Logic Matters

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!

Richard Zach, over at LogBlog, has posted this:

Exciting developments! The Association of Symbolic Logic has made the now-out of print volumes in the Lecture Notes in Logic (vols. 1-12) and Perspectives in Mathematical Logic (vols. 1-12) open-access through Project Euclid. This includes classics like

• Shoenfield’s Recursion Theory,
• Lindström’s Aspects of Incompleteness in the LNL,
• Sacks’ Higher Recursion Theory,
• Hájek and Pudlák’s Metamathematics of First-order Arithmetic,
• Shelah’s Proper and Improper Forcing,
• Barwise’s Admissible Sets and Structures, and
• Barwise and Feferman’s Model-theoretic Logics in the PiML.

I’m especially excited about the Hájek/Pudlák and Barwise/Feferman volumes, which are chock-full of useful material!

This is indeed an excellent development (I’m not sure why Project Euclid puts the books up in chapter-length chunks and then complains if you download too many chunks at once: but let’s not sound ungrateful, because I’m certainly not!).

Looking around online, you can in fact find a large number of logic books available, though most of them are there contrary to copyright. Frankly, I don’t feel guilty about having a bootleg e-book on my laptop if the hard copy acquired with hard cash is sitting on my shelves. But it would be wonderful if this is the beginning of a trend for out-of-print classics to be made freely available in high-quality PDFs.

Newly in to the CUP bookshop today, a second edition of Lawvere and Schanuel’s Conceptual Mathematics. This has a little new material over and above what was in the first edition: that looks a good move, as I found when new to category theory that the first version ended too soon, without enough pointers forward to where we were we being taken.