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
StatementThe Peano axioms of arithmetic can be derived in second-order logic from Hume's principle. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
In Branch
Source Frege's theorem, Wikipedia
Proved By
Source Frege's theorem, Wikipedia
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
In Branch: Logic and Foundations, Lead sentence
In metalogic and metamathematics, Frege's theorem is a metatheorem that states that the Peano axioms of arithmetic can be derived
In Group: Proof Theory and Methods of Proof, Lead section
In metalogic and metamathematics, Frege's theorem is a metatheorem
Proved By: Gottlob Frege, Lead
It was first proven, informally, by Gottlob Frege in his 1884 The Foundations of Arithmetic and proven more formally in his 1893 Grundgesetze der Arithmetik I (Basic Laws of Arithmetic I).
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