Sections VII and XIV
Gustav Theodor Fechner (1860 - 1912)
THE MEASUREMENT OF SENSATION
Weber's law, that equal relative increments of stimuli are proportional to equal increments of sensation, is, in consideration of its generality and the wide limits within which it is absolutely or approximately valid, to be considered fundamental for psychic measurement. There are, however, limits to its validity as well as complications, which we shall have carefully to examine later. Yet even where this law ceases to be valid or absolute, the principle of psychic measurement continues to hold, inasmuch as any other relation between constant increments of sensation and variable increments of stimulus, even though it is arrived at empirically and expressed by an empirical formula, may serve equally well as the fundamental basis for psychic measurement, and indeed must serve as such in those parts of the stimulus scale where Weber's law loses its validity. In fact such a law, as well as Weber's law, will furnish a differential formula from which may be derived an integral formula containing an expression for the measurement of sensation.
This is a fundamental point of view, in which Weber's law, with its limitations, appears, not as limiting the application of psychic measurement, but as restricted in its own application toward that end and beyond which application the general [p. 563] principle of psychic measurement nevertheless continues to hold. It is not that the principle depends for its validity upon Weber's law, but merely that the application of the law is involved in the principle.
Accordingly investigation in the interest of the greatest possible generalization of psychic measurement has not essentially to commence with the greatest possible generalization of Weber's law, which might easily produce the questionable inclination to generalize the law beyond its natural limitation, or which might call forth the objection that the law was generalized beyond these limits solely in the interest of psychic measurement; but rather it may quite freely be asked haw far Weber's law is applicable, and how far not; for the three methods which are used in psychic measurement are applicable even when Weber's law is not, and where these methods are applicable psychic measurement is possible.
In short, Weber's law forms merely the basis for the most numerous and important applications of psychic measurement, but not the universal and essential one. The most general and more fundamental basis for psychic measurement is rather those methods by which the relation between stimulus increments and sensation increment in general is determined, within, as well as without, the limits of Weber's law; and the development of these methods towards even greater precision and perfection is the most important consideration in regard to psychic measurement.
And yet a great advantage would be lost, if so simple a law as Weber's law could not be used as an exact or at least sufficiently approximate basis for psychic measurement; just such an advantage as would be lost if we could not use the Kepler law in astronomy, or the laws of simple refraction in the theory of the dioptric instruments. Now there is just the same difficulty with these laws as with Weber's law. In the case of Kepler's law we abstract from deviations. In the case of simple lens refraction we abstract from optical aberration. In fact they may become invalid as soon as the simple hypotheses for which they are true no longer exist. Yet they will always remain [p. 564] decisive for the principle relation with which astronomy and dioptrics are concerned. Weber's law may in like manner, entirely lose its validity, as soon as the average or normal conditions under which the stimulus produces the sensation are unrealized. It will always, however, be decisive for these particular conditions.
Further, just as in physics and astronomy, so...