Volume 5, Issue 2, Fall 2011
Jörgen Sjögren
Pages 99-116
Indispensability, the Testing of Mathematical Theories, and Provisional Realism
Mathematical concepts are explications, in Carnap’s sense, of vague or otherwise unclear concepts; mathematical theories have an empirical and a deductive
component. From this perspective, I argue that the empirical component of a mathematical theory may be tested together with the fruitfulness of its explications.
Using these ideas, I furthermore give an argument for mathematical realism, based on the indispensability argument combined with a weakened version of confirmational holism