Process and Reality — the Gifford Lectures, 1929

Actual entities atomize the extensive continuum. This continuum is in itself merely the potentiality for division ; an actual entity effects this division. The objectification of the contemporary world merely expresses that world in terms of its potentiality for subdivision and in terms of the mutual perspectives which any such subdivision will bring into real effectiveness. These are the primary governing data for any actual entity; for they express how all actual entities are in the solidarity of one world. With the becoming of any actual entity what was previously potential in the space-time continuum is now the primary real phase in something actual. For each process of concrescence a regional standpoint in the world, defining a limited potentiality for objectifications, has been adopted. In the mere extensive continuum there is no principle to determine what regional quanta shall be atomized, so as to form the real perspective standpoint for the primary data constituting the basic phase in the concrescence of an actual entity. The factors in the actual world whereby this determination is effected will be discussed at a later stage of this investigation. They constitute the initial phase of the ‘subjective aim.’ This initial phase is a direct derivate from God’s primordial nature. In this function, as in every other, God is the organ of novelty, aiming at intensification.

In the mere continuum there are contrary potentialities; in the actual world there are definite atomic actualities determining one coherent system of real divisions throughout the region of actuality. Every actual entity in its relationship to other actual entities is in this sense somewhere in the continuum, and arises out of the data provided by this standpoint. But in another sense it 1s everywhere throughout the continuum; for its constitution includes the objectifications of the actual world and thereby includes the continuum; also thep. 105 potential objectifications of itself contribute to the real potentialities whose solidarity the continuum expresses. Thus the continuum is present in each actual entity, and each actual entity pervades the continuum.

This conclusion can be stated otherwise. Extension, apart from its spatialization and temporalization, is that general scheme of relationships providing the capacity that many objects can be welded into the real unity of one experience. Thus, an act of experience has an objective scheme of extensive order by reason of the double fact that its own perspective standpoint has extensive content, and that the other actual entities are objectified with the retention of their extensive relationships. These extensive relationships are more fundamental than their more special spatial and temporal relationships. Extension is the most general scheme of real potentiality, providing the background for all other organic relations. The potential scheme does not determine its own atomization by actual entities. It is divisible; but its real division by actual entities depends upon more particular characteristics of the actual entities constituting the antecedent environment. In respect to time, this atomization takes the special form * of the ‘epochal theory of time.’ In respect to space, it means that every actual entity in the temporal world is to be credited with a spatial volume for its perspective standpoint. These conclusions are required by the consideration * of Zeno’s arguments, in connection with the presumption that an actual entity is an act of experience. The authority of William James can be quoted in support of this conclusion. He writes: “Hither your experience is of no content, of no change, or it is of a perceptible amount of content or change. Your acquaintance with reality grows literally by buds or drops of perception. Intellectually and on reflection you can divide these into components, but as immediately given,

? Cf. my Science and the Modern World, Ch. VII. * Cf. loc, ctt.; and Part IV of the present work.

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they come totally or not at all.”* James also refers to Zeno. Insubstance I agree with his argument from Zeno; though I do not think that he allows sufficiently for those elements in Zeno’s paradoxes which are the product of inadequate mathematical knowledge. But I agree that a valid argument remains after the removal of the invalid parts.

The argument, so far as it is valid, elicits a contradiction from the two premises: (i) that in a becoming something (res vera) becomes, and (ii) that every act of becoming is divisible into earlier and later sections which are themselves acts of becoming. Consider, for example, an act of becoming during one second. The act is divisible into two acts, one during the earlier half of the second, the other during the later half of the second. Thus that which becomes during the whole second presupposes that which becomes during the first half-second. Analogously, that which becomes during the first half-second presupposes that which becomes during the first quarter-second, and so on indefinitely. Thus if we consider the process of becoming up to the beginning of the second in question, and ask what then becomes, no answer can be given. For, whatever creature we indicate presupposes an earlier creature which became after the beginning of the second and antecedently to the earlier creature. Therefore there is nothing which becomes, so as to effect a transition into the second in question.

The difficulty is not evaded by assuming that something becomes at each non-extensive instant of time. For at the beginning of the second of time there is no next instant at which something can become.

Zeno in his ‘Arrow in Its Flight’ seems to have had an obscure grasp of this argument. But the introduction of motion brings in irrelevant details. The true difficulty is to understand how the arrow survives the lapse of time.

* Cf. Some Problems in Philosophy, Ch. X; my attention was drawn to this passage by its quotation in Religion in The Philosophy of William James, by Professor J. 8. Bixler.

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Unfortunately Descartes’ treatment of ‘endurance’ is very superficial, and subsequent philosophers have followed his example.