supposed to be determinate magnitudes, however great. But the essentially indeterminate, reasons Renouvier, cannot be real. The thought here involved is, of course, as old as Aristotle's answer to the Eleatic paradoxes.
Now without here criticising Renouvier's argument as he states it, let us apply to the question at issue our present line of considerations. Can a number that is not determinate, that is neither 1, nor 2, nor n, nor n±r, nor any other determinate number, be regarded as being really embodied in the actual world? Can there be in the external world a countless aggregate? Evidently, in the first place, even a comparatively small finite number of objects or events can appear as subjectively indeterminate or countless, when this number is represented in and by a given conscious being who is unable to count it, or who will not count it. To perceive multitudes and aggregates as such, and yet to be wholly unaware of what the experienced number is, is very common. The loose change at the bottom of a man's pocket may remain stubbornly countless for his consciousness so long as he merely feels it there, and fears to count lest his spending be checked. But now objectively, one says, the number of coins present must be determinate, just n, neither more nor less. Subjective experience, as such, is thus not subject to the law of determinate numbers; but objective or external experience is thus subject. Had we no objective criteria, the law of determinateness of number would never occur to us as necessary. The jar produced by a heavy sound can often be felt by the hand as a subjectively countless multitude of successive minor shocks. The clicking of a ratchet in a toothed wheel, the pickets of a fence, seen in indirect vision, as you walk rapidly past them, the phenomena of rattling sounds and of flickering lights generally, the crackling of an electric spark: all these are experiences of subjectively countless or indeterminate multitudinousness. How is it, then, that we pretend to know a priori, in advance of special tests, that the objective events which lie at the basis of our consciousness must, if real, be events whose number is in itself precisely determinate?
