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Re:What Even Is a Number? by FabHK on Tuesday February 19, 2019 @05:28PM (#19203516)
> How is it any different than believing that unicorns exist as physical objects, just in their own universe?

Good question, but I think there might be a difference. Suppose, in a galaxy far, far away, there are aliens. They probably don't have the concept of unicorns. However, they probably have discovered numbers, pi, Pythagoras theorem, e^(i pi) + 1 = 0, etc.

So, does the fact that something is discovered (rather than invented), and can be discovered many times independently in identical fashion, confer it some sort of elevated ontological status?

Re:What Even Is a Number? by stcredzero on Tuesday February 19, 2019 @05:43PM (#19203650)
However, they probably have discovered numbers, pi, Pythagoras theorem, e^(i pi) + 1 = 0, etc.

We can only be confident of that if they're in this universe. Also, this is only a conjecture. It's just something some of us imagine would be true. You can't elevate such an idea to the level of empirical data.

So, does the fact that something is discovered (rather than invented), and can be discovered many times independently in identical fashion, confer it some sort of elevated ontological status?

Unicorns. Kirin. Narwhals. Rhinos. So you have two independent origins in culture for such a creature, plus two appearances of something similar in nature. Does that confer it some sort of elevated ontological status?

Re:What Even Is a Number? by dragonwriter on Tuesday February 19, 2019 @06:03PM (#19203841)
> Unicorns. Kirin. Narwhals. Rhinos. So you have two independent origins in culture for such a creature, plus two appearances of something similar in nature.

It's not at all clear that the cultural constructs are independent of each other or real world creatures. Particularly in the Western case, some of the earliest Greek accounts of the unicorn as well as Marco Polo’s account confirming its existence and difference from the contemporary evolution of the image stem from the distant East (from the European perspective) and clearly are describing a rhinoceros. They are also very similar to accounts of the Kirin.

Re:What Even Is a Number? by ngcc_hk on Tuesday February 19, 2019 @07:11PM (#19204362)
Kirin is giraffe and upset Confucius as it should not appear in his chaotic time.
Re:What Even Is a Number? by dragonwriter on Tuesday February 19, 2019 @08:06PM (#19204685)
Some accounts of Kirin, yes, appear quite likely to be giraffes, others are nearly identical to the Western accounts of the monoceros of distant India (one of the original of the unicorn legend) and are almost certainly accounts of rhinoceros.
Re:What Even Is a Number? by kazinator on Tuesday February 19, 2019 @05:42PM (#19203644)
I would sadly have to say no. Because in some completely different universe unlike ours, the aliens have no concept of, say, "hemoglobin" because there isn't matter like ours: no atoms, no iron, no carbon. Unlike numbers, hemoglobin and unicorns contain a kind of arbitrary complexity. Yet one is definitely real. Some real entities are far removed from elementary math (even though they may ultimately rest upon it, many levels down). The question is: are unicorns bunk, or are they like hemoglobin.
Re:What Even Is a Number? by FabHK on Tuesday February 19, 2019 @06:49PM (#19204217)
I'm not claiming that if something exists (haemoglobin), we must have a notion of it and true statements about it in every universe.

Rather: if we have a notion of something and statements about it in every universe, then it must exist. However, come to think of it, that's bonkers.

Still, it's remarkable that mathematics allows us to make reproducible true statements about fictional objects.

Re:What Even Is a Number? by kansface on Tuesday February 19, 2019 @05:47PM (#19203684)
> They probably don't have the concept of unicorns.

What would happen to your epistemology if every alien civilization has unicorns but some lack π?

Re:What Even Is a Number? by FabHK on Tuesday February 19, 2019 @06:43PM (#19204167)
> every alien civilization has unicorns

I knew it, Unicorns are real!!11!

I am not sure I can conceive of aliens that don't have pi (how can they have cylindrical rockets?).

Anyway, maybe we should let the professionals deal with this.

https://plato.stanford.edu/entries/platonism-mathematics/

https://plato.stanford.edu/entries/intuitionism/

https://plato.stanford.edu/entries/mathphil-indis/

https://plato.stanford.edu/entries/nominalism-mathematics/

https://plato.stanford.edu/entries/philosophy-mathematics/