Definition:Naive Set Theory

Definition
Naïve set theory, in contrast with axiomatic set theory, is an approach to set theory which assumes the existence of a universal set, despite the fact that such an assumption leads to paradoxes.

A popular alternative (and inaccurate) definition describes this as a
 * non-formalized definition of set theory which describes sets and the relations between them using natural language.

However, the discipline is founded upon quite as rigid a set of axioms, namely, those of propositional and predicate logic.

Linguistic Note
The pronunciation of naive is in two syllables, approximately nigh-eeve, and means simple in the sense of unsophisticated. In natural language it is usually used in the sense of lacking worldly wisdom.

The word naive should strictly speaking be written naïve, with a diaeresis on the i. However, follows what appears to be standard practice and renders the word without it.