On Thu, 13 Jul 2006 14:20:01 -0400, Hatto von Aquitanien <abbot@AugiaDives.hre> wrote:
>lDontBother@nowhere.net wrote: > >> On Thu, 13 Jul 2006 09:33:58 -0400, Hatto von Aquitanien >> <abbot@AugiaDives.hre> wrote: >> > >>>A good number of people can master concepts of mathematics sufficiently to >>>solve difficult problems in, say, fluid mechanics without much grasp of >>>set >>>theory. That makes me wonder if set theory really is fundamental to >>>mathematics. >> >> I believe set theory is essential to modern math. > >What can you do with set theory which you can't do with symbolic logic >and/or some kind of BNF-like grammar? > >> Not exactly the same question. The historical or anthropological >> foundations of math are certainly interesting. But the more >> interesting question is why people are using intuitive assumptions in >> math at all? >> ~v~~ > >Because without intuitive assumptions they would have absolutely not concept >of existence.
Which in itself is an axiomatic assumption used to validate other axiomatic assumptions.
> That would make doing mathematics rather difficult.
Unless axioms are demonstrated instead of assumed.
> My >point is that if one were able to identify and codify these assumptions, it >may be possible to establish a good formal foundation that way.
Isn't that what modern math does? The only real difference seems to be that it codifies these axiomatic assumptions in various set terms instead of the geometric terms used in classical math.