[Footnote 56: Plato, Sophistes, pp. 261-262. [Greek: pha/sin kai\ a)po/phasin].--ib. p. 263 E. In the so-called Platonic 'Definitions,' we read [Greek: e)n katapha/sei kai\ a)popha/sei] (p. 413 C); but these are probably after Aristotle's time. In another of these Definitions (413 D.) we read [Greek: a)po/phasis], where the word ought to be [Greek: a)po/phansis].] [Footnote 57: Plato, Sophist. p. 263 A-C.] [Footnote 58: Ibid. p. 257, B: [Greek: Ou)k a)r', e)nanti/on o(/tan a)po/phasis le/gêtai sêmai/nein, sugchôrêso/metha, tosou=ton de\ mo/non, o(/ti _tô=n a)/llôn ti mênu/ei to\ mê\ kai\ to\ ou)/_ protithe/mena tô=n e)pio/ntôn o)noma/tôn, ma=llon de\ tô=n pragma/tôn, peri\ a(/tt' a)\n ke/êtai ta\ e)piphtheggo/mena u(/steron tê=s a)popha/seôs o)no/mata.] The term [Greek: a)nti/phasis], and its derivative [Greek: a)ntiphatikô=s], are not recognized in the Platonic Lexicon. Compare the same dialogue, Sophistes, p. 263; also Euthydêmus, p. 298, A. Plato does not seem to take account of negative propositions as such. See 'Plato and the Other Companions of Sokrates,' vol. II. ch. xxvii. pp. 446-455.] [Footnote 59: Aristot. Topica, I. xi. p. 104, b. 20; Metaphys. [Greek: D]. p. 1024, b. 32; Analytic. Poster. I. xxv. p. 86, b. 34.] [Footnote 60: Diogon. Laert. ii. 134-135. See the long discussion in the Platonic Theætêtus (pp. 187-196), in which Sokrates in vain endeavours to produce some theory whereby [Greek: pseudê\s do/xa] may be rendered possible. Hobbes, also, in his Computation or Logic (De Corp. c. iii. § 6), followed by Destutt Tracy, disallows the negative proposition _per se_, and treats it as a clumsy disguise of the affirmative [Greek: e)k metathe/seôs], to use the phrase of Theophrastus. Mr. John Stuart Mill has justly criticized this part of Hobbes's theory (System of Logic, Book I. ch. iv. § 2).]