Chapter One

The Language of Mathematics

Chapter Two

Metamathematics

Chapter Three

Zeno's Paradoxes and Infinity

Chapter Four

Binary

Chapter Five

Aristotle on Infinity, and Galileo on Infinity

Chapter Six

Finite Games, and Functions

Chapter Seven

Induction and Finite Games and Geometry

Chapter Eight

Bayes's Law and Constructivism

Chapter Nine

Defining Numbers, Decidable sets and Nice sets

Chapter Ten

Ordinal Numbers, Proof by Contradiction and Commensurability

Chapter Eleven

Ordinal Arithmetic and Infinite Nice Sets?

Chapter Twelve

Ordinal Multiplication, The Hydra, Set Theory and Undecidable Sets

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