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Is Mathematics Real? (2020)

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Re: Is Mathematics Real? (2020)

#21

Post by sethc2 »

sunstone wrote: post #7

Mathematics is not embodied by any of the entities of physics and to that extent it is not real.

Only to the extent “real” is defined by something being embodied by entities of physics. Though now we are simply describing a characteristic of what something is not. But the fact that we are describing what some thing is not, assumes then we are describing something that is, and therefore math is real. Though like many real things it’s embodiment varies.

By the platonic idea maybe: The shadow from the flower on the cave wall, does not smell like a flower, but the flower’s smell is a real thing.

Re: Is Mathematics Real? (2020)

#22

Post by yotamoron »

"Real" for humans, is whatever we experience directly. Therefore, colour is as real to a blind man as snow to a person who's born in the equator. Is anger "real"? is love "real"? is depression "real"? - all those are very real for those who directly experienced them. Mathematics is only real for those who experienced it directly.

Re: Is Mathematics Real? (2020)

#24

Post by hanslub42 »

For Plato mathematics was real, but not only that, the stuff we see around us was not.

In the Republic he therefore complains about mathematicians "... always talking in a narrow and ridiculous manner, of "squaring" and "extending" and "applying" and the like - they confuse the ways of geometry with those of daily life; whereas knowledge is the real object of the whole science."

I find it amazing that Plato wrote this 2000 years before it was taken up again (quite radically) by Brouwer's intuitionism, where "squaring", "extending", "applying" are the only way of doing mathematics (and proof by contradiction, one of Plato's favourite devices, is not admissible)

The article's conclusion "Just about everything [except basic number theory] in mathematics is determined by the society in which you live" is rather disappointing, and not at all contradicts the reality of mathematics, as those societies might just have made different discovery journeys in Plato's realm of eternal mathematical truth.

Re: Is Mathematics Real? (2020)

#26

Post by myWindoonn »

smokel wrote: post #20
teucris wrote: post #11

Earlier quoted context omitted.

That’s exactly what I’m saying. I’m glad you like it!

I have been entertaining this idea for years. First time I hear someone else voice it. Do you have an idea what the philosophical term for this idea is? It seems related to connectionism. One might assume that abstraction and pattern matching in the brain are required to determine that two "things" are the same. It is perhaps a small step to go from comparing things to comparing integers. Unfortunately, this line of…

The abstraction from counting to the natural numbers is called "decategorification", in category theory. The abstraction of sameness is called "equivalence" or "isomorphism".

Re: Is Mathematics Real? (2020)

#27

Post by myWindoonn »

ukj wrote: post #10

Category theorist: What is the universal property for “realness”? https://en.wikipedia.org/wiki/Universal_property

The abstract objects which aren't self-defeating [0] are real in this sense. Of course, note that we can't simply quantify over such objects since there is no universal way to decide whether objects are self-defeating, but it is nonetheless a simple criterion.

[0] https://terrytao.wordpress.com/2009/11/05/the-no-self-defeat...

Re: Is Mathematics Real? (2020)

#28

Post by gspr »

yotamoron wrote: post #22

"Real" for humans, is whatever we experience directly. Therefore, colour is as real to a blind man as snow to a person who's born in the equator. Is anger "real"? is love "real"? is depression "real"? - all those are very real for those who directly experienced them. Mathematics is only real for those who experienced it directly.

> "Real" for humans, is whatever we experience directly. Therefore, colour is as real to a blind man as snow to a person who's born in the equator.

This sounds like crazy talk to me. Of course those two things are entirely real.

The fact that we can deduce reality and communicate it to others in a truth-preserving manner is a fundamental underpinning of society. I think it's dangerous to suggest that reality is relative.

Re: Is Mathematics Real? (2020)

#30

Post by beebmam »

sethc2 wrote: post #18
teucris wrote: post #2

“God made the integers, all else is the work of man” I’m not sure if even that is true. Integer counts and succession seem like human constructs to me. An apple isn’t fundamentally a single unit. If I take a bite out of it, is it still one apple?

An apple is a single unit though. An apple is made up of constituent parts, but it is a singular thing. If you argue against an Apple being singular then you are essentially professing that nothing is singular. When you take a bite out of an apple you now have a subset of an apple “an apple with a bite out of it”. To me saying God made the integers is more akin to saying, there is and there isn’t, and all else is bui…

An apple is an abstraction. It's a combination of chemicals bonded together. Those chemicals are composed of atoms which are bonded together, each of which are composed of electrons, protons, and neutrons. Those particles are composed of quarks, and so on.

An apple is a singular thing because it is useful for us to think of an apple as a singular thing in most contexts. It is not a singular thing when it is more useful to look deeper.

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