(June 13, 2020 at 3:45 pm)Jehanne Wrote:(June 13, 2020 at 11:08 am)polymath257 Wrote: 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.
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.
In exactly what sense do numbers have an 'independent existence'? 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.
WLC does not accept ZFC, and in particular, the Axiom of Infinity. He is an ultra finitist, except, of course, when it comes to his God's attributes. Dr. James Lindsay's book Dot, Dot, Dot: Infinity Plus God Equals Folly has a in-depth look at this.
I didn't realize he had actually weighed in on that issue. I know he doesn't like an actual infinite past, but I wasn't aware he disliked either the axiom of infinity or, more broadly, ZFC.
On the other hand, there is a type of consistency there. It is pretty likely that Plato would be considered a finitist by today's standards. On the other hand, it is difficult to do an honest job of even Euclidean geometry without actual infinities.
