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God created the real numbers

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31 points EthanHeilman | 1 comments | | HN request time: 0.209s | source
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tshaddox ◴[] No.45055139[source]
Isn't this article conflating our formalism of a given abstract entity (like real numbers or integers) with the abstract entity itself? Surely quantities existed long before humans (e.g. there was a quantity of stars in the Milky Way 1 million years ago). And surely ordinals existed long before humans (e.g. there was a most massive star in the Milky Way 1 million years ago).

The article's claim seems to be about the mathematical formalisms humans have invented for integers and real numbers. And I agree that our formalism of integers is simpler and more elegant than our formalism of real numbers. But that could just be because we've done a worse job formalizing real numbers!

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crazygringo ◴[] No.45055693[source]
I mean, this is one of the deepest questions of philosophy. Do or can concepts and categories exist without the beings that create them?

Does tuna casserole exist independently of humans? If not, how is the idea of the number 7 different from the idea of a tuna casserole? Or what about the concept of decision by majority, which isn't as basic as 7, but doesn't have the physicality of a casserole?

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1718627440 ◴[] No.45061824[source]
> Do or can concepts and categories exist without the beings that create them

No of course not, but that's not the question. The question is whether the concepts were created by the beings.

In a system with 7 stars the number of stars doesn't change when all humans die or humans never even developed.

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crazygringo ◴[] No.45066502[source]
If humans never even developed, many philosophers would say the concepts of "number" and "7" and "star" would not exist.

Others would say they all exist independently of humans.

Some think abstract mathematical concepts are more privileged than physical categories like stars.

That is the question. I can't even tell if you're arguing one side or the other because you say "of course not" followed by "doesn't change" when those appear to be contradictory positions. But of course there are a lot of subtleties here. There's no "of course" to any of it. These things take entire books to argue one side and try to refute the other.

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1. 1718627440 ◴[] No.45069575[source]
> many philosophers

If only this was the stuff humans wasted their energy on not shooting explosives to improve their ego. :-)

> If humans never even developed, many philosophers would say the concepts of "number" and "7" and "star" would not exist.

Yes, I'm in the camp that thinks this is just plain wrong.

> abstract mathematical concepts are more privileged than physical categories like stars.

I agree to that.

> I can't even tell if you're arguing one side or the other

Sorry, if I was unclear. You wrote:

> Do or can concepts and categories exist without the beings that create them?

This takes it a priori, that the categories are created by the beings. If this is true, then I think by definition this categories can't precede the beings. That's why I wrote "of course not". When things are created by beings, they don't precede them, when they are not, they do.

What I already disagree with is what you already implied as a given. Honestly I don't even know how to argue for that, because this is what I think is part of the definition of the concepts and categories. When I coin some term it always happens in reaction to things I perceived with my senses. So given my senses don't lie to me, of course this is outside of me.

There are also things that are in fact invented by humans, for example color names. This doesn't mean that colors don't exist independently, but the exact boundary is arbitrary.

There are also concepts where I think they can be both. For example beauty. When applied to skin or shape, these are just invented, but the beauty of complexity or completeness exists outside of us. And beauty in general only exists as it points as to a thing that exists independently of us.