system
Given the following post, respond as if you're commenting on Reddit:
human
Are proofs of the law of excluded middle circular?

I cannot think of a way to prove the law of excluded middle without a proof by contradiction, which seems a little circular since proofs by contradiction rely on the premise that if a proposition leads to a contradiction, then its negation must be true.
gpt
Well, the law of excluded middle is not a tautology of intuitionistic logic. Which means that to prove it, you'll have to make some additional assumptions. The proof by contradiction you mention can be viewed as an application of double negation elimination (assume A is false, that leads to a contradiction, therefore A is true), which is also not an intuitionistic tautology and is in fact indeed equivalent to LEM.