Frege's Definition of Number: No Ontological Agenda?

Joan Weiner (2007) has argued that Frege’s definitions of numbers

constitute linguistic stipulations that carry no ontological commitment: they

don’t present numbers as pre-existing objects. This paper offers a critical

discussion of this view, showing that it is vitiated by serious exegetical

errors and that it saddles Frege’s project with insuperable substantive

difficulties. It is first demonstrated that Weiner misrepresents the Fregean

notions of so-called Foundations-content, and of sense, reference, and truth.

The discussion then focuses on the role of definitions in Frege’s work,

demonstrating that they cannot be understood as mere linguistic stipulations,

since they have an ontological aim. The paper concludes with stressing both

the epistemological and the ontological aspects of Frege’s project, and their

crucial interdependence.