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 ************************** Prof. Em. Jim Lambek, McGill, Montreal ************************************** 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. )