On the creative role of axiomatics. the discovery of lattices by Schröder, Dedekind, Birkhoff, and others

Dirk Schlimm

pp. 47-68

in: Arianna Betti, Willem de Jong, Marije Martijn (eds), The classical model of science II, Synthese 183 (1), 2011.

Abstract

Three different ways in which systems of axioms can contribute to the discovery of new notions are presented and they are illustrated by the various ways in which lattices have been introduced in mathematics by Schröder et al. These historical episodes reveal that the axiomatic method is not only a way of systematizing our knowledge, but that it can also be used as a fruitful tool for discovering and introducing new mathematical notions. Looked at it from this perspective, the creative aspect of axiomatics for mathematical practice is brought to the fore.

Cited authors

Schröder Ernst

Dedekind Richard