Wittgenstein's philosophy of mathematics: A reply to two objections

Southern Journal of Philosophy 26 (2):179-191 (1988)
Abstract
This paper has two main purposes: first to compare Wittgenstein's views to the more traditional views in the philosophy of mathematics; second, to provide a general outline for a Wittgensteinian reply to two objections against Wittgenstein's account of mathematics: the objectivity objection and the consistency objections, respectively. Two fundamental thesmes of Wittgenstein's account of mathematics title the first two sections: mathematical propositions are rules and not descritpions and mathematics is employed within a form of life. Under each heading, I examine Wittgenstein's rejection of alternative views. My aim is to make clear the differences and to suggest some similarities. As will become clear, Wittgenstein often rejects opposing views for the same or similar reasons. This comparison will provide the necessary background for better understanding Wittgenstein's philosophy of mathematics, for appreciating its many unappreciated advantages and, finally, for defending a conventionalist account of mathematics.
Keywords Wittgenstein  objectivity objection  consistency objection  conventionalism in mathematics
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DOI 10.1111/j.2041-6962.1988.tb00450.x
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