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The Foundations of Arithmetic

Die Grundlagen der Arithmetik

Gottlob Frege·1884·German

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Frege's attempt to show that arithmetic is logic in disguise. He defines number not in terms of counting or intuition but of one-to-one correspondence between concepts. The book was largely ignored in its time and recognized only when Russell and Whitehead built on it. It founded modern philosophy of mathematics.

Number is not abstracted from things in the way color, weight, and hardness are, nor is it a property of things in the external world: it belongs to a concept. The statement that a course of lectures has been given every Monday and Wednesday for three terms contains a numerical statement about a concept, not about a day or a week. If I say 'Venus has zero moons', there simply is no moon or agglomeration of moons for me to attach the zero to.

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