September 20, 2017, 6-7:30 PM in 234 Moses Hall
Douglas Marshall (Carleton College)
Impurity of Methods: Finite Geometry in the Early Twentieth Century
My talk aims to assess the reasonableness of various demands for purity of methods in mathematics by means of a historical case study of finite geometry in the early twentieth century. Work done in the foundations of algebra from 1900-1910 paved the way for corresponding advances in finite geometry. In particular, a geometric theorem on finite projective planes (Veblen and Bussey, 1906) was proved only with the help of an algebraic theorem on finite division rings (Wedderburn, 1905; Dickson 1905). In later years, several attempts were made to find a “pure” or “purely geometric” proof of Veblen and Bussey’s theorem, none of them entirely successful (Segre, 1958; Tecklenberg 1987). Given that it has already been proved, what exactly would be accomplished by the discovery of a “pure” or “purely geometric” proof of Veblen and Bussey’s theorem? What considerations favor or disfavor the devotion of research effort to a purely geometric development of finite geometry?
October 04, 2017, 6-7:30 PM in 234 Moses Hall
Barry Loewer (Rutgers University)
Perfectly Natural Properties and the Best System Accounts of Laws
David Lewis’ Best System account of fundamental laws requires there to be a preferred language relative to which the Best System (BS) is formulated. He proposes that the basic terms in this language (in addition to mathematical and logical terms) refer to what he calls “perfectly natural quantities.” Bas van Frassen objected that “perfectly natural properties” inolve a metaphysical posit that disconnects the Best System account from scientific practice and leads to an unwelcome skepticism about laws. In my talk I develop an alternative version of the BS account that avoids this objection and interestingly is neutral between Humean and non-Humean accounts of laws.
October 25, 2017, 6-7:30 PM in 234 Moses Hall
Robert May (UC Davis)
What is sense? Frege’s answer is this: Sense is what makes a reference thinkable such that in virtue of thinking this way an agent has grounds for making a judgement. In this talk, I explore this conception, which places sense at the crux of Frege’s account of judgement. The central claim is that sense is a composite notion, split between what makes a reference thinkable (mode of determination) and how we think of references (mode of presentation). These are related via grasp: an agent who grasps a mode of determination of a reference has a mode of presentation of that reference, and accordingly has grounds for making a judgement. This is crucial to understanding how Frege responded to the threat to logicism posed by the identity puzzle, viz. that a = b requires a special act of recognition in judgement. But it does, perhaps surprisingly, leave open the analysis of a = a.