A slightly different reframing on a recurring philosophical question about #maths: what percentage of #mathematics do you believe is discovered versus invented?

#math #philosophy

@btcprox Mathematical concepts are 100% discovered, mathematical language is 100% invented.

@freemo then what % of mathematics comprises concepts, and what % comprises language?

@btcprox You cant compare incompatible types thats like asking "what percentage of the universe are physical objects vs what percentage are ideas. How do you even quantify ideas vs the physical things those ideas describe?

@freemo interesting. It doesn't really have to be an actual number though. I could also ask in a vaguer sense: how strongly do concepts dominate language (could be the other way round) in your perception/use of maths? Or perhaps they're equally fundamental?

@btcprox Language is simply any mechanism that conveys concepts. So they seem tangents of each other.

Without other humans I could do math entirely without the language component. In fact this is usually what I do. I only invoke the language when it is time to express these ideas in some way.

In math for any one concept we usually have multiple ways to describe it, because by having lots of synonyms in a language allows us to be more expressive and explain the same idea in different ways.

@freemo does that mean you consider math to be equivalent to the concepts, if language isn't necessary to do math? Or are the concepts part of but not the entirety of math?

@btcprox I am someone who is very good at math but very poor at math language, so im bias :)

@freemo haha that's fine, merely curious about your personal belief! And at least you recognise a bias shaping your opinion ;)

Just to ask again: how strongly do you believe that math IS just the concepts? Would a stronger belief in that also imply a stronger belief in math being discovered?

@btcprox well I think how well we can explain math (math language) helps but the math itself is the idea not the language explaining the idea then.

@freemo so summing up your beliefs:

* Math is the ideas you work with, and are purely discovered
* The language describing the ideas is invented; it is a conveying mechanism of math, but is not math itself

Is that a fair summary?

I may come up with other questions/thoughts later on to examine them further (in a friendly casual way!) 😉

@btcprox @freemo Interestingly enough, I find I disagree with this. My concept of math is it comprises of sentences within a formal system, that is, production made according to the rules of inference. The semantics, or how we understand the math is separate from the formal language. Additionally the formal language is clearly invented to make concrete patters that we perceived in our own reasons. That is, we were using the rules to reason before their formalization and the formalization is what we call mathematics.

@btcprox @freemo This is maybe an academic pretension, that I don't consider it math without proof but that is the tradition that I come from. It is the proof that makes it math. Building systems of reason without proof is either science, engineering, or philosophy depending on the aim.