impossible in perception; in perception, therefore, we substitute in place of an element of experience a very small event representing the perceptual limit of our sense faculties, and comprising the given element together with a number of elements which cannot be distinguished from it in perception; to determine such a perceptual element of experience a finite number of relations between this element and the other elements is sufficient. The sum of the relations of a given element to the remaining elements we call its position in a given Experience, and the sum of those relations which suffice for its approximate determination, in the way indicated above, its approximate position.
24.1. It may be, indeed, and it most probably is so, that, even apart from the imperfection of our senses, the mind is more limited in perception than in thought, and that there is inherent in Experience itself a certain characteristic, which uniquely divides Experience, or a given section of it, into a finite number of delimited events, which the mind can further divide in thought but not in perception. Since such a characteristic must needs be independent of the mind we cannot predict it a priori, and its existence or non-existence can only be proved empirically; this characteristic—without making for the present any assumption as to its existence or non-existence—we call the atomicity of Experience.
From the manner in which we arrived at elements of experience it is evident that these elements will form a continuum; this continuum will, however, only be conceptual and thus does not preclude the possible perceptual atomicity of Experience. Even if it were ascertained by exact perceptual analysis that Experience is atomic, it will nevertheless suit us better, from the point of view of facilitating mathematical analysis, to regard it as continuous, with the understanding, of course, that results based on this hypothesis are only approximately valid, like statistical averages within aggregates of great numbers of elements, the individual significance of which in relation to the whole is infinitesimally small.
25. The parts of perceptual and non-perceptual content of a given mind present a number of attributes which can be arranged in series and enable us to order these parts; such ordinal characteristics are, for example, pleasurableness, colour, sound, intensity, and soon. We facilitate the ordering of the parts of the mind’s content according to this or that characteristic by correlating the various “degrees” of the attribute with the series (or part of a series) of natural numbers, which is nothing but an ultimate abstraction from
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