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May 25th, 2014, 04:59 AM   #1
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Philosophy of math

I read a mathematician is a mathematician during week and a philosopher on sunday. Reffering to the Bible, I guess.

I wonder to what school, if any, you belong?

If to the question if mathematical statements refer to something we answer 'no', we're a pure formalist. If we answer 'yes', it's possible to claim that the things the statements describe is somethung the existence of which depends on the human mind, something the mind constructs. We're a constructivist then, who includes intuitionist. If we claim that the existence of things described by math statements doesn't depend on the human mind, that the mind doesn't construct it, but only discovers, more successfully or less succesfully, we're a platonist. If we claim math comes down to logic, we're a logicist.

https://en.wikipedia.org/wiki/Philosophy_of_mathematics
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May 25th, 2014, 09:56 AM   #2
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I'm a Platonist with a generous sprinkle of Cartesionist 'I think Therefore I am' peppered in.

I'm a Carté-Plato-Nisionist

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May 25th, 2014, 10:14 AM   #3
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I'm a mathstafarian.

Mathstafarian
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May 25th, 2014, 10:21 AM   #4
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Mostly a Platonist. Mathematics exists entirely independently of the human mind and is logically prior to it. I do have traces for formalism, though -- humans *do* have some measure of control as to which systems to study.

What I've heard is that most mathematicians are Platonists until a philosopher comes around, and then they pretend to be a formalist until they go away. "Oh no, just playing games with symbols here. No special significance here."

I'm very interested in the aesthetics of mathematics.
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May 25th, 2014, 10:34 AM   #5
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I'm a Physicist. Mathematicians are my slaves.

As a theorist (edging on being a Mathematical Physicist) I generally consider Math to be like Physics: a field that is fully formed from the beginning and we are exploring it to find out what's there and how it works.

-Dan
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May 25th, 2014, 11:19 AM   #6
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Originally Posted by agentredlum View Post
I'm a Platonist with a generous sprinkle of Cartesionist 'I think Therefore I am' peppered in.

I'm a Carté-Plato-Nisionist

I'm also a platonist. As for The famous Rene line, says who it's you who thinks? Maybe thought exists, you don't.

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I'm a mathstafarian.

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You're probably the wisest one!

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Originally Posted by CRGreathouse View Post
Mostly a Platonist. Mathematics exists entirely independently of the human mind and is logically prior to it. I do have traces for formalism, though -- humans *do* have some measure of control as to which systems to study.

What I've heard is that most mathematicians are Platonists until a philosopher comes around, and then they pretend to be a formalist until they go away. "Oh no, just playing games with symbols here. No special significance here."

I'm very interested in the aesthetics of mathematics.
I believe in God, Jesus and that God created everything. But I don't believe in free will.

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Originally Posted by topsquark View Post
I'm a Physicist. Mathematicians are my slaves.

As a theorist (edging on being a Mathematical Physicist) I generally consider Math to be like Physics: a field that is fully formed from the beginning and we are exploring it to find out what's there and how it works.

-Dan
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May 25th, 2014, 04:13 PM   #7
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I'd have to be a skepticist. I'm happy with the scientific method. Keeps my feet on the ground.
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May 25th, 2014, 06:27 PM   #8
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I would say that maths exists but that the maths we know represents a model of maths as it exists. It differs from a model in science in that, even when we simplify things by making assumptions we are exactly describing some area of maths. But the model is incomplete.

Research in maths is mostly driven by the requirements of scientific (or at least, practical) endeavour and so at birth, mathematical theorems do have some sort of meaning, but they quickly transcend that meaning when the results become useful in other areas of maths.

I don't think that formalism and Platonism are mutually exclusive. The entire body of maths might exist independently of humans without it meaning anything at all.

I'm an agnostic with atheistic leanings, or on other days, an atheist who is aware that he could be wrong. Not that it would make much difference if I were. Even if we assume that (a) God(s) exist, I see little reason why they should be worshipped. Conversely, I find mathematics worthy of worship due to it's essential beauty.
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May 26th, 2014, 01:46 AM   #9
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I would say that maths exists but that the maths we know represents a model of maths as it exists. It differs from a model in science in that, even when we simplify things by making assumptions we are exactly describing some area of maths. But the model is incomplete.

Research in maths is mostly driven by the requirements of scientific (or at least, practical) endeavour and so at birth, mathematical theorems do have some sort of meaning, but they quickly transcend that meaning when the results become useful in other areas of maths.

I don't think that formalism and Platonism are mutually exclusive. The entire body of maths might exist independently of humans without it meaning anything at all.

I'm an agnostic with atheistic leanings, or on other days, an atheist who is aware that he could be wrong. Not that it would make much difference if I were. Even if we assume that (a) God(s) exist, I see little reason why they should be worshipped. Conversely, I find mathematics worthy of worship due to it's essential beauty.
Interesting that about formalism and Platonism. Never thought of it that way. But I think this question, just like any else, comes down to "God or no God". I must specify that the only true God for me is the Biblical one, and Jesus the only true Messiah. I hope I'm not emposing my beliefs, I'm just stating them. I think that formalism inevitably comes down to atheism and Platonism to religion, even Christianity. It makes no sense that God would create something meaningless.

I wouldn't use the word worship in my case. My faith in Jesus is what gives me hope that good will eventually prevail over evil.
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