%0 Generic
%A Werndl, Charlotte
%D 2009
%F pittphilsci:4537
%K definitions in mathematics, justification of definitions, Lakatos, mathematical reasoning, chaos, dynamical systems theory, ergodic theory
%T Justifying Definitions in Mathematicsâ€”Going Beyond Lakatos
%U http://philsci-archive.pitt.edu/4537/
%X 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.
%Z Forthcoming in: Philosophia Mathematica