The Immanent Structural Laws of Appearances

Stumpf’s conclusion is that appearances are “objective,” that is, they are given outside of and before the subjects, and their properties do not arise by means of psychic functions but rather trigger and guide them. If psychic functions react to appearances, no perceptual change occurs that is not admitted among the variations allowed by the nature of appearances. Decomposing a simple sound into component tones is as impossible as finding a transition from blue to yellow that does not pass through red or green, or adding a dimension to the three-dimensional perceptual space.

The appearances, their parts and properties obey specific laws that the phe­nomenology has to discover and describe. Stumpf (1906) calls them “imma­nent structural laws” and distinguishes between the causal and the structural laws to define their nature. In general, a law differs from the expression of a se­ries of facts for the necessary connection it implies regardless of the nature of the considered objects. There are logical and physical laws whose necessity is respectively deduced apodictically by inference or probabilistically measured through experimental observation. There can even be laws on individuals, for instance “if the petiole is cut off, then this apple must fall.” In such cases a contingency on a specifiable condition is expressed, but the necessary content is provided by the conceptual form “if…, then….” If the Matterhorn height is expressed in the form of a law, the contingent initial conditions that led the mountain to have that very measure are taken into account but in necessary connection to the physical laws of nature.

A structural law regards the properties and the relations of the parts com­bined in a whole. If the whole is a physical body, as in mineralogy, zoology or botany, the law presupposes the physical causes but is applied to the forms of the possible combinations of entities deriving from them. A phenomenologi­cal structural law regards the features and structures of appearances. It may apply to single properties of the visual shape and size or to general questions like the invariant properties, connections and orders of colors, sounds and perceptual space and time. In opposition to causal laws, the structural laws are descriptive laws. By “description” Stumpf does not mean the statement of regularities that allow for exceptions. Indeed, the above descriptive natural sciences are no less a science than mechanics, while mathematics can be con­sidered a descriptive science as it deals with formal structures. Accordingly, he claims that phenomenological laws can be formulated in abstract terms to which algebraic operations can be applied. For example, acoustics studies the properties of the pressure waves that give rise to the perception of tones. Phenomenology studies the perceptual structures of given intervals in terms of the result of algebraic operations on (groups of) tones, such as the octave is the product of the fifth and the fourth, the fifth of major and the minor third, the major second is the division of a fourth by a fifth. So the perceptual structure is preserved whatever the nature of the tones involved.

The study of the relation of “betweenness” among tones is a fragment of an algebraic treatment of the nature of appearances (1883: 140ff.). Stumpf claims that successive tones are distinguished according to having lower or higher pitch. The relation of increment allows the ordering of tones so that if three tones are presented, then it is always the case that one is in-between. More­over, the pitch increment allows one to recognize by similarity a direction along which tones are localized in analogy with judgements on the positions of points in space. If the following sequence of points is given: x, y, z, (y), the posi­tion of y between x and z is expressed by either the equation of the straight line “xy + yz = xz” or the conjunction of “xz > yz” and “xz > xy,” because the first in­equality would remain valid if y was also located beyond z, for instance in the position designated by (y). The case that z is an in-between point is expressed by the conjunction of “xy > yz” and “xy > xz.”

Now let tones replace points. The equation of the straight line is meaning­less, because tones are not equivalent to segments whose limits are points which can be added to obtain another segment. The tones are not perceived as the end points of a tonal line, rather as distinct qualities. To be sure, they allow a continuous transition through which, for instance, E is located in-between when passing from C to G. However, this is not a perception of the tones’ posi­tion, because passing from C to G does not require one to perceive E. If the pas­sage is realized in discrete steps, the perception can be due to the knowledge of the direction in which one is required to move one’s fingers when playing the piano. Yet the perception of E does not occur, because intermediate tones need a just perceptible duration to stand out as stable, distinct tones in the passage from C to G. Instead, using inequalities makes sense to describe how the tones are perceived according to their relative positions. The inequality means the perceptual degree at which the tones approach pitch similarity and the judgements on their localization are founded on it. Stumpf puts forth the example of these two sequences of tones in bass clef: D3, G3, A3 and D3, B3, A3. In the first case, DA > GA and DA > DG, in which G is between D and A. In the second case, B replaces G and is substituted for it in the inequalities. The substitution does not preserve the validity of the second inequality, for which instead the inverse DB > DA holds, with A between D and B. If for any three distinct tones x, y and z the equality xy = yz holds, Stumpf calls “double­sidedness” the property that there is always a single tone between two other tones. Stumpf leaves undecided the question whether the perception is suf­ficient or the judgement is needed to grasp these inequalities. At any rate, the attributes of tones determine their degree of similarity, which the judgement can either accept or reject as a phenomenal state of affairs.

The double-sidedness is important to define the geometry that maps the nature of tones. It implies the existence of a single in-between tone. The “betweenness” does not satisfy this condition for colors or the points of planar spatial figures, hence the double-sidedness permits one to derive the dimen­sionality of perceptual domains. If tones are mapped onto a one-dimensional space, the domain of colors requires a higher dimensional space. If a series of red, orange and yellow is given, only the orange lays between the other two. Next, let red, blue and black be presented. They can be qualitatively ordered in various ways, like the three points of a triangle or a circle. For both points and color appearances it is not necessary that in all circumstances only one is bound to occupy the middle place. As each point occupies the middle place when projected on an arbitrary line, so each color may appear as the middle one, even though the in-between points and colors are univocally determined by the judgements of similarity according to the chosen projection line or to the qualitative respect under which colors are grouped so that one can have (blue, red, black), (blue, black, red) and (black, blue, red). Stumpf argues that in such cases the domain of appearances can be described as a space endowed with more than one dimension, but the number of dimensions narrows if appearances can be ordered as if their corresponding points were projected onto a straight line. For example, this happens if brightness is the qualitative respect of the above grouping. The ordering (black, blue, red) allows for the inequality [(blue-black) > (black-red)], but it contradicts the ordering (black, red, blue) that allows for the inequality [(black-red) > (blue-black)]. This result suggests that a map of the domain of colors may be a spherical solid.

Stumpf (1906: 20) claims that the algebraic and geometrical formulations of phenomenological laws preserve their validity independent of the knowl­edge of the physical or physiological correlates of appearances. Besides, he be­lieves that the structural laws of appearances become more meaningful just as the mechanistic interpretation of the physical world becomes more and more abstract. Stumpf (1906: 3if.) concedes that phenomenological structural laws may turn out to be connected to physiological laws under the assumption that the color and the sound appearances correspond to brain processes. If this leads to hypotheses that end up being completely proved and ultimately verified, then phenomenology gains generality and improves the connection of its propositions. Stumpf cites Hering as a case in point, who suggests that phenomenology, namely philosophical psychology, provides more important clues for research into the physiology of perception than does the study of the chemical or microstructural properties of nerve cells, even though this knowledge has to be integrated in the explanation. However, Stumpf’s phe­nomenology is also a constitutive part of experimental science, as the wealth of empirical measures and observations of his psychology of sound attests. This does not change the function of phenomenology. Stumpf believes that a complete account of perception requires a division and specialization of tasks rather than of actual scientific work.

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

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