Latimer & Stevens (1997) propose making order out of the prevailing disorder surrounding the terms "whole" and "part" by applying a conceptual framework developed by Rescher & Oppenheim (1955). The basic argument of the present commentary is that this framework is not suitable to explain the perception of part-whole because it is nothing other than a reflection and formalization of the physical system, which differs fundamentally from the system of human behavior. Whereas physical properties are founded on basic and natural units of measurement, psychological properties are not based on such measurement units.
1. In a very interesting article Latimer & Stevens (1997) suggest making order out of the conceptual muddle over the relationship between the whole and its parts. The confusion stems, among other things, from the absence of a clear definition for the terms "whole" and "part": researchers do not deal properly with the relations among the parts themselves and between them and the whole. Latimer & Stevens argue that these concepts are relative and that the whole may be divided in an infinite number of ways, depending on theoretical viewpoint.
2. Latimer & Stevens suggest using the conceptual framework developed by Rescher & Oppenheim (1955) to bring order into the disorder surrounding the whole and its parts. Their framework is based on three conditions: (a) the whole is endowed with a special and discernible property; (b) the parts of the whole entertain discernible and special relations; (3) the whole is endowed with a structure that makes it unique. On the basis of this framework, Latimer & Stevens stress, among other things, the primacy of the conceptual analysis, clarifying concepts associated with the whole and its parts, and suggesting that before the perception of the whole a perceptual analysis of its parts occurs.
3. Rescher & Oppenheim's conceptual framework for analyzing the relation of the whole to its parts is based on a deductive, mechanistic approach to scientific explanation, formalized in one of the best known articles on the subject, a cornerstone in the modern discipline of philosophy of explanation (see Hempel & Oppenheim, 1948, and critical reviews in Rakover, 1990, and Salmon, 1989). A fundamental question in Rescher & Oppenheim's article concerns whether it is possible to explain the special property of the whole through the properties of its parts, when the explanation is conceived as a logical deduction from a particular theory of the property of the whole and the properties of its parts. If the property of the whole cannot be logically deduced, then this property is perceived as emergent. If the property is logically deduced, then it is explained, and in certain cases a given property is said to be reduced to certain other basic properties (see Rescher & Oppenheim, pp. 93-94).
4. Even though Latimer & Stevens's target article clarifies several concepts having to do with the whole and its parts, and draws attention to the great importance of developing the subject theoretically, some doubt arises as to the effectiveness of applying Rescher & Oppenheim's conceptual framework to human behavior connected with the perception of the whole and its parts. In many respects the deductive approach to scientific explanation is a formalization of the mechanistic explanatory structure and theory of classical physics (and chemistry). Many scholars have therefore raised serious arguments against applying the deductive, mechanistic explanatory model to psychology. They state that to explain human behavior other kinds of explanatory models must be used, models that can manage the meaning of behavior, not just motor activity (see review and discussion in Rakover, 1990, 1997). The perception of the whole and its parts is meaningful human behavior; as such it calls into question the suitability of the conceptual framework proposed by Latimer & Stevens for treating this form of perception. In the present commentary I will try to give examples of this lack of suitability through a discussion of the all-important status of measuring concepts in the physical system. Then I will consider an example of how one can deal with the present subject theoretically and experimentally analysing an experiment on the perception of a face and its facial features (see Rakover & Teucher, 1997).
5. A repeated argument in Latimer & Stevens's target article is that any whole can be decomposed into an infinite number of components, out of which an infinite number of different groups of properties can be assembled. In my view this argument arises from an assumption about the "basic unit of analysis," or the "perceptual measurement unit," or the "perceptual atom." This is a basic unit from which all the complex perceptions can be construed; and the reverse - it is a unit reached at the end of a process of decomposition of the perceptual form. This assumption, imported from the natural sciences, creates conceptual problems when it is applied to the perception of forms and patterns. These problems are rooted in the simple fact that psychological properties do not have a basic and natural measurement unit. By contrast, physics is based on concepts that are built on natural measurement units (see Michell, 1990; Campbell, 1953; Coombs, Dawes, and Tversky, 1970; Rakover, 1990).
6. The conceptual system of physics is ultimately founded on a limited number of fundamental measurements based on natural and agreed upon units. This system represents the physical world and explains it by means of the deductive explanatory model designed by Hempel & Oppenheim. Let us take, for example, the variable of length. We can know not only whether object (a) is longer than object (b) but also by how many units of length (a) is longer than (b). If (a) is <---------->, (b) is <----->, and the measurement unit is <->, then (a) is longer by five units than (b), and (a) is twice the length of (b). <-> is therefore a natural measurement unit by means of which the length of any object can be measured. Length is considered a fundamental measurement, which sustains several important mathematical properties such as transitivity and additivity. By such basic measurements physics builds various theoretical structures such as velocity, acceleration, force, work, and energy, and develops theories of relations among these structures and between them and the physical world. For example, the theoretical structure called "kinetic energy" is based on the basic measurements of weight, length, and time. In the case under review, then, the whole is defined and explained by its components and the appropriate physical theory. In other cases the relations of components of a physical system are determined by the appropriate theory and laws. For example, Rescher and Oppenheim (p. 96) cite Van der Waal's law linking gas pressure to volume and temperature.
7. Can a mechanistic conceptual system such as that described here be used to explain the perceptual phenomena of whole and parts? In my view, it cannot. It is hard to see how one can construct a conceptual system for perception akin to the physical system if there exist no natural measurement units for perception such as what we find in the physical world. Take the following example (after Campbell 1953). We have a heap of 60 corn kernels. I add (or remove) 30 kernels. Without doubt, I have significantly altered the heap's weight and volume. But have I altered the taste of the corn by addition or removal of kernels? Obviously not. Not only does the addition of kernels not alter the "corny" taste, but no natural measurement unit for taste exists whereby we can increase or diminish the taste of the corn, as we did in the physical case. Two points should be noted here. First, psychologists are able to alter (e. g., magnify) a psychological property by modifying the physical stimulus. This alteration, although explainable in many cases, is not based on natural and basic measurement units but on a correlation between the modification of the stimulus and the change in response. Second, although in special cases mathematical models may be developed that create interval and ratio measurement scales, and that are often supported by statistical analysis of the data (see e.g. Michell, 1990; Coombs, Dawes, and Tversky, 1970), they are not theoretical/empirical demonstrations of natural measurement units in psychology.
8. In terms of the physical system, an explanatory symmetry exists between what can be decomposed and what may be assembled. For example, we break down water into two atoms of hydrogen and one atom of oxygen and we also create water by composing these three atoms. By contrast, the psychological system evinces no such symmetry. For example, while a visual structure such as a human face can be arbitrarily (and creatively) divided infinitely, the meaningful perception of the parts of the face is extremely limited. We cannot perceive a face in an infinite number of ways or see the lovely face of Mona Lisa as a field of thistle. I call this property of the psychological system "asymmetric decomposition-construction." While the physical system gives the same explanation for disassembly and assembly of the whole, psychology posits different explanatory processes for decomposing the structure into parts and constructing the whole from its parts.
9. These differences between the physical and the psychological system, which derive from the use of a natural measurement unit, can be summarized by the following distinction: while the physical system may be seen as being based on the equation W=F(P), where W is the whole, P is the parts, and F is a function, law or theory, the psychological system can be regarded as based on the equation W=F(Sc,P), where Sc is a cognitive schema that constrains us to perceive a collection of visual stimuli meaningfully and uniquely as, say, a human face. The psychological whole cannot be understood as constructed of perceptual components, as is the case in the physical system. If these arguments are correct, Latimer & Stevens's application of Rescher & Oppenheim's formalization to the perception of the whole and its parts stands on infirm foundations.
10. One conclusion arising from this theoretical discussion is that the search for a basic perceptual measurement unit and for a conceptual system to address the relation between the perception of the whole and its parts on the basis of this unit is fruitless. A second conclusion is that new methods must be developed that are suited to psychological research on the perception of the whole and its parts. Since the purpose of this commentary is not to present a detailed discussion of this topic (including a critical review of existing methods in the literature), I shall only describe briefly the study of Rakover & Teucher (1997) as an example of the kind of research that can be done on the subject.
11. This study attempted to propose an alternative explanation for the "facial inversion effect." Recognition of a face presented upright (U) is better than recognition of a face presented inverted (I) by about 25 percent. The prevailing theory developed by Diamond and Carey (1986) suggests that recognition of the I face is based principally (or exclusively) on featural information, while recognition of the U face is based on both featural and configurational information, the latter being defined by the spatial relations among the facial features.
12. Rakover & Teucher's study showed that face perception is principally featural, and that the inversion effect is explained by the perceptual scheme whereby we process facial information when it is in the upright position, the position of the head to which we are exposed from birth. The study supports this hypothesis with empirical evidence that (a) isolated parts of the face -- namely, the natural individual features of hair and forehead, eyes, nose, mouth, and chin -- each separately display the inversion effect, and (b) recognition of the whole face is based on recognition of each of these five isolated facial features (the study used the facial features of the "Photofit," an identification kit developed by Penry (1971a, b)).
13. Rakover & Teucher proposed that recognition of the whole face (W) is a function of recognition of one of the five features (V) separately: the function squares each V separately, sums these five squares, and divides this sum by the total of V. The W formula was compared with other formulae in which W was calculated from V, and was found to be the most efficient. The results predicted from this formula were not statistically different from the empirical results in three out of four experimental conditions. Moreover, in the fourth condition too, the formula successfully explained about 91 percent of the empirical results. On the basis of these data, Rakover & Teucher suggested that Diamond and Carey's explanation for the inversion effect was incorrect: configurational information is not a necessary condition for the inversion effect, and recognition of the whole face is based mainly on recognition of the individual facial features.
14. The W formula has several interesting implications for the topic at hand. Will it receive empirical support if we use different divisions of the face, and if the whole face is composed not in the natural way, but jumbled, for example, the eyes appearing in the place of the mouth? Rakover & Teucher argued that it will not. If the parts of the face are unnatural, such as if the eye shape is divided and broken up, the formula will not be able to predict recognition of the whole face; and if the whole face is jumbled the formula will be unable to predict recognition of the face from its natural parts. (These experiments are currently being run in my laboratory.) These predictions arise directly from the theoretical analysis given above. Since the perception of the face and its parts is not based on natural and fundamental measurement units, such as those we find in physics, it is not possible to compose the whole facial structure the way the physical system does. Furthermore, perception meaningfully interprets the complex of visual stimuli presented to us according to certain cognitive schemata. Hence we perceive the group of stimuli consisting of a horizontal banana, above it a vertical cucumber, with a tomato on either side, all placed on a watermelon, as a crying or laughing face depending on the position of the banana. The assembly of these objects, each of which is perceived meaningfully in isolation by means of the appropriate cognitive schema, is not perceived as a basket of fruit and vegetables but as a laughing (or crying) face. This analysis does not suggest that the given structure cannot be divided into substructures, or that each substructure cannot be divided yet again. Rakover & Teucher point out that a face can be divided into features, and each feature can be further divided. Here I wish to stress that the perceptual system composes the whole overall form, not in the same way the physical system does, but by providing a new interpretation, in many cases independent of the various interpretations given to the substructures that make up the whole. (Note that a similar problem exists in memory measurement. For example, it turns out that short-term memory contains "chunks of information" and not basic, atomic, units of memory.)
15. Since the methodology of physics cannot be applied to research on the perception of the face and its parts, theoretical, methodological, and empirical constraints have to be developed that this research must comply with. Relying on Rakover (1994), Rakover & Teucher proposed several constraints, two of which are worth brief consideration here. First, recognition of the whole face and recognition of its parts have to be measured by the same experimental method. This requirement does not exist in physics, as the same basic units can be measured by several appropriate physical methods. In psychology, however, as there are no natural perceptual measurement units, this requirement must be satisfied, otherwise we will never know whether the differences in results reflect nature or different measuring methods. Secondly, the W formula is based on the following inequality: on the one hand, W must be greater than or equal to Vl (the lowest recognition score), and on the other hand W must be smaller than or equal to Vh (the highest recognition score). This constraint reflects an important property of the cognitive mechanism that handles the perception of whole face and its parts. (The constraint has received strong empirical support.)
16. The model proposed by Rakover & Teucher is essentially stationary, not dynamic. The W formula describes how the recognition score for the whole face is to be calculated from the separate recognition scores of
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