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I have two further reflections. The first is that the paradigm for rightly thinking about this question, and thus about the distinction between "to presuppose" and "to anticipate," is what Hartshorne has to say about the meaning of "the possibility of particular P"!:

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[W]e mean, if we understand ourselves [, he says,] only that the previous phase of process defined itself as destined to be superseded somehow, within certain limits of variation, by a next phase of process. The 'somehow' is not, however, a wholly undifferentiated question mark, but involves some modes of contrast, of 'alternative possibilities,' none of which can coincide in character with the particular which later turns up, but some one of which, or some one region of the continuum of possible quality, will later be recognizable as the nearest alternative or region, the one which with the least further definition is equivalent to the particular. This relation between particular and its possibility is only a relation of reason for the possibility, but is a real relation for the particular. Process relates itself backwards to its potencies, not forward to particular actualizations of these potencies. It does relate itself forward to the general principle, there will be further actualization, some additional definiteness or other" (Reality as Social Process: 98 f.).

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