Beyond Sets 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. Set theory was born in paradox, was shaped by paradox, and continues to carry the threat of paradox into its current adolescence. Properly understood, we will argue, the threat of contradiction is not merely formal and is not to be evaded by merely formal techniques. The fact that there can be no set of all non-self-membered sets might be shrugged aside as a minor logical surprise. Beyond Russell’s paradoxical set, however, there lie the serious philosophical difficulties of coherently conceptualizing a set of all things, the realm of unrestricted quantification (or even the sense of restricted quantification), the totality of all events, all facts, all propositions, or all that is true. Sets are structurally incapable of handling any of these. As argued in later chapters, all of these are properly conceptualized as collectivities rather than sets, though even that conceptualization carries some surprising lessons regarding indeterminacy, the nature of such totalities, and the universe as a whole. CHECK IT OUT! BEYOND SETS back to pgrim.org