Relevance, Relatedness and Restricted Set Theory
Barry Smith
From G. Schurz and G. J. W. Dorn, eds.,
Advances in Scientific Philosophy. Essays in Honour of Paul Weingartner,
Amsterdam/Atlanta: Rodopi, 1991, 45–56.
What sort of set theory results when restrictions are placed on the sorts of elements which may form a set? Given an arbitrary relevance relation, one can formulate a notion of set which will apply only to totalities of mutually relevant entities. Relevance might signify for example: exists at the same time as, belongs to the same body as, is less than a certain distance from, etc. The resultant theory, which embodies topological constraints, can then be used as the basis for an account of relevance between propositions which is in the tradition of the relevant logics of analytic implication studied by M. Dunn and W. T. Parry.