Document Type
Article
Publication Date
9-10-2024
Published In
Journal For The Philosophy Of 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.
Keywords
Enumerative induction, Arithmetic, Non-deductive reasoning
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
Alan Richard Baker.
(2024).
"Enumerative Induction In Mathematics".
Journal For The Philosophy Of Mathematics.
Volume 1,
5-21.
DOI: 10.36253/jpm-2931
https://works.swarthmore.edu/fac-philosophy/619
Comments
This work is freely available under a Creative Commons license.