> If you can't prove something, it is treated as false. Maybe I'm being excessively literal in interpreting the phrasing here, but that doesn't seem like how I

> If you can't prove something, it is treated as false. Maybe I'm being excessively literal in interpreting the phrasing here, but that doesn't seem like how I would describe classical logic? There are plenty of cases where neither a thing nor its negation can be shown in some system which is based on classical logic (I'm sure you are well aware of this fact, so I'm probably just misinterpreting you by being too literal). But yes, I also share the sentiment that, for ordinary/day-to-day reasoning, classical logic is substantially more intuitive than intuitionistic logic, and makes things simpler. Can I think of a precise way to say the thing that I imagine you must have meant by that? In both classical logic and intuitionistic logic, if by assuming something you can derive False, then you can prove the negation of the thing. So that's not the distinguishing thing. If by assuming the falsehood of something you can derive False, in classical logic you can use that as a proof of the thing. (double negation elimination), while in intuitionistic logic you only get the double negation. This, I think at least mostly describes the difference (though not all the like, implications of it), but I'm not sure how to make it into something similar to "If you can't prove something, it is treated as false." Though, that statement does remind me of the idea of a/the Constructible universe in set theory..