Frege's theorem

From Wikipedia, the free encyclopedia

In metalogic and metamathematics, Frege's theorem is a metatheorem which states that the Peano axioms of arithmetic can be derived in second-order logic from Hume's principle. It was first proven, informally, by Gottlob Frege in his Die Grundlagen der Arithmetik (Foundations of Arithmetic), published in 1884, and proven more formally in his Grundgesetze der Arithmetik (Basic Laws of Arithmetic), published in two volumes, in 1893 and 1903. The theorem was re-discovered by Crispin Wright in the early 1980s and has since been the focus of significant work. It is at the core of the philosophy of mathematics known as neo-logicism.

Frege's theorem in propositional logic

In propositional logic, Frege's theorems refers to this tautology:

$(P\to (Q\to R))\to ((P\to Q)\to (P\to R))$

External links

Stanford Encyclopedia of Philosophy:
- "Frege's Theorem and Foundations for Arithmetic" — by Edward Zalta.

This article is issued from Wikipedia. The text is available under the Creative Commons Attribution/Share Alike; additional terms may apply for the media files.