[Footnote 99: That is, we do not consider the sophism of Zeno refuted by the fact that the geometrical progression _a_(1 + 1/_n_ + 1/_n_2 + 1/_n_3 +,... etc.)--in which _a_ designates the initial distance between Achilles and the tortoise, and _n_ the relation of their respective velocities--has a finite sum if _n_ is greater than 1. On this point we may refer to the arguments of F. Evellin, which we regard as conclusive (see Evellin, _Infini et quantité_, Paris, 1880, pp. 63-97; cf. _Revue philosophique_, vol. xi., 1881, pp. 564-568). The truth is that mathematics, as we have tried to show in a former work, deals and can deal only with lengths. It has therefore had to seek devices, first, to transfer to the movement, which is not a length, the divisibility of the line passed over, and then to reconcile with experience the idea (contrary to experience and full of absurdities) of a movement that is a length, that is, of a movement _placed upon_ its trajectory and arbitrarily decomposable like it.] [Footnote 100: Plato, _Timaeus_, 37 D.] [Footnote 101: We have tried to bring out what is true and what is false in this idea, so far as spatiality is concerned (see Chapter III.). It seems to us radically false as regards _duration_.] [Footnote 102: Aristotle, _De anima_, 430 a 14 [Greek: kai hestin ho men toioutos nous tô pynta ginesthai, ho de tô panta poiein, ôs hexis tis, oion to phôs. tropon gar tina ka to phôs poiei ta dynamei onta chrômata energeia chrômata].] [Footnote 103: _De caelo_, ii. 287 a 12 [Greek: tês eschatês periphoras oute kenon estin exôthen oute topos.] _Phys._ iv. 212 a 34 [Greek: to de pan esti men hôs kinêsetai hesti d' hôs ou. hôs men gar holon, hama ton topon hou metaballei. kyklô de kinêsetai, tôn moriôn gar outos ho topos].] [Footnote 104: _De caelo_, i. 279 a 12 [Greek: oude chronos hestin hexô tou ouranou]. _Phys._ viii. 251 b 27 [Greek: ho chronos pathos ti kinêseôs].] [Footnote 105: Especially have we left almost entirely on one side those admirable but somewhat fugitive intuitions that Plotinus was later to seize, to study and to fix.] [Footnote 106: See page 10.] [Footnote 107: Descartes, _Principes_, ii. § 29.] [Footnote 108: Descartes, _Principes_, ii. §§ 36 ff.] [Footnote 109: In a course of lectures on Plotinus, given at the Collège de France in 1897-1898, we tried to bring out these resemblances. They are numerous and impressive. The analogy is continued even in the formulae employed on each side.] [Footnote 110: "Le Paralogisme psycho-physiologique" (_Revue de métaphysique et de morale_, Nov. 1904, pp. 895-908). Cf. _Matière et mémoire_, Paris, 1896, chap. i.] INDEX (Compiled by the Translator) Abolition of everything a self-contradiction, 280, 283, 296, 298 idea of, 279, 282, 283, 295, 296. _See_ Nought Absence of order, 231, 234, 274. _See_ Disorder Absolute and freedom, 277 reality, 99, 228-9, 269, 358, 361 reality of the person, 269 time and the, 239, 240, 298, 340, 344