Dialogues Concerning Natural Numbers

Front Cover
Peter Lang, 2009 - Mathematics - 130 pages
0 Reviews
Dialogues 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.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

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
References
127
Copyright

Common terms and phrases

About the author (2009)

The Author: Charles Sayward received his B.A. from Bates College and his Ph.D. from Cornell University. He is currently Professor of Philosophy at the University of Nebraska-Lincoln, where he has taught since 1963.

Bibliographic information