Aristotle, however, does not always adhere closely to the distinction. Thus, if we compare the _logical_ or _dialectical_ reasons given, p. 82, b. 37, seq., with the _analytical_, announced as beginning p. 84, a. 8, seq., we find the same main topic dwelt upon in both, namely, that to admit an infinite series excludes the possibility of Definition. Both Alexander and Ammonius agree in announcing this as the capital topic on which the proof turned; but Alexander inferred from hence that the argument was purely _dialectical_ ([Greek: logiko\n e)pichei/rêma]), while Ammonius regarded it as a reason thoroughly convincing and evident: [Greek: o( me/ntoi philo/sophos] (Ammonius) [Greek: e)/lege mê\ dia\ tou=to le/gein _logika\_ ta\ e)picheirê/mata; e)narge\s ga\r o(/ti ei)si\n o(rismoi/, ei) mê\ a)katalêpsi/an ei)saga/gômen] (Schol. p. 227, a. 40, seq., Brand.).] [Footnote 62: Analyt. Post. I. xxii. p. 83, a. 20, b. 14. Only eight of the ten Categories are here enumerated.] [Footnote 63: Ibid. I. xxii. p. 84, a. 30-35. The paraphrase of Themistius (pp. 55-58, Spengel) states the Aristotelian reasoning in clearer language than Aristotle himself. Zabarella (Comm. in Analyt. Post. I. xviii.; context. 148, 150, 154) repeats that Aristotle's proof is founded upon the undeniable fact that there _are_ definitions, and that without them there could be no demonstration and no science. This excludes the supposition of an infinite series of predicates and of middle terms:--"Sumit rationem à definitione; si in _predicatis in quid_ procederetur ad infinitum, sequeretur auferri definitionem et omnino essentiæ cognitionem; sed hoc dicendum non est, quum omnium consensioni adversetur" (p. 466, Ven. 1617).]