Dale Jacquette, born in Sheboygan, Wisconsin, USA, in 1953. Ph.D. from Brown University, Providence. Professor of Philosophy at Pennsylvania State University, University Park.
Fellow (1 September 2005 – 30 June 2006)
AN INHERENCE ANALYSIS OF THE CONCEPT OF MATHEMATICAL ENTITY
My topic during my ten months research visit at NIAS has been the philosophy of mathematics. I worked to develop an Aristotelian inherence ontology of mathematical entities, which has been surprisingly under-represented among the varieties of approaches to understanding the metaphysics of mathematics. I succeeded in working out in detail the main lines of argument for the core of the theory and its most interesting implications in a draft of a substantial part of the final projected book, Mathematical Entity. I presented these ideas at lectures, seminar series, and conferences, which helped me also to further refine my positions. Much of my research was devoted to familiarizing myself with differences between the sub-schools of intuitionism in philosophy of mathematics, so that I would be able to make an informed comparison between intuitionism and Aristotelian inherentism, which notably similar in some ways, but classic forms at least in the work of the Dutch intuitionists L.E.J. Brouwer and Arend Heyting, it is still significantly different. Explaining the exact relation between the metaphysics of Aristotelian inherentism and the possibility and utility of applied mathematics mediated by a logic of analogical reasoning has been a particularly rewarding aspect of this research.