Meinong on Color Manifold

Meinong (1903) makes an analysis of the abstract structure of colors, which satisfies a general tenet on the study of experience derived from Brentano. He contends that the theory of experience is the analysis of the elements and the connections that are manifested in it. Meinong (1888: 134) holds that the phenomenal elements of experience are colors, sounds, tactile qualities, temperatures and extensions. Appearances are not the subjective seeming of physical objects, rather they are particular individual qualities that are com­bined with one another in things. They are ascertainable facts for the subjects and have a value independent of the physical existence of what they present; hence they can be studied without any preconceived view on what the physical reality is (Antonelli and Manotta, 2005: 126-127). The experience is articulated and ordered through “real” and “ideal” connections of phenomenal elements (Meinong, 1882, 1891, 1899). The relations binding together colors and surfaces, qualities and places, points in space and time are real connections. They are forced on subjects because the relations are due to the nature of the constitu­tive elements that cannot be perceived in isolation. The relations of identity, diversity between colors or the form of a set of points and the melody of a se­quence of tones are ideal connections. They require a mental operation to bring together the elements that can be perceived in isolation. Nevertheless, they do not yield an aggregate of separated elements but rather a “complex,” that is, a whole distinguishable from the elements, albeit not independent of them. The diversity between a red and a blue patch is not independent of their qualities that yet occur on their own. Meinong calls this kind of connection “Kollektiva.” Unlike the elements of Kollektiva, the points of a form and the tones of a melody cannot occur independently of one another because of the very sense of the complex. Indeed, the connection can be viewed from the standpoint both of the form or the melody that binds together the elements and of the relations among them in that particular form or melody. Meinong (1899: 387-389) calls these elements “Jundamenta” and the connections a “founded” complex to emphasize the difference with the elements that are mere terms of Kollektiva.

Since the meaning of concepts derives from experience, Meinong (1888: 134) maintains that the so-called sensation is a construct that does not correspond to anything that is presented in it. Instead, the elements of experience form a qualitative continuum (infra 3.2.1 for Brentano’s theory of continuum founded on experience). The continuum is the structure underlying their possible changes, for example the visual field is the constant system of localization of appearances. A thing may change position in the field and each point of the field may be filled by different qualities or parts of things. Nevertheless, the visual field remains the constant localization system on whose grounds the changes of position make sense. In general Meinong (1882: 46f.) claims that con- tinua are the reference systems in which appearances are ordered according to the possible changes that specify their features and connections. Accordingly, they permit analysis of the nature of appearances when their ordering is used to construct the abstract space that specifies the laws of the appearances (see also Selz, 1930: 533-534).

Meinong (1903) considers the abstract color space the system of possible colors in which all colors occurring in experience are ordered. The descrip­tion of the geometry of this space is not a visualization of knowledge that has already been acquired, rather it accounts for the empirical and a priori proper­ties of color. The empirical properties derive from the facts of the psychology of perception and are mapped into the color solid.

Meinong adopts Hofler’s octahedron, which maps suitably the mutual posi­tions of colors and accounts for their phenomenal distance as well as relations like the opposition between primary colors (see figure r). This is not possible in Runge’s color sphere. This map permits one to make legitimate use only of the surface of the sphere, since only the black-white series is placed in the inner solid, the middle grey is located at the center, and the transitions from red to grey, from grey to green and so on are located along the radii of the equator. This im­plies that the proportional length of the distance between colors, which stands for the magnitude of the diversity between colors, is mapped onto the length of the lines on the sphere which account for color distances in an arbitrary or, in all likelihood, incorrect manner (Hofler, 1897: ii2ff.).

Yet Meinong observes that as a spatial body partakes of the physical space in which is embedded, so the color solid partakes of the abstract space in which it is embedded. The description of the abstract space regards the a priori properties of colors, that is, the nature of possible colors, which is as independent of contingent perceptual circumstances as the concept of number is of reading numerals (1903: 3, 6). The analysis of the abstract space regards the features of all possible appearances, which contains as subset those occurring in the experience, just as geometry regards the properties of infinite space even if it is not an object of direct experience, in which of course only finite space occurs (1903: 9-11). However, psychology cannot be left out of consideration. The geometry of colors aims at providing the scientific foundation for psychological theories, because the dimensions of the abstract space are the respects under which appearances vary (see Mulligan, 1991; cf. Rollinger, 2001 for a different interpretation). Moreover, the justification of the geometric properties of the color solid needs the evidence of psychology. Meinong (1903: 10-11) emphasizes that the a priori analysis cannot explain why the color solid is delimited in a certain way, why the edges have to be straight or almost straight and the surfaces flat or almost flat. The sense of the color solid is derived from the empirical research. For instance, it is self-evident that the line drawn from orange to yellow bends at green, but the fact that it cannot continue in a different direction, for instance that taken up from orange, is not something that can be justified a priori.

Meinong (1903: 4ff.) maintains that the a priori analysis provides immediate and mediate evidence on the relations of colors’ similarity, distance and direction. It is immediately evident that the greatest distance takes place between red and green or yellow and blue. It is also self-evident that grey is reached from red without any change of direction and that the path from green to grey is a straight line. The coincidence and diversity of the direction of the lines joining colors are another example of a priori evidence: the line originating from red through orange leads to yellow, the line originating from red through violet leads to blue. Likewise, the fact that these two lines do not lie at an angle that could be stretched into a straight line is immediately evident. Instead, it is immediately evident that the black-white line takes up an intermediate position among chromatic colors, but that it intersects the lines connecting contrasting colors is a mediate evidence that has to be deduced by reasoning. Meinong suggests that the scheme to prove such kind of evidence is as follows. If red undergoes a change that does not alter its intermediate position between yellow and blue, then leaving the brightness out of consideration the changing red can move only along the red-grey line, and the same holds also for green and the green-grey line. Since both these lines involve yellow and blue, they cannot but make a straight line. This kind of evidence is part of the analysis that specifies the dimensions of the abstract color space, whose number and characteristics cast light on the nature of color and accordingly on appearances.

Meinong assumes that the concept of dimension means independent varia­tion of elements rather than a not decomposable quantity. A and B are ele­ments varying along two dimensions, if they are the same under one respect and different under another. Were they simple elements in the strict sense of having no further parts than themselves, they should be the same and different at the same time. Therefore Meinong (1903: 3) holds that the elements of an re­dimensional manifold must have the same n parts as the allowed dimensions. Since the variations of colors cannot be contained in a line or a surface, he constructs the color solid and space as a three-extended manifold. This entails that color elements are not simple in the strict sense, and that von Helmholtz’s reduction of color appearances to elementary sensations is contrary to the na­ture of colors (1903: 20).

Meinong argues that hue and saturation cannot be natural dimensions of color space. The hue varies on two dimensions and no closed line can be contained in one dimension. The saturation also varies in two dimensions, provided the grey belongs to the center of the color solid. Instead, the bright­ness (Helligkeit) can be qualified as one dimension if it is not reduced to the black-white line, although this line varies just inside brightness. This is clear if it is observed that chromatic colors do hold a position between black and white but not for their achromatic component, because the rationale of this position is not put into question if the achromatic component is reduced to as arbitrarily little noticeable a magnitude as possible. Meinong proves this observation as follows. Let a circular surface generated from the white point be included in the solid and its arbitrary radius stand for the distance from white – hence for whiteness. The points on the surface have more brightness the more distant they are from the black-white line. Given that black and white do not coincide with dark and light, it is sound to conclude that brightness is one di­mension of the color space rather than the color solid, while the black-white line is its main representative. Different colors for hue and saturation show the same brightness. Meinong holds that they lie on a perpendicular plane to the black-white line and that there must be infinitely many such planes.

Meinong employs a similar scheme of reasoning and evidence to specify the two further dimensions of the color space. Because it is at least three­dimensional, each color is a complex element that has three constitutive parts given the possible variations along the dimensions. Meinong exemplifies this point with visual space. Each visual place is determined by its variation along the dimensions of depth, breadth and elevation whose respective axes are: in front of vs behind, right vs left, high vs low. A visual place is a complex ele­ment of depth, breadth and elevation values. The elevation aside for the sake of simplicity, the visual place “in front of me” consists of the depth value d₁ and the breadth value b_n, where b_n is the neutral value for breadth, since what it is straight in front of me is neither at my right nor at my left. Accordingly, the visual place “to my right” has the depth value d_n and the breadth value b₁, where d_n is the neutral value for depth, since what it is just to my side is neither in front of nor behind me. Meinong concedes that it could seem strange that the visual place in front of the perceiver also has a breadth value and that the neutral value of appearing neither to the left nor to the right is a position in the breadth dimension. However, it is reasonable if the neutral value does not mean the absence of a spatial determination, rather the zero of a system of coordinates. The corner of a room located in front of and to the right of the perceiver cannot consist of these places that as a whole are incompatible. Rather, it must consist of their values that are consistent to each other, hence it is the complex of the values (d₁, b₁) belonging to distinct dimensions.

Meinong extends the treatment of visual places to the analysis of the other two dimensions of color space, which correspond to visual depth and breadth in defining the system of color coordinates. If a dimension is a range of in­dependent variation, each color is a complex that is specified by the values of the compatible components varying along it. Brightness put aside, a pure red or a pure yellow are as incompatible as the whole places “in front of” and “at the right.” Instead, each is a complex whose values are consistent because they belong to distinct dimensions. Pure red is the red-green complex (r₁, g₀), pure yellow is the yellow-blue complex (y₁, b₀), where g₀ and b₀ mean the neu­tral values of the complex, that is, respectively the zero for the axes of green and blue. The converse holds for pure green and pure blue. Therefore, the red-green and the yellow-blue lines are the main representatives of the two further dimensions of the color space, which cannot be respectively neither red nor green, neither yellow nor blue. Indeed, the black-white line is the rep­resentative of brightness because black and white denote only the end terms of this dimension. Of course, this does not mean that a dimension contains the negation of its possible values, rather that it has a neutral value. The fact that each color is a complex of two values is indirectly ascertained by the fact that pure colors yield grey. With respect to the chromatic brightness, grey is the black or white component of color. If the brightness assumes its neutral value, the grey is the so-called neutral grey.

Meinong’s theory of abstract color space is a phenomenological theory. It has meaningful implications for color perception and psychology. Firstly, the notion of neutral values accounts for the outstanding position of the black- white line and the particular meaning of saturation (1903: 23-24). Color purity derives from the coincidence of the neutral value of one dimension with the fairly extreme value of another. The importance of this fact is attested by the perceptual spontaneous distinction between primary colors and colors like violet or blue-green. Meinong suggests that the cognitive importance of satu­ration might depend on the greater phenomenal accessibility of the extreme value with respect to the neutral value and its neighbors that instead can be unnoticed. The black-white line presents the coincidence of two neutral val­ues. Secondly, the analysis of the phenomenal properties of the points that lie on the surfaces into which the octahedron is decomposable, which correspond to colors and depend on the structure of color space, account for the fact that the name denoting only one of the end of a color line is usually used to refer to the dimension it represents (1903: 14, 16). Finally, the theory explains the relations between colors regarding their natural properties and order. The po­sition of primary colors depends on the dimensions of the color space that are designated with the name of one of its representatives (1903: 17). It is true that Meinong argues that the theory of abstract color space deals with its structure without taking competing psychological theories into account (see 1903: § 9 for a neutral comparison of the localization of phenomenal color points and curves with respect to the spectral properties). Nonetheless he emphasizes that this abstract structure is consistent with the results of Hering’s theory. This is not surprising, because Meinong states that his analysis derives a compelling force from the evidence of perceptual experience, against which no theory is entitled to raise objections.

Colors can be incompatible according to their component values. Red and yellow are as incompatible as red and green or yellow and blue, but only as complexes, because their components should vary in the same dimension. If the same components do not occur together, they can be combined in other colors. The “betweenness” is another relation that is fundamental for color order. Meinong points out that it has two different meanings. In the case of orange, which lies between red and yellow, the betweenness replaces the un­satisfactory notion of “mixture” (1903: 25). Orange is not a mixture in which perceivers see simultaneously pure red and pure yellow. It is an intermediate color lying between red and yellow. Its position is determined by the compat­ible components of the red and yellow complexes that take values along dis­tinct dimensions. In this case, the components approximate the extremes, that is, the most saturated values of the pure red and pure yellow. Since the satu­rated values are also the most perceptually accessible, the subjects distinguish red and yellow inside orange. The same account holds for violet, which does not contain red and blue but is rather a third color lying between red and blue. Each intermediate color between two primary colors consists of the extreme values of two dimensions, such as red and yellow, one component of which yet varies to the neutral value. In the case of the pure red that lies between orange and purple, the betweenness has a different meaning. It denotes a turn­ing point in the direction of color variation, which is accordingly a corner in the color solid.

Psychological theories cannot but take the results on the nature of color into account. Meinong (1903: 33) claims that the so-called Young-von Helm­holtz theory is not consistent with perceptual experience. It aims at discover­ing the sensations of color that are assumed as the simplest sensory elements and ends up in hypothesizing the wrong set of basic sensations. Even after re­placing the violet with blue to make it less extraneous to experience, the funda­mental sensations of red, blue and green form the vertices of a triangle which, once transposed in the color solid, forces yellow to a place that conflicts with experience. Red, blue and green are fundamental sensations if considered the ends of bounded qualitative series, but then yellow should have the same func­tion, otherwise it is impossible that red, green and yellow lie on a straight line. Meinong claims that in general, psychological theories try to reconstruct the color appearances with the construct of simple sensations and an aggregate thereof. Yet sensations are not appearances, but rather “fictional correlates” of light “fundamental stimuli.” Sensations are theoretical posits introduced to subsume the correlation between light and color under sufficiently general laws (1903: 28-29).

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