Platitudes in mathematics

Thomas Donaldson

pp. 1799-1820

in: Synthese 192 (6), 2015.

Abstract

The term ‘continuous’ in real analysis wasn’t given an adequate formal definition until 1817. However, important theorems about continuity were proven long before that. How was this possible? In this paper, I introduce and refine a proposed answer to this question, derived from the work of Frank Jackson, David Lewis and other proponents of the ‘Canberra plan’. In brief, the proposal is that before 1817 the meaning of the term ‘continuous’ was determined by a number of ‘platitudes’ which had some special epistemic status.

Cited authors

Lewis David

Jackson Frank