> 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. That would make doing mathematics rather difficult. 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. -- Nil conscire sibi