>>11451388I agree with the second sentence, but why do you say the first doesn't make any sense?
I'm saying that, when arguing about the validity of a statement in a formal logic, showcasing how it plays out in two-valued semantics isn't a strong argument in my mind.
There's enough universally quantifyable statements that a provably undecidable and thus can have no demostrable proof value each of it's instances. E.g.
https://en.wikipedia.org/wiki/List_of_undecidable_problems#Problems_about_matricesTo say a proposition _is_ like a container holding either of two truth values is begging the question from the get-go.
Adopting LEM just hides nice math and has no gain except for shorter formulas. And for any statement A provable with LEM, there's also an intutionistically statement B such that LEM+B=>A imediatenly, e.g.
https://en.wikipedia.org/wiki/Double-negation_translationAnyway, I was just shitposting from the start in the sense that it doesn't quite fit the topic of the thread (it's just always fun to discuss the topic on /sci/, although where it leads to is questionable.)
My favorite "theorem", if I think about it, is probably some nice but completely basic analysis result..
