[sunsetdive]

This is post-modernism applied to math. It concludes in solipsism.

Since the mind and its mental constructs are a part of the objective reality, they will end up describing aspects of objective reality. If they don't, they break down, become chaotic and incomprehensible to those grounded in the objective reality.

[fnordsensei]

They don’t need to describe aspects of reality, they just need to describe something analogous that’s useful enough when applied.

I’m no physicist, but I understand that Newtonian physics aren’t strictly true as such, but they are a good enough analogy to put a person on a different planetary body.

So I think it’s fine to be agnostic and practical about the outcomes without needing say much about the metaphysics either way.

Anyway, both perspectives tickle my curiosity.

[wpietri]

For sure.

I'm of the "all models are wrong, some models are useful" school of thought. My best guess is that the platonic-ideals-are-real folks are mistaking something in their head for something outside it. That's not to deny that there is an objective reality out there, just that I have no particular reason to think that it's perfectly representable in 3 pounds of primate headmeat and expressible by squirting air through our meat-flaps. [1]

But ultimately, it doesn't matter too much to me, because the practical utility of both models is pretty high. It does make me wish to meet intelligent beings from different evolutionary backgrounds, though, as I think there would be a lot of "So you think what exactly?" that would be very revealing about which things are pan-human quirks and which are more universal.

[1] Credit goes to Terry Bisson here for the last bit: https://www.mit.edu/people/dpolicar/writing/prose/text/think...

[naasking]

No, you're reading too much into it. The origin of the idea was a skepticism around seemingly paradoxical mathematical constructions, like uncountable infinities. Intuitionism eliminates some methods of proving that such things exist without needing to construct a proof of their existence.

And via Curry-Howard, any intuitionistic proof is also a computer program. Intuitionism thus unifies computation and mathematics in a very direct way, which has been extremely useful.

[Schiphol]

Intuitionism is not at all chaotic, though. It's a fully cogent way of doing math, it's just not a perfect overlap with traditional mathematics: some things you can prove intuitionistically that you cannot prove otherwise, and vice versa.

[tunesmith]

I was initially surprised to read this because when I hear Intuitionism, I hear Intuitionist Logic. But IL doesn't have anything to do with denying objective reality; it can use facts on the way to proof. So I don't really know why Intuitionism is so much more adamant about denying constructive reality, or why it's thought to "give rise" to Intuitionist Logic, which at this point seems like a totally different thing. In other words, it's true that truth != proof, but that doesn't mean truth doesn't exist.

[cubefox]

If there is an independent source of truth (external reality), then classical logic makes sense and intuitionistic logic doesn't. But intuitionists say mathematics, unlike the physical would, doesn't have such an independent reality. There is no platonic mathematical reality apart from explicit mathematical construction. Then classical logic is inappropriate and intuitionistic logic has to be used for mathematics.

[mistercheph]

The offer of 'objective reality' as the antithesis to solipsistic mental constructs is exactly the naivety that give both of these impotent families of epistemology any continued sway. Both bad, both wrong, and the crowd swings from one to the other, and at each arrival, anew recognizes the flaws of the mode and turns back.

[mecsred]

Thank god a philosopher has arrived to tell us we're all wrong. Being so wise, you must have the correct answer for us. What's it going to be today "you're not smart enough to understand my genius solution" or "enlightenment can't be taught, only achieved"?

[wpietri]

Beautifully put.