| Description |
1 online resource (xix, 192 pages) : illustrations |
| Contents |
Cover Page -- Title Page -- Copyright Page -- Dedication -- Contents -- List of Boxes -- Preface -- Introduction -- Part I -- 1 Naive Sets and Russell's 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 |
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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 -- 4 Kinds of Truths -- 4.1 Three Distinctions among Truths -- 4.2 Analytic and Synthetic |
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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 |
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6.1 Two Readings of Statements of Necessity -- 6.2 Scope Distinctions -- 6.3 Julius and the Inventor of the Zip -- 6.4 Rigid Designators -- 6.5 The Causal Theory of Reference -- 6.6 Rigidity and the Causal Theory -- 6.7 De Dicto and De Re -- 6.8 Necessary and A Priori Again -- 6.9 A Limit to Scepticism about A Posteriori Necessity -- Further Reading -- Exercises -- Part III -- 7 Kinds of Probability -- 7.1 Probabilities of Propositions -- 7.2 Kolmogorov's Axioms -- 7.3 Some Consequences -- 7.4 Joint Probabilities -- 7.5 Subjective and Objective Probabilities -- 7.6 Subjective Probability |
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7.7 Action, Utility, and Subjective Probability -- 7.8 Dutch Books -- 7.9 Objective Probability -- Further Reading -- Exercises -- 8 Constraints on Credence -- 8.1 The Principal Principle -- 8.2 Conditional Probability -- 8.3 Updating Degrees of Belief-Conditionalization -- 8.4 Bayes' Theorem -- 8.5 Conditional Probabilities and Conditional Statements -- 8.6 Material Conditionals -- 8.7 Indicative and Subjunctive Conditionals -- 8.8 Rational and Metaphysical Changes -- Further Reading -- Exercises -- 9 Correlations and Causes -- 9.1 Probabilistic Independence -- 9.2 Probabilistic Dependence |
| Summary |
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 Devices is 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 Gödel's theorem. Philosophical Devices will 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 |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Philosophy, Modern.
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PHILOSOPHY -- History & Surveys -- General.
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Philosophy, Modern
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| Form |
Electronic book
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| ISBN |
9780191656248 |
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0191656240 |
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9780199651726 |
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0199651728 |
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