless, it would not follow that, if there is something which is sensible, then there is something which senses. In the same way it follows that, if there is something numerable, then there can be something which numbers. Hence, if it is impossible for there to be something which numbers, then it is impossible for there to be something numerable. But it does not follow that, if there is no one who numbers, then there is nothing numerable, as the Philosopher's objection proceeds.

             If, therefore, motion were to have a fixed existence in things, as a stone or a horse does, then one could say absolutely that, just as there is a number of stones, when soul does not exist, likewise there is a number of motion, which is time, when soul does not exist. But motion does not have a fixed existence in things. Nor is anything concerning motion actually found in things except a certain indivisible part of motion, which is a division of motion. But the totality of motion is established by a consideration of the soul which compares a prior disposition of the mobile object to a later one. Therefore, time also does not have existence outside the soul except in respect to its own indivisible part. For the totality of time is established by the ordering of the soul which numbers the before and after in motion, as was said above. Therefore the Philosopher significantly says that, if soul does not exist, then time is 'some kind' of being, that is, an imperfect being. In the same way, if there happens to be motion but no soul, motion is also said to be imperfect.

             And because of this the arguments given above to show that time does not exist because it is composed of non-existent parts are answered. For it is clear from the foregoing that time does not have a perfect existence outside the soul, as neither does motion.

             630. Next where he says, 'One might also raise . . .' (223 a 29), he raises a difficulty concerning the unity of time, or the relation of time to motion.

             Concerning this he makes three points. First he raises the difficulty. Secondly, where he says, 'Must we not say . . .' (223 a 30), he answers it. Thirdly, where he says, 'It is said rightly . . .' (224 a 2), he clarifies a certain point which he had supposed.

             He says, therefore, first that, since time is the number of motion, there is the problem of what motion or of what kind of motion it is the number.

             Next where he says, 'Must we not say . . .' (223 a 30), he answers the problem. First he refutes a false solution. Secondly, where he says, 'Now there is such . . .' (223 b 13), he gives the true solution.

             Concerning the first part he makes three points. First he gives the false solution. Secondly, where he says, 'But other things as well . . .' (223 b 1), he disproves it by reducing it to absurdity. Thirdly, where he says, 'Surely not' (223 b 3), he shows that this absurdity is an impossibility.

             631. The first answer, therefore, is that time is the number of any motion.

             To prove this he indicates that every motion, that is, generation, increase, alteration, and local motion, is in time. Now that which pertains to every motion pertains to motion as such. Moreover, to be in time is to be numbered by time. Therefore it seems that any motion, as such, has number. Hence, since time is the number of motion, it seems to follow that time is the number of all continuous motion, and not of just some special kind of motion.

             632. Next where he says, 'But other things as well . . .' (223 b 1), he disproves the above position. Sometimes it happens that two things are moved simultaneously. If, therefore, time is the number of each motion, it follows that there is a different time for two motions existing simultaneously. And it would follow further that two equal times exist simultaneously, for example, two days or two hours. However, it is not astonishing if two unequal times, for example, a day and an hour, exist simultaneously.

             633. Next where he says, 'Surely not' (223 b 3), he shows that it is impossible for two equal times to exist simultaneously. Every time which is simultaneous and equal is only one time. But time which is not simultaneous is not one in number, but is one in species, as for example, a day with a day, and a year with a year.

             He shows this by a comparison with other numbered things. If there are seven horses and seven days, they do not differ in respect to number but in respect to the species of the numbered things. Likewise there is the same time for all motions which are simultaneously terminated in respect to both beginning and end. But motions differ in respect to their proper natures [ratio], insofar as one happens to be fast and the other slow, or the one is local motion and the other is alteration. But the time is the same if the alteration and the local motion, supposing that they are simultaneous, have an equal number. And because of this it is necessary that although motions are different from each other, the time in all of them is the same. For there is one and the same number for things which are equal and simultaneous, wherever they might be.

             634. Next where he says, 'Now there is such . . .' (223 b 13), he gives the true answer.

             Concerning this he makes three points. First he sets forth certain things which are necessary for his answer. Secondly, where he says, '. . . if, then, what is first . . .' (223 b 18), he concludes his answer from these premises. Thirdly, where he says, 'This also is why . . .' (223 b 22), he proves his answer from what has been said by others.

             Concerning the first part he sets forth three points.

             The first point is that local motion is the first and more simple and regular of all other motions. And circular motion is the first and more simple and regular of all other local motions, as will be proven in Book VIII.

             The second point is that each thing is numbered by some one thing of the same genus. Thus unities are numbered by unity and horses by horse, as is clear in Metaphysics, X. Hence it is necessary that time be measured by some determinate time. Thus we see that all times are measured by the day.

             The third point which he sets forth is that time is measured by motion and motion by time, as was said above. This is so because the quantity of any motion and time is measured by some determinate motion and by some determinate time.

             635. Next where he says, '. . . if, then, what is first . . .' (223 b 18), he concludes from the above that, since that which is first is the measure of all things which are of that genus, then it is necessary that circular motion, which is most regular, is the measure of all motions. Moreover, that motion is called regular which is one and uniform. But this regularity cannot be found in alteration or increase, because they are neither constantly continuous nor of equal speed. However, this regularity can be found in local motion, because some local motions can be continuous and uniform. This is true only of circular motion, as will be proven in Book VIII.

             And among all other circular motions, the first motion which revolves the whole firmament in daily motion is the most uniform and regular. Hence that circular motion, as first and more simple and more regular, is the measure of all motions. Moreover, it is necessary that a regular motion be the measure or number of the others. For every measure ought to be most certain, and this is found in things which are uniformly related.

             Therefore, from this we can conclude that, if the first circular motion measures all motion, and if motions insofar as they are measured by some motion are measured by time, then it is necessary to say that time is the number of the first circular motion, according to which time is measured, and in regard to which all other motions are measured by time.

             636. Next where he says, 'This also is why . . .' (223 b 22), he proves the above position by means of the opinions of others.

             He does this first by means of the erroneous opinion of those who were motivated to say that time is the motion of the celestial sphere because all other motions are measured by this motion. For it is clear that we say that a day or a year is completed by looking to the motion of the heavens.

             He does this secondly by means of the common use of speech, where he says, 'This also explains . . .' (223 b 24).

             He says that, since time is the number of the first circular motion, it is customary to say that there is a certain circle in human affairs and in other things which are naturally moved and generated and corrupted. This is so because all such things are measured by time, and men take the beginning and end of time as if time occurs according to a certain circularity. For time itself seems to be a kind of circle. Furthermore, this seems to be so because time is the measure of circular motion, and is also measured by circular motion. Therefore to say that there is a certain circle of things which occur in time is nothing other than to say that time is a kind of circle; which is so because time is measured by circular motion. For that which is measured does not seem to be different from the measure. Rather many measures seem to make one whole, thus many unities make one number, and many measures of cloth make one quantity of cloth. This is true when the measure is taken from the same genus.

             Therefore, it is clear that time primarily measures and numbers the first circular motion, and through this it measures all other motions. Hence, there is only one time because of the unity of the first motion. Nevertheless whoever senses any motion senses time, because mutability in all mutable things is caused by the first motion, as was said above.

             637. Next where he says, 'It is said rightly . . .' (224 a 2), he shows how something which he said above must be understood.

             He said that the number of seven dogs and seven horses is the same. He shows how this is true. If the number of some diverse things, for example, sheep and dogs, is equal, then it can be truly said that the number of each of them is the same. For example, both the sheep and the dogs are ten. But it cannot be said that ten itself is the same as the dogs and the sheep. For the ten sheep and the ten dogs are not the same ten. This is so because a genus with the addition of unity or identity can be predicated of many individuals existing in one species. And likewise an ultimate genus can be predicated of many species existing under one proximate genus. Nevertheless one cannot predicate with the addition of unity or identity either the species of the individual or the proximate genus of diverse species.

             He next gives an example of this. There are two species of triangle: the equilateral which has three equal sides, and the scalene which has three unequal sides. Now figure is the genus of triangle. Therefore, we cannot say that the equilateral and the scalene are the same triangle. But we can say that they are the same figure, since they are both contained under triangle which is one species of figure. He gives the reason [ratio] for this. Since the same and the diverse are opposed, we can predicate identity where difference is not found, but we cannot predicate identity where difference is found. Moreover, it is clear that the equilateral and the scalene differ from each other by a differentia of triangle, that is, by a proper division of triangle. This is so because they are diverse species of triangle. But the equilateral and the scalene do not differ in respect to a differentia of figure. Rather they are contained under one and the same dividing differentia of figure.

             Thus the following is clear. If we divide figure into its species, which are constituted by the differentiae, it will be found that the circle is one thing and the triangle another, and thus they are different species of figure. But if we divide triangle, we will find that one of its species is the equilateral and the other is the scalene. Thus it is clear that the equilateral and the scalene are one figure, because they are contained under one species of figure, which is triangle. But they are not one triangle, because they are diverse species of triangle.

             This is similar to what was proposed above. Number is divided into diverse species, one of which is ten. Therefore, all things which are ten are said to have one number, because they do not differ from each other in respect to the species of number, but are contained under one species of number. But it cannot be said that they are the same ten, for the things to which the number ten is applied differ. For some of them are dogs and some horses.

             Aristotle seems to have introduced this lest someone, in upholding the unity of time, be content to say that there is one number of things equal in number, even though they are diverse. For although ten or three is the same because of the unity of the species, nevertheless ten or three is not the same because of the diversity in respect to number from matter. Hence it follows that in respect to its nature [ratio] time is one in species, but not in number. And, therefore, to establish the true unity of time, it is necessary to go back to the unity of the first

motion, which is primarily measured by time, and by which time is also measured.

             Finally he concludes that time and those things which are proper to the consideration of time have been treated.

Book V