that Fechner's originality exclusively consists, in his assumptions, namely, 1) that the just-perceptible increment is the sensation-unit, and is in all parts of the scale the same (mathematically expressed, Δs= const.); 2) that all our sensations consist of sums of these units; and finally, 3) that the reason why it takes a constant fractional increase of the stimulus to awaken this unit lies in an ultimate law of the connection of mind with matter, whereby the quantities of our feelings are related logarithmically to the quantities of their objects. Fechner seems to find something inscrutably sublime in the existence of an ultimate 'psychophysic' law of this form.
These assumptions are all peculiarly fragile. To begin with, the mental fact which in the experiments corresponds to the increase of the stimulus is not an enlarged sensation, but a judgment that the sensation is enlarged. What Fechner calls the 'sensation' is what appears to the mind as the objective phenomenon of light, warmth, weight, sound, impressed part of body, etc. Fechner tacitly if not openly assumes that such a judgment of increase consists in the simple fact that an increased number of sensation-units are present to the mind; and that the judgment is thus itself a quantitatively bigger mental thing when it judges large differences, or differences between large terms, than when it judges small ones. But these ideas are really absurd. The hardest sort of judgment, the judgment which strains the attention most (if that be any criterion of the judgment's 'size'), is that about the smallest things and differences. But really it has no meaning to talk about one judgment being bigger than another. And even if we leave out judgments and talk of sensations only, we have already found ourselves (in Chapter VI) quite unable to read any clear meaning into the notion that they are masses of units combined. To introspection, our feeling of pink is surely not a portion of our feeling of scarlet; nor does the light of an electric arc seem to contain that of a tallow-candle in itself. Compound things contain parts; and one such thing may have twice or three times as many parts as another. But when we take a simple sensible quality like light or sound, and say that there is now twice or thrice as much of it present as there was a moment ago, although we seem to mean the same thing as if we were talking of compound objects, we really mean something different. We mean that if we were to arrange the various possible degrees of the quality in a scale of serial increase, the distance, interval, or difference between the stronger and the weaker specimen before us would seem about as great as that between the weaker one and the beginning of the scale. It is these relations, these distances, which we are measuring and not the composition of the qualities themselves, as Fechner thinks. Whilst if we turn to objects which are divisible, surely a big object may be known in a little thought. Introspection shows moreover that in most sensations a new kind of feeling invariably accompanies our judgment of an increased impression; and this is a fact which Fechner's formula disregards.[459]
But apart from these a priori difficulties, and even supposing that sensations did consist of added units, Fechner's assumption that all equally perceptible additions are equally great additions is entirely arbitrary. Why might not a small addition to a small sensation be as perceptible as a large addition to a large one? In this case Weber's law would apply not to the additions themselves, but only to their perceptibility. Our noticing of a difference of units in two sensations would depend on the latter being in a fixed ratio. But the difference itself would depend directly on that between their respective stimuli. So many units added to the stimulus, so many added to the sensation, and if the stimulus grew in a certain ratio, in exactly the same ratio would the sensation also grow, though its perceptibility grew according to the logarithmic law.[460]
If A stand for the smallest difference which we perceive, then we should have, instead of the formula Δs = const., which is Fechner's, the formula Δs/s = const., a formula which interprets all the facts of Weber's law, in an entirely different theoretic way from that adopted by Fechner.[461]
The entire superstructure which Fechner rears upon the facts is thus not only seen to be arbitrary and subjective, but in the highest degree improbable as well. The departures from Weber's law in regions where it does not obtain, he explains by the compounding with it of other unknown laws which mask its effects. As if any law could not be found in any set of phenomena, provided one have the wit to invent enough other coexisting laws to overlap and neutralize it! The whole outcome of the discussion, so far as Fechner's theories are concerned, is indeed nil. Weber's law alone remains true, as an empirical generalization of fair extent: What we add to a large stimulus we notice less than what we add to a small one, unless it happen relatively to the stimulus to be as great.