This volume presents Wittgenstein's views on mathematics, which he progressively elaborated during a lifetime's reflections on the subject. Divided into three parts, it corresponds to the three distinct phases in the development of Wittgenstein's philosophy of mathematics.

Leading scholars discuss whether some of the main tenets or theses that are currently or traditionally ascribed to Wittgenstein are still both theoretically and exegetically viable, by focusing on three well-established Wittgensteinian themes: mind, meaning, and metaphilosophy.

Understanding Wittgenstein's Tractatus provides an accessible and yet novel discussion of all the major themes of the Tractatus.

The book starts by setting out the history and structure of the Tractatus. It then investigates the two main dimensions of the early Wittgenstein's thought, corresponding to the division between what language can say by means of its propositions and what language can only show. It goes on to discuss picture theory, logical atomism, extensionality, truth-functions and truth-operations, semantics, metalogic and mathematics, solipsism and...

Wittgenstein's role was vital in establishing mathematics as one of this century's principal areas of philosophic inquiry. In this book, the three phases of Wittgenstein's reflections on mathematics are viewed as a progressive whole, rather than as separate entities. Frascolla builds up a systematic construction of Wittgenstein's representation of the role of arithmetic in the theory of logical operations. He also presents a new interpretation of Wittgenstein's rule-following considerations - the community view of internal relations'.