Justifying Definitions in Mathematics---Going Beyond Lakatos
History and Overview
2013-10-08 v1 Dynamical Systems
Chaotic Dynamics
History and Philosophy of Physics
Abstract
This paper addresses the actual practice of justifying definitions in mathematics. First, I introduce the main account of this issue, namely Lakatos's proof-generated definitions. Based on a case study of definitions of randomness in ergodic theory, I identify three other common ways of justifying definitions: natural-world-justification, condition-justification and redundancy-justification. Also, I clarify the interrelationships between the different kinds of justification. Finally, I point out how Lakatos's ideas are limited: they fail to show that various kinds of justification can be found and can be reasonable, and they fail to acknowledge the interplay between the different kinds of justification.
Cite
@article{arxiv.1310.1625,
title = {Justifying Definitions in Mathematics---Going Beyond Lakatos},
author = {Charlotte Werndl},
journal= {arXiv preprint arXiv:1310.1625},
year = {2013}
}