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ekthesis, (Greek: “to expose,” or “to set forth”), in logic, process used by Aristotle to establish the validity of certain propositions or syllogisms. For example, in the Analytica priora he argued: “If A belongs to no B; neither will B belong to any A; for if it did belong to any A, say Γ (gamma), it would not be true that A belonged to no B; for Γ is one of the B’s.” Ekthesis refers in particular to the creation of a new term (in this case, Γ) that, together with the principle of reductio ad impossibile (a method of proving a proposition by showing that its denial leads to a contradiction), allows the deduction of the desired result.

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syllogism, in logic, a valid deductive argument having two premises and a conclusion. The traditional type is the categorical syllogism in which both premises and the conclusion are simple declarative statements that are constructed using only three simple terms between them, each term appearing twice (as a subject and as a predicate): “All men are mortal; no gods are mortal; therefore no men are gods.” The argument in such syllogisms is valid by virtue of the fact that it would not be possible to assert the premises and to deny the conclusion without contradicting oneself.

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