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    cPeter King & StewartShapiro, The Oxford Companion to Philosophy(OUP1995), 496500.

    THE HISTORY OF LOGIC

    Aristotle was the first thinker to devise a logical system. He drew uponthe emphasis on universal definition found in Socrates, the use of reductioad absurdum in Zeno of Elea, claims about propositional structure and nega-tion in Parmenides and Plato, and the body of argumentative techniquesfound in legal reasoning and geometrical proof. Yet the theory presentedin Aristotles five treatises known as the Organonthe Categories, theDe interpretatione, the Prior Analytics, the Posterior Analytics, and theSophistical Refutationsgoes far beyond any of these.

    Aristotle holds that a proposition is a complex involving two terms, asubject and a predicate, each of which is represented grammatically with anoun. The logical form of a proposition is determined by its quantity (uni-versal or particular) and by its quality (affirmative or negative). Aristotleinvestigates the relation between two propositions containing the sameterms in his theories of opposition and conversion. The former describesrelations of contradictoriness and contrariety, the latter equipollences andentailments.

    The analysis of logical form, opposition, and conversion are combinedin syllogistic, Aristotles greatest invention in logic. A syllogism consists ofthree propositions. The first two, the premisses, share exactly one term, andthey logically entail the third proposition, the conclusion, which containsthe two non-shared terms of the premisses. The term common to the two

    premisses may occur as subject in one and predicate in the other (called thefirst figure), predicate in both (second figure), or subject in both (thirdfigure). A given configuration of premisses and conclusions is called amood.

    In the scholastic period, mnemonic names for the valid moods canvassedin the Prior Analytics were devised. Two first-figure valid moods wereconsidered perfect and not in need of any further validation: BARBARA(consisting entirely in universal affirmatives) and CELARENT (consisting ina universal negative and a universal affirmative, concluding in a universalnegative). For the validation of the rest, Aristotle used three techniques:reduction, in which a given mood is transformed through conversions intoBARBARA or CELARENT; reductio ad absurdum; and k q e s i j , which proceeds

    by selection of an arbitrary individual. He regularly describes moods byusing variables in place of terms. To reject a proposed inference he typicallygives a list of terms that, when substituted as values of the term-variables,produce true premisseswith false conclusions. This is similar to the modern

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