Book note: Smullyan’s Theory of Formal Systems

When I wrote my Gödel book I did a lot of it from memory (on the principle that if I had to reconstruct proofs without too much cheating, the discipline of doing so would help me to explain the proofs). But lately, as I slowly work away at the second edition, I’ve been (re)reading some of the old literature around and about the incompleteness theorems.

I’ve had a copy of Smullyan’s Theory of Formal Systems (1961) for thirty years, but to be honest I don’t think I’ve ever read it properly before. And it does date from that time when many maths books were photo-printed from typewritten originals, and looked exceedingly uninviting. Moreoever, in some ways, this volume has been superseded by Smullyan’s Gödel’s Incompleteness Theorems (1992).

But still, as I’ve found with great enjoyment, the earlier book remains quite terrific stuff. It is just so very elegant and insightful in developing Post’s ideas on formal systems and in excavating one basic line of ideas underlying incompleteness proofs (I plan to write up some notes in due course). Impressive indeed — even more so when you remember the book is essentially Smullyan’s doctoral thesis. Still very worth reading after all this time.

(And how many philosophy books, as opposed to logic books, still stand up so well after fifty years?)