Philosophy Is maths part of the natural world?

Blobbenstein

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The only way that we can understand maths is with our brains, which are a part of nature, so I would say that maths is part of nature.

I used to think that somehow it was aloof from this reality, this world, but I now see it as being as subjective as anything else.
 

Indian Summer

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No, math is the language we use to describe the natural world. Numbers and operations on numbers don't really exist as objects.

By your line of thinking, it seems everything that we can understand with our brains is part of nature, which doesn't seem to make sense.
 
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Blobbenstein

Blobbenstein

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surely those things are part of nature because our understand only comes about because of of our brains, and minds, which are part of nature.

can numbers really exist with out objects?
 

Indian Summer

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I can imagine a society of talking, winged unicorns, inhabiting some distant planet, but that doesn't necessarily make them part of the natural world.

In the same way I can imagine numbers and complex, yet coherent rules for doing operations with numbers.
 
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Blobbenstein

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I didn't really mean part of the natural world in that way, although maybe it is that way...

I just mean in the same way as a computer program is part of the natural world, or what ever that program computes.

I'm not sure how computer memory works these days, but magnetic fields, and electric currents are part of the natural world, and what ever mechanism by which we think, be it chemical or electric signals, metaphysical properties, they too are part of the natural world.

I think it is an important point because I think we take our understanding of logic as being objective and separate from nature, where as in fact it is very much part of it, and what is logical to us may not be logical from another perspective.

I like the Gödel's incompleteness theorem stuff, or at least my understanding of it, which isn't very technical, but I like the idea that nothing can really be proved, and think that that might mean that logic is subjective, and in another reality/universe maybe the rules of a triangle are different to Pythagoras', or maybe pi has a different value, or maybe there is no such thing as a circle.
 
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Blobbenstein

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Partly what I an getting at is that our understanding of logic comes from millions of years of evolution, plus our individual experiences, which have moulded our minds, and which comes from our being part of this universe, and I don't think that would make it objective, but heavily subjective based upon the "laws",and behaviour, of nature.
 

cornsail

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Blobbenstein said:
I used to think that somehow it was aloof from this reality, this world, but I now see it as being as subjective as anything else.

Why subjective? Would that mean 2+2 has a different correct answer depending on who you ask?

I would say we have mathematical concepts in our brain/mind, but those concepts are not necessarily mathematics itself. Sort of like how I have a concept of "pole vaulting" and a concept of "apples" in my head, but we wouldn't say I have actual apples and pole vaulting in my head.

Indian Summer said:
No, math is the language we use to describe the natural world. Numbers and operations on numbers don't really exist as objects.

Plato and Roger Penrose would disagree. Personally, I'm inclined to agree with you, but I think the argument goes deeper than it appears on the surface.
 
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Blobbenstein

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Why subjective? Would that mean 2+2 has a different correct answer depending on who you ask?

yeah, it's difficult to see how that could be any different, but I try to stay open to the possibility.
I know all my life, from playing with toys as a kid; you get up bunch of toys and they add up to a total, but that is all in this universe, following the laws of this universe, so maybe it would be different from another perspective, in another universe, crazy as that may seem.
 

nog

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The only way that we can understand maths is with our brains, which are a part of nature, so I would say that maths is part of nature.

I used to think that somehow it was aloof from this reality, this world, but I now see it as being as subjective as anything else.

To "Is maths part of the natural world?" I think it entirely depends on what you mean by 'natural world' and 'part'.

I think people will disagree, because of the way they view those words.
 

Pickle Juice

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I think of "natural" as anything that has not been synthesized by humans, even though I see the ability of humans to synthesize as natural.

I see math as a language, and as a tool that gets applied to natural phenomena in order to understand them, but, unlike the languages people have developed in order to communicate with one another, math seems to me to be a body of logic that exists independently, something that is recognized by humans, but not created by them, in the same way English was created.
 

silva

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Maybe my take on this is ignorant, but I'm thinking other animals have a natural instinct towards math.
I'm thinking webs, cocoons, navigation.
Esp. insects-bees certainly have a better use of math.
 

FortyTwo

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Maybe my take on this is ignorant, but I'm thinking other animals have a natural instinct towards math.
I'm thinking webs, cocoons, navigation.
Esp. insects-bees certainly have a better use of math.

This. Golden ratio, anyone?

However, I have to ask... what do you mean exactly by "math"? Math is just the study of numbers. If you mean the natural world corresponds to our opinions of math, then yes, that makes sense, because that is where we derived them from in the first place.
 

jeneticallymodified

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To "Is maths part of the natural world?" I think it entirely depends on what you mean by 'natural world' and 'part'.

I think people will disagree, because of the way they view those words.

a whole big bunch of what he said.

maths isn't something that comes 'naturally' to me, at all. my brain gets horribly scrambled by it and things rapidly dissolve into hyperventilating and tears once we get past three figures and much beyond making change for a $20. i'm assuming i'm part of nature?

...and honestly i have no clue what 'the natural world' is supposed to be..... especially compared to some 'un-natural world'... *gets dizzy and tries not to think about sparkly vampires*.

i see a lot of complex pattern, number, and shape -related stuff IN nature... spiderwebs, bee hives, flowers, crystals, blah de blah. i don't hear many squirrels or blades of grass debating pythagoras or talking about squares on hypotenuses very loudly while i'm trying to sleep, or anything though. thankfully. in large part because i take my pills every day, no doubt. :D
 

schmencer

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I like the Gödel's incompleteness theorem stuff, or at least my understanding of it, which isn't very technical, but I like the idea that nothing can really be proved, and think that that might mean that logic is subjective, and in another reality/universe maybe the rules of a triangle are different to Pythagoras', or maybe pi has a different value, or maybe there is no such thing as a circle.

Although I also can't claim to have a technical understanding of Gödel's incompleteness theorem, I don't believe that it states you can prove nothing, just that no system can fully demonstrate its own consistency. Essentially, you will always have to make some assumptions. This is why mathematics must start off with a set of axioms from which other stuff can be proved. And manipulating these axioms is sometimes what makes math so interesting—for example non-Euclidean geometries which throw out the parallel postulate. [Which essentially is the assumption that two non-parallel lines will always intersect — and (I think) is a good example of the incompleteness theorem in that it cannot be proven from Euclid's other axioms].

In my opinion a better way to put this question is: "is math discovered or invented?" (not my phrasing, although I don't remember where I heard it). Not that I have a particularly good answer to that one either...
 
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schmencer

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Also, for anyone interested in this sort of stuff I recommend Logicomix, a history of early 20th century math (and the crazy—sometimes literally—people involved) in comic book form. It's very accessible and well written/drawn.
 

yally

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Also, for anyone interested in this sort of stuff I recommend Logicomix, a history of early 20th century math (and the crazy—sometimes literally—people involved) in comic book form. It's very accessible and well written/drawn.

Oh! I've had that sitting on my bookshelf for a while now, just haven't got round to it. Thanks for reminding me :)
 

Josh James xVx

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Well, this descended into things that make my head hurt pretty fast.

Math is simply the way we express our limited understanding of certain basic universal forces. It doesn't actually exist as a thing. It's like a sensory perception of a thing.
 

nigel1

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Why subjective? Would that mean 2+2 has a different correct answer depending on who you ask?

It does if you're speaking the same language. To someone not speaking a language based on arithmetic postulates, 2+2=4 could be wrong or, more likely, gibberish.
 

cornsail

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It does if you're speaking the same language.

Due to the contrast with your next sentence and this one, I think you mean "doesn't" here(?)

To someone not speaking a language based on arithmetic postulates, 2+2=4 could be wrong or, more likely, gibberish.

But you are focusing on the linguistic representation of 2+2=4, not the underlying meaning. You are also implying that something being correct is dependent on someone understanding or believing it to be correct.
 

nigel1

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Due to the contrast with your next sentence and this one, I think you mean "doesn't" here(?)

You are correct, sir.


But you are focusing on the linguistic representation of 2+2=4, not the underlying meaning. You are also implying that something being correct is dependent on someone understanding or believing it to be correct.

No, different maths are based on different postulates. Arithmetic or counting maths are so commonplace that we take them as intuitive and true. I believe that it is you who are focusing on a linguistic representation more than a formal one, but yes, you are absolutely right about my implication in your last sentence. Something being correct is dependent on someone understanding or believing it to be correct; they believe it as truth because they are taught so, or they believe the postulates necessary to reason that it is true. It is hard to use the very abstracted 2+2=4 as an example because it is so universally taken for granted. Instead, why not use the example, "parallel lines don't intersect." Most people with a basic knowledge of mathematics or reasoning skills would agree that this is true, self-evident, whatever, but if you ask a mathematician you will likely get, "it depends," or from a few, "absolutely not." It all depends on the postulates we believe going into the discussion.
 
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