Tuesday, August 04, 2009

Disappearing logic again

A footnote to my post, Logic disappearing over the horizon. I've just been reading Stephen Simpson's "Unprovable Theorems and Fast-Growing Functions" (an introductory piece in the 1987 AMS Contemporary Mathematics Logic and Combinatorics volume that contains some important papers on provably computable functions -- it is a pity that Simpson's very helpful and accessible survey isn't more readily available, e.g. on his website). I was struck by this remark:

Like most good research in mathematical logic, the results which I am going to discuss had their origin in philosophical problems concerning the foundations of mathematics.
And that's right: the most interesting work in mathematical logic is bound up with problems and projects of a more philosophical kind concerning the foundations of mathematics. All the more worrying, then, the seeming trend I was remarking on for logic courses to be less and less available even to graduate philosophy students. If the wonderfully fruitful long dialogue since Frege between philosophers and mathematicians (or often, between the philosophical and mathematical sides of the same individual) is to continue, then some philosophers at any rate do need to be logically well-educated!

4 comments:

Smith said...

I chanced upon to view your blog and found it very interesting. Great ... Keep it up!

Callicles said...

Hi, I'm a philosophy undergrad looking one day to specialise in philosophical logic and I wonder - does having a good background in formal logic help my eventual job prospects?

I have been warned that logic isn't so intellectually trendy at the moment, and I fear for my (already slender) job prospects!

Peter Smith said...

Callicles: If you want to work in philosophical logic, then you'll certainly want a good background in logic! As to job prospects, I can only report that our local Cambridge logic-minded grads have done at least as well as other groups in ending up with jobs in good places. Better, if anything.

You might think there's a tension between that and my anxieties about advanced formal logic being demoted in undergraduate courses. But remember that people get jobs largely on research ability.

Callicles said...

Ah. Well, thank you for the encouraging words!