Enumerative Induction in Mathematics

Abstract

In my 2007 paper, “Is There a Problem of Induction for Mathematics?” I rejected the idea that enumerative induction has force for mathematical claims. My core argument was based on the fact that we are restricted to examining relatively small numbers, so our samples are always biased, and hence they carry no inductive weight. In recent years, I have come to believe that this argument is flawed. In particular, while arithmetical samples are indeed biased, my new view is that this bias actually strengthens the inductive support that accrues from them. The reason is that small numbers typically provide a more severe test of general arithmetical claims due to the greater frequency of significant properties and boundary cases among such numbers. In this paper, I describe and defend this new view, which a call Positive Bias Pro-Inductivism.