Philosophical devices proofs probabilities possibilities and sets 1st Edition by David Papineau ISBN 9780199651726 0199651728
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Product details:
ISBN 10: 0199651728
ISBN 13: 9780199651726
Author: David Papineau
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 Godel’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.
Table of contents:
Part I
SETS AND NUMBERS
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
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
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
THE NATURE AND USES OF PROBABILITY
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
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
9.3 Correlation
9.4 Causation and Correlation
9.5 Screening Off
9.6 Spurious Correlations
9.7 Randomized Experiments
9.8 Survey Research
9.9 Simpson’s Paradox
Further Reading
Exercises
Part IV
LOGICS AND THEORIES
10 Syntax and Semantics
10.1 Validity
10.2 Logic and Metalogic
10.3 Different Kinds of Logic
10.4 Truth-Functional Connectives
10.5 Syntax and Semantics
10.6 Syntactic Consequence
10.7 Semantic Consequence
Further Reading
Exercises
11 Soundness and Completeness
11.1 Soundness and Completeness
11.2 Proving Soundness and Completeness
11.3 Reflections on Circularity
11.4 Predicate Logic
11.5 Predicate Syntax
11.6 Predicate Semantics
11.7 Predicate Logic-Soundness and Completeness
11.8 Predicate Logic-Undecidability
11.9 Second-Order Logic
11.10 The Incompleteness of Second-Order Logic
Further Reading
12 Theories and Gödel’s Theorem
12.1 Theories
12.2 Syntax and Semantics for Theories
12.3 Theoretical Completeness
12.4 Completeness for Theories versus Completeness for Logics
12.5 Gödel’s Theorem Stated
12.6 A Sketch of Gödel’s Proof
12.7 The Inescapability of Gödel’s Theorem
12.8 Meta-Theorizing
Further Reading
Solutions to Exercises
Index
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