Michèle Friend
The George Washington University
Abstract: Mathematical pluralism is a principled skeptical position. It is 'principled' in the sense that the mathematical pluralist accepts that it might turn out that there is one thing called 'mathematics' that it can be fully captured by one mathematical theory, such as a set theory, category theory, type theory or homotopy type-theory or something else. Should things turn out this way, then the pluralist will set aside his pluralism and will become a monist. The mathematical pluralist is a 'skeptic' because he thinks that the evidence for monism is not strong presently.
I discuss some of the reasons why one might think that the evidence for monism is lacking.
I also discuss what mathematical pluralism looks like at first sight. That is, there are several ways, and degrees within those ways, of being a pluralist. I discuss some of these ways. The list from which I shall probably draw is: epistemological, in truth, in ontology, in foundations and in methodology.
Lastly, I discuss some of the virtues or vices of being a pluralist, answering questions such as: Do we learn more as a pluralist? Are we more honest as a pluralist? Are we more clear and precise? And, of course, how it is that we can measure and compare such things.
