The subject of this paper is the general question of what role mathematics, or more particularly the philosophy of mathematics, plays in the work of Wittgenstein, and, also, in philosophy generally; a question I have tackled in a more extensive form, and not always very explicitly, in the book Filosofie čísla (The Philosophy of Number). Just as there, I take as my starting point Frege’s linguistic turn, beginning with the question “what is number?”, and I develop this is in a free relation (1) to Plato’s theory of ideas with mathematical objects as the middle entities, (2) Kant’s anchoring of mathematics in the pure intuitions of space and time, and (3) Wittgenstein’s conception of mathematics as one of many language-games, stemming from the understanding of a concept as rule.
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