A Theory of Aggregates

Abstract

Introductions to the mathematical notion of set standardly explicate that notion by distinguishing it from a vaguer, more ordinary notion of aggregation, collection, or combination. Since Cantor and Frege, students have been warned that sets are not located in space-time and cannot be perceived or acted upon, and that a set of, say, fifty-two playing cards is not to be confused with the set of the four suits. The severity of this warning-and the usefulness and power of set theory-have led to the neglect of the ordinary notion of aggregation. The purpose of this paper is to refine that notion and give it a place in semantical and philosophical analysis.' Refinement is worthwhile for two reasons. First, the notion is useful in giving semantically intelligible form to some of our descriptions involving plural constructions and mass terms. Second, the notion will serve to hone the distinction between concrete and abstract objects.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 86 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.