Work · Analytic Philosophy
The Foundations of Arithmetic
Numbers are logical objects – against psychologism and Kant.
Introduction
Frege wrote this short book, published in Breslau in 1884, in ordinary German almost without formulas for philosophers and mathematicians. It begins by criticising existing answers to the question “What is a number?”: Mill’s view of numbers as empirical facts, Kant’s view of arithmetic as synthetic, and the idea that numbers are mental images. The introduction states three methodological principles, among them the context principle: the meaning of a word is to be asked for only in the context of a sentence. A statement of number, Frege argues, is an assertion about a concept, and numbers can be defined as extensions of concepts. Little noticed at the time, it later became a classic of the philosophy of mathematics.
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Connections
Criticizes
- Critique of Pure Reason1781 · Immanuel Kant
- A System of Logic1843 · John Stuart Mill
Taken up in
- Logical Investigations1900 · Edmund Husserl
- Principia Mathematica1910 · Bertrand Russell
- Frege: Philosophy of Language1973 · Michael Dummett
More works by Gottlob Frege
- 1879Begriffsschrift
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