Comment by goldenkey | Hacker News Reader

Comment by goldenkey | Hacker News Reader

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Extremely naive thing to say. Mathematical truths are merely derived truths about complex structures. These structures borrow intuitive concepts like "sets" or "natural numbers" in their foundations. Mathematics has everything to do with the format of this universe. A statement is only meaningfully true if it is based on axioms that are intuitively true. The direct relationship between what mathematicians agree on as meaningful systems to derive truth from, ie. ZFC , has everything to do with the relstionship between the axioms and intuition that can only be provided by living in this world as a human being.

The old and tired tripe of mathematics being some ethereal detached mental masturbation is so sorely mistaken that I must ask you to respond in as much depth as I did. Because your viewpoint is not only wrong but also the reason so many children grow up to be adults that dislike mathematics. Its a sad disinformation to disconnect the properties of our universe from the science that studies the most abstract type cast of our universe: object.

Natural numbers need not be in scope of intuition. Imagine a diffuse intelligence formed in a fluid (such a thing is at least imaginable), it has no fingers, it recognises no individual things, not even itself, it has no intuition of the natural numbers. If this being makes statement on arithmetic, like 1+1=2, according to you this statement is not "meaningfully true". Yet it is true, and this being has derived it from (abstract) thought. So what is "meaningfully true"?

> need not be in scope of intuition.

> Imagine

Imagination is in principle intuitive.

> it recognises no individual things, not even itself,

self-awareness is part of the common definition of intelligence.

> Imagine [something that is patently made up]

> Yet it is true

utter nonsense

> it has no intuition of the natural numbers. If this being makes statement on arithmetic, like 1+1=2, ...

How?

You can't just say

> imagine Natural numbers need not be in scope of intuition

> then Natural numbers need not be in scope of intuition

I mean, sure you can, but that is circular reasoning and not at all convincing.

You prove his point with your fluid example. Integers have _everything_ to do with our world. If we lived in a fluid world, then the mathematics of that world will not have integers.

Take a look at this: https://en.wikipedia.org/wiki/Mathematical_universe_hypothes...

Perhaps my point is misunderstood here: it is that if we think of mathematical truth as being based on intuition, then since what can be intuited depends on the species, on the society, even on the individual (99% of what was intuitive to Grothendieck is completely beyond me), then mathematical truth becomes relative. I say no, 1+1=2 universally, whether it is intuitive to you or not.

Language too has nothing to do with the Universe - that doesn't prevent sentences in it from "mean"-ing something.

> that doesn't prevent sentences in it

The fact that it could mean the universe or the language pretty much lets your argument fall apart.

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