Theorem

Frege's Theorem

Logic and Foundations

In metalogic and metamathematics, Frege's theorem is a metatheorem stating that the Peano axioms of arithmetic can be derived in second-order logic from Hume's principle. Gottlob Frege first proved it informally in his 1884 The Foundations of Arithmetic and more formally in his 1893 Grundgesetze der Arithmetik I, and Crispin Wright rediscovered it in the early 1980s, since which it has been the focus of significant work at the core of the philosophy of mathematics known as neo-logicism.

Facts

Statement

The Peano axioms of arithmetic can be derived in second-order logic from Hume's principle. 1

Proof Year

1884 1

Sources

1. Frege's theorem, Wikipedia

Introduction, statement
Frege's theorem is a metatheorem that states that the Peano axioms of arithmetic can be derived in second-order logic from Hume's principle.
Introduction, first proof
It was first proven, informally, by Gottlob Frege in his 1884 The Foundations of Arithmetic

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Frege's Theorem