Why do we believe in math?

[JKDS]

No because with maths they are either right or wrong. With language they can take variable meanings from a phrase or more. There is a school of thought that what the artists mean is unimportant compared to what the critic takes from it. They are open to interpretation, some of my favourite quotes I know for a fact I don't take them as the artist means them, that doesn't mean that what I took from it is wrong. In Maths that is 100% not the case.

That just means the phrase wasnt as defined as you'd have liked. If a phrase has more than one meaning, it means either more than one meaning exists by definition...or it means someone failed in accurately conveying or understanding the idea.

How is "the set of all real numbers" any better than "fork"? Do you agree that my sofa would not qualify as a fork?

[Savy]

That just means the phrase wasnt as defined as you'd have liked. If a phrase has more than one meaning, it means either more than one meaning exists by definition...or it means someone failed in accurately conveying or understanding the idea.

How is "the set of all real numbers" any better than "fork"? Do you agree that my sofa would not qualify as a fork?

No it means it wasn't defined. I have no problem with stuff being defined in multiple ways either as long as it is consistent. Not accurately conveying something means it isn't a definition. You can misdefine things but this is exactly that a mistake.

Based on your definitions I see no reason to believe your sofa isn't a fork.

[JKDS]

No it means it wasn't defined. I have no problem with stuff being defined in multiple ways either as long as it is consistent. Not accurately conveying something means it isn't a definition. You can misdefine things but this is exactly that a mistake.

Based on your definitions I see no reason to believe your sofa isn't a fork.

We're at an understanding roadblock, but I think we're on the same page. I'll go to bed with this:

Unlike math, most people DONT agree on the definitions of words. Love means something different to me than to you. Part of this disagreement is because the definitions suck, or we rely on different definitions to begin with. Another part is that people, as a whole, suck at describing things (because of laziness, poor vocabulary, or what have you). But this doesn't mean words aren't like math, it means we have an unrefined and shitty language.

[a500lbgorilla]

I feel like I chose the wrong words to describe my thought.

When I say people have trouble understanding and conveying math, I don't fault math and I don't mean that math can't do it. I mean that people in general don't understand the definitions, and suck at describing things with math. If you've ever tried to explain something mathematical to another person, you've probably experienced the issue.

There are many who can competently do this though. And understand it. Those people exist for words too, and when they speak it's beautiful

Yeah, there are understandings that are wordless. And then we have to go through all the trouble of getting those understandings across to someone else.

Messy business. People could argue over the communicae for centuries. Oh right, they do, and they're called lawyers.

[OngBonga]

I believe in maths because I'm good at it.

I also believe in chess.

[Jack Sawyer]

I believe in maths because I'm good at it.

I also believe in chess.

I believe in morgandawson__ because I love chocolate.

Also in keyanajenaye.

[Jack Sawyer]

If somebody were to ask me to explain why we believe in math, I would say because it is consistent within its own assumptions and because it is useful. I don't know how accurate that is. What is your answer to the question?

It's more of a "prove me wrong" vibe. 1+1=2. It isn't? Prove me wrong.

You don't necessarily believe (have to believe?) . If you cannot prove it wrong, then you simply assume it as fact as best as you can understand it and move on

[MadMojoMonkey]

Hey wuf! This isn't exactly what you're looking for, but I think it'll give you plenty of food for thought when it comes to similarities in the mythological stories of many different cultures.

Crash Course: Mythology

[OngBonga]

Maths doesn't exist without someone to codify it.

Of course it does. The ratio of the circumference to the radius is pi, and that was true before someone figured it out.

Maths is like language. The word mountain describes something that it physical. The word itself is not the mountain, the word is merely the noise we associate with the physical object that is a mountain.

Without the word mountain, mountains still exist.

[a500lbgorilla]

Great, maths is discovered.

Just like a wheel was always a wheel before someone created it.

[OngBonga]

Great, maths is discovered.

Just like a wheel was always a wheel before someone created it.

No. Someone had to conceive the wheel, someone had to manipulate physical objects in order to create the object they conceive.

That is not what is happening with maths, nor with language. With language, we see something, then we create a word for it. We don't manipulate rock to create mountains so we can give it a name... mountains were discovered, not invented.

The wheel was invented becuase it wasn't "found" lying around, and then someone said "I'll call this the wheel".

[a500lbgorilla]

No. Someone had to conceive the wheel, someone had to manipulate physical objects in order to create the object they conceive.

That is not what is happening with maths, nor with language. With language, we see something, then we create a word for it. We don't manipulate rock to create mountains so we can give it a name... mountains were discovered, not invented.

The wheel was invented becuase it wasn't "found" lying around, and then someone said "I'll call this the wheel".

How didn't Newton manipulate a thing to develop his understanding of mechanics?

[OngBonga]

Further, where there are two mountains... it doesn't require someone to be able to count for there to be two mountains there.

All we invented was the words to descirbe the concpets that we're trying to describe. The mountain exists, just as one and two exist. All we need to do is create the language to communicate these concepts.

[OngBonga]

Newton didn't invent gravity, nor did he invent the laws of motion. He discovered the laws of motion, and observed gravity. He didn't even discover gravity, he just explained it (rather well but not nearly perfectly).

[a500lbgorilla]

Newton didn't invent gravity, nor did he invent the laws of motion. He discovered the laws of motion, and observed gravity. He didn't even discover gravity, he just explained it (rather well but not nearly perfectly).

He invented how to describe gravity.

And in the same vein, maths is both invented and discovered.

Just like how Goodyear invented a way to make wheels real.

[OngBonga]

He invented how to describe gravity.

No he didn't. He didn't invent the words he was using. He merely figured out how to apply the maths to his concepts, he solved the puzzle better than anyone else for a long, long time. But he didn't invent anything, with the possible exception of a slightly flawed intepretation of physical laws that already existed. I suppose that he was wrong means he did invent something! But, that's just pedantry.

There's a clear distinction between inventing and discovering. I know you like to wrestle with language and philosophy, but inventing something involves direct manipulation to create something that didn't previously exist, other than in theory.

The wheel actually isn't the best example, because it's possible that a circular piece of debris was found and used for the purpose, which would make it a discovery. Let's talk about the light bulb. That's a very clear "invention". Is it also a "discovery"? The discovery is what's going on inside the head. The invention is the creation of a concept, it's applying the discovery to the physical world.

Nobody is creating maths, just applying it or describing it.

nd in the same vein, maths is both invented and discovered.

Only the words used to describe maths are invented.

[wufwugy]

Why are the mathematics axioms assumed true?

[Savy]

Why are the mathematics axioms assumed true?

Because someone said if you assume a b and c then d, ohh shit e f g h i j too, maybe even x y and z.

And no one has had a problem with a b or c at any point in time and we're onto zzzzzzz

[MadMojoMonkey]

Pretty much what Savy said.

Mathematical statements begin, "If you assume..." which is formally saying, "For the sake of the following discussion, that statement is absolutely true."

The thing is that math is very tight with its axioms. Simpler, more intuitive statements are preferred in most cases.

E.g.
Assume identity is not an absurd idea, i.e., that 'things' in the broadest sense, can be told apart, i.e. that if we were to talk about "this" thing, we would know that we're not talking about "that" thing, and vise versa, because we can tell these are different things.

That's more formally stated in mathematical axiom, but that's the gist of the fundamental principle which gives rise to all of algebra.

Whether or not this is true, or any reflection of reality is coincidental. That coincidental relationship can make humans more or less interested in studying it, but it doesn't change that the relationship between reality and numbers is not formally required in any part of mathematics.

[OngBonga]

I dunno, I think maths is sort of science. I think it's like a chess opening database compared to an endgame tablebase... science is the study of openings... it develops, and new openings become superior to what were once considered optimal. Maths is like the tablebase, working backwards, slowly figuring out all possible outcomes, starting with the most basic and becoming ever more complicated.

Either way, it's all doing the same thing... figuring chess out.

[MadMojoMonkey]

I thought you'd like this, wuf.



2nd video
https://www.youtube.com/watch?v=S4zfmcTC5bM

[wufwugy]

Cool, thanks.

[MadMojoMonkey]

Mathematics is the queen of sciences, without it it is impossible, this is the basic science

Mathematics is not a science.

Mathematics is not based on experimental observations, but on propositions, or axioms. Mathematics supposes its axioms are true and draws logical conclusions based on those axioms. If an axiom causes inconsistencies, it is discarded from that corner of mathematics, which is reminiscent of scientific processes, but not enough. Whether or not those axioms represent anything which could be observed is not relevant. Only the internal consistency of the logical mathematical system is relevant.

In the sciences, for any statement to be considered "true" (true in quotes, because science doesn't produce true statements, only statements not yet shown to be false), it must match experimental observations. It is not enough that a statement adds or does not disrupt the logical consistency of the science's other statements.