## Dialogues Concerning Natural NumbersDialogues Concerning Natural Numbers advances a thesis made several years ago by Rudolph Carnap: The sentence There are numbers is a trivial truth if construed as an assertion from within mathematics. As such it cannot possibly divide philosophers of mathematics. It lacks sense if construed as an assertion outside of mathematics. Unfortunately, the truth and importance of Carnap’s thesis has not been fully appreciated by philosophers of mathematics. The six dialogues that compose Dialogues Concerning Natural Numbers were formed to bring attention and praise to Carnap’s theory. |

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### Contents

Introduction | 1 |

Chapter Two A Conversation about the Peano Axioms | 15 |

Chapter Three Why Axiomatize Arithmetic? | 33 |

Chapter Four A Conversation about Numbers and Knowledge | 47 |

Chapter Five A Conversation of Five | 81 |

Chapter Six A Conversation about Numbers and Existence | 105 |

127 | |

### Common terms and phrases

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