The Calgary Mathematics and Philosophy Lectures: Patricia Blanchette (CANCELLED)

One of the most important techniques provided by modern logic is the use of models to show the consistency of theories. The technique burst onto the scene in the late 19th century, and had its most important early instance in demonstrating the consistency of non-Euclidean geometries. This talk investigates the development of that technique as it transitions from a geometric tool to an all-purpose tool of logic. Prof. Blanchette argues that the standard narrative, according to which our modern technique provides answers to centuries-old questions, is mistaken. Once we understand how modern models work, she'll argue, we see important differences between the kinds of consistency-claims that would have made sense, e.g., to Kant and the kinds of consistency-claims that we can demonstrate today. We’ll also see some philosophically-interesting shifts, over this time period, in the kinds of things that we take proofs to demonstrate.