^{page 279 note 1} Owen, G.E.L., , in Aristote et les problèmes de méthode…(first) Symposium Aristotelicum(Louvain, 1961), 85–103.Google Scholar

^{page 279 note 2} Owen, , op. cit. 84.Google Scholar

^{page 279 note 3} e.g., Wieland, W., Die Aristotelische Physik(Göttingen, 1962).Google Scholar

^{page 279 note 4} The last instance does follow the close of ch. 9, which is the longest non-demonstrative passage in the book, but the plural , as it marks the close of the discussion of Zeno, may be taken to refer not to the immediately preceding section, which draws a distinction rather than giving any demonstration, but to the entire correction of Zeno's errors implied throughout the first nine chapters of the book.

^{page 280 note 1} e.g., Wieland, W., op. cit. 42, n. 1Google Scholar. Cf. Patzig, G., Die Aristotelische Syllogistik (Göttingen, 1959), 201.Google Scholar

^{page 282 note 1} Admittedly, there is also an attempt to prove this assumption, in Physics 222^b30–223^a15.

^{page 283 note 1} The mathematical character of the book has been noticed, e.g. by Leblond, J.M., Logique et mithode chez Aristote (Paris, 1939), 197Google Scholar

^{page 283 note 2} Both faster and slower are defined in 215^b15, but book 6 defines only faster.

^{page 285 note 1} Similarly, in 240^a19 ff., when the traditional problem of quality change (that a changing subject both has and does not have the quality in process) is solved by a distinction between the whole and the parts of the thing, Aristotle is depending on his basic principle that anything which changes is always divisible into parts.

^{page 287 note 1} There is one reduction whose alternatives are those of the universal principle ofcontradiction, but in this peculiar case the universal principle is itself proper to the subject, the argument being about the change ofopposites (235^b–17).

^{page 287 note 2} One might well ask how demonstrations can be admitted in a system in which a criterion of knowledge is the ability to give the reasons for the facts. Probably it is because Aristotle expects that any premisses which are necessary and which link terms defined to the subject must give at least some insight into the formal cause of the conclusion. Of course, that argument would not be entirely valid in subordinate sciences, which study mathematical properties inherent in physical subjects to which they are not (cf. p. 289). But even subordinate sciences, in so far as they study mathematical properties, grasp some aspect of formal causality. Hence Aristotle can characterize the same science, optics, as in relation to mathematics, but in relation to in 79^a10–13.

^{page 290 note 1} He implies a criticism of that definition in Physics 200^b 18–20, but he reverts to it in 232b24 and offers it also in On the Heavens 286^a6.

^{page 290 note 2} Owen, , op. cit. 95–6.Google Scholar

^{page 291 note 1} The Metaphysics passage offers interesting support for my hypothesis. There, continuous is ‘that whose movement is per se one and cannot be otherwise’, while ‘one is explained as ‘indivisible in time’. That definition of continuous is not given in Physics 5. 3 because, although it would have surpassed the latter‘s arrangement by defining continuous directly in terms of movement, it would have implied indivisibility rather than infinite divisibility!

^{page 292 note 1} Kullmann, W., ‘Zur wissenschaftlichen Methode des Aristoteles’, in Flascher and Gaiser, Synusia (Neske, 1965), 247–74Google Scholar, finds occasional demonstrations, which prove the inherence of certain properties in certain subjects by making deductions from previously proved propositions, in the treatise On the Heavens. These, too, seem to be largely a continuation of the system deduced in Physics 6.