Reification Fallacies and Inappropriate Totalities

Informal Logic 20 (1) (2000)

Nicholas Rescher
University of Pittsburgh
As Russell's paradox of "the set of all sets that do not contain themselves" indicated long ago, matters go seriously amiss if one operates an ontology of unrestricted totalization. Some sort of restriction must be placed on such items as "the set of all sets that have the feature F' or "the conjunction of all truths that have the feature G." But generally, logicians here introduce such formalized and complex devices as the theory of types or the doctrine of impredictivity. The present paper argues for the informal and elementary idea that the items invoked in a proper identification have themselves already been identified. Even as an explanation is not satisfactory that proceeds in terms of items that themselves require prior explanation, so the same holds with identification. And heed of this elementary idea suffices to sideline those otherwise paradoxical perplexities
Keywords totality, identification, self-identificlttion, sets, paradox, set theory paradox, Barber paradox, Russell, Russell's Paradox, Vicious Circle Principle, Kant's antinomies
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