More accurate would be "1+2=4" is a concept like "you are thor" is a concept. Neither is true by definition*
*Perhaps "thor" is sometimes defined merely as the costume? Perhaps dressing as thor on Halloween would make "you are thor" true?
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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.
What is much more common place in maths is for someone to make a list of assumptions and you go from there. This isn't thought to be true it's jus tthought to be a usable approximation of what is going on.
An example is if you drop a ball from a height you can assume gravity to be 9.81 and you can make great estimations on the speed at the point it makes contact with the earth at pretty much any situation in which you'd drop a ball. Newtons laws of gravity is fucking great, it lets you make loads of predictions which are so accurate but if you don't understand it's limitations you are wrong just like the theory is. Hence why science still uses it for most situations but it certinaly doesn't for those that are known to be wrong such as GPS systems. Einstein loads of great shit comes from it but we know it's not true that doesn't mean it doesn't make loads of great predictions we can use it for.
All of those thing make assumptions and say them. These are very important because if the assumption isn't true it's wrong this doesn't mean it isn't useful. Ideal gas law is a great example of this.
Economic models are actually a great example of this in most cases. They make so many assumptions that they are basically nonsense in any actual real life scenario. They aren't wrong but to draw larger conclusions would be. You may recall economics nobel prize giving it to 3 lots of people who all said different outcomes were true because of the same thing and how this was retarded because obviously all three can't be true. Well none of them were ever saying they were always true.
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.
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.
You're saying language could become a thing like maths where everything is defined etc. Yeah maybe it could. I personally don't think that's better than what we have now, or maybe I would and I just can't see it reaching that point which is fair. On a level language tries to convey shit that is much more complicated than maths but that's a different point I suppose.
Language is also ever evolving in a way I don't think maths possibly could. I think this is a great thing about language how words can evolve over time to the point where words can mean what they mean and the exact opposite at the same time.
It's important to realise that it isn't just people don't agree on a definition of a word like love but there is no actual definition. Dictionaries are a great attempt at this but fall so short compared to mathematical definitions it's just bollocks.
I also want to point out that language is fucking great at what it does. I think humans deserve a great pat on the back at the complexities of language and hwo well they understand them based on context.
I believe in maths because I'm good at it.
I also believe in chess.
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
Black holes can be sensed.
Multi-verses can't [to my limited knowledge].Quote:
I believe either math exists or the idea of identity is total hogwash. Either everything is all one, or countability is a property of the universe.
If it is meaningful to count things, then math exists.
I cannot accept that I am actually you and it is only a fault ofmyour perception which makes me think I'm not.
Furthermore, I posit that if there are multiple universes, then that is proof that math exists, at least in-between the universes (where there is clearly countable-ness going on)
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.
Well no, it's not like that. All I said was if something already exists you can't really invent it, you can only discover it. As far as giving people credit for one versus the other, there's no value judgment implied in what I said; you're reading things into my words that aren't intended.
If I had said something along the lines of "Newton didn't accomplish much because all he did was discover gravity, not invent it." then you would have a point.
The question was raised regarding whether maths are invented or discovered, and I offered an answer. If you prefer to believe people invent maths, then by all means feel free.
Of course it does. The ratio of the circumference to the radius is pi, and that was true before someone figured it out.Quote:
Maths doesn't exist without someone to codify it.
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.
Great, maths is discovered.
Just like a wheel was always a wheel before someone created it.
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.
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".
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).
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.
Only the words used to describe maths are invented.Quote:
nd in the same vein, maths is both invented and discovered.
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.
Why are the mathematics axioms assumed true?
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.
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.
I thought you'd like this, wuf.
https://www.youtube.com/watch?v=3gBoP8jZ1Is
2nd video
https://www.youtube.com/watch?v=S4zfmcTC5bM
Cool, thanks.