It has often been argued that the Syllogism involves a _petitio principii_, because the Major Premiss contains the Conclusion, and would not be true unless the Conclusion were true. But this is really an _Ignoratio Elenchi_. The fact adduced, that the Major Premiss contains the Conclusion, is indisputable; but this does not prove the Syllogism guilty of Petitio. _Petitio principii_ is an argumentative trick, a conscious or unconscious act of deception, a covert assumption, and the Syllogism, so far from favouring this, is an _expositio principii_, an explicit statement of premisses such that, if they are true, the conclusion is true. The Syllogism merely shows the interdependence of premisses and conclusion; its only tacit assumption is the _Dictum de Omni_. If, indeed, an opponent challenges the truth of the conclusion, and you adduce premisses necessarily containing it as a refutation, that is an _ignoratio elenchi_ unless your opponent admits those premisses. If he admits them and denies the conclusion, you convict him of inconsistency, but you do not prove the truth of the conclusion. Suppose a man to take up the position: "I am not mortal, for I have procured the _elixir vitae_". You do not disprove this by saying, "All men are mortal, and you are a man". In denying that he is mortal, he denies that all men are mortal. Whatever is sufficient evidence that he is not mortal, is sufficient evidence that all men are not mortal. Perhaps it might be said that in arguing, "All men are mortal, and you are a man," it is not so much _ignoratio elenchi_ as _petitio principii_ that you commit. But be it always remembered that you may commit both fallacies at once. You may both argue beside the point and beg the question in the course of one and the same argument. [Footnote 1: Cp. Mr. Sidgwick's instructive treatise on Fallacies, International Scientific Series, p. 199.] CHAPTER IX. FORMAL OR ARISTOTELIAN INDUCTION.--INDUCTIVE ARGUMENT. The distinction commonly drawn between Deduction and Induction is that Deduction is reasoning from general to particular, and Induction reasoning from particular to general. But it is really only as modes of argumentation that the two processes can be thus clearly and fixedly opposed. The word Induction is used in a much wider sense when it is the title of a treatise on the Methods of Scientific Investigation. It is then used to cover all the processes employed in man's search into the system of reality; and in this search deduction is employed as well as induction in the narrow sense. We may call Induction in the narrow sense Formal Induction or Inductive Argument, or we may simply call it Aristotelian Induction inasmuch as it was the steps of Inductive argument that Aristotle formulated, and for which he determined the conditions of validity.