Prof. Greg Lavers Presents History and Philosophy of Mathematics Paper
Prof. Greg Lavers presented a paper at the Canadian Society for the History and Philosophy of Mathematics Conference, hosted by the University of British Columbia on June 2nd, 2019. The paper was titled "Modal Logic and Philosophy of Mathematics in the Mid-Twentieth Century: Carnap, Quine and Barcan Marcus."
The abstract reads:
Quine’s 'Two Dogmas of of Empiricism' is generally seen a major turning point in the course of analytic philosophy in the twentieth century, one that is particularly concerned with overturning an epistemological picture of mathematics and the sciences. Under the influence of Wittgenstein, Poincaré and others, logical empiricists, including Carnap, had come to see mathematical claims as analytic statements that we could know a priori because they are true no matter how the world happens to be. The majority of the text of 'Two Dogmas...' is devoted to a criticism of the notion of 'analyticity' required by this picture. As a result 'Two Dogmas...' is seen as primarily as response to Carnap (despite Carnap being the target only of two, relatively minor, sub-arguments). What I wish to do in the present paper is stress how these arguments grew out of arguments not having anything to do with large scale epistemological concerns, but as a reaction to Ruth Barcan Marcus’s, then recently developed, quantified modal logic. In fact, as I will argue, 'Two Dogmas...' can be seen as growing out of a 1947 paper of Quine’s where Barcan Marcus is the explicit target.
Prof. Greg Lavers is Associate Professor of Philosophy at Concordia University.