"Zuhair" <email@example.com> wrote in message news:firstname.lastname@example.org... > On May 27, 6:51 pm, Charlie-Boo <shymath...@gmail.com> wrote: >> On May 26, 2:52 am, Zuhair <zaljo...@gmail.com> wrote: >> >> > Frege wanted to reduce mathematics to Logic >> >> What does it mean to "reduce mathematics to Logic"? > > It means that any mathematical discourse can be interpreted within a > logical discourse. > > Logic is responsible for laying down a set of rules that results in > generation of non contradictory statements in the most general manner.
Logic is not just mathematical logic: case in point, you can make of identity an axiom, but the notion of identity itself presupposes an existential stance, so it is not a purely logical notion (in the sense you have just stated). My take is that mathematics uses logic (as the language of mathematics is as well logical) and logic uses mathematics (as the logical calculus is mathematical), but neither can be reduced to the other. Mathematics is the study and applications of "numbers", which is not a purely logical endeavour, while logic is the study and applications of "rational discourse", which is not an essentially mathematical endeavour.
I'd think the only way to operate the "unification" you have in mind is by reducing *everything* to just its operational side, the calculus: then there is not even any difference left between logic and mathematics, indeed you'd have destroyed the very nature of both.