Hoffman (1998) and Mortensen (1998) do not appear to be in disagreement with our general remarks on wholes and parts; they extend discussion on relevant issues. We challenge Mortensen's claim that our position is not general by asking for examples of wholes that fail in any sense to conform to the Rescher & Oppenheim (1955) conditions. We argue against his view that there is no need to be over-concerned about the conditions under which an object X is to be considered as a part of object Y since the classical part-whole relation is invariant with respect to decomposition. We remain unconvinced by Rakover's (1998) argument that a mechanistic approach to whole-part perception cannot be taken because psychology necessarily lacks the measurement precision of the physical sciences. We challenge this view, but also suggest that inability to measure with precision is no excuse for the proliferation in psychology of vague, imprecise and ill-defined notions of wholes and parts.
2. Mortensen (1998) is in general agreement with our approach, but registers several disagreements, one of which is that R&O stipulate only a restricted class of wholes. Calling wholes "structured" marks their distinctiveness from wholes in general. Perhaps the best way to settle this would be for Mortensen to provide, if he can, examples of wholes that fail, in any sense, to conform to the R&O conditions. A similar challenge is issued in reply to the comment that it is an overstatement to claim that the meaning or definition of "whole" should be relativised to its decomposition, and that this would be appropriate if only structural wholes are wholes. Is there a whole that could in no sense be regarded as structured? Further to this point: it is not our intention to offer a general theory of meaning but simply to emphasize the necessity for a clear and precise delineation of what is meant by "whole" and "part" in each theoretical and experimental context. This can be done informally and ostensively or formally by analysis, but in experimental psychology, for example, it is rarely done at all.
3. Mortensen (1998) suggests that one should not be over-concerned with the conditions under which an object X is to be considered as a part or a whole of object Y or with which specific part relation is intended, since the classical part-whole relation is invariant with respect to decomposition. We, on the other hand argue (Latimer & Stevens, 1997, Para 8), that this is precisely the issue that one should be very concerned about in any theoretical or experimental context. If, for example, in experimental tests of Local versus Global Feature theories, some experimenters regard as local properties that others regard as global, how could meaningful evidence be brought to bear on the question of which theory provides the best explanation of the data? Clearly, in such a situation, the ambiguity associated with the terms "whole" and "part" will vitiate any tests of the theories.
4. On a related matter, Mortensen (1998) claims that our treatment of the colour wheel, "gets it a bit wrong too." The whole wheel when spun has the phenomenal attribute "white," which is not a phenomenal attribute of any of the components; but this, claims Mortensen, seems to be comparing unlike things, noting that the parts of the spun wheel look white too. When we stop the wheel, we again see the colours and cease to see the white. This comment underlines our suggestion (Para. 4) that great care is needed in the specification of just what wholes and parts are under consideration in any investigation. Are they real or hypothesized neurophysiological structures, objective units of input for perceptual systems (colour wheels) or phenomenal attributes reported by experimental participants?
5. In light of these remarks, reference to the static and spun wheels as "unlike things" can be misleading. In what sense are there two things and in what sense are they not alike? There is just one colour wheel and its component coloured parts endure and remain the same, but when the property of movement is added, the whole and its parts appear white. However, it is not as if the addition of movement has produced a physical change in the wheel, for example, in the reflective properties of its coloured parts. In the case of the colour wheel, the addition of movement changes the mixture of the wavelengths stimulating the visual system and since the phenomenal attribute of white is predictable from the Young-Helmholtz trichromatic theory, this attribute is rendered non-emergent. A similar situation requiring equal attention to the exact ontological status of wholes and parts arises in the phi phenomenon, where one light appears to be moving back and forth. Physically, of course, there are two adjacent, static lights. Finally, Mortensen (Para. 7) describes our discussion of the cork example (Para 25) as a "little infelicitous" for the same reason. We are unsure why the example is so described, because we are in agreement with Mortensen's claim that the orientation of a magnetized needle in a magnetic field is solely a function of local field strength and direction.
6. Rakover (1988) asks whether mechanistic concepts can be applied to part-whole perception, and again, it is necessary to emphasize the need to consider carefully just what wholes and parts are in question: physical, physiological, phenomenal? It is not clear whether Rakover has difficulty with physical measures of stimuli or the physical segmentation and description of stimuli according to accepted physical measuring systems. Such measures form a necessary precursor to most experimental studies in psychology where independent variables such as size, shape, brightness, contrast, duration, frequency and amplitude of stimuli must be measured and manipulated precisely. The physical wholes and parts to be considered at this stage of any experimental investigation are subject to all the strictures made in our target article.
7. Rakover (Para. 5) seems to think that our argument rests on the assumption of a "basic unit of analysis" or perceptual measurement unit reached at the end of a process of decomposition of the perceptual form. There may be such a unit, but its existence forms no part of our basic set of assumptions. Our paper emphasizes the relativity of wholes and parts and we remain neutral with regard to the existence of wholes and parts in any absolute sense, such as "perceptual atoms". It may be that the visual system analyzes stimuli into a particular set of parts e.g., the analysis of face stimuli in the Rakover & Teucher (1997) study. However, while future experimentation may confirm this decomposition, it could also suggest that it is context-dependent, and that the visual system uses some other decomposition or no decomposition of the same faces in another context. By context, we mean, among other things, the particular set of stimuli in use and the environmental context established by the nature of a task or specific instructions (given to participants). Perhaps Rakover means that we are assuming the existence of perceptual atoms from which all perceptual experience is derived, regardless of context. Again, our remarks are neutral with regard to what wholes and parts are proposed in any context or how they operate in theories and explanations of perception. Our concerns are with how exactly wholes and parts are defined in each context, and whether their definitions permit or do not permit derivation of other properties.
8. Rakover's claim may simply be that phenomenal and physiological wholes and parts do not admit of the sort of analysis advocated in our paper. Alterations in psychological properties are, "not based on natural and basic measurement units but on a correlation between the modification of the stimulus and the change in the response." (Para 7). Feyerabend (1975), of course, makes a convincing case that all measurement, physical and psychological, is theory-dependent, but Rakover's objection is too general. Using uniform colour scales (CIE lab), responses to colour can be related quite precisely to physical measures of colour. Judgements of the orientation of bar stimuli, axes of symmetry, and the relative pitch and loudness of tones can be measured with precision. Perhaps emotional strength or degree of arousal cannot be measured with the same accuracy, but even here, electrophysiological indices of these constructs are improving (see Wenderoth & Latimer 1978).
9. It remains unclear just how the issue of imprecise measurement bears directly on our plea for greater concern in the definition of wholes and parts. Not being able to measure psychological responses or to identify psychological constructs with the precision of physics is no excuse for vague and imprecise notions of wholes, parts and their relations. For example, Rakover (Para 14) invokes the notions of "cognitive schemata," "features," "chunks" and "atomic units" and refers to an explanatory model. One can still ask to what exactly these terms refer: How are they being used and what exactly do they mean? How does the "model" work? What precisely are its inputs and outputs? Models are supposed to be heuristic devices used to explain the processes of a theory. What is the theory? and which of its processes are being modelled? Answers to these questions are not barred by the possibility of imprecise measurement but by the unwillingness or inability of theorists to spell out in detail what they mean with their terms and constructs. The uses and abuses of terms such as "whole" and "part," "local" and "global" are good examples.
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