9. “A Number, a Measure, belonging to Movement?”
This, at least, is plausible since Movement is a continuous thin; but let us consider.
To begin with, we have the doubt which met us when we probed its identification with extent of Movement: is Time the measure of any and every Movement?
Have we any means of calculating disconnected and lawless Movement? What number or measure would apply? What would be the principle of such a Measure?
One Measure for movement slow and fast, for any and every movement: then that number and measure would be like the decade, by which we reckon horses and cows, or like some common standard for liquids and solids. If Time is this Kind of Measure, we learn, no doubt, of what objects it is a Measure – of Movements – but we are no nearer understanding what it is in itself.
Or: we may take the decade and think of it, apart from the horses or cows, as a pure number; this gives us a measure which, even though not actually applied, has a definite nature. Is Time, perhaps, a Measure in this sense?
No: to tell us no more of Time in itself than that it is such a number is merely to bring us back to the decade we have already rejected, or to some similar collective figure.
If, on the other hand, Time is [not such an abstraction but] a Measure possessing a continuous extent of its own, it must have quantity, like a foot-rule; it must have magnitude: it will, clearly, be in the nature of a line traversing the path of Movement. But, itself thus sharing in the movement, how can it be a Measure of Movement? Why should the one of the two be the measure rather than the other? Besides an accompanying measure is more plausibly considered as a measure of the particular movement it accompanies than of Movement in general. Further, this entire discussion assumes continuous movement, since the accompanying principle; Time, is itself unbroken [but a full explanation implies justification of Time in repose].
The fact is that we are not to think of a measure outside and apart, but of a combined thing, a measured Movement, and we are to discover what measures it.
Given a Movement measured, are we to suppose the measure to be a magnitude?
If so, which of these two would be Time, the measured movement or the measuring magnitude? For Time [as measure] must be either the movement measured by magnitude, or the measuring magnitude itself or something using the magnitude like a yard-stick to appraise the movement. In all three cases, as we have indicated, the application is scarcely plausible except where continuous movement is assumed: unless the Movement proceeds smoothly, and even unintermittently and as embracing the entire content of the moving object, great difficulties arise in the identification of Time with any kind of measure.
Let us, then, suppose Time to be this “measured Movement,” measured by quantity. Now the Movement if it is to be measured requires a measure outside itself; this was the only reason for raising the question of the accompanying measure. In exactly the same way the measuring magnitude, in turn, will require a measure, because only when the standard shows such and such an extension can the degree of movement be appraised. Time then will be, not the magnitude accompanying the Movement, but that numerical value by which the magnitude accompanying the Movement is estimated. But that number can be only the abstract figure which represents the magnitude, and it is difficult to see how an abstract figure can perform the act of measuring.
And, supposing that we discover a way in which it can, we still have not Time, the measure, but a particular quantity of Time, not at all the same thing: Time means something very different from any definite period: before all question as to quantity is the question as to the thing of which a certain quantity is present.
Time, we are told, is the number outside Movement and measuring it, like the tens applied to the reckoning of the horses and cows but not inherent in them: we are not told what this Number is; yet, applied or not, it must, like that decade, have some nature of its own.
Or “it is that which accompanies a Movement and measures it by its successive stages”; but we are still left asking what this thing recording the stages may be.
In any case, once a thing – whether by point or standard or any other means – measures succession, it must measure according to time: this number appraising movement degree by degree must, therefore, if it is to serve as a measure at all, be something dependent upon time and in contact with it: for, either, degree is spatial, merely – the beginning and end of the Stadium, for example – or in the only alternative, it is a pure matter of Time: the succession of early and late is stage of Time, Time ending upon a certain Now or Time beginning from a Now.
Time, therefore, is something other than the mere number measuring Movement, whether Movement in general or any particular tract of Movement.
Further: Why should the mere presence of a number give us Time – a number measuring or measured; for the same number may be either – if Time is not given us by the fact of Movement itself, the Movement which inevitably contains in itself a succession of stages? To make the number essential to Time is like saying that magnitude has not its full quantity unless we can estimate that quantity.
Again, if Time is, admittedly, endless, how can number apply to it?
Are we to take some portion of Time and find its numerical statement? That simply means that Time existed before number was applied to it.
We may, therefore, very well think that it existed before the Soul or Mind that estimates it – if, indeed, it is not to be thought to take its origin from the Soul – for no measurement by anything is necessary to its existence; measured or not, it has the full extent of its being.
And suppose it to be true that the Soul is the appraiser, using Magnitude as the measuring standard, how does this help us to the conception of Time?