Quite. Mathematics is a tool - a language for discussing, describing, and deducing.
In itself it says nothing about the concepts being discussed. It's not a model - it's the language we use to describe the model. Some other hypothetical intelligence probably wouldn't use exactly the same language we do, but it would be relatively straightforward to come up with a way of translating between the two languages. "one plus one equals two" isn't a statement open to verification; it's a definition of the operation of addition - a verb in the language of mathematics. Of course you need to define "one" and "two" as well. That's actually quite a bit harder to do in an unambiguous fashion, and you need to get into some fairly advanced concepts. But it can be done. > I venture to suggest that some might disagree with this, but I will leave > it to others better qualified to do so. > > John > > On Mon, 10 May 2004 14:07:27 -0500, William Kane <[EMAIL PROTECTED]> > wrote: > > > > > On Monday, May 10, 2004, at 10:51 AM, Bob W waxed: > > > >> Hi, > >>> > >> > >> surely the purpose of mathematics is to remove this dependency. There > >> are almost certainly things that our minds cannot comprehend that > >> other minds could, in just the same way that there are things we can > >> comprehend that dogs and chimpanzees cannot. But mathematics and logic > >> allow us to explore ideas that are otherwise beyond our grasp. They > >> allow us to take ideas that we *can* grasp and stretch them beyond our > >> limitations, while keeping them consistent. This is why they seem > >> weird to us. But to schoolchildren on the planet Tralfamadore they may > >> be no weirder than building blocks are to human children. > >> > >> -- Cheers, > >> Bob > > > > As we wax philisophically, I would like to note that Math is an > > invention of humans. Sure, we can apply math to natural phenomenon, but > > this makes it no less of a model that describes a portion of the > > universe any more than quantum physics, or any other theory for that > > matter. Just a thought, not a criticism or a comment. > > > > IL Bill > > > > > > > > -- > Using M2, Opera's revolutionary e-mail client: http://www.opera.com/m2/ >
