Jon Cogburn has a nice short post on Graham Priest here.
New realists have got to have an honest confrontation with the Kantian problems of totality, and Priest’s characterization of such problems in terms of varieties of Russell’s Paradox is an essential step forward. Russellian paradoxical proofs have two moments: one of Transcendence where a set A is provably not a member of some set B, and one of Closure where A is provably a member of B (with Russell’s paradox A and B are the same set; the problem concerns whether the set of all sets that are not members of themselves is itself a member of itself). This provides a rigorous model of precisely what always goes wrong with transcendental idealism, limiting what can be said or known (Closure) and having to surpass those limits (Transcendence) in order to state or think the initial limitation. Continue reading