Definition:Naive Set Theory

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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.

Also see

  • Results about naïve set theory can be found here.

Linguistic Note

The pronunciation of naïve is in two syllables, approximately naa-eeve, and means simple in the sense of unsophisticated.

Try not to pronounce it nigh-yeeve.

In natural language it is usually used in the sense of lacking worldly wisdom.

The correct rendition of the word naïve is with a (diacritic) diaeresis on the i, that is: ï.

This has the effect of indicating that the pair of letters involved need to be pronounced as separate syllables. Spelt naive, the word would be expected to be pronounced something more like nave.

$\mathsf{Pr} \infty \mathsf{fWiki}$ usually follows what appears to be standard practice, and renders the word with the normal unadorned i, but on occasion the correct form can be seen.