Abstract

An attempt to vindicate naive set theory by postulating a universal set V which is describable in two distinct description languages: predicative and extensional. The extensional description of a set consists of describing all its elements whereas its predicative description consists of describing what sets it is an element of. Extensionally described V has an uncapturable description length, akin to its cardinality. But predicatively described, in virtue of being the set that is not contained in any set whatsoever, V has a minimal description length, a counterbalance to its cardinality. Descriptive efficiency can genuinely be attributed to V (achieved in a third description language) only if it contains predicatively indiscernible but extensionally discernible sets.