# Mathematical Concepts: Fruitfulness and Naturalness

# Mathematical Concepts: Fruitfulness and Naturalness

This chapter addresses the question of when one concept or definition is properly regarded as more ‘natural’ than another with reference to the principle that a mark of good definitions is their theoretical fruitfulness, especially as incorporated in the methodology implicit in the work of Riemann and Dedekind. It explores the suggestion that the objectivity of imputations of ‘naturalness’ of concepts/definitions/properties can be underwritten at least in part by quasi-empirical mathematical practices of conjecture and verification, in a mathematical analogue of Goodman's ‘New Riddle of Induction’.

*Keywords:*
concept, definition, natural property, fruitfulness, methodology, Bernhard Riemann, Richard Dedekind, conjecture, verification

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .