Déductifs

Déductifs is the plural form used in French to refer to deductive approaches. In logic and philosophy, déductifs describes reasoning that derives specific conclusions from general premises via valid forms of inference. A deductive argument is valid if the conclusion follows necessarily from the premises; it is sound if the premises are true and the argument preserves truth.

Deduction proceeds within a formal system characterized by axioms and inference rules. In mathematics and related fields, proofs are deductive: starting from accepted axioms, one deduces theorems through a sequence of justified steps.

Historical and scope: The deductive method has roots in Aristotle’s syllogistic and Euclidean geometry; in the 19th and 20th centuries, Frege, Russell, and Hilbert formalized deduction as a foundational tool of logic and mathematics.

Applications and contrasts: Deductive reasoning aims for certainty, in contrast to inductive reasoning that generalizes from experience and abductive reasoning that infers explanations. In computer science, deduction underpins formal verification, automated theorem proving, and many logical programming paradigms.

In French-language usage, déductifs may describe procedures, arguments, or systems that rely on deduction. Thus déductifs encompasses classical syllogisms as well as modern axiomatic proofs.