The Evolution of the “a Priori Proof” and “a Posteriori Proof” from Logic to Philosophy in the Discourse of Ibn Sīnā and Mullā Ṣadrā

The terms proof, a priori proof, a posteriori proof, absolute a posteriori proof, and argument have specific definitions in logic. However, when some of these terms are transferred from logic to philosophy, philosophers have applied changes to these terms, retaining the division of proof in logic into a priori and a posteriori. There is evidence in the discourse of Ibn Sīnā and Mullā Ṣadrā that indicates the evolution of these terms in philosophy. In philosophy, proof (burhān) represents an “absolute a priori proof” and argument represents a “non-absolute a priori proof”.  The syllogism similar to proof in the discourse of Ibn Sīnā corresponds to the “absolute a posteriori proof” of the third kind in logic. The accidental proof in the discourse of Mullā Ṣadrā is a kind of "non-absolute a priori proof". Mullā Ṣadrā's burhān-i siddīqīn (Proof of the Veracious), which begins with the reality of existence, corresponds to the "absolute a posteriori proof" of the third kind. Mullā Ṣadrā calls it as the "proof similar to a priori". In philosophy, proof is divided into two branches: "essential" and "accidental." The argument specific to the argument from contingency to prove the necessary being, is considered by Mullā Ṣadrā as an "accidental a priori proof", and not an "essential a priori proof." Paying attention to the evolution of these terms from logic to philosophy opens the way for a precise interpretation of expressions that philosophers have used in philosophy.