Aristotle on the Motion of Projectiles: a Reconsideration
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Ancient Philosophy 38 (2018) ©Mathesis Publications 1 Aristotle on the Motion of Projectiles: A Reconsideration Pantelis Golitsis Aristotle is still credited in several studies dealing mostly with medieval sci - ence with the so-called theory of antiperistasis , by which he allegedly explained the motion of the projectiles. 1 Nonetheless, antiperistasis is the first of two theo - ries to which Aristotle refers with regard to the motion of the projectiles, pass - ingly in Physics iv 8 and more amply in Physics viii 10, where it is actually rejected in favour of the second theory. Several commentators fail to notice the strict analogy between the two passages and wrongly take Aristotle as expound - ing and endorsing just one theory in Physics viii 10, which would be (a refined version of) the theory of antiperistasis . As a result, Aristotle’s account of forced motion has been repeatedly misunderstood. 2 As is well known, according to the Stagirite, the natural elements that consti - tute the universe are either heavy or light or weightless; the heavy elements, i.e., earth and water, naturally move towards the centre, the light elements, i.e., air and fire, naturally move away from the centre, and the weightless element, i.e., the ether that occupies the supralunary region of the universe, naturally moves around the centre. 3 The problem with the projectiles, which are heavy by nature (φύσει ), was not that they do not immediately move downwards, since this was explained as the result of a forced, unnatural ( βίαιος or παρὰ φύσιν) motion pro - vided by the thrower’s hand. The real problem was that the projectile continued to move for some time, while there was no mover to move it. Here is how a histo - rian of science presents the difficulty that Aristotle had to face: Projectile motion posed a…problem for Aristotle. In the case of a thrown object, the force was provided by the hand of the thrower as long as the object was in contact with the hand. But one needed an explanation of why the object continued to move once it had left the thrower’s hand. Aristotle concluded that the medium through which the projectile moved provided the force that kept it moving. This occurred either by antiperis - tasis (replacement), in which the medium rushes around the 1 See, for instance, Gabrovsky 2015, 40: ‘There were many problems with Aristotle’s theory of antiperistasis : in Aristotle’s argument a stone that is thrown moves the air, and the air propels the stone as it fills in the vacuum left behind.’ 2 Various accounts of medieval science treat the theory of antiperistasis as a standard part of a general Aristotelian theory of motion; see, e.g., Grant 1974, 275-280. Nevertheless, medieval thinkers themselves, such as Thomas Aquinas and Jean Buridan, clearly distinguished between the two theo - ries in both passages; cf. Maggiòlo 1965, §1163; Benoît 1996, IV, q. 2, 21-28. 3 For a concise presentation of this theory, see Aristotle On the Heavens i 3. 2 body to prevent the formation of a void or vacuum and pushed the body from behind, or by the medium itself having acquired the power to be a mover from the original projector… The medium itself does not have to move, but rather possesses the power to move something else. This power is, however, imper - fectly transmitted from one layer of the medium to the next and gradually dies away. (Franklin 1998, 251) I would like to revisit the two relevant Aristotelian passages and argue three things: (i) that Aristotle was not heavily concerned by the theory of antiperistasis as such; (ii) that he rejected this theory and proposed a different explanation of the motion of the projectiles, which corresponds to the second of the two expla - nations described above by Allan Franklin but is not fully grasped in his account; and (iii) that Aristotle’s explanation was a preliminary excursus from a larger argument, which sought to establish that there is an eternally continuous motion in the universe, of one thing and due to one thing, namely, the diurnal motion of the outer celestial sphere, a motion that is eternally generated by the First Unmoved Mover. Franklin, presumably following W.D. Ross, correctly specifies that the theory of antiperistasis was in reality not Aristotelian but probably Platonic in origin. 4 Plato does not use this specific term but he explains nonetheless the mechanics of respiration in Timaeus 79a-e as a round pushing ( περιωθεῖν) of air exhaled and inhaled, which goes on without interruption because there can be no void left in the universe. 5 Plato also invites his readers to explain by a similar reasoning, among other phenomena, the motion of the projectiles. 6 It was the Platonist Plutarch (2nd cent. AD) who first undertook the task to expand the teaching of the Timaeus by describing the kind of round motion that keeps the motion of the projectiles, a round motion that he precisely calls antiperistasis : In what sense does Plato say [in the Timaeus ] that, because there is void nowhere, the antiperistasis of motion is the cause of what happens in the case of medical-cupping instruments and in that of swallowing and of weights that are thrown and of flowing waters and of thunderbolts and of the apparent attrac - 4 See Ross 1936, 726. Other scholars trace the origins of the theory back to Empedocles, who also argued from the mutual replacement of bodies that there can be no void in the universe (cf. DK 31 A5); see Taylor 1934, 558, and Barnes 1982, 399-401. I believe, however, that what we see in Empedocles is not an antecedent of the specific theory of antiperistasis but a more general case of antimetastasis (see below). Although pseudo-Aristotle ( MXG 976b22-29 = DK 31 A5) uses the verb περιίστασθαι to explain Empedocles’ doctrine, other doxographers (see DK 31 A35) refer to it more properly with such verbs as μεταλαμβάνειν and ἀντιπαραχωρεῖν, which have the more general mean - ing of changing places (and not of round displacement). 5 See Opsomer 1999. Opsomer rightly speaks of the Platonic ‘concept of periôsis ’. Note, how - ever, that this word, too, does not appear as a technical term in Plato but in Aristotle; cf. Aristotle, On Respiration 472b6: ἡ δ᾽ ἐν τῷ Τιμαίῳ γεγραμμένη περίωσις… 6 Plato, Timaeus 80a1-2: καὶ τὰ τῆς καταπόσεως τά τε τῶν ῥιπτουμένων [sc . αἴτια] , ὅσα ἀφεθέ - ντα μετέωρα καὶ ὅσα ἐπὶ γῆς φέρεται, ταύτῃ διωκτέον. 3 tion to amber and the lodestone and of the consonances of sounds? …Weights that are thrown cleave the air and separate it because of the impact with which they have fallen upon it; and the air because of its nature always to seek out and fill up the space left empty flows around behind and follows along with the object discharged , helping to accelerate its motion. 7 The theory of antiperistasis , therefore, was not considered to be Aristotelian in antiquity. The word antiperistasis , however, is first found in Aristotle, who also uses the related term antimetastasis . Most scholars tend to treat the two terms as synonymous but they are not (see Barnes 1982, 400). On the one hand, antimetastasis relates to the impossibility of having any void left in the universe, since when a body leaves its place, another body immediately occupies the place left. Aristotle uses it as an endoxon in order to establish the existence of place in Physics iv .8 To take Aristotle’s example: when I pour water from a vessel into a bowl, the vessel does not remain void but is instantaneously filled with air; thus, air and water change places ( ἀντιμεθίστανται ). On the other hand, antiperistasis occurs twice in Aristotle’s Physics and is used to refer not to a mere interchange of bodies, which could happen in any direction, but to a round displacement of bodies until the last displaced body occupies the place of the first displaced body. 9 (This is more or less equivalent to the action of periôthein , with which Plato explains the process of respiration: the air, which is heated in the body and thus exhaled, pushes around several portions of air that are outside the body until a freshly inhaled air occupies inside the body the place left by the exhaled air.) Aristotle uses the term antiperistasis in a context that relates specifically to the motion of the projectiles: Moreover, the projectiles move when the thrower is not in con - tact with them either (i) because of antiperistasis , as some say, or (ii) because the air pushed [by the thrower] pushes [the air] 10 7 Plutarch, Platonicae Quaestiones 1004d9-1005a: Πῶς ποτέ φησιν ὁ Πλάτων τὴν ἀντιπερίστα - σιν τῆς κινήσεως διὰ τὸ μηδαμοῦ κενὸν ὑπάρχειν αἰτίαν εἶναι τῶν περὶ τὰς ἰατρικὰς σικύας παθημά - των, καὶ τῶν περὶ τὴν κατάποσιν καὶ τὰ ῥιπτούμενα βάρη καὶ τὰ τῶν ὑδάτων ῥεύματα καὶ κεραυνούς, τήν τε φαινομένην πρὸς ἥλεκτρα καὶ τὴν λίθον τὴν Ἡρακλείαν ὁλκην τάς τε τῶν φθόγγων συμφω - νίας; …Τὰ δὲ ῥιπτούμενα βάρη τὸν ἀέρα σχίζει μετὰ πληγῆς ἐμπεσόντα καὶ διίστησιν· ὁ δὲ περιρ - ρέων ὀπίσω, τῷ φύσιν ἔχειν ἀεὶ τὴν ἐρημουμένην χώραν διώκειν καὶ ἀναπληροῦν συνέπεται τῷ ἀφιεμένῳ τὴν κίνησιν συνεπιταχύνων . Cherniss 1976, 63 trans., which renders antiperistasis by ‘cyclical replacement’. 8 Cf. Phys . iv 1.208b1-8: ὅτι μὲν οὖν ἔστιν ὁ τόπος, δοκεῖ δῆλον εἶναι ἐκ τῆς ἀντιμεταστάσεως· ὅπου γὰρ ἔστι νῦν ὕδωρ, ἐνταῦθα ἐξελθόντος ὥσπερ ἐξ ἀγγείου πάλιν ἀὴρ ἔνεστιν, ὁτὲ δὲ τὸν αὐτὸν τόπον τοῦτον ἄλλο τι τῶν σωμάτων κατέχει· τοῦτο δὴ τῶν ἐγγιγνομένων καὶ μεταβαλλόντων ἕτερον πάντων εἶναι δοκεῖ· ἐν ᾧ γὰρ ἀὴρ ἔστι νῦν, ὕδωρ ἐν τούτῳ πρότερον ἦν, ὥστε δῆλον ὡς ἦν ὁ τόπος τι καὶ ἡ χώρα ἕτερον ἀμφοῖν, εἰς ἣν καὶ ἐξ ἧς μετέβαλον.