Department of Philosophy
Issues in the History and Philosophy
of Non-Archimedean Geometry
I won an National Science Foundation Scholars Award to work on Part II of a lengthy work on the history and philosophy of non-Archimedean mathematics.The first part was published as:
"The Rise non-Archimedean Mathematics and the Roots of a Misconception I: the Emergence of Non-Archimedean Systems of Magnitudes," Archive for History of Exact Sciences 60 (2006), pp. 1-121.
In addition, I have completed the following forthcoming works that can be downloaded from my web site at OU.
"The Absolute Arithmetic Continuum and its Peircean Counterpart," in New Essays on Peirce's Mathematical Philosophy, edited by Matthew Moore, Open Court Press (forthcoming).
"The Absolute Arithmetic Continuum," Synthese (forthcoming).
6 August 2010
This year I continued to work on non-Archimedean mathematics including its history and philosophy and have three new forthcoming papers on the subject which can be obtained from my website.
I have established a body of new results on surreal numbers and have given a number of talks on surreal numbers including talks at Cambridge University and University of Évora, Portugal. In addition, my paper "A Re-examination of Zeno’s Paradox of Extension: An Essay in Honor of Adolf Grünbaum on his 90th Birthday" has been accepted by Philosophy of Science.