1519. I have argued that for universals . . .

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I have argued that, for universals to be somehow "embodied" (this being required by "the Aristotelian principle," or Whitehead's "ontological principle") is for them "to be included [sc. in some actuality] —being instantiated as actuality being one mode of [such] embodiment or inclusion, being entertained as possibility being the other" (Notebooks, 16 November 1993).

But what is exactly, for a universal to be "entertained as a possibility," as distinct from its being "instantiated as an actuality"? It is for the universal to belong to the aspect of an actuality relative to its future, wherein the actuality foreshadows or anticipates but does not define or determine successor actualities, as distinct from belonging to the other aspect of an actuality relative to its past, wherein an actuality further defines or determines what was but foreshadowed or anticipated by its own predecessor actualities

Otherwise put: for a universal "to be entertained as a possibility" is for it to be required by an actuality, not by the specific and definite necessity wherewith an actuality requires its predecessor actualities, and so on, but by the merely generic and indefinite necessity wherewith an actuality requires its successor actualities. This means, among other things, that any and every universal whatsoever is always embodied or included in God, not by being instantiated as an actuality, or required by the specific and definite necessity wherewith God requires the past, but by being entertained as a possibility, or required by the merely generic and indefinite necessity wherewith God requires the future.

Still otherwise put: an actuality embodies, or includes, universals both by instantiating some among those constituting the future of the actualities preceding it and by entertaining those constituting its own future, some of which can and must be instantiated by the actualities succeeding it.

12 May 2009 

The following passage well expresses the understanding of the actual as having two aspects—relatively to the past and relatively to the future—that presuppose in explaining what it is for a universal to be "entertained as a possibility," as distinct from being "instantiated as an actuality" (Notebooks, 12 May 2009).

"[T]he actuality of the present is the possibility of the future] that such and such an event is here and now possible is because a suitable predecessor of such an event is here and now actual. . . .The actuality of the present involves the antecedent actuality of its past, but it involves merely the potentiality of later events.  It is their potentiality. . . . [T]he present as a whole is the condition for later events. So one and the same event as one whole or unity is actuality, relatively to the past, and potentiality, relatively to the future. It has a retrospective face of Secondness and a prospective face of Firstness" ("The Relativity of Nonrelativity": 219).

13 May 2009