Bill Craig died early Thursday morning at the age of 97. He was a member of Berkeley’s philosophy department since 1961, and a central figure in Berkeley’s logic community. He was warm, supportive, approachable, just really a wonderful person. Berkeley’s memorial notice is here. We were office mates of sorts for two years. I was a graduate student, he was already retired, but still had an office in Moses Hall. He wasn’t on campus all that much, so he let me use it. It was such a nice gesture on his part, and for me, it was really inspiring to work at his desk.
Logicians know him best for the Craig interpolation theorem, and philosophers of science know him for what they also call “Craig’s theorem” (logicians usually call it “Craig’s trick,” and according to Bill, Robin Gandy called it “Craig’s swindle”). Stathis Psillos, in his Philosophy of Science A-Z, describes it thus:
The logician William Craig (born 1918) constructed a general method according to which given any first-order theory T and given any effectively specified sub-vocabulary O of T, one can construct another theory T’ whose theorems are exactly those theorems of T that contain no constants other than those already in the sub-vocabulary O. What came to be known as Craig’s theorem is the following: for any scientific theory T, T is replaceable by another (axiomatisable) theory Craig(T), consisting of all and only the theorems of T which are formulated in terms of the observational vocabulary V0. Craig showed how to construct the axioms of the new theory Craig(T). There will be an infinite set of axioms (no matter how simple the set of axioms of the original theory T is), but there is an effective procedure which specifies them. The new theory Craig(T) is ‘functionally equivalent’ to T, in that all observational consequences of T also follow from Craig(T). So, for any V0-sentence O0, if T implies O0 then Craig(T) implies O0. This point was seized upon by instrumentalists, who argued that theoretical commitments in science were dispensable: theoretical terms can be eliminated en bloc, without loss in the deductive connections between the observable consequences of the theory.
For more context, see also Ch. 2 of his Scientific Realism.
His colleagues honored Bill’s life and work with a conference in 2007, and the essays of that conference are collected in a special issue of Synthese (Springer, JSTOR). I recommend Paolo Mancosu’s introductory essay, Bill’s two essays about his own work, Sol Feferman’s “Harmonious Logic” about the interpolation lemma (free preprint!), and Michael Friedman’s paper “Wissenschaftslogik: The role of logic in the philosophy of science,” about the place of Craig’s theorem/trick/swindle in the history of philosophy of science. I’ll attach a preprint of Bill’s paper “The road to theorems of logic” here, in case you don’t have access to Synthese.
[Photo credit: Steve Givant]