Process and Reality — the Gifford Lectures, 1929

In his ‘Achilles and the Tortoise’ Zeno produces an invalid argument depending on ignorance of the theory of infinite convergent numerical series. Eliminating the irrelevant details of the race and of motion—details which have endeared the paradox to the literature of all ages— consider the first half-second as one act of becoming, the next quarter-second as another such act, the next eighthsecond as yet another, and so on indefinitely. Zeno then illegitimately assumes this infinite series of acts of becoming can never be exhausted. But there is no need to assume that an infinite series of acts of becoming, with a first act, and each act with an immediate successor is inexhaustible in the process of becoming. Simple arithmetic assures us that the series just indicated will be exhausted in the period of one second. The way is then open for the intervention of a new act of becoming which lies beyond the whole series. Thus this paradox of Zeno is based upon a mathematical fallacy.

The modification of the ‘Arrow’ paradox, stated above, brings out the principle that every act of becoming must have an immediate successor, if we admit that something becomes. For otherwise we cannot point out what creature becomes as we enter upon the second in question. But we cannot, in the absence of some additional premise, infer that every act of becoming must have had an immediate predecessor.

The conclusion is that in every act of becoming there is the becoming of something with temporal extension; but that the act itself is not extensive, in the sense that it is divisible into earlier and later acts of becoming which correspond to the extensive divisibility of what has become.

In this section, the doctrine is enunciated that the creature is extensive, but that its act of becoming is not extensive. This topic is resumed in Part IV. Howp. 108ever, some anticipation of Parts III and IV is now required.

The res vera, in its character of concrete satisfaction, 1s divisible into prehensions which concern its first temporal half and into prehensions which concern its second temporal half. This divisibility is what constitutes its extensiveness. But this concern with a temporal and spatial sub-region means that the datum of the prehension in question is the actual world, objectified with the perspective due to that sub-region. A prehension, however, acquires subjective form, and this subjective form is only rendered fully determinate by integration with conceptual prehensions belonging to the mental pole of the res vera. The concrescence is dominated by a subjective aim. which essentially concerns the creature as a final superject. This subjective aim is this subject itself determining its own self-creation as one creature. Thus the subjective aim does not share in this divisibility. If we confine attention to prehensions concerned with the earlier half, their subjective forms have arisen from nothing. For the subjective aim which belongs to the whole is now excluded. Thus the evolution of subjective form could not be referred to any actuality. The ontological principle has been violated. Something has floated into the world from nowhere.

The summary statement of this discussion is, that the mental pole determines the subjective forms and that this pole is inseparable from the total res vera.

SECTION III

The discussion of the previous sections has merely given a modern shape to the oldest of European philosophic doctrines. But as a doctrine of common sense, it is older still—as old as consciousness itself. The most general notions underlying the words ‘space’ and ‘time’ are those which this discussion has aimed at expressing in their true connection with the actual world. The alternative doctrine, which is the Newtonian cosmology, emphasized the

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‘receptacle’ theory of space-time, and minimized the factor of potentiality. Thus bits of space and time were conceived as being as actual as anything else, and as being ‘occupied’ by other actualities which were the bits of matter. This is the Newtonian ‘absolute’ theory of space-time, which philosophers have never accepted, though at times some have acquiesced. Newton’s famous Scholium * to his first eight definitions in his Principia expresses this point of view with entire clearness:

“Hitherto I have laid down the definitions of such words as are less known, and explained the sense in which I would have them to be understood in the following discourse. I do not define time, space, place and motion, as being well known to all. Only I must observe, that the vulgar conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which, it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common.

“T. Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without regard to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.

“TJ. Absolute space, in its own nature, and without regard to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies, and which is vulgarly taken for immovable space; . . . absolute and relative space are the same in figure and magnitude; but they do not remain always numerically the same. . .

S)Veateiear. As thesordersofirthe parts of time is

5 Andrew Motte’s translation; new edition revised, London, 1803.

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