Abstract
Intensive magnitudes are not measurable in themselves, because the establishment of an equivalence between different steps in a scale of intensity does not make any sense without further clarification. Where intensive magnitudes are determined in a domain of the natural sciences, von Kries claims this is only a matter of counting, and of the measurement of temporal and spatial magnitudes. Every measurement of intensity should then be reduced to these operations by explicit conventions. Likewise, we can only speak of the measurement of sensations once we have established an arbitrary convention that determines what we will consider equal. The debate whether sensation varies with the logarithm of stimulus intensity, is then not a difference over matters of fact. Instead it is an empty dispute over words that is rooted in misunderstanding.
1882. Ueber die Messung intensiver Grössen und über das sogenannte psychophysische Gesetz. Vierteljahrsschrift für wissenschaftliche Philosophie, 4(3), 257–294.
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Notes
- 1.
Counting operations are not restricted to the determination of similar masses only, as when a lump of gold is designated to be x times another lump of gold. We can use counting operations on various kinds of things to establish composite units, and we can find valid methods to establish a basis for measuring these magnitudes. It is easy to see that population density is one intensive magnitude (among others) that is entirely measurable; it is composed of a number (of people) and a planar area.
- 2.
Zeller ’s (1881) recent article is also directed against the performance of actual measurements. It leaves unmentioned what I must take to be the core of the whole matter. When Zeller (1881, p. 9) says ‘that psychological processes are not measurable in the same sense as magnitudes of space and time, because they have no invariant standard of measure...’, then it is evident he considers a situation similar to that which would hold for space if there were no rigid bodies. To this one might justifiably counter that in the domain of sensations we could produce at least close or approximate values that might serve as such ‘invariant standards of measure’. Nor am I ready to concede that psychological processes may be unmeasurable because appearances in consciousness can only ever be compared with appearances in consciousness. No form of measurement does anything else, but to establish the relations of like with like. So we measure space only by space, and time only by time. Compare Wundt ’s (1883, pp. 253–254) comments on the subject, which I endorse wholeheartedly.
- 3.
It is assumed these oscillations occur in a plane, without the formation of nodes, so that the process can be described as a function of a single variable.
- 4.
I rely here on Aubert ’s report (Aubert & Foerster, 1857). The comparison of a bright spot in central vision with one in peripheral vision appears to me a rather shaky business, though I do believe Aubert’s report to be correct.
- 5.
I hardly need point out that one of these two propositions f = φ(a b c…) could itself be the defining equation. And under certain circumstances, it can remain arbitrary which of several propositions is regarded as the defining equation and which as a law. Thus it is arbitrary whether one regards the electrostatic, the electrodynamic, or the electromagnetic determination of current intensity as definitive (by analytic judgment). In any case the remaining two will then be subjects of synthetic judgment.
- 6.
Here I disregard any consideration of the small correction introduced for the natural light of the retina. [Trans.: for spontaneous phosphenes].
- 7.
Wundt (1883, p. 254) has objected to an apparently similar argument by Zeller (1881) as follows: [Naturally psychology must forever renounce the hope of determining by measure or in numbers the boringness of a conversation as greater or less. Psychology should be all the readier to do so, because such a determination would be as useless as it is hopeless. Why didn’t Zeller also reproach physicists for being in no position to count the number of water droplets in the ocean, or to predict the course that a storm-tossed boat will travel on the high seas?]. This objection finds its target in Zeller’s perspective on the subject, but does not impinge at all on the explanation given above. Here we are not concerned whether or not a measurement can be made practically in a specific case; rather we are concerned that such reports as may be made offer anything meaningful, quite apart from their material truth or falsity. The proposition that the amount of liquid water on the face of the earth amounts to exactly 100 kilograms at a given time is simply false. It is false only because it has a fully determinate sense, like the proposition that that boat will move at a uniform speed along a cubic curve. Yet the proposition that one conversation is ten times as boring as another is neither true nor false, but is simply a string of words to which no sense may be attached.
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Niall, K.K. (2023). Conventions of Measurement in Psychophysics. In: Johannes von Kries: Principles of the Probability Calculus. Studies in History and Philosophy of Science, vol 59. Springer, Cham. https://doi.org/10.1007/978-3-031-36506-5_12
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