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 biweekly 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
MathematicsPhilosophy 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
197172 (as a regular Assistant Professor, actually), and Matthew Foreman
(now at UC Irvine) in 198182. 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 worldwide
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 of Keith 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 halftime 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 Schlenker came 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.
