Werndl, Charlotte (2009) Justifying definitions in mathematics: going beyond Lakatos. Philosophia mathematica, 17 (3). pp. 313-340. ISSN 0031-8019
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 how various kinds of justification can be found and can be reasonable, and they fail to acknowledge the interplay among the different kinds of justification.
|Additional Information:||© 2009 The Author|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Philosophy, Logic and Scientific Method|
Actions (login required)
|Record administration - authorised staff only|