Beyond Sets: A Venture in Collection-Theoretic Revisionism

Heusenstamm, Germany: Ontos Verlag (2011)
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Abstract

Our target is collectivities--all types of collectivities, beyond formal treatment in terms of sets alone. Collectivities are collections that can have members under all modalities: actual and potential members, definite and indefinite members, past and future members, members identifiable or unknown. The null collectivity aside, collectivities will indeed have members, but their membership need not be enumerable individual by individual or identifiable with precision. Collectivities are pluralities we generally access in terms of qualifying features and modalities rather than lists of identifiable members. Our attempt is to do justice to collectivities in their generality and indeterminacy, with plena as a specific focus: large-scale macro-totalities on the order of all facts, all truths, and all things...a collectivity well beyond the technical machinery of sets.

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Patrick Grim
University of Michigan, Ann Arbor

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