Abstract

A further reformulation of Naive Set Comprehension related to that proposed in “Resolving Insolubilia: Internal Inconsistency and the Reform of Naive Set Comprehension” is possible in which contradiction is averted not by excluding sets such as the Russell Set but rather by treating sentences resulting from instantiation of such sets as the Russell Set in their own descriptions as invalid. So the set of all sets that are not members of themselves in this further revision is a valid set but the claim that that set is or is not a member of itself is not validly expressible. Such an approach to set comprehension results in a set ontology co-extensive with that permitted by the Naive Set Comprehension Principle itself. This approach has as strong a claim to consistency as that formulated in “Resolving Insolubilia: Internal Inconsistency and the Reform of Naive Set Comprehension.”