  Metaphysical interpretations of set theory are either inconsistent or
incoherent. The uses of sets in mathematics actually involve three distinct
kinds of collections (surveyable, definite, and heuristic), which are governed
by three different kinds of logic (classical, intuitionistic, and minimal). A
foundational system incorporating this analysis and based on the principles of
mathematical conceptualism accords better with actual mathematical practice
than Zermelo-Fraenkel set theory does.
