80-150 The Nature of Reason

Summer Two, 2001

Overview

Introduction

What is philosophy?
History of western philosophy

Deductive reasoning

Examples of reasoning
Euclid's geometry
The structure of deductive theories
Arguments for the existence of God
Reasoning about the infinite

Aristotle's logic: The syllogisms
Soundness and validity of arguments

Hobbes, Descartes, and Leibniz
Ideas and combinations

Boole's logic
Modern logic and some of its limitations
Propositional logic
Predicate logic

Inductive reasoning

Induction vs. deduction
The theory of probability
Hume and skepticism
Bayesian solutions
Kantian solutions
Knowledge and reliability

Mind and computation

Mind and meaning
Philosophy of mind overview
Sense and reference; Quine's holism
Computability
Turing machines
Mathematical induction