A brief history of logic at UCLA

Logic started in UCLA in the period 1954 – 1956, with the arrival of Rudolf Carnap and (more significantly) Richard Montague in Philosophy, and C. C. Chang in Mathematics. Montague and Chang were both students of Alfred Tarski in Berkeley. They started the training of graduate students in logic, and they established the bi-weekly Logic Colloquium, which has been since then the main “meeting place” for logicians in Southern California. The group expanded considerably in the early 60’s, with the arrival of Abraham Robinson in 1962, (initially) on a joint Mathematics-Philosophy appointment, and Yiannis Moschovakis in Mathematics (1964). Robinson left for Yale after only three years, and was (fortuitously) replaced as “resident living legend” by Alonzo Church, who moved to the UCLA Philosophy Department from the Princeton Mathematics Department in 1967. By example if nothing else, these two men set very high standards for the local logicians, in research, scholarship, and the concern for deep foundational questions.

In terms of results obtained, the most fundamental work in logic produced in UCLA in the sixties was Montague’s development of semantics for natural language. There was also a great deal of related research in modal logic and the application of “formal methods” in philosophy of language, for example by David Kaplan. This period was characterized by a great deal of interaction between logicians in Philosophy and in Mathematics; Montague and Moschovakis held joint seminars (in abstract computability theory), and the strong philosophy Graduate students studied logic in the Mathematics Department. One of the best was Hans Kamp, who subsequently moved to linguistics.

Mathematical Logic in Los Angeles matured in a period of some twenty years, starting at about 1967. In terms of “human resources,” Alexander Kechris (a 1972 Ph.D. of Moschovakis) came to Caltech in 1975, and John Steel and Tony Martin came to UCLA in the following two years;Hugh Woodin was also active in Caltech during most of that period, first as an Undergraduate student and later on the faculty. These logicians worked as a cohesive research group in Descriptive Set Theory, especially the study of determinacy and large cardinal hypotheses, and the mathematical and foundational consequences of these hypotheses. The quality of Post. Docs. in Logic improved dramatically, e.g., Saharon Shelah was in UCLA in 1971-72 (as a regular Assistant Professor, actually), and Matthew Foreman (now at UC Irvine) in 1981-82. There were also some excellent students, including Chris Freiling (1981), Steve Jackson (1983) and Yo Matsubara (1985) who worked with Martin, and Alexander Kechris (1972), Lefteris Kirousis(1978), Phokion Kolaitis (1978), Howard Becker (1979), Michel de Rougemont (1984), Larry Moss(1984) and Greg McColm (1986) who worked with Moschovakis. It was during this period that “the Los Angeles school of set theory” attained a world-wide reputation and its members earned high honors, including, most prominently, the award by the Association for Symbolic Logic of the Karp Prize jointly to Martin, Steel and Woodin in 1988.

The interaction between logicians in Mathematics and Philosophy waned during these years of rapid mathematical development, partly because nobody really “did logic” in Philosophy after the death of Montague in 1971, and also because of the preoccupation of the mathematical logicians with the exciting technical developments of the period. On the other hand, the study of Philosophy of Language blossomed in the Philosophy Department, especially by the work ofKeith Donnellan and David Kaplan; and the Semantics of Natural Language (a voracious “consumer” of logic) started receiving serious attention in the Department of Linguistics, initially with Barbara Partee and Ed Keenan.

Towards the end of the eighties, the Mathematical Logic group in Los Angeles started losing its tight cohesion, partly because Woodin and (later) Steel moved to Berkeley, but also because its remaining members developed new (or returned to old) scientific interests which were not shared by the group. Moschovakis has been working (primarily) on the foundations of computer science; Martin has returned to problems in the Philosophy of Mathematics, although without abandoning completely technical work in set theory; and Kechris is a leader (and one of the creators) of a very successful research program which applies Descriptive Set Theory to other areas of Mathematics, especially Analysis. He and Greg Hjorth (who came to UCLA in 1995) received the Karp Prize for this work in 2004.

At the same time, the interaction between Mathematics and Philosophy has taken off again, especially after Martin’s half-time move to the Philosophy Department in 1991. Philosophy students have started again learning their logic in the Mathematics Department, and the Workshop in Philosophy of Mathematics is regularly attended by some faculty and students in Mathematics. In addition, there is some (and a promise of substantially more) interaction between Logic, Philosophy and Linguistics, especially after Terry Parsons came to the Philosophy Department (from UC Irvine) in 2000, and Marcus Kracht and Philippe Schlenkercame to Linguistics in 2003.

The situation in 2006. In addition to Moschovakis, Martin and Hjorth, already mentioned, the current (2006) group of logicians with “regular” appointments in the UCLA Mathematics Department also includes Itay Neeman, a student of John Steel who joined the faculty in 2000 (only the third UCLA Ph.D. ever to be appointed to a regular faculty position in the history of the UCLA Mathematics Department). They are supported by two Logic Center Fellows,Benjamin Miller and Alex Usvyatsov. The philosophers whose work is most closely related to logic are David Kaplan, Terry Parsons and (of course) Tony Martin, and the linguists with knowledge of and interest in logic are Ed Keenan, Marcus Kracht, Philippe Schlenker and Ed Stabler.

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