Philosophical Devices Proofs, Probabilities, Possibilities, and Sets

This book is designed to explain the technical ideas that are taken for granted in much contemporary philosophical writing. Notions like "denumerability," "modal scope distinction," "Bayesian conditionalization," and "logical completeness" are usually only elucidated deep within difficult specialist texts. By offering simple explanations that by-pass much irrelevant and boring detail,Philosophical Devicesis able to cover a wealth of material that is normally only available to specialists. The book contains four sections, each of three chapters. The first section is about sets and numbers, starting with the membership relation and ending with the generalized continuum hypothesis. The second is about analyticity, a prioricity, and necessity. The third is about probability, outlining the difference between objective and subjective probability and exploring aspects of conditionalization and correlation. The fourth deals with metalogic, focusing on the contrast between syntax and semantics, and finishing with a sketch of Godel's theorem. Philosophical Deviceswill be useful for university students who have got past the foothills of philosophy and are starting to read more widely, but it does not assume any prior expertise. All the issues discussed are intrinsically interesting, and often downright fascinating. It can be read with pleasure and profit by anybody who is curious about the technical infrastructure of contemporary philosophy.

David Papineau was educated in Trinidad, England, and South Africa. He has a BSc in mathematics from the University of KwaZulu-Natal and a BA and PhD in philosophy from Cambridge. He has lectured at Reading University, Macquarie University, Birkbeck College London, and Cambridge University. Since 1990 he has been Professor of Philosophy at King's College London.

He was President of the British Society for the Philosophy of Science from 1993 to 1995. In 1999-2000 he was a Leverhulme Research Fellow and in 2007 a Mind Fellow. He was President of the Mind Association for 2009-10. In 2010 he gave the Rudolf Carnap Lectures in Bochum, Germany and in 2011 the Gottlob Frege Lectures in Tartu, Estonia.

Preface
Introduction
Part I: Sets and Numbers
1. Naive Sets and Russell's Paradox
2. Infinite Sets
3. Orders of Infinity
Part II: Analyticity, a prioricity, and necessity
4. Kinds of Truths
5. Possible Worlds
6. Naming and Necessity
Part III: The Nature and Uses of Probability
7. Kinds of Probability
8. Constraints on Credence
9. Correlations and Causes
Part IV: Logics and Theories
10. Syntax and Semantics
11. Soundness and Completeness
12. Theories and Godel's Theorem