Is mathematics invented or discovered ?

[Ero]

I challenge all of you to work long enough on a math problem until you start hallucinating.

The degree of imagination you need to comprehend higher levels of mathematics is not one accessible to normal humans.

[AION]

Everything is i-magi-nation but not all imagination is the same.

[Natasha Tori Maru]

Both? 

Deep structures appear to exist whether we're here or not..  pythag, primes, geometry, limits. They appear to behave the way they do regardless of human opinion. 2 bananas + 2 bananas = 4 bananas long before anyone counted... Or so it would seem.

But also invented in the sense that the language is ours. I like to think of mathematics as a universal language. Symbols, axioms, co-ordinate systems - human made tools. Calculus didn't 'exist' until someone framed it. Even though change and motion always did.

So I think we built a map to help navigate what was always there... So there was always constraints and patterns & we supplied the formal systems to describe them.

 

[UnbornTao]

23 hours ago, Salvijus said:

 As far as I'm concerned, I see no problems with my definition of what language is. I'm open to hearing opposite views than my own but so far I found none of it more convincing than mine. That's my side of the story at least. Perhaps your experience is different. It's okay. We can just agree to disagree. 

That's the thing, it's a definition. Could you have come up with it if this possibility didn't exist?

Ironically, without language, our knowledge about language might never have come to pass in the first place. Without a reference to the content of language, what is language? 

I ran out of synonyms this morning. 

 

Edited 24 minutes ago by UnbornTao

[gettoefl]

Invented maths is possible. That will model a different universe to this one. Maths just discovers whatever works here. Nothing more, nothing less. I can make different universes if I choose.

[UnbornTao]

20 hours ago, Carl-Richard said:

There are reasons for thinking they are invented and reasons for thinking they are discovered. You can heed both of those while also choosing which ever frame you prefer the most for your everyday epistemology.

But what's true? If it were possible to know what language really is, then that understanding would take a different form than just a notion about it.

Isn't that kind of thinking itself dependent on the thing being investigated?

When we examine our knowledge of language, how much of it relies on language simply to exist?

I haven't done this successfully, but we could ask (as a meditation, perhaps): What is an experience without - or prior to - the existence of language? The goal being creating "language" from the ground up. 

Not an easy topic.

Edited 50 minutes ago by UnbornTao

[UnbornTao]

 

7 hours ago, Natasha Tori Maru said:

Both? 

Deep structures appear to exist whether we're here or not..  pythag, primes, geometry, limits. They appear to behave the way they do regardless of human opinion. 2 bananas + 2 bananas = 4 bananas long before anyone counted... Or so it would seem.

But also invented in the sense that the language is ours. I like to think of mathematics as a universal language. Symbols, axioms, co-ordinate systems - human made tools. Calculus didn't 'exist' until someone framed it. Even though change and motion always did.

So I think we built a map to help navigate what was always there... So there was always constraints and patterns & we supplied the formal systems to describe them.

 

This seems to me like a balanced take, in principle.

For example, if we were to temporarily eliminate the entire possibility of language, what would we then have, relative to a banana? A perception of something? And then - what is a "thing"?

To what extent does language not only influence, but create, our experience?

It's difficult to separate what is there from what is added. I'd rather not speculate too much, and instead proceed step by step - like a meditation.

Edited 17 minutes ago by UnbornTao