Editorial preface to the fourth edition and modified translation -- The text of the Philosophische Untersuchungen -- Philosophische untersuchungen = Philosophical investigations -- Philosophie der psychologie, ein fragment = Philosophy of psychology, a fragment.

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, (...) and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field. (shrink)

The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers.

A respected Harvard logician and philosopher gathers together twenty-nine writings dealing with the foundations of mathematics, Rudolf Carnap, lin-guistics, ...

Drawing on writers as diverse as Saul Kripke, Stanley Cavell, G. E. M. Anscombe, Jonathan Lear, and Bernard Williams, I offer an interpretation of Wittgenstein's key notion of a form of life that explains why Wittgenstein was so enigmatic about it. Then, I show how Hilary Putnam's criticism of Wittgenstein's philosophy of mathematics and Richard Rorty's support of (what he takes to be) Wittgenstein's legacy in the philosophy of mind both require mistaken assumptions about Wittgenstein's idea of a form of (...) life. Finally, I consider the extent to which the idea of a form of life is subject to Donald Davidson's critique of the idea of a conceptual scheme. (shrink)

In this book Saul Kripke brings his powerful philosophical intelligence to bear on Wittgenstein's analysis of the notion of following a rule.

This paper has two main purposes: first, to compare Wittgenstein's views to the more traditional views in the philosophy of mathematics; second, to provide a general outline for a Wittgensteinian reply to these two objections. Two fundamental themes of Wittgenstein's account of mathematics title the following two sections: mathematical propositions are rules and not descriptions and mathematics is employed within a form of life. Under each heading, I examine Wittgenstein's rejection of alternative views. My aim is to make clear the (...) differences and too suggest some similarities. As will become soon clear, Wittgenstein often rejects opposing views for the same or similar reasons. This comparison will provide the necessary background for better understanding Wittgenstein's philosophy of mathematics, for appreciating its many unappreciated advantages and, finally, for defending a conventionalist account of mathematics. (shrink)