Chris Partridge wrote: (01)
> EB>While logic is the foundation for all of mathematics
>
> Is it really?
>
> I was taught, some time ago, that after Russell and Whitehead's failure,
> people were a little less optimistic about these kinds of claims. I have
> heard since some (maybe cynical) logicians say that they see mathematical
> logic as a branch of mathematics.
> I recall one saying that mathematical logic tended to focus on FOL as one
> could prove interesting results, but if you wanted to formalise any
> interesting mathematics, you needed to go higher order, but this was less
> tractable. (02)
Philosophically, "logic" is the study of reasoning mechanisms -- "how to
think". Mathematical logic _is_ a branch of mathematics: It is about
formalization of logic itself as a set of theories -- reasoning about
reasoning (and the artifacts of reasoning). First-order logic is a
formalization of one such mechanism, and is intentionally constrained in
certain regards. I didn't say that FOL was the foundation for all of
mathematics, and I agree that it isn't. (03)
[Pat and John will doubtless correct my less-than-well-educated
exposition. So I should probably have simply left the answer to them.] (04)
-Ed (05)
--
Edward J. Barkmeyer Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263 Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263 FAX: +1 301-975-4694 (06)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (07)
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