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'.

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 value, metaphysics, and finally, Wittgenstein's idea of the duty of maintaining silence. Frascolla also proposes a new interpretation of the ontology of the Tractatus. Based on the identification of objects with qualia, the argument put forward in the book challenges the currently prevalent ideas of the New Wittgenstein'. The paradoxical nature of the Tractatus itself, and the theme of "throwing away the ladder," are thus revisited in a new key. Understanding Wittgenstein's Tractatus is essential reading for anyone wishing to further their insight into one of the most influential works of twentieth-century philosophy.

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 value, metaphysics, and finally, Wittgenstein's idea of the duty of maintaining silence. Frascolla also proposes a new interpretation of the ontology of the Tractatus. Based on the identification of objects with qualia, the argument put forward in the book challenges the currently prevalent ideas of the 'New Wittgenstein'. The paradoxical nature of the Tractatus itself, and the theme of "throwing away the ladder", are thus revisited in a new key. Understanding Wittgenstein's Tractatus is essential reading for anyone wishing to further their insight into one of the most influential works of twentieth-century philosophy.

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. The first part is devoted to the "Tractatus" and contains a systematic construction of the representation of arithmetic in logical operations. The second part is concerned with the so-called "intermediate phase" (1929-33), which is characterized by strong verification and by a conception of the relation between the particular and the general in mathematics which forms the basis of Wittgenstein's later reflections on rule-following. The final section deals with the writings on mathematics in the decade 1934-44. The main themes of Wittgenstein's later philosophy of mathematics are understood as consequences of his considerations of rule-following.