The nature of mathematics.

[Johnny]

I'm sitting here in my room slightly baked with no one to talk to and I got to thinkin'. Does mathematics exist to be discovered, or does man invent it? As far as I know Plato was the first to claim that it already exists. I would agree with him, but would not know how to prove it one way or the other.

I have thought of this:

-Physical existence is a subset of the laws of math. That is, math exists for which it would seem no physical example does.
-Math is a subset of mental concepts.
-The mind is a subset of physical reality.

Thus we have three legs, each a subset of the previous coming back to the original, regardless of which one we start with. I'm not sure this can be possible. One leg of the triangle must be false, i.e. that math is a sub set of mental concepts... or something.

What say you?

[40oz]

Well simple mathematics im pretty sure already existed, but the way it was coded by way of determining the value of digits and plus signs and subtraction signs all had to be recorded and taught over generations.

[Creaphis]

Well! It just so happens that I took a philosophy of math discussion course last year. Let me throw a few thoughts in here so that Myk can show up and make them look stupid.

The author of one of our class' main texts categorized all mathematical philosophies as realist or non-realist - essentially, for each philosophy, he made the claim, "This philosophy states that mathematics are objectively real," or "This philosophy states that mathematics are not real in any way." However, some modern philosophies are difficult to categorize. This author labeled naturalism as "realist," because noted naturalists declare math as a fundamental part of our web of knowledge, but I found this label to be highly debatable. Eventually, the conclusion that the class came to was: Whether math is real or not depends on how you define "real." And that's another mess. We also learned that philosophical questions don't get answered, which is something I had already figured out, but this left several of the more innocent students severely disappointed.

In my own personal philosophy of math, which the course helped me to substantiate, I would say that the first leg in your post is the weak one. I believe mathematics to be a linguistic tool, created by human minds, to describe reality to a much higher accuracy than would otherwise be possible. As reality appears to work in ordered, predictable ways, we are able to use this language of math to predict as well as to describe. Reality does not follow mathematical rules, but math can be used to make a sufficiently accurate model of reality. Much math is also done without any intent to measure reality, but just to further mathematical systems - this doesn't discover previously-existing mathematical truths, but just further explores the consequences of math's foundational linguistic rules.

There are some common arguments against non-realist philosophies, but none of them are bulletproof. Some of these arguments have become dated, but others are still poignant, such as: if math is not real, existing and eternal, then why do no "alien mathematics" exist? Many cultures in early history, fully separated from each other, have arrived at the same set of arithmetical and geometrical axioms. Isn't this strong evidence that there is ONE set of mathematical truths, eternal and existing separately from ourselves?

To respond to this, I would argue that, while we have created our mathematical languages based on a certain set of rules, and "alien mathematics" founded on other rules could hypothetically exist, the physical laws of the universe have shaped our own brains to favour one set of rules over any other. Imagine a human brain that is fully convinced that 1=2, and his own personal mathematics includes this fact, even though such a system would not be useful to describe our reality. As math is an extension of language, and thus is a reflection of the mathematician's conceptual knowledge about his world, this shows a fundamental conflict between how our reality works and how our "alien mathematician" perceives it. Such disconnects between perception and reality are not advantageous to survival, and any brain that is capable of a system of math that is incompatible with conventional systems will quickly be weeded out via natural selection. This is a rough example but I hope you follow.

Now, the funny thing is: Declaring that there is only one set of mathematical rules which intelligent species can develop is close to saying that this one set of mathematical rules is the only true set, so it could be argued that this one set of rules is objectively correct, and existent within the universe itself. So, is our math "Real?" "True?" It's really up to you. Now, it's possible that an intelligent species could flourish with a fully different system of mathematics, but this would require that the species live in an environment where fundamentally different perceptions of the structure of reality would be best for survival. Now, what environment in this universe could possibly be different enough from ours for this to be the case? Past the edge of the universe? The core of a black hole?

[GreyGhost]

Johnny said:

-Physical existence is a subset of the laws of math. That is, math exists for which it would seem no physical example does.
-Math is a subset of mental concepts.
-The mind is a subset of physical reality.

Birds fail the second leg because they can't count. Does that mean they cease to exist?

[Creaphis]

GreyGhost said:

Birds fail the second leg because they can't count. Does that mean they cease to exist?

Sure, why not.

[Butts]

im not sure why, but i have definitely thought about this before. everything is pretty much based on math too... im taking physics class and the answer to everything is math, well thats what it seems like. math was not an invention, it just simply existed. i just forgot what i was typing.

[Lüt]

I find that it exists for the primary function of stealing valuable career-oriented education time for the purpose of meeting an irrelevant and stale core curriculum requirement.

[Creaphis]

Or perhaps career-oriented education steals time from learning the conventions by which the universe is measured. Take that



You have a point, though. I can respect those who just want to learn how to do a job, even though my future career is one of the things I have a hard time caring about.

[exp(x)]

Math was invented, and if you don't agree with me, then fuck you.

[Butts]

so you would like to fuck me? bring it on!

just dont hurt me...

[Fredrik]

"Mathematics is part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap." - Vladimir Arnold

[Creaphis]

exp(x) said:

Math was invented, and if you don't agree with me, then fuck you.

YES! Now THAT is philosophy.

[Doom Marine]

Lüt said:

I find that it exists for the primary function of stealing valuable career-oriented education time for the purpose of meeting an irrelevant and stale core curriculum requirement.

A lot of engineers, chemists, physicists, and Asians are sad because of your hurtful statement.

[Doom Marine]

Mathematics is the perfect language, and if you don't agree with me, then fuck you.

[myk]

Lüt said:
I find that it exists for the primary function of stealing valuable career-oriented education time for the purpose of meeting an irrelevant and stale core curriculum requirement.

Do they make you study it even for non-scientific careers? In the University I went to you don't need it for humanities.

[Sharessa]

That's one of the many reasons I dropped out of college. Fucking math. All I want to do is make music.

The funny thing is that if humans didn't have 10 fingers, we'd most likely not be using a base-10 system. Digital. Digits. Fingers. Ten.

[magicsofa]

I've had plenty of digital sex...

Anyway, exp(x) is right. "Math" is, first of all, a -word- referencing a concept. Obviously people have different words for what we consider math. They also have different words to represent numbers, operations, functions, and whatever else.

Math is really no different from a language in and of itself. People see stuff, and start naming it. I know it takes a long time and it's not instantaneous, but you get the point. Similarly, it took gradual human evolution to start naming quantities - one, two, etc. It took even longer to come up with the concept "zero." Arithmetic obviously came after the numbers, and so on until we have totally wacky theoretical math going on that probably has no bearing on reality.

But the point is, the concept of math did have to be "invented." If I have two apples and throw one away, the state of affairs (that is, me having only one apple left) doesn't change depending on my ability to describe the quantity of apples I have.

Get it?

By the way, I consider math an ultimate representation of truth. It's the same as logic. It's just a system we define in order to examine truth value. 1+1=2 because we set it up that way, and therefore it must be true.

[Csonicgo]

Doom Marine said:

Music is the perfect language, and if you don't agree with me, then fuck you.

Fixed

[Sharessa]

Csonicgo said:

Fixed

Seconded.

[Creaphis]

Doom Marine said:

Klingon is the perfect language, and if you don't agree with me, then fuck you.

Fixed better.

[fraggle]

You can never prove that anything in maths is "correct", because of Gödel's incompleteness theorems - you can only prove that a mathematical system is self-consistent. Our "conventional" system of mathematics is based on several fundamental axioms which are held to be true; everything else follows from there. If you use different axioms, you can get different mathematical systems that are also consistent.

The axioms that form the mathematical system that we normally use are arguable based on our real world conceptions of what we intuitively believe to be true; as such, it's really based in our subjective experience of reality.

[chungy]

I never thought of that, but it strangely makes sense. It's hard to think of different axioms that would also make sense, however...

[Technician]

Danarchy said:

That's one of the many reasons I dropped out of college. Fucking math. All I want to do is make music.

Heh funny. I'm staying in college in hopes to make music.

[fraggle]

MikeRS said:

I never thought of that, but it strangely makes sense. It's hard to think of different axioms that would also make sense, however...

I believe modular arithmetic is one example of a system that uses different axioms.

Euclidean geometry is another system that is based on a set of axioms, like "parallel lines never meet"; if you change them, you get different systems, like spherical geometry.

[andrewj]

magicsofa said:

Similarly, it took gradual human evolution to start naming quantities - one, two, etc. It took even longer to come up with the concept "zero."

Indeed. I've heard about isolated tribes being discovered who had no words for numbers over three, and three itself was ambiguous for a "group of more than two". [something like that anyway]. It suggests that even simple arithmetic is not inevitable (just highly probable) for sentient beings.

[Sharessa]

Technician said:

Heh funny. I'm staying in college in hopes to make music.

Well I'm going back...to a different college that doesn't teach math or English.

[exp(x)]

Danarchy said:

Well I'm going back...to a different college that doesn't teach math or English.

I don't think you can call it college then. Besides, any respectable degree in music involves music theory which involves math.

[Fletcher`]

Doom Marine said:

Mathematics is the perfect language, and if you don't agree with me, then fuck you.

[Creaphis]

I'm confused. Why wasn't that funny?

[GreyGhost]

Kentucky maths might be more to your liking if no less confusing. :-)