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Aristotle's Topics introduces a deductive argument as follows: "a deduction [sullogismos] is an account [logos] in which, some things being supposed, something other than that which is assumed results of necessity [ex anagkês sumbainei] in virtue of that which has been assumed.'" The translation of sullogismos as "deduction," instead of "syllogism," is a matter for discussion, but the term "deduction" here exclusively pertains to Aristotle's conception of deduction in the same way as epagôgê, translated as "induction," is confined to his view on induction. We then avoid Keyt's criticism that the word "deduction" fails to assert the difference between a syllogism and the modem notion of deduction.2 As for logos, its translation as "account," instead of "argument," aims to stress the role of deduction in language. Indeed, the first meaning of logos is "sentence" in spoken language, as explained in De Interpretation,e.3 The Topics does not explain further the notion of deduction, as it immediately focuses on the distinction between demonstration and dialectical deduction, namely the contrast between knowledge and opinion.
On the other hand, the Prior Analytics is concerned with deductions simpliciter, which are neither demonstrative nor dialectical.4 Aristotle suggests a same formulation of deduction, despite the slightly different wording: "a deduction is an account in which, some things being supposed, something other than that which is assumed results of necessity [ex anagkês sumbanei] in virtue of these being so."5 A deduction simpliciter is a necessary inference from given premises. Aristotle adds: "I mean by 'these being so' [tôi tauta einai] that which results because of these, and I mean by 'that which results because of these' that which stands in need of no term outside in order for that which is necessary to be produced."6 An inference is necessary when the conclusion is drawn from the terms of the premises alone, without referring to anything outside of them. Thus, a conclusion is deducible when it has been necessarily inferred from its premises. If two distinct conclusions were inferred from the same premises, the two inferences could not be necessary, since a necessary inference cannot be otherwise. If no conclusion "results of necessity" (ex anagkês sumbainei) from the premises, then the account cannot be a deduction.
Modern logicians, in their logical réévaluation of...