> A and not A are not necessarily contradictions Nobody was saying p OR !p is necessarily true. The argument was about p AND !p. It really seems to me like you

> A and not A are not necessarily contradictions Nobody was saying p OR !p is necessarily true. The argument was about p AND !p. It really seems to me like you're confusing AND and OR... The intuitionist will accept that "A and not A" cannot be true https://en.wikipedia.org/wiki/Intuitionism#Truth_and_proof https://en.wikipedia.org/wiki/Intuitionism#Truth_and_proof