Die Grundlagen der Arithmetik (The Foundations of Arithmetic) is a book by Gottlob Frege, published in 1884, in which he investigates the philosophical foundations of arithmetic. In a tour de force of literary and philosophical merit, Frege demolished other theories of number and developed his own theory of numbers. The Grundlagen also helped to motivate Frege's later works in logicism. The book was not well received and was not read widely when ...
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Die Grundlagen der Arithmetik (The Foundations of Arithmetic) is a book by Gottlob Frege, published in 1884, in which he investigates the philosophical foundations of arithmetic. In a tour de force of literary and philosophical merit, Frege demolished other theories of number and developed his own theory of numbers. The Grundlagen also helped to motivate Frege's later works in logicism. The book was not well received and was not read widely when it was published. It did, however, draw the attentions of Bertrand Russell and Ludwig Wittgenstein, who were both heavily influenced by Frege's philosophy.
Frege objects to any psychological account of mathematics. Psychological accounts appeal to what is subjective, while mathematics are purely objective. Mathematics are completely independent from human thought. Mathematical entities have objective properties regardless of humans thinking of them. It is not possible to think of mathematical statements as something which evolved naturally...
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