1 I defended the basic thesis of this article at the meeting of the CPA in Halifax in 1981. Jack Macintosh made very useful comments on that occasion. That paper lay asleep in a drawer for several years until Kant's remarks on density (in the Anticipations of Perception) sent me back to it. Andrew Lugg has read several approximations to this final version, and has given me careful and generous comments on them.

2 καὶ καθ' αὑτὸ δὲ σκοποῦσιν φανείη ἄν τὸ λεγόμενον κενὸν ὡς ἀληθῶς κενόν.

3 Friedrich Solmsen, for example, calls Aristotle's treatment of the void a digression. See Aristotle's System of the Physical World (Ithaca: Cornell University Press 1960), 135.

4 Hussey, Edward, Aristotle's Physics, Books III and IV, Clarendon Aristotle Series (Oxford: Oxford University Press 1983)Google Scholar: ‘The discussion of theories of void looks like a not very well-integrated sum of two residues: arguments left over from a criticism of space theories, and arguments left over from a discussion of Atomism’ (xxxvi).

5 Solmsen writes, ‘The gist of Aristotle's arguments against [the void's] existence is simply that it does not fit into his own cosmic system’ (137).

6 Commentators have sought to discover these real reasons. Joseph Moreau thinks the real reason Aristotle rejected the void is that it would have meant that some movements were without cause, undetermined, and that this was repugnant to Aristotle, ; L'Espace et le Temps selon Aristote (Padova: Antenore 1965), 182ffGoogle Scholar. Solmsen writes, ‘His objections are not of a metaphysical or ontological nature; they keep strictly to the sphere of physics. If deeper reasons account for his antipathy to the void, one may surmise that it offended either his aesthetic sense or his religious belief that some degree of perfection must obtain even in the subcelestial regions’ (143). Duhem, Pierre (Système du monde [Paris: Hermann 1913] i, 190-1)Google Scholar thinks that the real reason for Aristotle's rejection of the void is that it would provide for no absolute directions in space, and Aristotle cannot conceive of movement without absolute directions.

7 I speak of the standard views of people with a basic scientific literacy; no doubt more sophisticated reflection on atomism will complicate this commitment considerably. In what follows I shall use the unusual phrase ‘plena-and-void’ instead of the more usual ‘atoms-and-void’ to denote atomism. The reason is that the feature of atoms which will preoccupy me is not their indivisibility - a feature that is variously understood - but the fact that they are all plena, equally, perfectly, and utterly dense.

8 I shall use the phrase ‘continuum theory’ to mean the theory that the world is full, that there are no gaps between one jot of matter and the next. It is not part of this view that there are no sharp boundaries between middle-sized objects or tracts of substance.

9 Of course his viewing the world as a continuum straight forwardly precludes the void. But it only directly precludes one of the three kinds of void. My argument will be that its implications led Aristotle also to preclude the other kinds.

10 213a33ff. The punctuation of the OCT text, as that of most others, must be altered to give sense: οὔτε χωριστόν, οὔτε ἐνεργείᾳ ὄν ὄ διαλαμβάνει τό πᾶν σῶμα ὥστε εἷναι μὴ συνεχές: a merely separable but not actually separate void would not constitute a discontinuity in body. The translation should be: it is not then the existence of air that needs to be proved, but the nonexistence of an extension, different from bodies, whether separable, or actually separate so as to break the continuity of body …. I know of no English translation which has reflected this point.

11 217b21

12 I think that Aristotle has in mind this threefold distinction throughout the chapters on the void, though there has long been thought to be a textual difficulty here. The problem is that Aristotle's labels for these three sorts of void are not settled, and in particular, the (notoriously slippery) word XWlm:6v seems to be used to label different sorts at different places. The labels can be summarized as follows:

13 Aristotle, the Physics, Loeb Classical Library, tr. Wicksteed, Philip H. (Cambridge, MA: Harvard University Press 1958), 364Google Scholar

14 These two different understandings of what Aristotle means by potential void have a history. Wicksteed's interpretation of it as very small but still discrete pockets of void goes back to Philoponus and to Simplicius in the 6th century. But the other view, my view, also has a pedigree. In the 4th century the commentator Themistius, in his In Aristotelis Physics Paraphrasis, ed. Schenkl, H. (Berlin 1900) (vol. 5/2 of the Commentaria in Aristotelem Graeca) 136, 13ff.Google Scholar, expressing the idea of the potential void in Physics, 216a30ff., writes: ‘if the void is not separate, but rather mixed into (ἐγκεκραμένον) and, as one might say, pervading (συγκεχυμένον) rare bodies, then this is less impossible …. ‘A millennium later, Aquinas’ In Octo Libras Physicorum Aristotelis Expositio, ed. Maggiόlo, P.M., O.P. (Rome: Marietti 1954)Google Scholar quite unambiguously interprets the potential void as perfect diffusion(¶ 546): ‘Dicit ergo primo quod illi qui dicunt vacuum esse in corporibus, dupliciter possunt hoc intelligere; uno modo quod in quolibet corpore sint multa quasi foramina vacua, quae sint separata secundum situm ab aliis partibus plenis, sicut est videre in spongia vel in pumice vel in aliquo alio huiusmodi: alia modo quod vacuum non sit separatum secundum situm ab aliis partibus corporis, utpote si dicamus quod dimensiones, quas dicebant esse vacuum, subintrent omnes partes corporis’ (267). I think that Themistius, Aquinas and I have a better interpretation than do Simplicius, Philoponus and Wicksteed, for the following reason. Aristotle says (216b30ff) that the idea of the potential void is less impossible than the idea of the separate void in the rare, but that nonetheless it must be rejected, for two reasons. The first of these is that the void will turn out to be the condition not of all movement but only of movement upwards; but this would not be true of interatomic voids, for they are a condition of all movement: it is the voids in a fluid which (on the atomists’ theory) allow a body to move through it, by allowing the atoms to move out of the way. Only a void which does not break the continuity of body, a void coterminous with body, would fail to be a condition of all movement and so be confined to being a condition of movement upwards, as a lightening agent. Aristotle's first reason for rejecting the idea of this kind of void is incompatible with Simplicius’ and Philoponus’ and Wicksteed's understanding of this kind of void.

15 Newton thought that all the matter in the universe could be compressed into a thimble. Descartes, who identified matter with extension, held that matter was utterly rigid. It seems clear that Aristotle allows the compressibility of matter, even though, as we shall see, he identifies matter with extension; extension for Aristotle is not absolute space, of course, but space dependent on and constituted by bodies.

16 This is made clear by Aristotle at 216b33 ff, and again at de Caelo 313a1 ff. The void is thought of as a sort of lightening agent, like helium in a balloon.

17 217a3. Another joke? The argument is repeated at de Caelo 309b17ff.

18 214b6, 217a10 ff.

19 Kant points this out, in his Critique of Pure Reason, tr. Norman Kemp Smith (London: Macmillan 1929), 206.

20 214a29 ff.

21 The permittivity of a substance is a measure of the degree to which it permits the buildup of electrical charge on the plates of a capacitor when it fills the space between those plates. It is measured in farads per metre. The permittivity of empty space is 8.854 x 10^-12 farads per metre. This seems a nontrivial value. One could adjust the value of the unit of charge in such a way as to give a unit value to the permittivity of empty space, but then another property of empty space, magnetic permeability, would have a nontrivial value. In other words, empty space inescapably has some properties of nontrivial quantity. This argument is taken from Hinckfuss, Ian, The Existence of Space and Time (Oxford: Oxford University Press 1975) Chapter II.CrossRefGoogle Scholar

22 E.g. 208b2 ff.

23 Stocks seems to take it that chapter 8 of Book IV is about this kind of void. See his note to de Caelo 305a21 in his translation of that work (in Volume II of The Works of Aristotle Translated into English, ed. W.O. Ross). But surely all Aristotle's arguments in that chapter are based on the things we do or do not observe in the sublunary sphere.

24 de Caelo 279a12 ff.

25 Ibid. 271b25 ff.

26 Ibid. 305a21 ff.

27 Physics 203b22 ff.

28 Ibid. 208a15 ff.

29 E.g. Physics, 204b20; Metaphysics, 1066b32; de Caelo, 268b6, 274b20, 284b23. Topics 142b25ff. criticizes the definition of body as ‘that which has three dimensions’ for not mentioning the genus; at first glance this might suggest that if the genus were mentioned we might have found the elusive difference between spatial extension and body. But I think that in fact Aristotle has in mind merely the genus ‘figure.'

30 E.g. in the definition of void as place in which there is no body (213b34), or again in his description of a less dense and resistant medium as ἀσωματώτερον, less bodily.

31 E.g. 216b6.

32 E.g. 213a16.

33 E.g. de Caelo, 268a7, Metaphysics, 1020all.

34 E.g. de Gen. et Corr., 321b16.

35 E.g. in the discussion of place as matter in Physics, 2096b20ff.

36 E.g. Metaphysics, 1029a20.

37 E.g. in the elegant argument that if the world were not spherical but rectilinear there would have to be empty space beyond the world: as the world rotates its angular projections would alternately fill a tract of space and leave it empty (de Caelo, 287a15ff.).

38 The concept of mass as quantity of matter, different from weight or volume, was not settled until the work of Aquinas’ disciple Aegidius Romanus in the 13th century. On Aristotle's lack of the concept of mass or quantity of matter, and on its development in mediaeval thought, see Jammer, Max, Concepts of Mass (Cambridge, MA: Harvard University Press 1961) chapters 2 & 4.Google Scholar

39 Insofar as Aristotle has a conservation principle, it must be or turn out to be a principle of conservation of volume. Otherwise, the universe would bulge (as Xuthus said), or it will grow and diminish, so that there must be empty space around its periphery.

40 de Caelo, 310a12

41 216b12ff., 326b20

42 I wonder if this argument lies behind his apparent equation of void with sizeless incorporeal matter in the difficult chapter on growth in the de Gen. et Corr., 1,5. Commentators do not generally take this equation seriously, but it may be seriously meant.

43 ἔστι δὲ πυκνὸν μανοῦ διαφέρον τῷ ἐν ἴσῳ ὄγκῳ πλεῖον ἐνυπάρχειν. Barnes’ revision of the translation keeps the word ‘matter.'

44 I say ‘appears to define’ because the phrase is KEVOV … καὶ σῶμα οὐκ αἰσθητόν, and the question is whether the Kai is epexegetic or not. Most commentators think it is.