Gödel's theorems: an incomplete journey (10/18)

Gary Mar and colleagues will present their project “A Year of Magical Thinking” that uses new media and AI to introduce students, as well as logicians, mathematicians, and linguists to the breadth and depth of Gödel’s Theorems. Gödel is widely regarded as the greatest logician of the 20th century and dreamed of establishing philosophical theses and ontological results with the rigour and precision of mathematics. His dream was to a remarkable extent fulfilled. Despite their technical sophistication, Gödel’s logical theorems such as the Completeness Theorem [1930] and his Incompleteness Theorems [1931] have perennially managed to escape mere mathematics and shed light on larger philosophical issues.

A number of popular accounts of Gödel’s Incompleteness Theorems misrepresent the scope of Gödel’s ideas and their mathematical and philosophical significance. This workshop explores ways of presenting Gödel’s Incompleteness theorems using modal provability logics. Modal principles characterize properties of proof, time, and God reveal logical interconnections among Gödel’s theorems and philosophical conclusions about the unreality of time in the General Theory of Relativity [1949-1952] and in his Ontologischer Beweis [*1970], a modal ontological argument. Gödel’s success has often been attributed to his philosophy of mathematics, but his success is as much a tribute to his “mathematics of philosophy”, i.e., his ability to formulate philosophical problems in a manner that made them amenable to mathematical methods.