Solid Klein bottle: Difference between revisions

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In [[metalogic]] and [[metamathematics]], '''Frege's theorem''' is a [[metatheorem]] which states that the [[Peano axiom]]s 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'' ([[Frege's Foundations of Arithmetic|Foundations of Arithmetic]]), published in 1884, and proven more formally in his ''Grundgesetze der Arithmetik'' ([[Frege's Grundgesetze|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 calculus|propositional logic]], Frege's theorems refers to this [[tautology (logic)|tautology]]:
 
:<math>(P \to (Q \to R)) \to ((P \to Q) \to (P \to R))</math>
 
==External links==
* [[Stanford Encyclopedia of Philosophy]]:
** "[http://plato.stanford.edu/entries/frege-logic/ Frege's Theorem and Foundations for Arithmetic]"&nbsp;— by [[Edward Zalta]].
 
{{DEFAULTSORT:Frege's Theorem}}
[[Category:Theorems in the foundations of mathematics]]
[[Category:Theorems in propositional logic]]
[[Category:Metatheorems]]
 
{{Logic-stub}}

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