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Comment by sunsetdive | Hacker News Reader

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.

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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.

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...

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.

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.

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.

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.

So then what kind of logic is the following:

"Socrates is a male" has a value of True; "All men are mortal" has a value of True; and a conclusion of "Socrates is mortal" that is "True" because a True "and" a True yields a True.

And then an immortal man is discovered, making that first premise "False". And False "and" a True yields a "False".

This causes "Socrates is mortal" to have a truth value of "False", which doesn't make sense unless you consider it "proof" instead of "truth": it used to be proven (by the premises) that Socrates is mortal, but now it is "false that it is proven". It might still be true, but it's not proven.

This is closer to intuitionist logic than classical logic, but it still relies on facts like "Socrates is male".

> "Socrates is a male" has a value of True; "All men are mortal" has a value of True; and a conclusion of "Socrates is mortal" that is "True" because a True "and" a True yields a True.

No, for a logical argument the conclusion must be true if the premises are true. A valid argument (proof) only shows: necessarily, if the premises are true, the conclusion is true.

> And then an immortal man is discovered, making that first premise "False". And False "and" a True yields a "False".

> This causes "Socrates is mortal" to have a truth value of "False"

No...

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.

Beautifully put.

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"?

Yeah. There are some approaches in philosophy of mathematics which try to avoid platonism (the view that mathematical objects have a mind independent existence) but while also retaining classical logic. That's not easily done though. (Currently popular is "structuralism", but this theory has its own problems.)

I do appreciate you providing some relevant information instead of just telling everyone else they're wrong. You still haven't put any of your own ideas on the line though. Is there an approach you believe is correct, and why?

Here's one of mine so I play by my own rules: philosophical questions don't have any testable hypothesis by nature, they'd be scientific questions if they did. The goal is to massage the question into an answerable one if you can. It's not really possible to have a "wrong" answer if the question is unknowable or malformed.

I could have made the original post with less melodrama but I like to snub philosophers when they swoop in like they have answers to these questions. Either it's a matter of science or you don't have answers, just perspectives.

What is testing a hypothesis?

If you'd like to ponder this question and more, please sign up for a course called "Philosophy of Science". It won't help answer it, but it's easy marks.

Sorry, I just figured from all your chest puffing that you had something to say, it appears you don't.

I made my point above. You're the one with nothing to say, you lead with a generic question.

> I do appreciate you providing some relevant information instead of just telling everyone else they're wrong. You still haven't put any of your own ideas on the line though. Is there an approach you believe is correct, and why?

I think a form of logicism (the view that mathematical statements are logical tautologies in disguise) is true at least for arithmetic. There are some ways to interpret them using logical truths from pure higher-order logic. I'm not sure about most other parts of mathematics.

> Here's one of mine so I play by my own rules: philosophical questions don't have any testable hypothesis by nature

I think they are testable by performing conceptual analysis, which consists in organizing data from semantic intuitions about the involved concepts.

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