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Whether you take those approaches, that’s up to you. “that approach won’t work, for such and such a reason”: Aldo would provide technical results that opened those approaches up again. One can think of them as playing a role in an intellectual infrastructure to which spaces are regularly wrongly closed off. Aldo’s work was about exploring new possibilities, alternatives to views that could otherwise calcify into mere dogmas.

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It comes to seem dogmatic: one’s reputation is connected with one’s intellectual position, and thus changing your mind comes with the loss of professional status.Īldo was not like this. The result is a literature that moves quickly and as a result yields little change, little persuasion, little clarification, little wisdom.

These are bold statements, and they draw attention. ZFC is the right foundation of mathematics, first-order logic is the true logic, the nature of mathematical knowledge is intuitionist, the axiom of projective determinism is true, nominalism is true. These days people are quick to take positions, “hot takes”. 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.

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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. 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). 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.įor more context, see also Ch. So, for any V 0-sentence O 0, if T implies O 0 then Craig(T) implies O 0. The new theory Craig(T) is ‘functionally equivalent’ to T, in that all observational consequences of T also follow from 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.

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Craig showed how to construct the axioms of the new theory Craig(T). 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 V 0. 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. Stathis Psillos, in his Philosophy of Science A-Z, describes it thus: 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”).

It was such a nice gesture on his part, and for me, it was really inspiring to work at his desk. He wasn’t on campus all that much, so he let me use it. I was a graduate student, he was already retired, but still had an office in Moses Hall. We were office mates of sorts for two years. He was warm, supportive, approachable, just really a wonderful person. He was a member of Berkeley’s philosophy department since 1961, and a central figure in Berkeley’s logic community. Deadline to apply is April 18.īill Craig died early Thursday morning at the age of 97. So far the visiting faculty confirmed are Liam Kofi Bright (Carnegie Mellon University), Margaret Cuonzo (Long Island University), and Gillian Russell (University of North Carolina). Classes and workshops are led by visiting faculty and Graduate Assistants. Guest speakers will address Self-Referential, Set-Theoretic, Epistemic and other types of paradoxes, presenting current research from a variety of perspectives. This program is an opportunity for students to investigate a range of formal techniques and systems aimed at solving paradoxes. Logicians and philosophers work at solving or dissolving paradoxes. Paradoxes present the ultimate challenge-contradictions. The program is open to undergraduates and recent graduates from underrepresented groups there are 10 spaces and travel & lodging are provided. Maureen Eckert is organizing Summer Program for Diversity: Logic at the University of Massachusetts Dartmouth from May 22-28, 2016.

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