Aristotle’s unlimited dunamis argument: an unrecognized proof of the immobility of the prime mover

ABSTRACTAccording to the standard view, the function of the unlimited dunamis argument (Physics VIII.10, Metaphysics Λ.7 1073a5–11) is to introduce a new property of the first immovable mover, namely its lack of magnitude. The paper challenges this view and argues that the argument at issue serves to prove that the eternal motion of the first heavenly sphere is caused by an immovable mover rather than by a moved mover. Further, the paper shows that, at least in Phys. VIII, the unlimited dunamis argument is the main argument for the immobility of the Prime Mover.KEYWORDS: AristotlemetaphysicsPrime Moverunlimited dunamis argument AcknowledgementI am grateful to the anonymous referees for reading the paper and for their useful suggestions.Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 A partial exposition can be found in De caelo I.7 275b21–23, where Aristotle mentions two parts of the unlimited dunamis argument and refers to its Physics VIII.10 full version (ἐν τοῖς πϵρὶ κινήσϵως).2 The argument concerns the Prime Mover but is clearly extendable to all immovable movers that cause motion for an unlimited time. This is confirmed by the fact that, after summarizing the argument in Metaph. Λ.7 1073a5–11, in Metaph. Λ.8 1073a38 Aristotle attributes the lack of magnitude to all heavenly immovable movers. Of course, the scholars who (like e.g. Ross, Aristotle’s Physics, 101–2) think that, when writing the Physics, Aristotle had not yet theorized the existence of a plurality of heavenly immovable movers (and that therefore maintain that passages such as 259b28–31 are later additions) would claim that the target of the unlimited dunamis argument, in its first formulation, is the Prime Mover alone.3 In Phys. VIII.10 and Metaph. Λ.7 Aristotle understands these three properties (lack of parts, lack of magnitude, and indivisibility) as equivalent to each other, since by “parts” he means the parts into which a magnitude can be divided (for this meaning, see Metaph. Δ.13 1020a7–14, V.25 1023b12–17, Phys. VI.10 240b12–13). Further, when he claims that the mover of an eternal motion lacks parts and magnitude, he means that it is such both by itself and by accident. This is shown by the fact that he conceives the mover as a subject (i.e. the subject of a dunamis, which is the form whereby a mover causes motion: see below note 21) and that one of the hypotheses about the Prime Mover’s position is the geometrical centre of the first sphere (267b6–7), namely a point. This excludes that he understands the lack of magnitude as only per se.4 Against the traditional interpretation, Lang maintains that this argument concerns the position of the primary eternal motion, not that of the first immovable mover (Lang, Aristotle’s Immaterial Mover). For a criticism (successful in my view) of Lang’s proposal, see Judson, Heavenly Motion, 168 note 48.5 Here I focus on modern scholarship. On the Neoplatonic interpretation and use of the unlimited dunamis argument, see Sorabji, Infinite Power Impressed.6 As the title of his article shows, Solmsen includes the argument about the position of the Prime Mover among what he considers some “Misplaced passages at the end of Aristotle’s Physics” (Solmsen, Misplaced Passages).7 See Judson, Heavenly Motion, 169–71, and Aristotle. Metaphysics Book Λ, 193–4, who maintains that the unlimited dunamis argument is incompatible with the immobility of the Prime Mover, on the grounds that it requires that the Prime Mover causes motion by expending, and so, losing energy (i.e. dunamis) – which implies that it changes (i.e. it is not immovable). I shall come back to this point of Judson’s interpretation in note 51.8 In Phys. VIII.5 Aristotle formulates two arguments to prove that not all movers are moved: the first at 256a4–b3 (the so-called ‘infinite regress argument’) and the second at 256b3–257a27. Then, in Phys. VIII.6 he argues for the existence of a numerically unitary motion that goes on for an unlimited time. He also states that this motion is caused by an eternal immovable mover but does not provide any argument for this latter claim ­– which suggests that he implicitly grounds it on the results of the two Phys. VIII.5 arguments.9 On the distinction between immovable movers and moved movers, and between immovable movers and affections such as the hot, see De generatione et corruptione I.7 324b4–22.10 On the above-mentioned De motu animalium 9 passage, see Gregoric, The Origin, 425. Of course, as the city analogy of De motu animalium 10 shows, the point-like nature of the soul is fully compatible with the fact that it is the form of the whole ensouled body.11 See above note 3.12 Phys. VIII.7 260a20–21. On this point, see Section 2 below.13 The situation of Metaph. Λ is more complicated and I shall not cover it here. The main difficulty is given by the fact that, according to Aristotle's own statements (1071b3–5), the demonstration of the existence of an eternal and immovable substance should be found in chapter 6, but until now interpreters have not been able to identify in this chapter an argument for the immobility of the Prime Mover.14 διωρισμένων δὲ τούτων φανϵρὸν ὅτι ἀδύνατον τὸ πρῶτον κινοῦν καὶ ἀκίνητον ἔχϵιν τι μέγϵθος. ϵἰ γὰρ μέγϵθος ἔχϵι, ἀνάγκη ἤτοι πϵπϵρασμένον αὐτὸ ϵἶναι ἢ ἄπϵιρον. ἄπϵιρον μὲν οὖν ὅτι οὐκ ἐνδέχϵται μέγϵθος ϵἶναι, δέδϵικται πρότϵρον ἐν τοῖς φυσικοῖς· ὅτι δὲ τὸ πϵπϵρασμένον ἀδύνατον ἔχϵιν δύναμιν ἄπϵιρον καὶ ὅτι ἀδύνατον ὑπὸ πϵπϵρασμένου κινϵῖσθαί τι ἄπϵιρον χρόνον, δέδϵικται νῦν. τὸ δέ γϵ πρῶτον κινοῦν ἀΐδιον κινϵῖ κίνησιν καὶ ἄπϵιρον χρόνον. φανϵρὸν τοίνυν ὅτι ἀδιαίρϵτόν ἐστι καὶ ἀμϵρὲς καὶ οὐδὲν ἔχον μέγϵθος.15 δέδϵικται δὲ καὶ ὅτι μέγϵθος οὐδὲν ἔχϵιν ἐνδέχϵται ταύτην τὴν οὐσίαν ἀλλ' ἀμϵρὴς καὶ ἀδιαίρϵτός ἐστιν (κινϵῖ γὰρ τὸν ἄπϵιρον χρόνον, οὐδὲν δ' ἔχϵι δύναμιν ἄπϵιρον πϵπϵρασμένον· ἐπϵὶ δὲ πᾶν μέγϵθος ἢ ἄπϵιρον ἢ πϵπϵρασμένον, πϵπϵρασμένον μὲν διὰ τοῦτο οὐκ ἂν ἔχοι μέγϵθος, ἄπϵιρον δ' ὅτι ὅλως οὐκ ἔστιν οὐδὲν ἄπϵιρον μέγϵθος)·16 According to some scholars (e.g. Ross, Aristotle’s Physics, 721–2; Solmsen, Misplaced Passages, 271 and n. 9; Judson, Heavenly Motion, 169–70, and Aristotle. Metaphysics Book Λ, 193–4), this premise is the conclusion of the second of the three sub-arguments of Phys. 8.10 that Aristotle presents as preliminary (266a24–b6). The first (266a12–24) would instead be aimed at demonstrating a different thesis, which does not involve the notion of dunamis, i.e. that a limited magnitude cannot cause an unlimited motion. This interpretation, however, is incompatible with the fact that, at 266a24–26, Aristotle introduces the second sub-argument as a generalization of the first and that, at 266b25–26, he presents the two sub-arguments as having one and the same conclusion. Further, it is very unlikely that the first sub-argument does not implicitly use the notion of dunamis, because according to Aristotle's physics it is not the variation in magnitude of a mover that determines a variation in duration (or speed) of the movement it causes, but the variation in quantity of the mover’s dunamis, which is directly proportional to the magnitude of the body to which it belongs (see e.g. Phys. VII.5; on Aristotle’s employment of proportionality principles, see Gregory, Aristotle, Dynamics, and note 21 below). Therefore, to say that 'a limited magnitude cannot cause an unlimited motion' is equivalent to saying that 'a limited magnitude cannot cause an unlimited motion because it cannot have an unlimited dunamis', i.e. is equivalent to saying what is expressed by premise 4 above.17 On the dunamis as the form or entelecheia whereby a mover causes motion, see e.g. Metaph. Θ.1 1046a9–13, 26–28. The (accidental) quantification of the dunamis is based on a principle of proportionality between the amount of dunamis and the magnitude of the body the dunamis is a dunamis of (as well as either the minimum or the maximum time of the motion) that Aristotle employs in various passages of his physical investigation (see, e.g. Phys. VII.5) including Phys. VIII.10 (see e.g. 266a26–28, 266b7–8). On this principle of proportionality, see e.g. Gregory, Aristotle. Dynamics.18 This is because, according to Aristotle, the body is that which is per se movable (see e.g. Phys. IV.4 211a17–23).19 Phys. VII.2 243a16–17, b16–17, 244a2–4; Phys. VII.10 267b12.20 This strongly suggests, against the standard interpretation, that the unlimited dunamis argument does not presuppose the immobility of the Prime Mover. If the immobility of the Prime Mover were presupposed, there would be no reason to argue against the hypothesis that an eternal motion can be caused by a bodily mover, i.e. by a moved mover.21 This is because, according to Aristotle, everything that is in motion is moved by something (see e.g. Phys. VIII.4).22 Aristotle does not consider the hypothesis that an eternally rotating sphere is moved by a self-mover, like for instance the traditional Atlas. Arguably, this is because in Phys. VIII.6 he has already established that this kind of self-mover cannot cause motion for an unlimited time (259b20–22). Further, claiming that an eternally rotating sphere is moved by a self-mover (on the assumption that a self-mover is able to cause motion for an unlimited time) would amount to claiming that its first mover is an immovable mover, since a self-mover is such because it is moved by an internal immovable mover.23 ὅτι μὲν οὖν οὐκ ἐνδέχϵται ἄπϵιρον ϵἶναι δύναμιν ἐν πϵπϵρασμένῳ μϵγέθϵι […] ἐκ τούτων δῆλον.24 The latter point is accomplished in the section on the motion of projectiles (266b27–267a20; see e.g. Menn, Aristotle’s Theology, 440; Falcon, The Argument of Physics VIII, 281). Later, at 267b9–17, Aristotle also excludes the hypothesis that an eternal motion can be caused by a single bodily mover that moves by pushing and/or pulling repeatedly. Both options (i.e. the pushing and/or pulling by one or several movers) are excluded for the same reason: they would compromise the unity of the motion.25 ἐπϵὶ δ' ἐν τοῖς οὖσιν ἀνάγκη κίνησιν ϵἶναι συνϵχῆ, αὕτη δὲ μία ἐστίν, ἀνάγκη δὲ τὴν μίαν μϵγέθους τέ τινος ϵἶναι (οὐ γὰρ κινϵῖται τὸ ἀμέγϵθϵς) καὶ ἑνὸς καὶ ὑφ' ἑνός (οὐ γὰρ ἔσται συνϵχής, ἀλλ' ἐχομένη ἑτέρα ἑτέρας καὶ διῃρημένη), τὸ δὴ κινοῦν ϵἰ ἕν, ἢ κινούμϵνον κινϵῖ ἢ ἀκίνητον ὄν. ϵἰ μὲν δὴ κινούμϵνον, συνακολουθϵῖν δϵήσϵι καὶ μϵταβάλλϵιν αὐτό, ἅμα δὲ κινϵῖσθαι ὑπό τινος, ὥστϵ στήσϵται καὶ ἥξϵι ϵἰς τὸ κινϵῖσθαι ὑπὸ ἀκινήτου.26 See e.g. Simplicius In PH. 1353, 4–7; Ross, Aristotle’s Physics, 727; Solmsen, Misplaced Passages, 274; Lang, Aristotle’s Immaterial Mover, 331; Graham, Aristotle. Physics Book VIII, 177; Blyth, Aristotle’s Ever-Turning World, 344.27 See Phys. VIII.5 256a16–17, 26–29: ϵἰς ἄπϵιρον ἰέναι.28 To my knowledge, Solmsen, Misplaced Passages, 274–5 is the only scholar who stresses that the section of Phys. VIII.10 from 267a21 to 267b9 contains an argument for the immobility of the Prime Mover. He maintains, however, that this section is out of place and that it has nothing to do with the unlimited dunamis argument. Further, he speculates that it was put where we find it by an editor inspired by Eudemus’ work.29 Note that the property of not moving itself per accidens holds not only for the Prime Mover but for all other heavenly immovable movers, too. The difference between the Prime Mover and the other heavenly immovable movers is that the former, unlike the latter, is not moved per accidens by something else either (259b28–31).30 ἐξ ὧν ἔστιν πιστϵῦσαι ὅτι ϵἴ τί ἐστι τῶν ἀκινήτων μὲν κινούντων δὲ καὶ αὑτὰ κατὰ συμβϵβηκός, ἀδύνατον συνϵχῆ κίνησιν κινϵῖν. ὥστ' ϵἴπϵρ ἀνάγκη συνϵχῶς ϵἶναι κίνησιν, ϵἶναί τι δϵῖ τὸ πρῶτον κινοῦν ἀκίνητον καὶ κατὰ συμβϵβηκός.31 In T6 Aristotle does not claim overtly that the motion of the first sphere is uniform (ὁμοία, ὁμαλής). However, the hypothesis that T6 tackles this point is suggested by the parallelism between it and De gneneratione et corruptione II.10 336a29–b10 (as well as Phys. VIII.10 267b2–6) where such a claim is explicit.32 τὸ μὲν γὰρ ἀκίνητον [τὴν αὐτὴν] ἀϵὶ τὸν αὐτὸν κινήσϵι τρόπον καὶ μίαν κίνησιν, ἅτϵ οὐδὲν αὐτὸ μϵταβάλλον πρὸς τὸ κινούμϵνον. τὸ δὲ κινούμϵνον ὑπὸ τοῦ κινουμένου μέν, ὑπὸ τοῦ ἀκινήτου δὲ κινουμένου ἤδη, διὰ τὸ ἄλλως καὶ ἄλλως ἔχϵιν πρὸς τὰ πράγματα, οὐ τῆς αὐτῆς ἔσται κινήσϵως αἴτιον, ἀλλὰ διὰ τὸ ἐν ἐναντίοις ϵἶναι τόποις ἢ ϵἴδϵσιν ἐναντίως παρέξϵται κινούμϵνον ἕκαστον τῶν ἄλλων, καὶ ὁτὲ μὲν ἠρϵμοῦν ὁτὲ δὲ κινούμϵνον.33 (1) τοῦτο γὰρ οὐκ ἀνάγκη συμμϵταβάλλϵιν, ἀλλ' ἀϵί τϵ δυνήσϵται κινϵῖν (ἄπονον γὰρ τὸ οὕτω κινϵῖν) (2) καὶ ὁμαλὴς αὕτη ἡ κίνησις ἢ μόνη ἢ μάλιστα· οὐ γὰρ ἔχϵι μϵταβολὴν τὸ κινοῦν οὐδϵμίαν. (3) δϵῖ δὲ οὐδὲ τὸ κινούμϵνον πρὸς ἐκϵῖνο ἔχϵιν μϵταβολήν, ἵνα ὁμοία ᾖ ἡ κίνησις34 On this point, see Bodnar, Movers, 112 and note 53.35 According to this interpretation, lines 267b2–3 should be paraphrased as follows: it is not necessary for an immovable mover to be moved together with what it moves (i.e. to be moved by itself per accidens) and, if an immovable mover is not moved together with what it moves, it will move for an unlimited time (for moving in this way is effortless). Note that Aristotle uses the clause “it is not necessary that” also in Phys. VIII.6 258b24–26 to distinguish between the movers endowed with magnitude (i.e. the moved movers) and those devoid of magnitude (i.e. the immovable movers).36 In Phys. VIII.10, after T7, Aristotle goes on arguing that the Prime Mover must be in the circumference of the first sphere (267b6–9). Here I shall not tackle the issue of how this claim is related to the Phys. VIII.6 thesis that the Prime Mover is not moved per accidens by itself.37 τὰ μὲν ὑπὸ ἀκινήτου κινϵῖται ἀϊδίου, διὸ ἀϵὶ κινϵῖται, τὰ δ' ὑπὸ κινουμένου καὶ μϵταβάλλοντος, ὥστϵ καὶ αὐτὰ ἀναγκαῖον μϵταβάλλϵιν. τὸ δ' ἀκίνητον, ὥσπϵρ ϵἴρηται, ἅτϵ ἁπλῶς καὶ ὡσαύτως καὶ ἐν τῷ αὐτῷ διαμένον, μίαν καὶ ἁπλῆν κινήσϵι κίνησιν.38 See above note 10.39 Οὐ μὴν ἀλλὰ καὶ ἄλλην ποιησαμένοις ἀρχὴν μᾶλλον ἔσται πϵρὶ τούτων φανϵρόν.40 It is worth noting that, in Metaph. Λ.6 1071b36–37, Aristotle underlies the necessity to apply this methodological principle when dealing with the arche of everything and criticizes Plato for not having investigated circular motion sufficiently.41 Note that in Phys. VIII.6 (at 259b28–31) Aristotle already presupposes that the eternal and numerically unitary motion whose existence he argued for is the circular motion of the heavenly spheres.42 σκϵπτέον γὰρ πότϵρον ἐνδέχϵταί τινα κίνησιν ϵἶναι συνϵχῆ ἢ οὔ, καὶ ϵἰ ἐνδέχϵται, τίς αὕτη, καὶ τίς πρώτη τῶν κινήσϵων·43 In Phys. VIII.8 Aristotle argues that all sublunar motions (i.e. all non-local motions and all local rectilinear ones) are temporally limited.44 For instance, concerning the first argument of Phys. VIII.5 (256a4–b3), i.e. the so-called ‘infinite regress argument’, given that an infinite regress is not necessarily fallacious, it is unclear on what grounds and in what sense Aristotle refuses unlimited causal chains of moved movers.45 Concerning Metaphysics Λ, see above note 17.46 As already mentioned (see above note 9), Judson, Heavenly Motion, 169–71, and Aristotle. Metaphysics Book Λ, 193–4, maintains that the unlimited dunamis argument is incompatible with the immobility of the Prime Mover, on the grounds that it requires that the Prime Mover causes motion by expending, and so, losing energy (i.e. dunamis). More generally, according to Judson, no immovable mover causes motion thanks to a dunamis, since causing motion in this way (i.e. qua ‘energetic efficient cause’) means changing (i.e. expending and losing dunamis or energy). This interpretation, however, neglects the fact that it is a general thesis of Aristotle’s physics that a mover causes motion thanks to a dunamis (see above note 21). Further, the decrease or loss of dunamis only applies to moved movers, as it is due to the simultaneous and inverse action of the moved on the mover (Phys. III.1.201a19–27): e.g. when a hot body heats a cold one, the mover’s dunamis (i.e. its heat) decreases progressively because the mover is cooled progressively by the moved. This means that, if a mover is immovable (i.e. is not moved by anything, not even by the body it moves), it does not lose dunamis (when it causes motion). Arguably, the quantification of the dunamis of the Prime Mover (i.e. its unlimitedness) must be understood in a different sense than the quantification of the dunamis of a moved mover (on Aristotle’s application in Phys. VIII of physical concepts to a metaphysical entity and their consequent modification, see Quarantotto, From Physics to Metaphysics). In the latter case, the dunamis is quantified (by accident) on the basis of the magnitude of the mover and the duration of the process, whereas in the former case it can only be quantified on the basis of the duration of the process (for the Prime Mover has no magnitude). According this interpretation, claiming that the Prime Mover has an unlimited dunamis amounts to claiming that it is in actuality (and, therefore, causes motion) for an unlimited time. Clearly, this point requires further development. I shall come back to it in a future work.