It’s not intuitive, it’s intuitionist. I’m not saying that to nitpick it’s just important to make the distinction in this case because it really isn’t intuitive at all in the usual sense.

Why you would use it is it’s an alternative axiomatic framework so you get different results. The analogy is in geometry if you exclude the parallel postulate but use all of the other axioms from Euclid you get hyperbolic geometry. It’s a different geometry and is a worthy subject of study. One isn’t right and the other wrong, although people get very het up about intuitionism and other alternative axiomatic frameworks in mathematics like constructivism and finitism.

▲

BigTTYGothGF 2 hours ago | parent | next [-]

> if you exclude the parallel postulate but use all of the other axioms from Euclid you get hyperbolic geometry

No, you don't.

(You need to replace the parallel postulate with a different one)

	▲	seanhunter an hour ago \| parent [-]
		Thank you for the correction I actually didn't realise that so have learned something. Specifically for people who are interested it seems you have to replace the parallel postulate with a postulate that says every point is a saddle point (which is like the centre point of a pringle if you know what that looks like). https://en.wikipedia.org/wiki/Pringles

▲

smj-edison 2 hours ago | parent | prev [-]

I think they called it intuitive, because I called it intuitive in my original post, so that's on me :)