Kevin Doran wrote to me requesting a reading list on logic. He recommends an introductory guide to logic by Peter Smith. Smith's appendix lists several textbooks on logic, but misses my two favourites.
- Jean-Yves Girard, Yves Lafont, and Paul Taylor. Proofs and Types. CUP, 1989. The master logician (discoverer of System F and linear logic), aided by two superb computer scientists, covers the basics. Explains additive and multiplicative proof rules, and the fundamentals of propositions as types.
- Jean van Heijenoort, From Frege to Gödel A Source Book in Mathematical Logic, 1879-1931, Harvard University Press, 1967. My favourite entry is the correspondence between Russell and Frege---it is only a few pages long and so a quick read; don't skip van Heijenoort's introduction. See also Anita Feferman's biography of van Heijenoort, who lived quite a life: he served as Trotsky's secretary and was shot to death by a jealous lover.