Table of Contents
of
Thinking Things Through
by
Clark Glymour

 

Part I: The Idea of Proof

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1. PROOFS

• Introduction
• Forms of reasoning and some fundamental questions
• The Socratic method
• Geometry
• Plato and Euclid
• God and Saint Anselm
• God and Saint Thomas
• Aquinas and Aristotle
• Infinity
• Spinoza and Euclid
• *Infinity and cardinality
• Conclusion

2. ARISTOTLE'S THEORY OF DEMONSTRATION AND PROOF

• Aristotle and Greek science
• The Platonic conception of knowledge
• Aristotle's conception of nature
• Aristotle's conception of science
• The axiomatic method
• Aristotle's logic
• The theory of the syllogism
• Limitations of Aristotle's syllogistic theory of deductive argument
• After Aristotle
• Aristotelian reasoning in artificial intelligence*
• Two puzzles

3. IDEAS, COMBINATIONS, AND THE MATHEMATICS OF THOUGHT

• Introduction
• Combinations
• The IDEA idea
• Thomas Hobbes
• The binomial theorem
• Leibniz and the mathematics of reason
• Conclusion

4. THE LAWS OF THOUGHT

• Introduction
• The universe of discourse and fields of sets
• Language and the world
• The laws of Boolean algebra
• Truth, propositions, and Boolean algebra
• Use of Boolean logic
• Some limitations of Boole's logical theory

5. FREGE'S NEW LOGICAL WORLD

• Introduction
• Frege,Logicism, and Logic
• The theory of meaning: language and the world
• Implications of Frege's theory
• Mysteries
• Conclusion

6. MODERN LOGIC*

• Relational structures
• Formal languages
• Truth and satisfaction
• Proofs
• Soundness and completeness
• Theories and models
• Two paradoxes
• The Finite and the Infinite
• The Liar

Part II: Experience, Knowledge, and Belief

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7. SKEPTICISM

• Introduction
• Bacon's inductive method
• The Newtonian revolution
• Ancient inductive skepticism
• Hume's inductive skepticism
• Metaphysical skepticism
• Conclusion

8. BAYESIAN SOLUTIONS*

• Natural religion
• The theory of probability
• Bernoulli trials
• The binomial distribution
• What is probability?
• Bayes, Price, and Hume
• The modern revival
• Bounded rationality and Bayesian problems
• Conclusion

9. KANTIAN SOLUTIONS

• Introduction
• The Kantian picture
• Constructional systems
• Conventionalism and analytic truth
• Doubts
• Idealism, skepticism, and relativism
• The History of Knowledge
• After Kant
•  Language Games
•  Primitivism
•  Naturalized Epistemology

10. KNOWLEDGE AND RELIABILITY

• Introduction
• Knowledge
• Reliability and justification
• The mathematics of reliability
• Putnam's framework
• Reliability when truth is relative
• Conclusion

Part III: Minds

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1. MIND AND MEANING

• Introduction
• Some metaphysical views
• Personal identity
• Reduction
• The Intensional and the Extensional
• Functionalism, Physicalism, and the Cartesian Fallacy
• What are meanings?
• Truth conditions
• Meanings as use
• The private-language argument
• Conclusion

12. THE COMPUTABLE*

• The development of computation theory from logic
• Goedel's theorems
• Turing machines
• Church's thesis
• Recursive and recursively enumerable sets
• Decision problems
• What is a computation?
• Complexity

13. THE COMPUTATIONAL CONCEPT OF MIND

• Introduction
• The compuational conception of mind
• The argument of Lucas and Penrose
• Are mental states in the head?
• The Chinese room
• Challenges of the computational conception of mind
• Can the computational conception of mind be wrong?
• Bounded rationality
• Rationality and Computationally Bounded Systems
• Conclusion: Android epistemology and android norms

14. THE ENTERPRISE OF PHILOSOPHY