Koffka (1917) starts from Kohler’s arguments to focus his criticism on Stumpf’s paradox. Stumpf (1883: 33-34) introduces the paradox to support the existence of noticing thresholds and to defend the view that noticing is not equivalent to attention. Stumpf conceives the paradox as an extreme case in which a series of appearances change so smoothly that differences might not be explicitly perceived as such. He supposes to produce a continuous series of tones a, b, c, …z that range from the lowest to the highest limit of perceivable pitch by smoothly varying the stimulus frequency. He claims that even the most skilled musicians listening with the utmost attention to the tones would hardly succeed in distinguishing any two neighboring tones for pitch; hence, they will judge that they are equal. Yet this judgement of perceptual equality is false. If it were true, appearances should force inconsistent judgements upon the subjects. The tones form a phenomenally continuous series. Since two neighboring appearances of any pair are always judged equal to one another, all the appearances of the series likewise should be judged to be equal. This is obviously not true: a is never judged to be equal to z, otherwise the series would be equivalent to perceiving one and the same single sound as if one perceived a glissando. In fact, the tones in the pairs (a-b) and (b-c) are judged to be equal, but a and c are judged to be different. If this difference were thoroughly ascribed to appearances, this would violate the transitivity of equivalence relation. Therefore, it can be concluded that for each neighboring tone of the first two pairs there is no part – that is, the pitch attribute – that stands out so explicitly that three appearances are noticed as equally differing in pitch. This means that the cause of the erroneous responses lies in judgement in a condition in which the variation in pitch of the first three appearances does not have an equally noticeable magnitude. Given the principle of independent variation, Stumpf concludes that appearances are the same across successive comparative judgements despite the difference in subjects’ reports.
Koffka’s criticism is addressed to theoretical and methodological issues. He assumes that Stumpf’s account belongs to the second solution of the paradox (supra § 4.1.1); hence, it is consistent with the constancy hypothesis and the assumption of unobservable sensations. He maintains that Stumpf does not recognize that perception faces a real phenomenal difference, which consequently is treated as an error of the judgement applied to constant sensations that fall under the threshold of a hypothetical psychic function. In reality, according to Koffka, the paradoxical consequences of Stumpf’s argument arise because he derives the truth of the pairwise comparison from the knowledge of the stimuli difference. The judgements on the pairs (a-b), (b-c) and (a-c) are paradoxical because he assumes that the appearance of the tone a must be the same in the first comparison with b and in the third with c, for the frequency of the stimulus A is the same in both cases. Koffka remarks that Stumpf does not admit a change of appearances: he derives this belief from the constant stimulation and does not recognize that they form a relational structure in each comparison in which they play a new perceptual role. Stumpf assumes that a1 = a2, b1 = b2, c2 = c3, for A, B and C are held constant in the three successive comparisons. The assumption introduces a spurious asymmetry that leads to the arbitrary selection of observations. The observation of the difference between a and c decides on the observations (a = b) and (b = c), because the first captures the barely noticeable difference that Stumpf knows to hold assuming the non-perceptual criterion of the difference between the frequencies of the corresponding stimuli.
Like Kohler, Koffka has a methodological point in testing whether Stumpf’s constructs consist of observable constituents in order for the functional equivalence of description and explanation to obtain. However, the phenomenological core of Stumpf’s theory is overlooked. Koffka (1917: 2 n. 1) is aware of the tenet that appearances do not depend on psychic functions, but he decides to leave it out of consideration. He raises the objection that the concept of noticing is contradictory because it implies that what is perceived has unobserved parts. However, Stumpf uses this concept to denote the perceptual explication of the parts that cannot have the same relief simultaneously. In this sense, the criticism that Stumpf does not recognize a real phenomenal difference is ill-founded. Stumpf (1907: 35) remarks that there are differences that belong to appearances, because they occur while the function of noticing remains constant. A piano following a pianissimo does not show a loudness equal to that of a fortissimo after a forte, though the intensity difference in the stimulation is the same. In accord with Brentano, Stumpf contends that loudness, rather than physical intensity, has to vary its magnitude to let the sounds appear equally dissimilar to the dynamical increase in the way they are played. Instead of assuming a physical model for the differential threshold, as Koffka claims, Stumpf employs Brentano’s phenomenological reformulation of the psychophysical law. If objects appear equal when the difference between them is equally noticed, that is, when they appear equally dissimilar, then the magnitude of change (increase/decrease) under the respect of a phenomenal quantity must be proportionally rather than absolutely equal as in Fechner’s law (supra § 7.3) It is noteworthy that Brentano’s reformulation can be expressed by a power function with the consequence that it does not admit positive values of stimuli for which there are negative values for sensations, that is, unnoticed sensations, because the threshold is the value at which there is a sensation, however small it may be, and below which the stimulation is simply not sufficient to bring about anything perceivable. For each value above threshold there is always an appearance (Stumpf, 1883: 35; cf. Antonelli and Zudini, 2010). Accordingly, when Stumpf talks of “unnoticed sensations” in the paradox of the smooth pitch shift, he means the insufficient magnitude of change in a phenomenal attribute, which might affect the subjective reliability of the comparative judgements of the second class on pure tonal appearances unless a determinate increment ratio is established. He is somehow aware of this equivocal expression and maybe too confident in relying on the context to avoid misinterpretations by readily adding the distinction between objective and subjective senses of tone appearances (1883: 34). He interprets this distinction as stemming from the phenomenal domain, because it corresponds to the grammatical distinction between a sentence like “This tone appears_” and a sentence like “It seems to me that this tone is_,” where the empty place “_” stands for a qualitative or quantitative part of the perceived object (1883: 32, 1907: 36). Far from introducing unobservable contents in appearances, Stumpf thinks of the paradox as an extreme case allowed by the language employed to talk about appearances, in which the two senses cannot be distinguished with certainty to decide the trustworthiness of reports. In such cases he admits of an indirect control of the hypothesis by manipulating the stimulation (cf. 1907: 21, for the conditions allowing the indirect hypothesis and control in the science of observable data). The reference to the stimulus frequency does not seem to attest a stimulus error.
Koffka reproaches Stumpf for not conceding that appearances can change when they become part of distinguished structures according to the new functional role they play. He extends Rubin’s discussion of the figure – ground inversion to the structures of comparative judgements. Koffka (1922: 383-385) emphasizes that the alternate appearance of figure and ground is not explained by saying that an unnoticed ground becomes noticed as a figure and vice versa. The articulation of the field in a figure and a ground is a phenomenal distinction and its inversion is equivalent to a phenomenal change; hence, it is correct to talk of “noticing differently” rather than “noticing so and so” the parts of the field. The correct description would say that the phenomenon has changed, rather than that some unnoticed parts of the field have become noticed. Something perceptually really new occurs in the figure – ground inversion, because the ground or parts thereof that become figure cannot be reduced to something that was already “contained” in it, albeit unobserved. It is doubtful that Stumpf would not have accepted this account. “Noticing differently” is the sense of the explication of parts of appearances as perception goes along. However, Stumpf does not accept the immediate extension without restriction of the evidence obtained for visual perception to other fields like sound perception or to a general theory of perception.
As regards sound perception, Stumpf does not concede that there is always a phenomenal change in appearances any time they come to hold new relations because of his earlier refusal of the “theory of sensory relativity,” according to which perceiving something is always sensing something in relation to something else (1883: 7-22). This theory implies that appearances have no intrinsic properties, but Stumpf holds that this is contrary to experience. He points out, for example, that dissonance is an absolute property of tones because its perception does not contain any relation to the consonance by which it is bound to be resolved. The dominant seventh does not imply any of the consonant chords by which it is accompanied in a perfect cadenza. A fortiori, it is wrong to maintain that a tone acquires its properties of pitch and loudness as a function of the other tones that happen to precede or follow it. In this sense, Stumpf (1883: 20-21) warns against the unrestricted extension of Hering’s account of the simultaneous or successive visual contrast. He recognizes that the loudness of a tone is modified by other tones. This is an objective perceptual fact and one may look for its causal physiological mechanism. However, this cannot mean that each feature of a tone undergoes a phenomenal change in every condition in which the contrast might occur. If a lower dominant precedes a C that is then followed by a higher dominant, the C is perceived with the same pitch, even if either of the dominant tones alternatively is presented simultaneously with it. The pitch quality of a tone itself seems to be unaffected by contrast.
As regards the general theory of perception, Stumpf warns against the theoretical and methodological implications of the theory that relations always bring about the alteration of appearances. The theoretical implication involves the reconstruction of the order of phenomena. If the constituent tones and the chord C-E-G are different appearances, the chord itself should be considered a simple appearance not coincident with any of its tones. Yet it is not localizable in any position along the continuous series of tones along the pitch height. One could add another ordering dimension, but this is not demanded by a complete description of tone appearances. If for a part x0 of the appearance A, each distinction D(0,1,…, (n _ 1),n) should change a so that it would give rise to new appearances of simple qualities X(0,1,…,(n _ 1), n), no sound could be per-ceived on its own, the fundamental classes of appearances of a domain could not be specified, the “mixture laws” of tones could not be determined and phenomena like timbre could not be accounted for (1907: 19). The methodological implication regards the sense of the comparative task. It is of course true that appearances cannot be studied without being observed. However, if observing them in conditions in which they hold relations necessarily brought about a modification of them, the comparison would become meaningless. It would change eo ipso what it is meant to compare (1907: 22).
In conclusion, if one discounts the issues peculiar to the scientific debate in early 20th-century psychology, the dispute can indeed be reduced to common phenomenological grounds. Kohler, Koffka and Stumpf point to phenomenological evidence and arguments to support their views. It is noteworthy that Stumpf refuses to interpret all phenomena by analogy with vision, because he does not admit that the study of tones takes for granted the model of the simultaneous excitation of nervous cells that is assumed for visual contrast. The divergence on relational structures could be settled only by the phenomenology of comparative perceptual judgements that has been independently outlined in theoretical and experimental contributions by Meinong (1882), Benussi (1913), Kohler (1923, 1933), Lauenstein (1933, 1938), Husserl (1939) and Ehrenstein (1977).
Source: Calì Carmelo (2017), Phenomenology of Perception: Theories and Experimental Evidence, Brill.
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