Compare, about Petitio Principii, Aristot. Topic. VIII. xiii. p. 162, b. 34, in which passage Aristotle gives to the fallacy called Petitio Principii a still larger sweep than what he assigns to it in the Analytica Priora. Mr. Poste's remark is perfectly just, that according to the above passage in the Analytica, every syllogism with a problematical (_i.e._ real as opposed to verbal) premiss would be a Petitio Principii; that is, all real deductive reasoning, in the syllogistic form, would be a Petitio Principii. To this we may add, that, from the passage above referred to in the Topica, all inductive reasoning also (reasoning from parts to whole) would involve Petitio Principii. Mr. Poste's explanation of this difficult passage brings into view the original and valuable exposition made by Mr. John Stuart Mill of the Functions and Logical Value of the Syllogism.--System of Logic, Book II. ch. iii. sect 2:--"It must be granted, that in every syllogism, considered as an argument to prove the conclusion, there is a Petitio Principii," &c. Petitio Principii, if ranked among the Fallacies, can hardly be extended beyond the first of the five distinct varieties enumerated in the Topica, VIII. xiii.] [Footnote 23: Analyt. Prior. II. xvi. p. 65, a. 23-27: [Greek: to\ ga\r e)x a)rchê=s ti/ du/natai, ei)/rêtai ê(mi=n, o(/ti to\ di' au(tou= deiknu/nai to\ mê\ di' au(tou= dê=lon.--tou=to d' e)/sti, to\ mê\ deiknu/nai.] The meaning of some lines in this chapter (p. 65, a. 17-18) is to me very obscure, after all the explanations of commentators.] [Footnote 24: Ibid. p. 65, a. 35; Topic. VIII. xiii. p. 162, b. 31.] We must be careful to note, that when Aristotle speaks of a _principium_ as knowable in itself, or true in itself, he does not mean that it is innate, or that it starts up in the mind ready made without any gradual building up or preparation. What he means is, that it is not demonstrable deductively from anything else prior or more knowable by nature than itself. He declares (as we shall see) that _principia_ are acquired, and mainly by Induction.