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Aristotle's Theory of ΤΟΠΟΣ

Published online by Cambridge University Press:  11 February 2009

H. R. King
H. R. King
Affiliation:
Christ Church, Oxford
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Extract

Diogenes Laertius relates the tale that Aristotle, upon being reproached for giving alms to a debased fellow, replied, ‘It was not his character, but the man, that I pitied.’ Some such reply is equally apt in apology for a paper paying homage to an idea long discredited in the philosophical world, Aristotle's theory of Place. I have been moved, not indeed by the apparent character of Aristotle's theory, for that is easily reproached, but by what has proved for the philosophical tradition of infinite worth, what we may call the theory's ‘latent virtue’. There is a danger, of course, as hard-headed philologists and commentators are always reminding us, that in attending to this latent virtue we may be paying sentimental homage to the dead. Thus it will be important that we first carefully and coldly examine the overt character of the Aristotelian doctrine before attempting to justify any philosophical compassion felt in its presence. More than likely in such a disinterested inquiry it will be found that our ‘debased fellow’ is a good deal more of a man than the modern reformers have allowed.

Type
Research Article
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The Classical Quarterly , Volume 44 , Issue 1-2 , January 1950 , pp. 76 - 96
Copyright
Copyright © The Classical Association 1950

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References

page 76 note 1 Diogenes Laertius 5. 17: see Loeb Library edition, Hicks, R. D., Diogenes Laertius, Lives of Eminent Philosophers, vol. i, p. 460Google Scholar: ⋯νειδιζ⋯μεν⋯ς ποτε ὅτι πονηρῷ ⋯νθρώπῳ ⋯λεημοσ⋯νην ἔδωκεν, “οὐ τ⋯ν τρ⋯πον”, εἶπεν, “⋯λλ⋯ τ⋯ν ἄνθρωπον ἠλ⋯ησα”. Laertius gives a second and clearer but less elegant version of the anecdote (ibid., p. 462): πρ⋯ς τ⋯ν αἰτιασ⋯μενον ὡς εἴη μ⋯ ⋯γαθῷ ἔρανον δεδωκώς—ϕ⋯ρεται γ⋯ρ κα⋯ οὕτως—“οὐ τῷ ⋯νθρώπῳ”, ϕησ⋯ν, “ἔδωκα, ⋯λλ⋯ τῷ ⋯νθρωπ⋯νῳ”.

page 76 note 2 By far the best and most extensive study of the history and development of the theory of Place will be found in the Revue de Philosophie, vol. xi (12 1907)–vol. xiv (May 1909)Google Scholar, sixteen articles published under the title, ‘Le mouvement absolu et le mouvement relatif’ by Pierre Duhem. With some omissions and addition, the substance of these articles was later included in his Le Système du Monde: Histoire des doctrines cosmologiques de Platon à Copernic, 5 vols. (Paris, 1913–1917)Google Scholar.

page 76 note 3 Mathematics, apart from arithmetic and geometry, is complicated for Aristotle by what he calls the ‘more physical’ branches (τ⋯ ϕνσικώτερα τ⋯ν μαθημ⋯των), optics, harmonics, and astronomy. Thus, he says (Physics 194a9–12), ⋯ μ⋯ν γ⋯ρ γεωμετρ⋯α περ⋯ γραμμ⋯ς ϕυ;σικ⋯ς σκοπεῖ, ⋯λλ' οὐχ ᾗ ϕυσικ⋯, ⋯ δ' ⋯πτικ⋯ μαθηματικ⋯ν μ⋯ν γραμα⋯ν, ⋯λλ' οὐχ ᾗ μαθηματικ⋯ ⋯λλ' ᾗ ϕνσικ⋯. This means, of course, that for some mathematical sciences the subject-matter will be ‘inseparable’ even for thought.

page 76 note 4 Cf. Metaphysics 1064a32–3.

page 77 note 1 Physics 193b24–35; De Caelo 299a15 ff.; De Anima 403b14 ff.; cf. Metaphysics 1061b21–6: ⋯ μαθηματικ⋯ δ' ⋯πολαβο⋯σα περ⋯ τι μ⋯ρος τ⋯ς οἰκε⋯ας ὕλης ποιεῖται τ⋯ν θεωρ⋯αν οἷον περ⋯ γραμμ⋯ς ἢ γων⋯ας ἢ ⋯ριθμοὺς ἢ τŵν λοιπŵν τι ποσŵν, οὐχ ᾗ δ' ⋯ντα ⋯λλ' ᾗ σννεχῢς αὐτŵν ἕκαστον ⋯ϕ' ἕν ἢ δ⋯ο ἢ τρ⋯α, and ibid. 1061a28–36: ⋯ μαθηματικ⋯ς περ⋯ τ⋯ ⋯ξ ⋯ϕαιρρ⋯σεως τ⋯ν θεωρ⋯αν ποιεῖται … π⋯ π⋯θη τ⋯ το⋯των ᾗ ποσ⋯ ⋯στι κα⋯ σννεχ⋯, κα⋯ οὐ καθ' ἔτερ⋯ν τι θεωρεῖ, κα⋯ τŵν μ⋯ν τ⋯ς ἄλληλα θ⋯σεις.… Thus the mathematician has no concern for what is the ontological status of the elements whose formal properties he is investigating. In this sense, in Bertrand Russell's well-known phrase, ‘Mathematics is the science in which we do not know what we are talking about, and do not care whether what we say about it is true.’

page 77 note 2 Aristotle's use of χώρα was one familiar enough to Greek philosophy; it connoted a receptive δι⋯στημα, or locus of hypostasized extension within which bodies were placed. Cf. Stoicorum Veterum Fragmenta, ed. Arnim, Ioannes ab (Lipsiae, 1905), vol. i, No. 95, p. 26Google Scholar: Ζ⋯νων κα⋯ οἱ ⋯π' αὐτο⋯ ἄντ⋯ς μ⋯ν το⋯ κ⋯σμον μηδ⋯ν εἶναι κεν⋯ν, ἔξω ω' αὐτο⋯ ἄπειρον … διαϕ⋯ρειν [δ⋯] κεν⋯ν, τ⋯πον, χώραν κα⋯ τ⋯ μ⋯ν κεν⋯ν εἶναι ⋯ρημ⋯αν σώματος, τ⋯ν δ⋯ τ⋯πον τ⋯ ⋯πεχ⋯μενον ὑπ⋯ σώματος, τ⋯ν δ⋯ χώραν τ⋯ ⋯κ μ⋯ρονς ⋯πεχ⋯μενον. Cf. Aristotle's remark (Physics 209b15) that Plato identified χώρα and τ⋯πος, and see Timaeus 52. Duhem, (Le Système du Monde, vol. i, pp. 189–91)Google Scholar notes that “χώρα” had come to connote something ‘semblable aux figures dont raisonne le mathématicien’.

page 77 note 3 Physics 208b26–7.

page 77 note 4 Cf. ibid. 216b3–5: μ⋯γεθος … ὂ εἰ κα⋯ θερμ⋯ν ἤ ψνχρ⋯ν ⋯στιν ἤ κο⋯ϕον, οὐδ⋯ν ἧττον ἕτερον τῷ εἶναι π⋯ντων τŵν παθην⋯των ⋯στ⋯, κα⋯ εἰ μ⋯ χωριστ⋯ν λ⋯γω δ⋯ τ⋯ν ⋯γκον. Cf. De Gen. et Corr. 326b19–21.

page 78 note 1 Cf. Physics 208a27 ff., with ibid. 193b22 ff.

page 78 note 2 Cf. ibid. 211a12–13; 214a21 ff.

page 78 note 3 Ibid. 208b1–2; cf. Simplicius, 631. 1–6 (references to Simplicius will always be to his Commentaria on the Physics edited by Diels, H., Berlin, 1882)Google Scholar.

page 78 note 4 Physics 208b3–5.

page 78 note 5 Ibid. 214a24–5.

page 78 note 6 Newton's Principle, Cajori, Florian (a revision of Motte's, trans., 1946, Univ. of Calif.), in the Scholium, pp. 6–12Google Scholar. It is interesting to note that Locke supposed the possibility of motion necessitated a void. Cf. his Essay, bk. ii, ch. xiii, § 23.

page 78 note 7 Physics 211a20–33.

page 78 note 8 Ibid. 212a5–6.

page 79 note 1 Physics 211b11–14; cf. 209b1–4.

page 79 note 2 Physics 212a31–2.

page 79 note 3 Ibid. 212b12–22: ⋯ δ' οὐραν⋯ς οὐκ⋯τι ⋯ν ἄλλῳ.

page 79 note 4 Ibid. 204b5–7.

page 79 note 5 Ibid. 205b24–5.

page 79 note 6 Ibid. 205b35–206a2.

page 79 note 7 Ibid. 206a2–3.

page 79 note 8 Ibid. 207a13 ff.

page 79 note 9 Ibid. 207a7–8; cf. 207a1–2: σνμβα⋯νει δ⋯ τοὐναντ⋯ον εἶναι ἄπειρον ἢ ὡς λ⋯γουσιν, οὐ γ⋯ρ οὗ μηδ⋯ν ἔξω, ⋯λλ' οὗ ⋯ε⋯ τι ἔξω ⋯στ⋯, το⋯το ἄπειρ⋯ρ ⋯στιν. Aristotle's amusing reference is to the Stoics who said that though the void was outside the οὐραν⋯ς, there was nothing beyond this infinite void. Cf. Doxographi Graeci, Diels, H. (Berol., 1879), p. 460, 25Google Scholar; or Ioannis Stobaei Eclogarum Physicarum et Ethicarum, ed. Meineke, A., vol. i (Lipsiae, 1860), p. 107, 31 ff.Google Scholar; p. 103, 13 ff.

page 80 note 1 Physics 212b14–18: cf. De Caelo 279a11 ff. The precise meaning of the word οὐραν⋯ς, like many words Aristotle uses, must often be divined from the context. The word has three general senses, which he gives in the De Caelo 278b10–21: (i) οὐραν⋯ν λ⋯γομεν τ⋯ν οὐσ⋯αν τ⋯ τ⋯ς ⋯σχ⋯της το⋯ παντ⋯ς περιϕορ⋯ς, (ii) τ⋯ συνεχ⋯ς σ⋯μα τῇ ⋯σχ⋯τῃ περιϕορᾷ το⋯ παντ⋯ς, ⋯ν ᾧ σελ⋯νη κα⋯ ἥλιος κα⋯ ἔνια τ⋯ν ἄστρων, (iii) τ⋯ περιεχ⋯μενον σ⋯μα ὑπ⋯ τ⋯ς ⋯σχ⋯της περιϕορ⋯ς· τ⋯ ⋯λον κα⋯ τ⋯ π⋯ν. … The confusion of meaning (i) with (iii) complicated unnecessarily the problem of the motion of the outer sphere for the tradition. The heaven (the all) is not in place essentially (Physics 212b7 ff.), for non-entity is no container. However, the heaven (the all) is in place accidentally, since all of its parts are in place (ibid. 212b13). But the heaven (the outer sphere) is a part of the whole; therefore the outer sphere is in place, even though nothing contains it; but having nothing outside it, its only motion can be rotation (ibid. 212b14), not translation, a rotation consisting in a successive change of relation of its parts to the contained bodies, since it is in place in virtue of its relation to that contained.

The commentators, who stuck to the letter of Aristotle's definition of Place, asked how the heaven (the outer orb) could move (rotate) since, if nothing contained it, it was not in place, and all motion was reducible to locomotion (Simplicius, 601. 25 ff.; Philoponus, 564–5; all references to Philoponus will be to the Berlin edition by Vitelli, H. (1898) of the commentary to the PhysicsGoogle Scholar). The problem remained in the tradition until the Copernican revolution, but became one of finding what it was, relative to which the outer sphere was in place. Averroes rightly recognized that the rotation of the outer sphere assumed an immovable centre, the earth, and so said that the sphere was placed in reference to the earth. But to unimaginative minds this meant that the earth was at rest relative to some absolute Space within which the heavens rotated. Thus Richard of Middleton would argue that God might well extend this Space beyond the world and so translate the whole heavens. Bacon recognized, in his excellent Communia naturalium, that, on Aristotle's assumptions, the immobility of the earth meant simply the maintenance of a constant relation of situation to the sphere as a whole while the parts composing the whole were successively changing their rapport with that centre. It would be equally meaningful to say that the earth rotates as that the outer sphere rotates, since there was nothing apart from the whole with which to relate the changing of rapport. (I cannot agree with Duhem in thinking that Bacon merely restated Averroes' notion of an immovable centre.)

Aquinas followed the solution of Themistius (see the latter's In Arist. Phys. Paraphrasis, ed. Schenkl, H., Berol. 1900, pp. 120–1Google Scholar) in the following interpretation (Aquinatis, Thomae, Opera Omnia, ii, Comm. in Phys. Arist. (Leonine, ed., Rome, 1884), pp. 166–9Google Scholar, Synopsis): ‘ultima sphaera est in loco per suas partes. … In motu autem recto totum unum corpus dimittit unum locum, et in ipsum totum aliud corpus subintrat; corpus ergo quod hoc modo movetur, est in loco secundum se totum. Sed in motu circulari non totum corpus mutat locum subiecto, sed ratione tantum; partes autem mutant locum et ratione et subiecto. Ergo corpori circulariter moto debetur locus non secundum totum, sed secundum partes.’ None the less, Bacon's rapport between the sphere and the earth is necessary in order to place the parts; and it is not sufficient to say, as does Aquinas, that the parts are potentially in place as parts of one continuous sphere.

page 80 note 2 Physics 212b9–15.

page 81 note 1 Physics 207a13–15.

page 81 note 2 Ibid. 207a30 f.; cf. also Aristotle's arguments that the admission of an infinite Universe would make ‘nature’ impossible, De Caelo, bk. i, chs. 2–7.

page 81 note 3 Physics 207b15–21.

page 81 note 4 Ibid. 208a11–13.

page 81 note 5 It is significant, however, that science has reintroduced a finite Universe.

page 81 note 6 De Caelo 279a10–22.

page 81 note 7 Cf. SirRoss, David, Arist. Physics, pp. 7–8Google Scholar.

page 81 note 8 Hardie and Gaye, in the Oxford translation, write ‘in contact’ for τ⋯ ἄπτεσθαι and ‘contiguous’ for τ⋯ ⋯χ⋯μενον. These translations have helped to give the impression, which I shall contest below, that Aristotle calls continuity a species of touching things, and for this reason I have abandoned them. I have introduced the rather artificial word ‘togetherness’ in order to emphasize the affinity of ⋯χ⋯μενον with ἅμα rather than with ἅπτεσθαι the reason for this should become clear in the sequel.

page 82 note 1 Physics 227a17 ff.; 227a29 f.

page 82 note 2 Ibid. 226b34 ff.; 227a18, 29 f.

page 82 note 3 If it be objected that houses are bodies and can be ⋯ϕεξ⋯ς (no other house between) and yet not be touching, it must be replied that houses as such (definitions) can not be ⋯χ⋯μενα; houses can touch, or be ⋯χ⋯μενα only qua body, and qua body, if ⋯ϕεξ⋯ς, they are ἄμα. Otherwise, to admit the objection, one must admit its converse, that two bodies, e.g. a house and a barn, may touch and yet not be ⋯ϕεξ⋯ς because not ⋯μογεν⋯; and this contradicts 227a18: τ⋯ μ⋯ν γ⋯ρ ⋯πτ⋯μενον ⋯ϕεξ⋯ς ⋯ν⋯γκη εἶναι.

But perhaps I have been ‘over-subtle’ in this interpretation. Aristotle may intend simply, as Aquinas says, to define ⋯χ⋯μενον by reference to that restricted class of things ⋯ϕεξ⋯ς which have nothing between them, i.e. things which at least touch. The class is the same in either case. Both interpretations exclude geometrical elements from a relation of togetherness, elements which in any case ‘touch’ and are ‘in place’ only analogy.

page 82 note 4 Physics 221a21–7. Some element of time, generation, is inseparable from the relations of continuity and contiguity, and for this reason to translate ἅπτεσθαι as ‘in contact’ in 227a21 is misleading. The relation is genetic rather than logically generic.

page 83 note 1 Simplicius (877. 11) says: ⋯ γο⋯ν χιτὼν ⋯πτ⋯μενος το⋯ σώματος δι⋯ τ⋯ μ⋯ ⋯ϕεξ⋯ς εἶναι οὐ λ⋯γεται ⋯χ⋯μενος αὐτο⋯. … That is, only things ⋯μογεν⋯ can be ⋯ϕεξ⋯ς, and things ⋯χ⋯μενα are ⋯ϕεξ⋯ς, but the coat and man are not ⋯μογεν⋯. Simplicius apparently had forgotten Aristotle's words in 227a18: τ⋯ μ⋯ν γ⋯ρ ⋯πτ⋯μενον ⋯ϕεξ⋯ς ⋯ν⋯γκη εἶναι. The fallacy in his argument is that he has things touching in virtue of their (non-homogeneous) definitions: whereas they touch qua body and as such are ⋯μογεν⋯. Ross, (Arist. Physics, p. 626)Google Scholaremploys Simplicius' erroneous example as giving Aristotle's meaning and then finds Aristotle contradicting himself in 227a18. This leads Ross to his two ‘confused arrangements of terms’ (ibid., p. 626, and A.'s Metaphysics, vol. ii, p. 345). The ‘confusion’, I think, is not Aristotle's, and arises from (i) construing continuity as a mere species of contiguity, (ii) a misreading of the definition of τ⋯ ⋯χ⋯μενον. Magnus, Albertus (Opera Omnia, ed. Borgnet, A., Parisiis, 1890, vol. iii, p. 381b)Google Scholar corrected the relation of ⋯χ⋯μμενον and ⋯πτ⋯μενον by simply saying, ‘Habitum [⋯χ⋯μενον] autem est quod addit aliquid consequenti [⋯ϕεξ⋯ς]’, viz. it adds the requisite that the successive entities be bodies (or touch), not, as Simplicius (and Averroes) had said, that ⋯χ⋯μενον adds something to ⋯πτ⋯μενον, viz. that the touching entities be ⋯ϕεξ⋯ς. Not only did this account for the form of the definition of ⋯χ⋯μενον, but it explained 227a18.

page 83 note 2 This interpretation, however, has the tradition against it in that, though concerned with a controversial issue, it was not advanced, so far as I know, until Magnus, Albertus (op. cit., pp. 378b–9a)Google Scholar: … ‘cum dicuntur aliqua simul esse secundum eundem proprium locum, intelligitur locus proprius non unus, sed duorum, et hoc est, quando contingunt se in loco utriusque proprio’. An interpretation allied to this was suggested by Alexander, and apparently followed by Philoponus, that by τ⋯ ἄκρα in the definition of ἅπτεσθαι Aristotle may have meant τ⋯ π⋯ρατα, i.e. the bodies' bounding surfaces. The ἄκρα would then be ἄμα, Alexander says (Simpl. 870), ⋯ν τῷ αὐτῳ τ⋯πῳ κατ⋯ συμβεβηκ⋯ς … ἅπτεται οὖν τα⋯τα ⋯λλ⋯λων, ὧν τ⋯ π⋯ρατα ⋯ϕαρμ⋯ζει ⋯λλ⋯λοις κα⋯ οὔτως ⋯στ⋯ν ἅμα. But this, as Alexander admits (and despite Simplicius), is immediately to construe ἅμα in a sense other than Aristotle has just defined, besides confusing the usage of ἄκρα.

page 84 note 1 This interpretation was first advanced by Alexander: cf. Simpl. 868–9: εἷς [τ⋯πος] μ⋯ν οὖν ⋯στιν, ὥς ϕησιν Ἀλ⋯ξανδρος, ⋯ μ⋯ διῃρημ⋯νος, ⋯λλ⋯ συνεχ⋯ς, τῷ κα⋯ αὐτ⋯ τ⋯ ἅμα λεγ⋯ενα ⋯ν τ⋯πῳ συνεχ⋯ ⋯λλ⋯λοις εἶναι ὡς τ⋯ το⋯ συνεχο⋯ς μ⋯ρη. Undoubtedly Alexander meant by the bodies being continuous that, since their places are continuous, there can be no ‘gap’, or other body, between them (a use Aristotle also employs); but his terminology suggested to Simplicius that, on such an interpretation, bodies could not be together, i.e. be contiguous, without being also continuous. Simplicius rightly criticized the theory on this assumption, and interpreted ἅ μ α … ⋯ν ⋯ν⋯ τ⋯πῳ πρύτῳ to mean something like ‘together in one city’, or ‘within the walls’, or being together as are parts of a mixture (Eudemus' choice example), in all these instances the bodies being not necessarily contiguous. SirHeath, Thomas (Math, in Arist., Oxford, 1949, pp. 122–3)Google Scholar apparently thought Simplicius' interpretation correct. However, apart from unsatisfactorily accounting for πρύτῳ, this interpretation makes useless Aristotle's definition of ἄπτεσθαι (and those definitions dependent upon it), for supposedly two bodies could be contiguous if their extremities were simply in the same room (ἅμα). And finally, Alexander adds a sentence to his interpretation given above, which Ross apparently follows: ἔν γ⋯ρ ⋯στι κα⋯ συνεχ⋯ς κα⋯ τ⋯ το⋯ περι⋯χοντος π⋯ρας τ⋯ περι⋯χον τ⋯ οὕτως ⋯νωμ⋯να ⋯λλ⋯λοις. (Cf. Ross, , Arist. Phys., p. 627Google Scholar.) But taken by itself, this equally raises difficulties in the definition of ἄπτεσθαι, for what can it mean to say that the extremities of two bodies are contained by one surface?

page 84 note 2 Physics 211a1.

page 85 note 1 Physics 206b19–20; cf. 206b3–20, 28; 207b4 ff.

page 85 note 2 De Caelo 271b9–11.

page 85 note 3 Ibid. 305a26.

page 85 note 4 Physics 212b24–5.

page 85 note 5 Ibid. 209a10 ff.

page 85 note 6 Cf. Categoriae, 5a1–6.

page 85 note 7 Physics 212b27–8.

page 85 note 8 De Caelo 268b5–8.

page 85 note 9 Cf. De Gen. et Corr. 321a6–7: ⋯δ⋯νατον δ⋯ μεγ⋯θους ὕλην ηἶναι χωριστ⋯ν.

page 85 note 10 Physics 214b17–19.

page 85 note 11 Ibid.212a31–2; cf. also 214b30–1: ἄν τις ⋯πισκοπῇ, μ⋯ ⋯νδ⋯χεσθαι μηδ⋯ ἔν κινεῖσθαι ⋯⋯ν ᾖ κενόν. The fact that ‘velocity in a void’ was for Aristotle, as it has proved for modern physics, meaningless (cf. 215a), gave him an effectual argument against the void from the nature of motion. His argument (215a29–216a21) may be put briefly: A body decelerates in a medium A at a rate dependent, other things being equal, upon its initial momentum, i.e. ‘weight’ and velocity, and the resistance of the medium. Now if the body enters a medium B contiguous with A, its rate of deceleration relative to that in A will be in direct proportion to that of the densities of A and B. Thus if the density of B is less than that of A, the rate of deceleration will decrease, until, Aristotle says, when B has no density, i.e. is void, we should have to say that the body will traverse B in no time at all, which is absurd, since all motion takes time. The Newtonian answer to this, which was given by Philoponus in the sixth century (and restated with admirable clarity by Aquinas), is that in the void, when the deceleration = o, the body will traverse the space with the velocity it had at the moment it entered B. Thus, in respect to deceleration, Philoponus says (684. 5–11), οὐδ⋯ποτε τ⋯ κεν⋯ν λόγον τιν⋯ ἔξει πρ⋯ς τ⋯ πλ⋯ρες… Indeed Newton's, dynamics, if not, as Duhem observes (Revue de Phil., 8e Année, No. 12, 12 1908, p. 643)Google Scholar, ‘autre que l'antique doctrine de Jean Philopon’, is based upon the same assumptions and same conclusions which Philoponus had enunciated with a precision and narrowness possible only to scientific genius. Drabkin, I. E. (‘Notes on the Laws of Motion in Aristotle’, American Jour. of Philology, vol. lix, No. 233, pp. 60–84)Google Scholar, with somewhat less clarity than Philoponus, says that Aristotle should have considered ‘resistance as a term to be subtracted from velocity under ideal conditions rather than as a experifactor by which to divide the velocity …’. But this is, in actual fact, to put the cart before the horse: velocity is the abstract ideal arrived at in subtracting the medium. That is, by decreasing the density of the medium, we can make any motion apparently approach a constant; viz. the velocity. But subtract the medium completely—and who knows? Aristotle's argument was not against fictitious and useful tools (cf., e.g., the concept of infinity), but against hypostasizing these abstractions. Assuming the dependence of motion upon forces, Aristotle's argument is a logical reductio ad absurdum: there is no mere velocity. It is not important that this should seem reasonable; logical arguments seldom do. In fact, since what seems reasonable is the hypostasized velocity, or conversely, an actual void, Aristotle based a second reductio ad absurdum upon this assumption (215219–22): in a void οὐδε⋯ς ἂν ἔχοι εἰπεῖν δι⋯ τ⋯ κινηθ⋯ν στ⋯σετα⋯ που τ⋯ γ⋯ρ μ⋯λλον ⋯ντα⋯θα ἤ ⋯ντα⋯θα; ὥστε ἤ ἠρεμ⋯σει ἤ εἰς ἄπειρον ⋯ν⋯γκη φ⋯ρεσθαι ⋯⋯ν μ⋯ τι ⋯μποδ⋯σῃ κρεῖττον. It is not ‘tantalizing’ (in Wicksteed's words) to find Aristotle stating Newton's first Law of Motion and then calling it absurd. Anyone who admits an actual void will have equally to hypostasize velocity, and Newton's ‘Law’ obviously follows. Aristotle calls the law absurd because it is not illustrated in everyday experience; and since to deny hypostasized velocity is to deny an actual void, he concluded from it that there was no actual void.

page 86 note 1 Physics 216b17–20. This passage has been rendered suspect by the fact that it is omitted by the Greek commentators. But whether spurious or not, the obserrvation that fish would quite likely find water a void, were they made of iron, is good enough to be Aristotelian.

page 86 note 2 Ibid. 214a7.

page 86 note 3 See Duhem's, P. ‘Roger Bacon et l'horreur du vide’, in Roger Bacon Essays (7th centenary), ed. Little, A. G. (Oxford, 1914), pp. 241–84Google Scholar, for a brief survey of the Scholastic concern, theoretically and experimentally, with the void.

page 87 note 1 Descartes, , Principles of Philosophy, 11. xviiiGoogle Scholar. Cf. Magnus, Albertus (op. cit., p. 273a)Google Scholar: ‘… sed ideo quia nihil est vacuum: et ideo oportet superficies corporum esse conjunctas [if all body be removed from between two bodies].’

page 87 note 2 It cannot be too often emphasized that the void for pre-field (and pre-ether) physics is not simply what we mean now by a vacuum. A void for Aristotle meant hypostasized extension, an absolute Space. Cf., e.g., de Brabant, Siger (Quaestiones super libros Physicorum I–IV et VIII, ed. Delhaye, Philippe, Louvain, , 1941, p. 179)Google Scholar: ‘Cum igitur vacuum sit dimensiones, et dimensiones non sint, ergo nee vacuum erit.’ Hence to admit of a void was to admit of an absolute Space, unlike such an admission in the present day. As long as Science ceases to believe in absolute Space, it cannot afford, as could Locke, to poke fun at Aristotle's denial of a ‘void’.

page 87 note 3 Categories 5a1–6.

page 87 note 4 Ibid. 5a8–14. Duhem, (Le Système du monde, vol. i, p. 198Google Scholar) mistakes Aristotle's interest here in one character of π⋯πος for a definition, and thus supposes Aristotle to say that ‘le lieu d'un corps, c'est la partie de l'espace que ce corps occupe’. Ross quotes Duhem, and says (Arist. Physics, p. 53 n.)Google Scholar, ‘This seems to support the view that the Categories are an early work. …’

page 88 note 1 Physics 212a13–14.

page 88 note 2 Ibid. 211a12–29.

page 88 note 3 Ibid. 211a2; cf. 211a25 ff.

page 88 note 4 Ibid. 211a3–6.

page 88 note 5 Ibid. 212a20–1.

page 88 note 6 Ibid. 212a16–20.

page 88 note 7 Simplicius 583. 12–14; cf. 583. 16–584. 28.

page 89 note 1 Duhem, P. (Le Système du Monde, i, p. 200)Google Scholar follows Alexander in so interpreting Aristotle's final definition of place. If this interpretation entailed only, as Duhem says, a revision of Aristotle's earlier theory in which he stated that the contained and its containing place must be contiguous, it might be admissible; but it also violates the very axioms Aristotle set to be fulfilled by his theory of Place.

page 89 note 2 Simplicius 584. 18–20: … δι⋯ το⋯ “πρ⋯τον” τ⋯ προσεχ⋯ς δηλώσας συντ⋯μως, ὅπερ πρ⋯τερον ⋯σ⋯μανε δι⋯ το⋯ “κοθ' ὅ συν⋯πτει τῷ περιεχμ⋯νῳ”. This las phrase is from 212a6 f. and appears only, as Ross tells us, in the Arabo-Latin translation, Themistius, Simpl., and Philoponus.

page 89 note 3 Simplicius 607. 8–9.

page 89 note 4 Physics 211a34–b1.

page 89 note 5 Ibid. 219a11; Metaph. 1020a11 ff.

page 89 note 6 Physics 231b15–18; cf. 239a23 ff.

page 90 note 1 Ibid. 212b3–6.

page 90 note 2 In actual fact, Aristotle uses the word συνεχ⋯ς as a. generic term which covers the gamut of specific relations between a complete organic unity of bodies and simply a relation when no other body is between the related bodies.

page 90 note 3 Cf., e.g., De Gen. et Cart. 314b27 ff. Cf. also Physics 245a5 ff., where he says that the body must be continuous with the air and the air with the object as the basis of sensation.

page 92 note 1 Simplicius (in his Corollarium de Loco, 601–45), 628. 34–629. 3.

page 92 note 2 Ibid. 629. 3–5.

page 92 note 3 Ibid. 626.35 ff.; cf. 625. 23 ff.

page 92 note 4 Ibid. 630. 30.

page 92 note 5 Ibid. 631. 14–15; cf. 627. 14–16: ἒοικεν οὖν ⋯τ⋯πος μ⋯τρον εἶναι τ⋯ς κειμ⋯νων θ⋯σεως, ⋯σπερ ⋯ χρ⋯νος ⋯ριθμ⋯ς λ⋯γεται τ⋯ς τ⋯ν κινουμ⋯νων κιν⋯σεως.

page 92 note 6 Ibid. 635. 23–5.

page 92 note 7 Cf. ibid. 635. 28–33; 626. 28–32; 645. 8–10.

page 92 note 8 Ibid. 637. 25–9; cf. 639. 19 ff.; 641. 21; 638. 26–30; 637. 36 ff.; 628. 26–34.

page 93 note 1 StAquinas, Thomas, Comm. In Arist. Phys., Cap. IV, Lect. VI, § 14Google Scholar.

page 93 note 2 Cf. Aristotelis Philosophia, selecta expositio Thomistica, de Prado, Franciscus Manca (Messanae, 1636), p. 454Google Scholar: ‘locus ergo si sumatur materialiter, mutabilis, ac variabilis dicitur, quia sic importat superficies quae fluunt, et refluunt, si vero sumatur formaliter, locus dicitur immobilis…’. This distinction between formal and material Place, a device with which the medievals covered a multitude of sins, was apparently first suggested, without comment, by R. Grosseteste, Bishop of Lincoln, in his compendious Physica: ‘locus est immobilis formaliter, mobilis veto malerialiter’ (I take this on Duhem's authority, since I have been unable to procure a copy of this work). Cf. de Brabant, Siger, op. cit., p. 156Google Scholar; Magnus, Albertus, op. cit., vol. iii, p. 265Google Scholar.

page 94 note 1 Physics 212a6–7; cf. 212b29.

page 95 note 1 De Gen. et Corr. 319b8–18.

page 96 note 1 I am not suggesting that Aristotle ‘anticipated’ the Whiteheadian theory of Organism. But the point is that Whitehead's cosmology may be conceived as a development from the Aristotelian; whereas the Newtonian system—still the presupposed natural ontology of most modern philosophy—can be looked upon only as a high abstraction from both.