Wittgenstein on Infinity, Mathematical Propositions and Proofs

In this paper we discuss some of the most important themes Wittgenstein is concerned with in his extensive remarks about the foundations of mathematics, such as the conceptual difference between mathematical propositions and empirical propositions. The differences that Wittgenstein brings to our attention have impact on philosophical issues about the concept of infinity in mathematics and about the nature of mathematical proof. They are also significant for our understanding of mathematics as a science, and especially for how it differs from the natural sciences. These themes are dealt with in this paper with the aim of bringing to light the originality and sensitivity of Wittgenstein’s thinking, and to show how it differs from the received views and ways of approaching the issues that have dominated the discussion within the philosophy of mathematics in the last 100 years.

Keywords: aspect-perception, extension, formalism, generality, internal relation, operation, realism, Rule, surveyable.