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.