The argument, so far as it is valid, elicits a contradic- tion from the two premises: (i) that in a becoming some- thing (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 presup- poses 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.
The Extensive Continuum 107
Unfortunately Descartes’ treatment of ‘endurance’ is very
superficial, and subsequent philosophers have followed
his example.
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 eighth- second as yet another, and so on indefinitely. Zeno then illegitimately assumes this infinite series of acts of becom- ing 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 arith- metic 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 imme- diate 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. How-
108 Process and Reality
ever, 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 prehen- sion in question is the actual world, objectified with the perspective due to that sub-region. A prehension, how- ever, acquires subjective form, and this subjective form is only rendered fully determinate by integration with con- ceptual 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 deter- mining 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 noth- ing. 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.
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 doc- trine, which is the Newtonian cosmology, emphasized the
The Extensive Continuum 109
‘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 dis- course. 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 dura-
tion: relative, apparent, and common time, is some sen-
sible and external (whether accurate or unequable)
measure of duration by means of motion, which is com-
monly 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 deter- mine 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.
210 Process and Reality
immutable, so also is the order of the parts of space. Sup- pose those parts to be moved out of their places, and they will be moved (if the expression may be allowed) out of themselves. For times and spaces are, as it were, the places as well of themselves as of all other things. All things are placed in time as to order of situation. It is from their essence or nature that they are places; and that the primary places of things should be movable, is absurd. These are, therefore, the absolute places; and translations out of those places are the only absolute motions. . . . Now no other places are immovable but those that, from infinity to infinity, do all retain the same given positions one to another; and upon this account must ever remain unmoved; and do thereby con- stitute, what I call, immovable space. The causes by which true and relative motions are distinguished, one from the other, are the forces impressed upon bodies to generate motion. True motion is neither generated nor altered, but by some force impressed upon the body moved: but relative motion may be generated or altered without any force impressed upon the body. For it is sufficient only to impress some force on other bodies with which the former is compared, that by their giving way, that relation may be changed, in which the relative rest or motion of this other body did consist. . . . The effects which distinguish absolute from relative motion are, the forces of receding from the axis of circular motion. For there are no such forces in a circular motion purely rela- tive, but, in a true and absolute circular motion, they are greater or less, according to the quantity of motion. . . Wherefore relative quantities are not the quantities them- selves, whose names they bear, but those sensible meas- ures of them (either accurate or inaccurate) which are commonly used instead of the measured quantities them- selves.) 9°30?
I have quoted at such length from Newton’s Scholium
because this document constitutes the clearest, most
definite, and most influential statement among the cos-
THE EXTENSIVE CONTINUUM Lid
mological speculations of mankind, speculations of a type which first assume scientific importance with the Pythagorean school preceding and inspiring Plato. New- ton is presupposing four types of entities which he does not discriminate in respect to their actuality: for him minds are actual things, bodies are actual things, absolute durations of time are actual things, and absolute places are actual things. He does not use the word ‘actual’; but he is speaking of matter of fact, and he puts them all on the same level in that respect. The result is to land him in a clearly expressed but complex and arbitrary scheme of relationships between spaces inter se; between durations inter se; and between minds, bodies, times and places, for the conjunction of them all into the solidarity of the one universe. For the purposes of science it was an extraordinarily clarifying statement, that is to say, for all the purposes of science within the next two hundred years, and for most of its purposes since that period. But, as a fundamental statement, it lies completely open to sceptical attack; and also, as Newton himself admits, diverges from common sense—“the vulgar conceive those quantities under no other notions but from the relation they bear to sensible objects.” Kant only saved it by reducing it to the description of a construct by means of which ‘pure intuition’ introduces an order for chaotic data; and for the schools of transcendentalists derived from Kant this construct has remained in the inferior position of a derivative from the proper ultimate sub- stantial reality. For them it is an element in ‘appearance’ ; and appearance is to be distinguished from reality. The philosophy of organism is an attempt, with the minimum of critical adjustment, to return to the conceptions of the ‘vulgar.’ In the first place, the discussion must fasten on the notion of a ‘sensible object,’ to quote Newton’s phrase. We may expand Newton’s phrase, and state that the com- mon sense of mankind conceives that all its notions ultimately refer to actual entities, or as Newton terms them, ‘sensible objects.’ Newton, basing himself upon