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 19 hours 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 20 hours ago by UnbornTao

[UnbornTao]

 

14 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 also 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 12 hours ago by UnbornTao

[Salvijus]

8 hours ago, UnbornTao said:

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

Whether you define existence or not, it still exists. Same is true with communication. Is there a form of communication that is not invented but universal? According to me - yes. Hopefully I don't have to explain myself all over again. If you disagree, it's okay. We can agree to disagree. 

Edited 17 hours ago by Salvijus

[Joseph Maynor]

There's real analysis and complex analysis as subjects today.  Real analysis concerns real numbers and complex analysis concerns imaginary numbers.

This is fascinating!
https://en.wikipedia.org/wiki/Complex_analysis

[UnbornTao]

3 hours ago, Salvijus said:

Whether you define existence or not, it still exists. Same is true with communication. Is there a form of communication that is not invented but universal? According to me - yes. Hopefully I don't have to explain myself all over again. If you disagree, it's okay. We can agree to disagree. 

I disagree with your point about communication somehow existing on its own. How would that even come about?

Is language really limited to defining and labeling reality - as if reality were there as an immutable object, and language merely added commentary on top of it? Or is the relationship far more intertwined?

Communication isn't a fact of the universe, but an activity. Bring to mind how much projection and conceptualization is involved in such an assumption. 

Language actively contributes to our experience in a creative way. It makes possible entire worlds for us to inhabit: science, philosophy, art, religion, belief, communication, comedy, metaphor, symbolism, talking with yourself. These are huge aspects of our shared experience of reality, and yet, without language, they couldn't exist. Think about it.

The fact that a sound can represent something beyond or different from itself already points to language being invented.

I get that written exchanges may not be especially effective, but at the very least they can leave us with a question or an opening to delve deeper into the topic, rather than simply assuming that all this means we actually comprehend what language is.

[UnbornTao]

Also, I'm not exactly sure that its being universal (in the sense of being broadly applied, perhaps) has to be incompatible with its being invented.

But in my experience, I keep bumping into assumptions about language. Like: it is objective, it is just an add-on, it is absolute, etc. 

[UnbornTao]

@Salvijus

Watch the fart language video above.

Edited 13 hours ago by UnbornTao

[Natasha Tori Maru]

6 hours ago, UnbornTao said:

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.

Hmmmm language in my eyes... appears to mediate/filter/stabilize experience (while not having anything to do with the generation of consciousness itself). But I definitely think it is an element in creating out social reality; money, laws, contracts, gender roles, job titles, borders... all exist because of shared language. It also frames perception - we don't experience raw reality, we experience an 'interpreted' reality. Language supplying categories... so I imagine if our language had 10 words for a feeling, we might notice that feeling more precisely. But if the language had no words for the feeling the experience still happens. It would just be more nebulous/fuzzy and harder to hold... maybe even easier to dismiss?

Language also creates psychological objects - ego, anxiety, trauma, success, failure.

Mathematics as a language would operate the same I imagine... the raw experience of one banana, then two bananas... we can use 'plus' as the operator. It is a tighter cleaner language. Less wiggle room and brutal consistency. Raw experience would be one banana, then another banana. It is  'pre-mathematical' - no numbers required. Even animals can get that far - my little miniature poodle certainly can. Mathematics enters in when we abstract 'one', 'two', 'plus'. Then instead of dealing with the experience of the bananas we are dealing with relationships stripped of content.

And that is the key move there - once we say 1 + 1 = 2 the bananas disappear. Apples work... fingers work - anything works! So it turns into structure...

Anyway dunno where I was going there  

[zurew]

Its often times an ill-formed question.

This is one move that I usually use, when I have a categorization problem:

Think through a couple of  examples where the categorization (in this case invented/discovered categorization) is crystal clear for you and try to analyze and explicate what made the categorization easy in those cases. Once you finish that, try to work yourself backwards from there  (try to apply that gained understanding/insight to progressively harder examples and eventually to math).

[Natasha Tori Maru]

21 hours ago, Ero said:

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.

No offence, but this sounds like a full parrot of something Leo would say... 

[Salvijus]

7 hours ago, UnbornTao said:

I disagree with your point about communication somehow existing on its own.

That's okay. We can agree to disagree. 

Quote

How would that even come about?

I don't want to repeat myself for the 10th time. 

Edited 7 hours ago by Salvijus