Aristotle (384–322 BC)

DOI: 10.4324/9780415249126-A022-1
Version: v1,  Published online: 1998
Retrieved October 16, 2018, from

5. Deduction

Part of logic, as Aristotle conceives it, is the study of good and bad arguments. In the Topics Aristotle treats dialectical arguments in general. In the Prior Analytics he examines one type of argument, a ‘deduction’ (syllogismos; literally, ‘reasoning’, hence the standard term ‘syllogism’). This is an argument in which, if propositions p and q are assumed, something else r, different from p and q, follows necessarily because of the truth of p and q (Prior Analytics 24b18–20, paraphrased). Aristotle insists that it is not possible for the premises of a deduction to be true and the conclusion false (‘follows necessarily’); that a deduction must have more than one premise (‘if p and q are assumed’); that the conclusion cannot be identical to any premise (‘different from p and q’); and that no redundant premises are allowed (‘because of the truth of p and q’). He takes deductions to express affirmative or negative relations between universals, taken either universally (‘Animal belongs to every (no) man’) or not universally (‘Animal belongs (does not belong) to some man’). He takes the affirmative and negative claims to imply existence (so that ‘Biped belongs to some dodo’ follows from ‘Biped belongs to every dodo’; the latter affirmation is not equivalent, therefore, to ‘If anything is a dodo, it is biped’).

These different features of an Aristotelian deduction differentiate Aristotle’s account of a deduction from a more familiar account of deductively valid arguments. An argument may be valid even if it is redundant, or a premise is identical to the conclusion, or it has only one premise, or it is about particulars, or it contains neither ‘some’ nor ‘every’ nor ‘belongs’; but no such argument is an Aristotelian deduction. Aristotle’s theory of the different forms of deduction (often called ‘the moods of the syllogism’) examines the various forms of argument that necessarily preserve the truth of their premises. He begins from ‘complete’ (or ‘perfect’) deductions whose validity is evident, and classifies the different types of arguments that can be derived from (shown to be equivalent to) the complete deductions. He also explores the logical relations between propositions involving modalities (‘Necessarily (possibly) animal belongs to every man’ and so on). Since Aristotle accepts this relatively narrow account of a deduction, his exploration of the different forms of deduction is not a theory of valid arguments in general; the Stoics come much closer to offering such a theory (see Stoicism §11; Logic, ancient).

Aristotle’s theory of deduction is developed for its own sake, but it also has two main philosophical applications. (1) Deduction is one type of argument appropriate to dialectic (and, with modifications, to rhetoric; see §29). Aristotle contrasts it with inductive argument (also used in dialectic), in which the conclusion does not follow necessarily from the premises, but is made plausible by them. (2) It is essential for demonstration (apodeixis), which Aristotle takes to be the appropriate form for exhibiting scientific knowledge.

Citing this article:
Irwin, T.H.. Deduction. Aristotle (384–322 BC), 1998, doi:10.4324/9780415249126-A022-1. Routledge Encyclopedia of Philosophy, Taylor and Francis,
Copyright © 1998-2018 Routledge.

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