Remark on the hypothetical judgment

Abstract

What is the proper explanation of intuitionistic hypothetical judgment, and thence propositional implication? The answer is unclear from the writings of Brouwer and Heyting, who in their lifetimes propounded multiple (sometimes conflicting) explanations of the hypothetical judgment. To my mind, the determination of an acceptable explanation must take into account its adequacy for the expression of the bar theorem and, more generally, the development of an open-ended framework for transcendental arguments in mathematics.