The Logic of Constructivism

In this paper I dispute the current view that intuitionistic logic is the common basis for the three main trends of constructivism in the philosophy of mathematics: intuitionism, Russian constructivism and Bishop’s constructivism. The point is that the so-called ‘Markov’s principle’, which is accepted by Russian constructivists and rejected by the other two, is expressible in intuitionistic first-order logic, and so it appears to have the status of a logical principle. The result of appending this principle to a complete intuitionistic axiom system for first-order predicate logic constitutes a new logic, which could well be called ‘Markov’s logic’, and which should be regarded as the true logical system underlying Russian constructivism.