Abstract

Wittgenstein's conceptions considered, from a more general point of view not only classic positions in philosophy of mathematics such as formalism, but the controversy between realism and antirealism as well. The treatment of arithmetic in the Tractatus Logico‐Philosophicus reveals a radically antirealist stance, where by “radical antirealism” which means a conception that deprives arithmetical propositions, identified with equations, of assertability and truth‐aptness, by construing them as expressions of rules of syntax, of rules dealing with signs. The Tractatus’ radical antirealism results in a conception of mathematics that has remarkable points of contact with Hilbert's formalism, even though important qualifications will have to be added to that statement in order to make it minimally acceptable. In virtue of the characterization of the notion of a thought as the logical picture of states of affairs, a mathematical proposition, insofar as it does not express a thought, is not even the logical picture of a state of affairs.