Philosophical devices : proofs probabilities possibilities and sets Cover Contents List of Boxes Preface Introduction Part I: SETS AND NUMBERS 1 Naive Sets and Russells Paradox 1.1 Sets 1.2 Membership and the Axiom of Extensionality 1.3 Unions Intersections and the Empty Set 1.4 Subsets 1.5 Members versus Subsets 1.6 Power Sets 1.7 The Axiom of Comprehension 1.8 Russell s Set 1.9 Russell s Paradox 1.10 Barbers and Sets 1.11 Alternatives to Naive Set Theory Further Reading Exercises 2 Infinite Sets 2.1 Some Infinite Sets 2.2 Different Kinds of Numbers 2.3 Two Senses of  More 2.4 Denumerability 2.5 More Denumerable Sets 2.6 The Non Denumerability of the Real Numbers 2.7 The Abundance of the Real Numbers Further Reading Exercises 3 Orders of Infinity 3.1 Some Harder Stuff 3.2 The Numerical Size of Sets 3.3 The Reals and the Power Set of the Natural Numbers 3.4 The Continuum Hypothesis 3.5 An Infinity of Infinities 3.6 The Generalized Continuum Hypothesis Further Reading Exercises Part II: ANALYTICITY A PRIORICITY AND NECESSITY 4 Kinds of Truths 4.1 Three Distinctions among Truths 4.2 Analytic and Synthetic 4.3 A Priori and A Posteriori 4.4 Synthetic A Prioris 4.5 How is Synthetic A Priori Knowledge Possible 4.6 Pure and Applied Geometry Further Reading Exercises 5 Possible Worlds 5.1 Necessity and Contingency 5.2 A Posteriori Necessities 5.3 A Priori Contingencies 5.4 Possibility and Necessity 5.5 Possible Worlds 5.6 Necessity and Possibility in terms of Worlds 5.7 Constraints on Possible Worlds 5.8 Essential Properties 5.9 The Nature of Necessity 5.10 Different Kinds of Possibility Further Reading Exercises 6 Naming and Necessity 6.1 Two Readings of Statements of Necessity 6.2 Scope Distinctions. Philosophical Devices introduces the technical ideas that are taken for granted in contemporary philosophical writing. It offers simple explanations and covers a wealth of material that is normally available only to specialists. This original distinctive book will appeal to anyone who is curious about the technical infrastructure of philosophy.