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## Main Question or Discussion Point

Hi, all.

Wikipedia says:

(emphasis added)

My question is, can we prove that the bolded claim is true? For some many-valued logic, can we show that for some condition, there is P with ¬(P∨¬P) ?

Thanks!

Wikipedia says:

In logic, the law of the excluded middle states that the propositional calculus formula "P ∨ ¬P" ("P or not-P") can be deduced from the calculus under investigation. It is one of the defining properties of classical systems of logic. However, some systems of logic have different but analogous laws, while

**others reject the law of excluded middle entirely**.(emphasis added)

My question is, can we prove that the bolded claim is true? For some many-valued logic, can we show that for some condition, there is P with ¬(P∨¬P) ?

Thanks!