Philosophy of Arithmetic [Book Review]

Review of Metaphysics 59 (2):428-431 (2005)
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Abstract

In the late nineteenth and early twentieth centuries, philosophy of mathematics was a relatively new subject divided into a variety of dynamically opposed research programs. Edmund Husserl’s Philosophie der Arithmetik joined the ensuing debate by offering a unique phenomenological perspective on the psychological origins of arithmetical concepts. Husserl’s theory, apparently going against the grain of what was to become the dominant Platonist and extensionalist force majeure, was destined to be misunderstood, its purpose and arguments sometimes willfully misrepresented. As a result, despite its brilliant down to earth discussions of the nature of mathematical ideas, Husserl’s text has remained obscure, virtually unacknowledged except as an illustration of how not to explain the principles of arithmetic by mainstream analytic movements in the philosophy of logic and mathematics.

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