December PASHoM meeting
Posted by tbartlow on 12/11 at 09:29 AM
The Philadelphia Area Seminar on History of Mathematics (PASHoM) met on December 10 at Villanova University. Thirteen people heard a wonderful lecture by John W. Dawson Jr. on “Compactness in Logic and Topology.” Dawson traced the history of compactness in logic (In first-order logic, if every finite subset of a set of sentences is satisfiable then the whole set is satisfiable) and related it to compactness in topology (a covering with closed sets has a finite subcover, or if every finite subset of a collection of closed sets fails to cover a set, the whole collection also fails). A lively discussion followed touching on both technical and social aspects of Dawson’s talk, including interaction among logicians in the 1930s, possible parallels between Godel’s habits of thought and Newton’s, and the possiblity of making the logic-topology connection more explicit by imposing a topological structure on the sentences of a language.