Which Mathematical Objects are Referred to by the Enhanced Indispensability Argument?

Abstract

This discussion note points to some verbal imprecisions in the formulation of the Enhanced Indispensability Argument (EIA). The examination of the plausibility of alternative interpretations reveals that the argument's minor premise should be understood as a particular, not a universal, statement. Interpretations of the major premise and the conclusion oscillate between de re and de dicto readings. The attempt to find an appropriate interpretation for the EIA leads to undesirable results. If assumed to be valid and sound, the argument warrants the rationality of the belief in an unusual variant of Platonism (partial and mutable domain admitting gaps and gluts). On the other hand, if taken as it stands, the argument is either invalid or is unsound or does not support the mathematical Platonism. Thus, the EIA in its present form cannot serve as a useful device for the Platonist.