Description
Wittgenstein once said that his aim was to make the philosophical problems 'completely disappear', a remark that has baffled philosophers ever since. In this book, Sorin Bangu reconstructs and defends Wittgenstein's unusual idea, and applies it to the traditional problems in philosophy of mathematics, setting out and explaining the subtleties of what is considered the most difficult area of Wittgenstein's views. He also considers how, according to the later Wittgenstein, we should think of the relation between philosophy and mathematics, articulating Wittgenstein's 'normativist' dissolution strategy and explaining his 'therapeutic' vision of the relation between the two disciplines. His book shows how these controversial views sit within the context of current debates in the philosophy of mathematics, and mounts a detailed and convincing defence of the radical eliminative claim – that philosophy of mathematics after Wittgenstein is devoid of its traditional problems.
Table of Contents
Introduction: a disappearing act; 1. Wittgenstein's normativism about mathematics; 2. Normativism as eliminativism: three illustrations; 3. Basic mathematical rules (I): hardening; 4. Basic mathematical rules (II): objectivity, agreement, and skepticism; 5. Advanced rules: proofs and concept-formation; 6. Cantor's proof (I): a 'style of thinking'; 7. Cantor's proof (II): reluctant nonrevisionism; 8. Logicism, number and the infinite; 9. Conclusion: a cleared ground; Bibliography.
