80150 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