Math, Music, and Philosophy

Is anyone else freaked/amazed at how closely related the three are?

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OMG EVERYTHING IS RELATED

>>3
But only 50% of relations are more related than average.

>>1
No. I'm not. But I understand how fundamental the relationship between philosophy and mathematics is.

People really need to stop reading GEB if they're going to be so impressed by it.

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the relationship between music and philosophy is nicely exposed in the first part of the Simarillion concerning the creation of Arda

>>8
Tolkien succesfully envisaged M-theory, so it's more to do with physics and the creation of the universe than who/what created the universe.

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Music (as opposed to acoustics) and maths aren't really related, it's just that music theory can sometimes have a logical structure.

Music which is purely based on maths (various works by Xenakis, Boulez and Stockhausen come to mind) usually pushes the limits of what is considered music, which suggests that music and maths are not just two sides of the same coin.

ps DIX!

>>11
I've always thought this too. Everyones always like wow music and math! But no. Just because sound can be described using physics/math, does not in anyway make them very related. Logically and computer generated music is largely unappealing.

Have you ever read Godel, Escher, Bach: Eternal Golden Braid? It kinda has the same idea.....check it out.

>>10
I agree with this basic principle, but a lot of people would syill disagree

Math and philosophy maybe.
But music? No. How the hell did you come to that conclusion?

>>13
Please review >>6.

>>16
*shrug* Just kinda skimming and thought I'd suggest a good read. I admit it's nothing revolutionary, but I see no reason not to be at least slightly impressed by his ability to describe what would normally be a rather abstract concept mundanely....it's no book for the college-level mathematician, but nearly anyone else could only benefit from reading it.

>>17
It really is amazing at finding so many parallels and connections between godel escher and bach, but the same cannot be said about music, art, philosophy and math in general.

>>18
Well, I wouldn't say every aspect of them are intermingled, but there are surprisingly many similarities. For the most part, the artistic aspect of human beauty has been defined mathematically, as have some of the prominent patterns in music. On the other hand, some would say that the beauty of an equation has an artistic balance to it. Philosophy also has a large impact on all three of these in the stylistic expression of art, the impact of music's mood, and some of the theories behind math (take the implications of some of set theory for example). On the other hand, this is all a matter of opinion. Some people simply don't think the similarities defined enough to say they are interwoven, and others see the subtlety as proof in itself. I, for one, believe in the latter.

Philosophy is liberal arts bullshitting, it has nothing to do with math aside from abstracted reality which has no bearing on the physical world

>>20
Tell me why 1 + 1 = 2 without using philosophy.

>>21

because that's how we defined the symbol for the multiplicative identity, the binary relation of addition, the symbol used to denote equality and the successor to multiplicative identity.

Fuck all to do with philosophy.

>>22
Ahhh the axiomization of mathematics. You make it sound so simple, but this was a philisophical problem for mathematics only settled in the 19th century. All was going well until Gödel proved in the 20th century that there are things in mathematics that are true and can't be proved with the axiom system. There are still many Platonic mathematicians who hold that numbers are real objects, and not just a language we use axioms to play games with.

Logic is also philosophy. Deductive reasoning, the basis of all formal proofs from axioms, relies on Aristotlean logic. However, most proofs are not stated so formally and are at the mercy of human language and its imperfections and ambiguities. This makes most written mathematical proofs fallible. If written proofs were written axiomatically they could simply be entered into a computer and checked using a simple program, without professors having to spend weeks in some cases agonizing over them just to be hopefully "convinced" by the arguments presented.

>>23

I told him why 1 + 1 = 2. It's because that's how the symbols are defined.

That's nothing to do with philosophy. Many similar questions are, but that one isn't.

>>24
It's because that's how the symbols are defined.
I guess you didn't take on board the previous post. Your view is that of a formalist, a philosophical view, which happens to be the dominant view of our time (hence why you share it). Gödel proved formalism is untenable when applied to the entire field of mathematics.

>>25

I know what godel proved, that doesn't changed why 1 + 1 = 2.

I guess you didn't take on board my previous post.

Oh look what I did there, intellectual stalemate (except I'm obviously right)

>>26
I really don't think you understand philosophy. This is like talking to a school kid who just learned his additional tables or something.

>>27

>>27

I really don't think you understand philosophy.

This is like talking to a school kid who just read a undergraduate textbook on philosophy and didn't really understand it.


The fact that 1 + 1 = 2 has EXTREMELY little to do with philosophy, it has very little to do with the axiomisation of mathematics as well.

1 + 1 = 2 just because of how the symbols 1, +, = and 2 are defined. It's not a question of philosophy.

>>22
"because that's how we defined the symbol for the..." What do we do this based off of? It's either based off of an axiom, and so is the product thereof, or it is an axiom in itself, being a truth taken for granted. If you can prove that 1+1=2 without using axioms, then you've just won, but I think you'll find that impossible. Now, unless you're going to contest that axioms lie in the domain of philosophy, it can be shown that the most basic mathematical equations are completely reliant upon the creation of philosophy. It seems reasonable to, if that conclusion is met, say that math is reliant on philosophy.

>>27
You're trying to bullshit your way through this conversation in the hopes that nobody will realise that you don't actually know what you're talking about, and couldn't hold your own in a real discussion of axiomatic theory.

>>30
Ignorant cunt. The fact some philosophers decided to pretend mathematics is actually what their domain is about in a desperate attempt to steal some credibility doesn't make it true.

>>31
I'll give you one more chance to offer some logic behind your thoughts. You've given me nothing but a heap of opinionated garbage, add some evidence, logic, citation, anything to show that what you're saying is true. At least try to refute my logic. That's kinda how post-junior high debates go......or so I hope. I'll give you a hint: I gave evidence for why math was the philosopher's domain, now you should return with something along the lines of counter-evidence, not merely your thesis restated.

>>32

>>31 isn't me, the original person arguing with you, just to point that out.

However he agrees that you're an idiot.

You haven't given any logic, there's nothing to refute. Our argument is just really that fucking simple that it's easy to re-state.

Deciding on axioms is not a philosophical process. In maths you don't pick axioms because you believe them to be fundamentally true, you pick axioms because you want to study systems that you believe have those axioms.

>>33
You don't appreciate the implications of Godel's incompleteness theorem. Do some reading faggot.

>>34

You're an idiot. Godel's incompleteness theorem means that no system can be consistent and complete.

But that doesn't mean a system can't be consistent and prove certain statements true.

Even then, it doesn't matter if my particular construction of the integers is consistent or complete as to whether 1 + 1 = 2.

The statement 1 + 1 = 2 doesn't mean anything except within a system where 1, +, = and 2 have been defined. Whether or not that system is complete or consistent doesn't (In the system of integers we're familiar with) affect either way whether or not the statement 1 + 1 = 2 is a true statement, within that axiomatic system.

Do you even understand Godel's incompleteness theorem yourself, you seem to be throwing it around like some sort of philosophical buzzword.

>>35

Be wary of bridges, and what lie beneath.

>>36

You seem to underestimate how much fun an argument is.

>>33
Perhaps it's merely the semantical nature of the argument that leads to this confusion. It doesn't matter what the name of what defines mathematics is, but it can be said with certainty that mathematics does not define itself. "In maths you don't pick axioms because you believe them to be fundamentally true, you pick axioms because you want to study systems that you believe have those axioms." I've neither said, thought, nor implied that axioms are any sort of truths, in fact, they quite possibly contain the least amount of truth. They're merely truthy. Still, this fact does nothing to refute axioms' roots outside mathematics. To assert an axiom, you must use procedures derived outside of the field of mathematics, such as assumption. Mathematics only deals with the relationship between properties, which means that the actual basis for these relationships must be developed by an outside entity, for axioms are derived from no other property. Just think of philosophy and logic creating the axiom and mathematics creating the theorems; in a purely numerical instance, of course.

>>38
I'm not confused, you're just wrong.

"Why does 1 + 1 = 2"

Tell me then, how would you answer this?

I'm assuming you agree with me that the question would be better worded,

"Why is the statement "1 + 1 = 2" true".

And obviously you could say, that depends on the axiomatic system you are working in.

However, he's almost certainly, without knowing, asking about the standard construction of the natural numbers, let's take peano's as it's an obvious choice.

Now, within that system, we can assign truth values to a statement. The fact that the statement "1 + 1 = 2" is true, follows pretty simply from the axioms.

Godel's incompleteness theorem does not come into it. Peano's axioms have in fact been proved to be consistent by referring to a different mathematical system, but that's irrelevant here.
While there are statements that can be expressed in our system here that are undecidable, the statement "1+1=2" is not one of them.


I don't see where you are expecting philosophical questions to enter into this. "Why those axioms" is hardly a philosophical question. Just because it may or may not be outside the realms of mathematics, which is debatable, does not place it inside the realms of philosophy, and even if it were, it would still be irrelevant to the matter at hand. (HORRIBLE sentence structure there, I apologise)

>>1
Not particularly.

If you ask a Philosopher they'll say Math and Music root from Philosophy. If you ask further where Philosophy comes from they roughly say it comes from either dedicating many brain cycles to big questions, or from God.

If you ask a Mathematician or a Musician where Math/Music comes from, they'll roughly say it comes from either taking the time to figure out a problem, or it's influence from God, or something they feel is God-like.