Two Logic Classes This Coming Fall
Gary Mar will be teaching two logic classes this semester that should be of interest to MLRG attendees. One is his Introduction to Symbolic Logic (PHI 220, MWF 10-11), the other his Gödel seminar (M 4--7). An outline of the seminar is given at the end of this message.
This is an excellent opportunity to learn more about logic in general, and Gödel's revolutionary work in particular. Logic plays an important role in computational linguistics (e.g. in model-theoretic syntax), and we might also encounter some logic in my phonology seminar. So even if you don't fancy yourself a semanticist, it's good to know some basic logic --- I'd go so far as to say that familiarity with logic and Gödel's work in particular is an essential requirement for every modern intellectual.
Also, the last time two linguistics students took a class with Gary, it resulted in a joint paper on "Unless and Until" that was published in the proceedings of the Symposium on Logic, Language, and Computation.
The first three sessions of Goedel seminar will cover the
- history of logic from Aristotle to Frege,
- the emergence of paradoxes in logic and semantics from Russell and Frege to Goedel,
- applications of the philosophy of language to the history of philosophy.
We'll also cover the Goedel completeness and incompleteness theorems, with the latter presented using modal provability logics.
There will be an informal introduction to Cantorian, in contrast to Fregean, set theory and how the axioms of ZFC articulate the Cantorian "iterative conception of set." As a sidebar, we'll show why Grim's "Cantorian Atheistic Arguments" are based on a fundamental misunderstanding of the Cantorian conception and how Goedel's Modal Ontological Argument parallels certain constructions he used to prove his completeness theorem.