Applicability of Maths to the Universe

[Belacqua]

Yes, there is an aspect of math that cuts across cultures. But this is also true of other basic linguistic concepts. So, cat, chat, gato, mao, etc as opposed to two, deux, dos, er. 

The word "cat" and its cognates refers to material objects of a certain type. The question we're working on now is: what does "two" refer to?

One difference is that math  is a *formal* language: it has internal rules that are not present in most natural languages. And, for mathematicians, playing with and exploiting those formal rules are the essence of the game.

And, yes, mathematics really is like a very complex game for those doing mathematics. It has rules about what 'plays' are legal, it has goals (theorems), etc. It can even be helpful to *think* of the mathematical concepts visually and in other ways.

You use words that sound unserious when you talk about pure mathematics -- "playing with," "game," "plays," etc. 

Would you say that math is only serious when it is used to describe the material world? That any other time it's just a game? 

I think that many mathematicians would disagree with you. I'm also concerned that if we define seriousness as utility, we're repeating a common anti-intellectual assumption.

In exactly what sense do numbers have an 'independent existence'? 

Since you've already ruled out all of Plato (without bothering to explain why), we can talk about numbers having independent existence in exactly the way that Popper describes. I suppose I could type that all out in my own words, but the original paper is not long. And if you're going to go around declaring that Popper is wrong it might make sense for you to read what he says. 

https://tannerlectures.utah.edu/_documen...pper80.pdf

From what I can see, the 'number 2' is a shorthand for all the cases where counting two objects is a useful thing to do. And the mathematical object 2 allows for such modeling.

So a number is the memo we use after looking at two objects and counting them? If that's all numbers are, then you're begging the question and assuming that they only exist when used in reference to physical objects. 

But then, you use the term "mathematical object 2." Is this the same as the number 2? Do people doing pure mathematics use "mathematical objects" but not numbers?

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I really want to see some one counting in 'Cat'!

  

No one counts in "cat." 

The question is: does a word like "two" refer to an object in the same way that a word like "cat" does.