The Leo Apostel Center
invites everyone to the 47st of its interdisciplinary seminars in the
Foundations series. In this series CLEA invites scholars that are actively
engaged in the research on the foundations of a particular discipline.
Their lectures will always be directed to an interdisciplinary audience,
and the discussions aim at confronting the foundations of the different
disciplines.
Grammar, Algebra and Logic
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Prof. Em. Jim Lambek, McGill, Montreal
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Monday, April 10, 17.00h, 10F734.
About the lecture and speaker:
Prof. Lambek is author of some monographs in mathematics, eg. "Completions
of categories" (1966), "Torsion theories, additive semantics, and rings of
quotients" (1970), but in particular a standard mathematical reference work
"Lectures on Rings and Modules" (1966) of which there was a third edition
in 1986. He obtained all his degrees at McGill, Montreal. In 1958, he
published his first paper on the syntactic calculus, and for a while the
"Lambek Grammars" were an essential opponent to "Chomskian Grammars",
essentially supported in Europe - contrary to the North Americans who made
Chomski win the day. Prof. Lambek then turned his thoughts for most of a
decade to ring theory, particularly to rings of quotients, including the
above mentioned monographs. Around 1965 he got interested in categories,
resulting in a monograph with Phil Scott "Introduction to Higher order
Categorical Logic". That same time he renewed his interest in mathematical
linguistics, studying formally verb conjugations in French and Latin. Also
to be mentioned is a paper "How to program the abacus" in which he invents
independently and simultaneously with Marvin Minsky the Minsky machine,
which is Turing complete, but conceptually much simpler than the Turing
machine. Currently Prof. Lambek still publishes regularly on categorical
logic, still producing highly valued papers, and on linguistics, returning
to the grammars of syntactic types. In this lecture he will outline his
ideas on the latter. (An appreciation of Prof. Lambek by Prof. Barr on the
occasion of Jim Lambek's 75th birthday can be found on
http://euclid.math.mcgill.ca/triples/lambek/Lambek.biography.html. )