The late 1960s saw the emergence of new philosophical interest in Kant's philosophy of mathematics, and since then this interest has developed into a major and dynamic field of study. In this state-of-the-art survey of contemporary scholarship on Kant's mathematical thinking, Carl Posy and Ofra Rechter gather leading authors who approach it from multiple perspectives, engaging with topics including geometry, arithmetic, logic, and metaphysics. Their essays offer fine-grained analysis of Kant's philosophy of mathematics in the context of his Critical philosophy, (...) and also show sensitivity to its historical background. The volume will be important for readers seeking a comprehensive picture of the current scholarship about the development of Kant's philosophy of mathematics, its place in his overall philosophy, and the Kantian themes that influenced mathematics and its philosophy after Kant. (shrink)

In their recent paper “Do Accelerating Turing Machines Compute the Uncomputable?” Copeland and Shagrir draw a distinction between a purist conception of Turing machines, according to which these machines are purely abstract, and Turing machine realism according to which Turing machines are spatio-temporal and causal “notional" machines. In the present response to that paper we concede the realistic aspects of Turing’s own presentation of his machines, pointed out by Copeland and Shagrir, but argue that Turing's treatment of symbols in the (...) course of that presentation opens the door for later purist conceptions. Also, we argue that a purist conception of Turing machines plays an important role not only in the analysis of the computational properties of Turing machines, but also in the philosophical debates over the nature of their realization. (shrink)