What's the point of theories like the following? how have they benefited humans?

Question

do not bother to explain technical details, i've been reading up on them since 3 years back.

law of the excluded middle, false dilemna, syllogism.

how would it seriously benefit human beings to study these theories ? granted, false dilemna makes sense in arguement, so does syllogism. but whats the point of making them so similar, and the most questionable(i think) law, law of the excluded middle. like, huh, you need someone to tell you that?

at least theories like Pythagoras' theorm does benefit us, i really cannot picture someone spending weeks on a thesis explaining that if a = b, and b != c, then a != c.

Answer 1

I guess so that if someone's trying to trick you with a bad argument, you're more likely to notice.

Funnily enough, if someone DOESN'T already believe in these theories, there's no way to convince them.

"So you see now why this can't both be a basketball and not be a basketball at the same time?"

"No. Why?"

"Because it can't be a and not-a."

"Why?"

"Because... because... oh, shut up!"

Answer 2

If you've ever seen a creationist argue, you'll see the value of the law of the excluded middle. They'll find some laughable claim against evolution and parade it around as though they've proved creation.

Answer 3

They're for working with logic, which is extremely close to mathematics. In both, you can't just assume something, you have to have a proof to back up every single step. Just because it makes complete sense to anyone to say a=a or a=~~a doesn't mean you don't have to prove it to make your work legitimate. It may seem superfluous to you, but that how they make sure everything is correct.