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Dialogues Concerning Natural Numbers

Charles Sayward

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.