Popper’s Correspondence with Stephen Cole Kleene

Abstract

Stephen Cole Kleene (1909–1994) was an American logician, well-known for his fundamental work in various fields of theoretical computer science, such as formal language theory, automata theory and recursion theory. The letter to Kleene reproduced in this chapter shows Popper’s continued interest in Boolean algebra. In that letter Popper claims to have found a proof of a theorem in Boolean algebra that contradicts propositions which are widely believed to be true; similar letters were sent to various other researchers. A typescript entitled “The Distributivity of Lattices with Unique Complements” was enclosed, but the alleged proof contains an error. As mentioned in the Preface, Popper’s work on Boolean algebra is outside the scope of this edition. This episode, part of a larger critical examination of the logic of quantum mechanics, is discussed more fully in an article by (Del Santo, F. (2020). An Unpublished Debate Brought to Light: Karl Popper’s Enterprise against the Logic of Quantum Mechanics. In: Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 70, pp. 65–78.).