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Math, An invention, or discovery?

drpiek
Posts: 589
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8/4/2015 11:35:15 PM
Posted: 1 year ago
Mathematical platonism is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thoughts, and practices, in essence math is something real that always existed and we discovered and not an invention like language. Thoughts?
Ramshutu
Posts: 4,063
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8/5/2015 1:54:00 AM
Posted: 1 year ago
At 8/4/2015 11:35:15 PM, drpiek wrote:
Mathematical platonism is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thoughts, and practices, in essence math is something real that always existed and we discovered and not an invention like language. Thoughts?

This is quite an interesting topic. And in the process of disagreeing with you in places, I'll probably end up agreeing with you in others.

In my opinion, Maths is actually very much like language; albeit a much more formal language (J'ai etudie la francais maintenant! Maths est moins deficile que francais!).

A house is a physical object represented by physical properties, and exists whether there is a name for it or not; and you can say the same for almost everything in maths. Language in this context is a mechanism of describing things that exist; although obviously you are able to use it to describe things that do not.

Maths, in this respect is exceptionally similar. In that it is a formal language of describing things that exist and more specifically I beleive the relationships between things.

At a basic mathematical level, Pi exists as a fixed relationship between the width and circumference of a circle, or it's area, and indeed pretty much everything relating to circles. It's not so much that Pi as an irrational number actually exists, but there is a relationship it describes.

Even getting into the weirdness of imaginary numbers and S-Domain interpretation of inductance and capacitance; having studied a lot of pure and applied mathematics for signal processing and electronics; while weird and curious and giving the appearance that they should not really exist; in a way they do, because even imaginary numbers are used to describe the real relationships between various real things.

In this way, the answer is really related to what would happen if you restarted humanity from scratch; it's possible that we would not write the same songs, have the same games on our phones, have the same sorts of tools with the same purpose because these would all be inventions and products solely reliant on human imagination.

Our languages would not be the same, almost undoubtedly, but we would still have words for human, dogs, cats, grass, the sky, beauty, ugliness.

In the same way, our maths would still be the same; we would still have an equivalent of multiplication, division, probably calculous and almost certainly most of the more advanced mathematic principles (although when you get into the really weird stuff I cannot say, because in all honesty some of the crazy maths I simply do not understand). The reason is that while the language of maths was invented; for example Newton and the-other-guy-we-can-never remember both invented calculus but had different ways of representing it; the relationships that it represents are the same and as such many new theorems, and mathematical advances would still be the same.

As shakespear would say, a beta-function by any other name would still have a symettric identity. And probably something about roses.

So yes, essentially I agree to a point with this position, but you could probably stretch the point too far (I don't think second order integrals "exist", but the relationship that is described by them does).
August_Burns_Red
Posts: 1,253
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8/5/2015 2:14:23 AM
Posted: 1 year ago
At 8/4/2015 11:35:15 PM, drpiek wrote:
Mathematical platonism is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thoughts, and practices, in essence math is something real that always existed and we discovered and not an invention like language. Thoughts?

Math IS a language. It is a form of communication and a way to put into defined words and equations things that other wise couldnt be conveyed. just like all language does. If you look up the def for language you'll see the Mathematics meets all criteria.
God Bless.
Tomorrow's forecast: God reigns and the Son shines!
Sidewalker
Posts: 3,713
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8/5/2015 4:18:45 AM
Posted: 1 year ago
At 8/4/2015 11:35:15 PM, drpiek wrote:
Mathematical platonism is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thoughts, and practices, in essence math is something real that always existed and we discovered and not an invention like language. Thoughts?

The questions for mathematical realism are difficult to answer. If mathematical objects exist independent of the human mind, where and in what form do they exist? If there is an abstract realm that exists, is it another dimension of reality, in what way can it be said to exist,? If so, how do we find out about them? In what way do we have access to this dimension of abstraction? This process of discovery, does it involve observation, do we have the ability to perceive mathematical objects in some other dimensional space? How exactly does that work?

Claiming that mathematics exists independently of mind raises more questions than it answers. Just saying that mathematical objects "exist" and we "discover" them just isn't enough, it requires some kind of an explanation to be meaningful.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
RuvDraba
Posts: 6,033
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8/5/2015 6:17:00 AM
Posted: 1 year ago
At 8/5/2015 1:54:00 AM, Ramshutu wrote:
At 8/4/2015 11:35:15 PM, drpiek wrote:
Mathematical platonism is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thoughts, and practices, in essence math is something real that always existed and we discovered and not an invention like language. Thoughts?

Maths [...] is a formal language of describing things that exist and more specifically I believe the relationships between things.

I agree that this is where maths comes from, and that it remains the grounding of mathematics today. To paraphrase Ramshutu: maths is a language creating structure for describing abstractions of things we already know.

But we can invent abstractions for which we know no physical analog, and if such abstraction nevertheless has structure, then maths can describe that too.

So I'd (mostly) agree with Ramshutu (mostly) agreeing with you, Dr P. :D Maths is normally a language describing the structure of things we know, but it can happily extend to the structure of things we don't yet know, and might might never know.
kp98
Posts: 729
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8/5/2015 6:20:54 AM
Posted: 1 year ago
Just saying that mathematical objects "exist" and we "discover" them just isn't enough, it requires some kind of an explanation to be meaningful.

Perhaps an example would help. Put two stones in a box, and then put another two stones in the box. There will be four stones in the box. Of course there is nothing special about stones. Two things and another two things make four things is built into the very fabric of reality. We didn't invent the fact that two things and another two things make four things. We discover it through our interaction with reality.

Mathematical objects, then, exist in the sense of being reifcations. Two is a reification of a quality shared by all pairs of things, addition is a generalisation of the act of collecting together.

All we truly invent is a notation to describe such aspects of reality. But what that notation refers to is independent of the notation. 7 and VII refer to the same aspect of reality and we are not free to invent what mathematics we like - at least not what mathematics apply to reality.