ABSTRACT
In this note I discuss two specific issues raised by Mark van Atten in his review of my book Logic and Philosophy of Mathematics in the Early Husserl, both concerning my reconstruction of Husserl’s elaboration of the notion of “conceivable arithmetical operation” in chapter 13 of his Philosophy of Arithmetic. The first issue is more technical in nature: it concerns the role of a kind of restricted inversion operator in the proof of the equivalence between the class of partial recursive functions and that of the Husserl-computable functions (as I defined them in my book). The second issue has to do with the absence, in Husserl’s reflections on computable operations, of a sort of “Husserl thesis” analogous to the Church–Turing thesis. I argue that the theoretical issues and the philosophical context which underlie Husserl’s reflections on the totality of “conceivable arithmetical operations” are completely different from those motivating the elaboration of computability theory in the 1930s by Gödel, Church, Kleene, Turing and others.
