Oskar Becker - Intuitionistic and Modal Logic

Intuitionistic and Modal Logic

Becker made a start toward the formalization of L. E. J. Brouwer's intuitionistic logic. He developed a semantics of intuitionistic logic based on Husserl's phenomenology, and this semantics was used by Arend Heyting in his own formalization. Becker struggled, somewhat unsuccessfully, with the formulation of the rejection of excluded middle appropriate for intuitionistic logic. Becker failed in the end to correctly distinguish classical and intuitionistic negation, but he made a start. In an appendix to his book on mathematical existence, Becker set the problem of finding a formal calculus for intuitionistic logic. In a series of works in the early 1950s he surveyed modal, intuitionistic, probabilistic, and other philosophical logics.

Becker made contributions to modal logic (the logic of necessity and possibility) and Becker’s postulate, the claim that modal status is necessary (for instance that the possibility of P implies the necessity of the possibility of P, and also the iteration of necessity) is named for him. Becker's Postulate later played a role in the formalization given, by Charles Hartshorne, the American process theologian, of the Ontological Proof of God's existence, stimulated by conversations with the logical positivist and opponent of the alleged proof, Rudolf Carnap.