Perceiving the Difference and the Phenomenal Basis of Judgments

It may be quite surprising that despite a common phenomenological back­ground, Kohler (1913a) and Koffka (1917) address, contra Stumpf, arguments against the constancy hypothesis and the construct of unnoticed sensations. In fact, their criticism consists in charging Stumpf with a theory that might imply similar theoretical and methodological problems. Kohler ([1913a] 1971: 19 n. 12) acknowledges that Stumpf “pay[s] due respect to observable phenom­ena.” For example, Stumpf does not account for perceptual constancies by re­sorting to an inferential integration of sensory data and specifies the criteria for distinguishing such cases from those that seem to require the introduction of the notion of judgement. In addition, Kohler remarks that Stumpf’s defi­nition of “elementary judgement” is not as vague as that of the theories that explain perception through inference. Nevertheless, he suggests that the con­cept of “noticing” in Stumpf’s theory of perceptual judgements induced him in certain cases to admit of the disputable constructs of unnoticed sensation and error judgements.

Stumpf derives the concept of “noticing” from Brentano (1982), for whom it denotes the possibility of making the elements of perception explicit and available to observation through analysis. Analysis indeed is not a reduction to the less complex or even atomic terms, but, rather, the partition of an in­stance of perception into the minimal structural elements that are able to un­dergo an independent variation (supra, § 2.1). Thus a perception is modified in a phenomenon analyzed in the correlated parts of reference and appearance. Stumpf employs this concept in connection with the perception of parts of a unitary object, which can also be noticed, for example, when the tones in the chord C-E-G are explicitly made to stand out(supra, § 2.2). This concept is cen­tral in the Tonpsychologie (1883) that is a phenomenological contribution to the psychophysics intended as the science of the intersubjective trustworthi­ness of perceptual judgements. As Stumpf himself recognized, this work was devoted more to the reliability (Zuverlassigkeit) of perceptual judgements than to the phenomenological analysis of tones (1883: 3, 22). Stumpf (1930: 425) re­marks that it is to be considered a piece of the phenomenological psychology that starts from judgement rather than from appearances.

Stumpf (1883: 22-23) defines reliability as the measure of the confidence subjects have in the truth or accuracy (Genauigkeit) of statements regarding judgements of appearances. The concept of perceptual judgement is different from that of von Helmholtz’s inferential theory. It is derived from Brentano’s theory that judgements are founded on appearances and consist in approving or rejecting their features correctly or not. On this basis, Stumpf introduces the notion of “state of affairs” as the specific object of judgement. A state of affairs is equivalent to the proposition “that S is p” or to the infinitive form “the being p of S.” Then, a judgement is true if it correctly approves or rejects the state of affairs that represents what is objectively the case according to the appearances forced upon the subjects. Stumpf (1883: 22f.) distinguishes be­tween two kinds of reliability and two classes of perceptual judgements. Ob­jective reliability regards judgements made about objects on the basis of how they appear. Subjective reliability regards judgements on the appearances themselves, which are involved in tasks requiring categorization like identi­fying a tone by reporting its name. The first class of judgements includes af­firmative or negative judgements that are either true or false. For instance, if subjects are asked which of two tones has a higher pitch, each of the two possible answers may be true. The second class includes judgements whose either affirmative or negative form is always false. For instance, if subjects are asked whether two tones have the same pitch, the affirmative answer is always false, while the negative is always true because of the differences that may be too small to appear explicitly as such. For this reason, Stumpf holds that equality and diversity are asymmetrical with respect to judgement reliability. Consider the judgement by eye of the length of two lines. The judgement that they have equal length is always false because of the differences, for example of a millimetre order of magnitude, that must pass unobserved. However, if the judgement on length is expressed through sentences in which numerals denote integers that are multiples of the smallest observable unit, it becomes either true or false because the differences that are too small to appear can be neglected. Likewise, the affirmative judgement in response to such questions as “is this interval a fourth?” is always false if “fourth” has an absolute meaning. If “fourth” denotes the interval that is distinguished from the others by musi­cal theory, affirmative and negative judgements become either true or false, because they will be founded on the comparison through fixed steps between diverse appearances. Indeed, affirmative judgements on the equality of pitch height are necessarily false, but if subjects are asked to judge which piano key yields the closest sound to a previously heard tone, the judgements are either true or false because the fixed steps on the keyboard permit one to neglect the differences too small to appear explicitly as such. In general, the judgements that can be expressed through numerals designating integers belong neces­sarily to the first class. Accordingly, when a tone is judged to appear equal to another, the judgement of equality should be rephrased in terms of the high­est perceivable similarity or the least perceivable diversity as possible given something as a scale.

These two classes of judgements have different implications for measuring objective reliability. The objective reliability of the first class is equivalent to its degree of probability, that is, the ratio of the likely cases of true and false judgements calculated as the number of correct and wrong answers in a se­ries of judgements. The objective reliability of the second class is equivalent to the degree of accuracy of the affirmative judgements on equality, that is, to the degree at which they approach the correct state of affairs on the basis of explicit or noticed differences. To obtain this measure, one needs to know how the perception of difference varies in connection with how much the stimuli depart from the equality in an absolute sense; for instance, for judgements on the equality of intervals one should measure the function that connects the perceptual magnitude of interval difference with how much the frequency of the corresponding stimuli departs from the pure ratio 1:2, 2:3 and so forth.

Stumpf introduces the concept of noticing in the framework of the mea­surement of the objective reliability of perceptual judgments. He observes that subjects happen to take a tone in two distinct presentations as C or D. Fur­thermore, if the same number of tones is presented twice in rapid sequence (or a row of dots for a brief time), subjects report hearing first 15 and then 20 tones (1883: 31-32). He reasoned that the variability is accounted for by admit­ting various degrees of noticing. In categorization and enumeration tasks the conditions of presentation may have an influence on the ability to notice the parts and properties of appearances, making them explicit to various extents in order to be represented or not in the state of affairs. Since this question deals with the second class of judgements, an indirect control of appearances through the stimulation confirms that they are the same across the conditions; hence, the different reports should depend on perceptual noticing judgements.

Stumpf argues that it is necessary to introduce noticing thresholds for per­ceptual judgements by analogy with sensory thresholds (1883: 33-34). Stumpf extends the treatment of noticing in connection with Brentano’s phenomeno­logical re-interpretation of the construct of sensory thresholds and the formu­lation of Fechner’s psychophysical law (Brentano, 1874: 10-11). Brentano argued that Fechner’s law consists in reality of two sides. The first side regards the correlation between the stimulus increment and the barely noticeable sen­sory differences. The second side regards the correlation between the barely noticeable differences and their perception as different or equal appearances. Considering the two sides of the psychophysical law, Brentano ([1874] 1995: 51) concluded that if the strengths of the physical stimuli increase by the same number of times, the intensities of the sensations also increase by the same number of times. […] Our law does not require that, whenever the stimulus in­creases by a certain number of times, the sensation increases by the same number of times. It would be satisfied if, whenever the stimulus increases by one half, the sensation increases by one third.

Accordingly, the sensory thresholds tell us which differences in the stimula­tion correspond to the barely noticeable differences by which two sensations are discriminated, but not that sensations are equal in perception. Indeed, for two sensations discriminated by a barely noticeable difference to appear equal, every equal stimulus increment should be equally noticeable and every equally noticeable increment should appear equal. This question cannot be decided on the basis of the correlation between stimuli and sensations, be­cause it requires taking into account the mutual relation between sensations, that is, how they appear. This is a phenomenological question that involves the variable magnitude of the changes of appearances. For instance, if a segment of a tenth of an inch is added to an inch’s length line, this increment is more noticeable than if the same segment were added to a foot’s length line. A foot lengthened by a tenth of an inch appears more similar to a foot than an inch lengthened by the same amount appears similar to an inch. Only if the foot appears different at the same magnitude after the addition as the inch will the difference be perceived, that is, it is noticed as equal to the difference in the inch before and after the addition ([1874: 97f.], 1995: 50-51). Therefore, the psychophysical law must be qualified by specifying that it is not sufficient for varying appearances to be equal that the barely noticeable sensory differences are equal, but it is required that the magnitude of the variation appears equally noticeable. The hypothesis of noticing thresholds stems from this conclusion. The perception of equality depends on the magnitude of the change in appear­ances that is equally noticed. This implies that the parts and attributes of ob­jects, be they lines, tones or colors, have to be explicit so to make their bearers appear equally dissimilar. Likewise, the smallest observable unit for the mea­surement of the first class of judgement must be intended as a phenomenal yardstick. Therefore the reliability of perceptual judgements is a function of the threshold of noticing, that is, of the extent to which differences become phenomenally explicit for the judgement to be true to them.

Kohler does not attack this reasoning, which he does not even reconstruct. He focuses rather on the notion of noticing itself to claim that it entails epis­temological and methodological problems for the experimental research, like those which stem from admitting the constancy hypothesis and the unnoticed sensations. He makes the case of masking low tones through the simultane­ous presentation of other tones ([1913a] 1971: 20-21). He reports that Stumpf (1910: 79) is inclined to account for masking as the effect of the interference be­tween sensations of different intensity. Kohler suggests that unless there is evi­dence of a mixture law for sounds and colors alike, this account explains away masking as a proper phenomenon. In his reconstruction, Stumpf treats mask­ing as an unexpected effect on the basis of the intensities of the single sensa­tions due to constant stimuli, which is reduced to their interaction. Stumpf tries to prove that the masked tone is unnoticed by showing that the low tone becomes noticed if its intensity is increased with respect to the masking tone.

Kohler takes this argument as a commitment to the existence of unobservable sensations whose properties are univocally fixed by the stimulation. Therefore, he considers the noticing thresholds as unnecessary a construct as that of at­tention traditionally used to account for changes in appearances despite the alleged constant sensations. Claiming that the unnoticed intensities that inter­fere with one another can be singled out from the tonal aggregate is equivalent to claiming that a constant sensory material can be variously caught up in the focus of attention. The observational meaning of a phenomenon is reduced to a psychic function that acts on the unobservable constant sensory basis. More­over, if this account of perceptual judgements is correct, Stumpf should ex­tend the construct of noticing thresholds to every case of phenomenal change. However, this undermines its explanatory power, because it cannot rule out the opposite account. Since by definition noticing implies unobserved entities, it cannot be excluded that in hearing out an overtone, in reality it “has brought into existence” a tone that did not exist before. Finally, Kohler claims that the theory of noticing leads to undecidable methodological problems. He cites the study of the pitch change of a tone in a chord slightly out of tune (Stumpf, 1910: ii7f.). One may ask whether the different pitch depends on a change in the ap­pearance of the tone or on a false judgement. Stumpf either adjusted the tone to a tuning fork through successive comparisons or presented it simultaneous­ly with each of the other tones of the chord and then again in isolation. Hav­ing found no perceptual change in the tone pitch, Stumpf concluded that the pitch shift is due to a deceptive judgement (Urteilstauschung) because in the chord out of tune, the single tone had fallen under the noticing threshold for a correct judgement. In contrast, Kohler argues that if the evidence is decided on the basis of unobservable constructs of entities that may turn from being under to being above threshold, this affects even the validating evidence. It cannot be ruled out that the tone heard in isolation becomes so strengthened through noticing that it sounds louder and deceptively higher pitched than when it goes unnoticed in the chord. This means that there is no available cri­terion to preclude that the isolated tone has set a mistaken reference point for pitch perception, which is used to compare it simultaneously with the other tones of the chord. The conclusion that the tone does not really change is not meaningful because the whole question is not decidable.

Kohler’s objections contain meaningful points concerning the equivo­cal use of terms that belong to a long-established empiricist and inferential theory and the ensuing problems for deciding univocally the experimental questions. Yet they often miss a fair interpretation of Stumpf. Stumpf (1907: 16, 1930: 425) states that noticing is not a further psychic function that amounts to perception by adding something to mere sensations. Moreover, perceiving itself means making explicit the parts and the relations in a whole. What may be unnoticed is not the unobservable sensation but the part or attribute of ap­pearances that does not have a phenomenal relief with respect to other parts and the whole. Stumpf does use the term “sensation,” but he makes clear that it denotes the “pure” appearances considered without the bias of common- sense or scientific interpretations (1930: 425). He suggests that the distinction between unnoticed and noticed parts is as perceptual as that between figure and ground. Being unnoticed is a phenomenal state due to the fact that ap­pearances are independent of psychic functions and are not “transparent” to subjects under every respect, although they are immediately and directly giv­en. Perceiving pitch and loudness requires the appearance of a tone, but the latter does not imply that pitch and loudness appear as distinguishable proper­ties of the tone. Conversely, it is not true that if pitch is not perceived as a dis­tinguishable part of a tone, it is not a phenomenal attribute of it. The parts and attributes of appearances emerge through manifold changes and Stumpf (1873: 139) calls them “distinction[s] cum fundamento in re,” in the sense that they come to be forced upon the subjects as perception goes along (supra § 2.2). Therefore, noticing is not equivalent to attention intended as the psychic func­tion that explains away phenomena that do not seem derivable from stimula­tion. Stumpf concedes that attention is an external psychic condition that may facilitate noticing. However, he argues against the theory that parts of appear­ances are singled out through attentional scrutiny (1907: 18). This theory means either that an appearance shows previously non-perceived new parts, as if it were changed by attention, or that the perceivable parts of appearances be­come more or less noticeable according to a distance function of the different degrees of attention. However, consider the chord C-E-G. Should perceiving these component tones consist of three new appearances once attention is di­rected to them? If instead the parts of appearances become explicit depending on the continuous increase of attention, should the same parts stand out even if the distance between the ends of low and high attentional scrutiny varies?

Kohler contests Stumpf’s account in conditions of tones interference or in comparative tasks in which tones are presented in isolation. He criticizes Stumpf’s hypothesis and experiments for assuming that tones have the proper­ties of single sensations, hence for reducing the correct response to the isolated property derived from the stimulation. In fact, Stumpf holds that appearanc­es have inherent features and that the relations between them are objective, namely directly perceived in and with appearances. Tonal fusion is a clear ex­ample. The fusion does not change the tones between which it holds, because it needs the particular properties of individual tones. On the contrary, com­binations of different tones bring about various degrees of fusion. Thus the properties that appear in isolation are phenomenal and not properties as­cribed to unobserved sensation. The judgement of unity that is made in the case of fusion may correctly accept this relation if the properties of tones allow for it. Therefore, fusion is not equivalent to a judgement of unity. This is also the principle according to which Stumpf ascribes the variability of responses in categorization tasks to judgements. He reports that when fine musicians are asked to judge the pitch of successive tones, even they are likely to take tones as pitched about an octave lower than they would if presented with the isolated tones. He is inclined to explain the different responses as an error of judgement that could be induced by a phenomenal feature, for instance tim­bre. For the different response about the pitch of a tone in a slightly out of tune chord with respect to the isolated tone, Stumpf cannot admit that the tone ap­pearance has changed one of its attributes simply for belonging to the chord; hence, he ascribes the difference to an error of judgement, because the tone remains the constituent of the state of affairs but the appearance of the whole chord replaces the tone as the phenomenal foundation of judgement. Kohler is right in pointing out that Stumpf’s theory may have difficulty in deciding the univocal interpretation of the evidence in these two extreme cases. However, this regards the empirical adequacy of the theory rather than the commitment to the unnoticed sensations.

As Kohler correctly remarks, Stumpf sometimes resorts to the disputable construct of the “judgement illusion” to account for the observations that ap­pearances may not be represented as they are in the state of affairs in condi­tions of tones interaction or comparative tasks (see Benussi, 1904: 389b, for a discussion of the inadequacy of this construct in the Brentano School). In such cases, Stumpf calls “illusion” the judgement that mistakenly rejects the percep­tual properties of tones and their combination. The “illusion” is so dependent on judgement that the skills of musical education may help in making explicit what they really are (1883: 35, 1907: 26, 35-36, 1910: 77). However unsuitable the use of this construct may be in Stumpf’s theory, Kohler’s reconstruction of it as a theory that admits the interpretation of the effects of unnoticed sensa­tions through habits and past experience is unfair. Stumpf does not claim that judgements are illusory because they are about unnoticed sensations and that practice and education modify perception so that an experienced subject can observe their effects regardless of the common-sense interpretation. On the contrary, musical training might help in singling out the real properties of ap­pearances and judging them correctly. Then the external aid of practice has a phenomenal basis. If appearances did not have intrinsic properties, even when they did not appear explicitly, the musical ability to hear them should lead subjects to always perceive different pitch and loudness of the same tone in different contexts, while the opposite is true and the tone is usually recognized as the same if heard in isolation.

Source: Calì Carmelo (2017), Phenomenology of Perception: Theories and Experimental Evidence, Brill.