Note 446 — Chapter XIII · (continued 2)

Stumpf, pp. 116-7. I have omitted, so as not to make my text too intricate, an extremely acute and conclusive paragraph, which I reproduce here: "We may generalize: Wherever a number of sensible impressions are apprehended as a series, there in the last instance must perceptions of simple likeness be found. Proof: Assume that all the terms of a series, e.g. the qualities of tone, c d e f g, have something in common,—no matter what it is, call it X; then I say that the differing parts of each of these terms must not only be differently constituted in each, but must themselves form a series, whose existence is the ground for our apprehending the original terms in serial form. We thus get instead of the original series a b c d e f ... the equivalent series Xα, Xβ, Xγ,... etc. What is gained? The question immediately arises: How is α β γ known as a series? According to the theory, these elements must themselves be made up of a part common to all, and of parts differing in each, which latter parts form a new series, and so on ad infinitum, which is absurd."