LECTURE 3

IN LOCAL MOTION THE MOVER AND THE MOVED MUST BE TOGETHER

             897. Since in the preceding demonstration the Philosopher assumed that the mover is either contiguous or continuous with the mobile object, he intends here to prove this.

             First he proves the proposition. Secondly, where he says, 'All things which are . . .' (Appendix A, 697), he proves a certain thing which he assumes in this proof.

             Concerning the first part he makes two points. First he states his intention. Secondly, where he says, 'Since there are three . . .' (Appendix A, 683), he proves the proposition.

             He says, therefore, first that the mover and the thing moved are together. But a thing is said to move in two ways. First a thing can move as an end moves an agent. A mover of this kind is sometimes at a distance from the agent which it moves. Secondly, a thing can move as that which is the principle of motion moves. It is this kind of mover which he discusses here. And because of this he adds, '. . . not as the cause for the sake of which but as the principle of motion . . .' (Appendix A, 682).

             Further, the mover as the principle of motion is sometimes proximate and sometimes remote. He is speaking here of the proximate mover, and therefore he calls it the first mover. By 'first' he means that which is proximate to the mobile object and not that which is first in the order of movers.

             And since he has said in Book V that those things are together which are in the same place, then when he says that the mover and the moved are together, one might think that, when one body is moved by another, they are both in the same place. Therefore, in order to reject this, he adds that by 'together' he here means not that they are in the same place but that there is no intermediary between the mover and the moved. Thus they are either touching or are continuous since their termini are together or are one.

             And since in the preceding demonstration he has discussed only local motion, one might think that he holds this to be true only of this kind of motion. Therefore in order to reject this, he adds that it is said universally that the mover and the moved are together and not just specifically in regard to local motion. For it is common to every species of motion for the mover and the moved to be together in the manner indicated.

             898. Next where he says, 'Since there are three . . .' (Appendix A, 683), he proves the proposition.

             Concerning this he makes two points. First he enumerates the species of motion. Secondly, where he says, 'Whatever is moved . . .' (Appendix A, 684), he proves the proposition in respect to each type of motion.

             He says, therefore, first that there are three motions: one with respect to place, which is called change of place; another with respect to quality, which is called alteration; another with respect to quantity, which is called increase or decrease. He makes no mention of generation and corruption because these are not motions, as was proven in Book V. But since there are termini of motion, i.e., of alteration, as was considered in Book VI, then when the proposition has been proven in regard to alteration, the same conclusion follows in regard to generation and corruption.

             Therefore, just as there are three species of motion, so there are three species of mobile objects and movers. And in all of these cases it is true to say that the mover and the moved are together, as will be shown for each one of them. But this must first be shown in respect to local motion, which is the first of motions, as will be proven in Book VIII.

             899. Next where he says, 'Whatever is moved . . .' (Appendix A, 684), he proves the proposition in regard to each of the three kinds of motion mentioned above.

             First he treats local motion. Secondly, where he says, 'Neither is there . . .' (Appendix A, 693), he treats alteration. Thirdly, where he says, 'And that which is increased . . .' (Appendix A, 696), he treats increase and decrease.

             Concerning the first part he makes two points. First he proves the proposition in things in which it is more obvious. Secondly, where he says, 'That which is moved . . .' (Appendix A, 685), he proves the proposition in things in which it is more obscure.

             He says, therefore, first that it is necessary to say that everything which is moved in respect to place is moved either by itself or by another. The statement that a thing is moved by itself can be understood in two ways. This can be understood in one way by reason of the parts. Thus he will show in Book VIII that in regard to things which move themselves one part moves and another part is moved. Secondly, a thing can be understood to move itself primarily and per se. For example, the whole itself moves the whole itself. He has proven above that nothing moves itself in this way. If, however, it is conceded that a thing is moved by itself in either way, it is clear that the mover will be in the very thing which is moved, either as the same thing is in its own self, or as a part is in a whole as a soul is in an animal. And so it will follow that the mover and that which is moved are together so that there is nothing intermediate between them.

             900. Next where he says, 'That which is moved . . .' (Appendix A, 685), he shows the same thing with respect to things which are moved in place by another, concerning which it is less obvious.

             Concerning this he makes three points. First he distinguishes the modes in which a thing happens to be moved by another. Secondly, where he says, 'Therefore it is clear . . .' (Appendix A, 690), he reduces these modes to two. Thirdly, where he says, 'This is clear from . . .' (Appendix A, 691), he proves the proposition in regard to these two modes.

             Concerning the first part he makes two points. First he divides the modes in which a thing is moved by another. He says that there are four modes, namely, pushing, pulling, carrying and twirling. For all motions which are from another are reduced to these.

             901. Secondly, where he says, 'Pushing is either . . .' (Appendix A, 686), he explains the four modes mentioned above.

             First he explains pushing, which occurs when the mover by its moving makes a mobile object to be at a distance from the mover. He divides pushing in two, namely pushing on and pushing off. Pushing on is said to occur when the mover so strikes a mobile object that it does not break free of it when driving it on, but tends together with it toward the place to which it leads. Pushing off occurs when the mover so moves the mobile object that it breaks loose from it and does not accompany it up to the end of the motion.

             902. Secondly, where he says, 'Carrying will be . . .' (Appendix A, 687), he explains 'carrying'. He says that carrying is based on the three other motions, namely, pushing, pulling, and twirling, just as that which is per accidens is based on that which is per se. For that which is carried is not moved per se but per accidens insofar as some other thing is moved in which it itself is (as when someone is carried by a boat in which he is), or on which it is (as when one is carried by a horse). However, that which carries is moved per se, because things which are moved per accidens cannot go on to infinity. And so the first carrier must be moved per se by some motion, either by a pushing, or a pulling, or a twirling. From this it is clear that carrying is contained in the three other motions.

             903. Thirdly, where he says, 'Pulling occurs when . . .' (Appendix A, 688), he explains the third mode, namely pulling.

             It should be understood that pulling differs from pushing because in pushing the mover is related to the mobile object as the terminus from which of its motion. But in pulling the mover is related to the mobile object as the terminus to which. That, therefore, is said to pull which moves another toward itself.

             To move something toward one's self with respect to place occurs in three ways.

             This happens first in the way in which an end moves. Hence an end is also said to pull. Thus the poets say, 'Pleasure attracts each man.' In this way it can be said that place pulls that which is naturally moved to a place.

             In another way it can be said that a thing pulls because it moves something toward itself by altering it in some manner, from which alteration it happens that the thing altered is moved with respect to place. In this way a magnet is said to pull iron. For just as a generator moves heavy and light things insofar as he gives them a form through which they are moved to a place, so also a magnet imparts some quality to iron through which the iron is moved toward the magnet.

             And that this is true is evident from three things.

             First a magnet does not pull iron from any distance, but only from nearby. But if iron were moved to a magnet only as to an end, as a heavy thing is moved to its own place, it would tend toward it from any distance.

             Secondly, if a magnet is greased with other things, it cannot attract iron. It is as if these other things either impede the alterative force of the iron or else change it to its contrary.

             Thirdly, in order for a magnet to attract iron, the iron must first be rubbed with the magnet, especially if the magnet is small. It is as if the iron receives some power from the magnet in order to be moved to it. Thus a magnet attracts iron not only as an end, but also as a mover and an alterer.

             In a third way a thing is said to attract something because it moves it toward itself by local motion only. And thus pulling is defined here as one body pulling another such that that which is pulling is moved together with that which is pulled.

             904. He says that pulling occurs when the motion of that which pulls something toward itself or toward another is faster and is not separated from that which is pulled. He says, moreover, 'toward itself or toward another' because a voluntary mover can use another as itself. Hence it can push from another as from itself, and pull toward another as toward itself. But this does not happen in natural motion. For natural pushing is always from the pusher, and natural pulling is toward the puller.

             He adds, moreover, 'when the motion is faster'. For it sometimes happens that that which is pulled is also moved per se to the place to which it is pulled, but it is forced to move by the faster pulling motion. And since the puller moves by its own motion, the motion of the puller must be faster than the natural motion of that which is pulled.

             He also adds, '. . . it is not separated from that which is pulled' in order to distinguish it from pushing. For in pushing, the pusher is sometimes separated from that which it pushes and sometimes it is not. But the puller is never separated from that which it pulls. Rather the puller is moved together with that which is pulled.

             He also explains why he said 'toward itself or toward another'. For in voluntary motions pulling occurs both toward one's self and toward another, as was said.

             905. And since there are certain motions in which the nature [ratio] of pulling is not so manifestly seen, he next shows that these are reduced to the modes of pulling which he has proposed, namely, toward itself and toward another. He says that all other pullings, which are not named pullings, are reduced to these two modes of pulling. For they are the same in species with them to the extent that motions receive their species from their termini. Even these pullings are toward themselves or toward another, as is evident in inhaling and exhaling. For 'inhaling' is a pulling in of air; 'exhaling' is a pushing out of air; and similarly, 'spitting' is an expulsion of spit. And the same can be said of all other motions in which some bodies are taken in or expelled. For an emission is reduced to a pushing, and a receiving to a pulling.

             And similarly 'striking' [spathesis] is a pushing, and 'combing' [kerkisis] is a pulling. For 'spathe' in Greek means either a sword or a spatula. Hence 'spathesis' is the same as 'spathatio', that is, striking with a sword, which occurs by pushing. And therefore the other text which says 'speculation' seems to be corrupt through the fault of the transcriber, because for 'spathatio' he has written 'speculatio'. 'Combing', moreover, is an attraction. In Greek 'kerkis' is a certain instrument which the weavers use. In weaving they draw this instrument toward themselves. In Latin this instrument is called a 'radius'. Hence the other text has 'radiatio'.

             Among these two and other motions of ejecting or receiving, 'combination', which pertains to attraction because a combiner moves something toward another, is different than separation, which pertains to pushing, because pushing is the motion of one thing from another. Therefore it is clear that every local motion is a combination or a separation. For every local motion is either from something or to something. Consequently, it is clear that every local motion is either a pushing or a pulling.

             906. Next where he says, 'Twirling is composed . . .' (Appendix A, 689), he explains what twirling is. He says that twirling is a motion composed of pulling and pushing. For when something is twirled, it is pushed from one side and pulled from another.

             Next where he says, 'Therefore it is clear . . .' (Appendix A, 690), he shows that all of the four motions mentioned above are reduced to pushing and pulling. And the same thing must be said of all of these and of these two. For since carrying consists of the three others, and since twirling is composed of pushing and pulling, it follows that all local motion which is from another is reduced to pushing and pulling. Hence it is clear that if in pushing and pulling the mover and the moved are together, such that the pusher is together with that which is pushed and the puller with that which is pulled, consequently it is universally true that there is nothing intermediate between a mover in respect to place and the moved.

             907. Next where he says, 'This is clear from . . .' (Appendix A, 691), he proves the proposition in regard to these two motions.

             First he gives two arguments to prove the proposition. Secondly, where he says, 'There is throwing . . .' (Appendix A, 692), he refutes an objection.

             The first argument is taken from the definition of each motion. Pushing is a motion from the mover itself or from something else to something else. And so at least at the beginning of the motion the pusher must be together with that which is pushed, until the pusher moves that which is pushed from itself or from another. But pulling is a motion toward one's self or toward another, as was said; and the puller is not separated from that which is pulled. From this it is clear that in these two motions the mover and the moved are together.

             The second argument is taken from combination and separation. It was said that pushing is a separation and pulling is a combination. And he says that 'thus far there is coming together, i.e., combination, and going apart, i.e., division' (Appendix A, 691). Now it is not possible for something to combine or separate unless it is present in those things which are being combined or separated. And so it is clear that in pushing and pulling the mover and the moved are together.

             908. Next where he says, 'There is throwing . . .' (Appendix A, 692), he refutes a certain objection which can be raised concerning pushing. In regard to pulling it was said that the motion of the puller is not separated from that which is pulled. But in regard to pushing it was said that sometimes the pusher withdraws from that which is pushed. And this type of pushing is called pushing away, a species of which is 'throwing', which occurs when a thing is thrown to a distance through violence. And so in throwing it seems that the mover and the moved are not together. Therefore, in order to refute this, he says that throwing occurs when the motion of that which is moved is swifter than its natural motion, and this occurs because some strong pushing has been done. For when something is thrown by a strong impulse, the air is moved by a swifter motion than its natural motion; and the thrown body is carried toward the motion of the air. And as long as the impulse of the air remains, the thrown object is moved. He says that, when such an impulse has been made, a thrown object is carried along as long as there is in the air a motion which is stronger than its natural motion.

             Having removed this difficulty, he concludes that the mover and the moved are together and there is no intermediate between them.