Negation in Popper's theory of deductive inference

David Binder (Tübingen)

I will present the results of my investigations into Popper's treatment of
negation in his articles on deductive logic in the 1940s. Popper gives
definitions for classical, intuitionistic and dual-intuitionistic negation and
shows that intuitionistic and dual-intuitionistic negation do not necessarily
collapse into classical negation if both exist in the same system, thus
providing probably the first formal account of a bi-intuitionistic logic.
Further topics are the analysis of Popper's notion of duality, his analysis of
weaker negations that lead him to reject Johansson's minimal negation and his
treatment of modal logic and the anti-conditional.