Abstract

I defend the “settist” view that set theory can be done consistently without any form of distinction between sets and “classes” (by whatever name), if we think clearly about belief and the expression of belief—and this, furthermore, entirely within classical logic. Standard arguments against settism in classical logic are seen to fail because they assume, falsely, that expressing commitment to a set theory is something that must be done in a meaningful language, the semantics of which requires, on pain of Russellian paradox, a more powerful set theory. I explore the consequences of this response to the standard argument against “classical logic settism” for our notion of belief, and argue that what is revealed is that representationalist theories of belief cannot be right as long as it is possible to believe that every set is self-identical.