Formal knowledge
Classical logic
Logic that permits principles such as excluded middle for every proposition.
Definition
Classical logic
Classical logic accepts principles that are not derivable in a purely constructive core, including unrestricted excluded middle.
Classical reasoning supports many standard mathematical proofs. Axeyum records when imported or reconstructed results depend on classical axioms instead of treating the entire library as one undifferentiated foundation.
01
Example
A proof may split on P or not P even when it has no procedure for deciding P.
02
Important distinction
Calling a theorem classical identifies assumptions in its proof route, not a defect in the theorem.
After reading this article, you should be able to
- Define Classical logic in the sense used on this site.
- Recognize a use of excluded middle or choice in a proof outline.