Abstract

To leave matters in no doubt, we obligingly assert that the Russell class R, i.e. {x : x 6∈ x}, both belongs to itself and also does not belong to itself; in short, we assert R ∈ R & ∼ . To be quite explicit, we assert the contradiction r & ∼ r, where r abbreviates R ∈ R. Thus, in convenient symbols, `δ r & ∼ r, where δ is the group of dialethicians comprising Priest and Routley. Now Goldstein asserts not, or not just, that we should not do what we have naughtily done, but that we cannot; it “is not that people should not assert contradictions, but that they cannot, even though they may purport to do so”