alt Hacker NewsThere are other forms of logic? is intuitionistic logic as rigorous? fascinating
edit: the link says it is a weakening. if it is weakened, how can you prove the same stuff? i am a bit confused but i can see how it is useful for smarter people than me!
Replies
black_knight • yesterday at 6:53 PM
Having a weaker base system means you can distinguish more fine grained between statements.
For example, in an intuitionistic setting there is a difference between a set being non-empty and a set having an element.
IsTom • yesterday at 6:22 PM
Intuitionistic logic can prove less than classical logic, but what you gain is that proofs are constructive. Also you can use it to reason about things for which law of excluded middle doesn't hold (typically types).
> if it is weakened, how can you prove the same stuff?
Sometimes, you can't. In particular, so-called "non-constructive" proofs don't work in intuitionistic logic. Some mathematicians like to work in intuitionistic logic: for philosophical reasons, pragmatic technical considerations, or just because they think it's interesting.