Ekthesis

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.