Table of Contents

of

Thinking Things Throughby

Clark Glymour## Part I: The Idea of Proof

## 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

## 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

## 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