Opie (1999) suggests that our our claim that there must be prior local analysis in part-whole processing stems, not from our suggestions about whole/part analysis, but from our assuming extrinsic rather than intrinsic representations. He argues that the assumption of intrinsic representation in the brain allows an escape from the need for prior local analysis and offers a framework for simultaneous, parallel processing of local and global properties of patterns. We challenge his claim and demonstrate how, on Opie's connectionist examples of intrinsic representation, and from what we know about the real visual system, the need for prior local analysis is evident.
2. We are reluctant to use the term "representation" in reference to brain states, and prefer the direct realist notion of such states standing in direct relationships with objects and events in the world. Representation is a ternary relation requiring three terms: the thing represented (e.g., x, an object in the world); the thing representing x (e.g., y, a brain state) and a third entity that knows y to be a representation of x. It is the third entity that causes concern in theories of cognition. What could the third term of the representative relation refer to other than an homunculus? We therefore prefer to conceive of brain states standing in the binary relation of isomorphism with states of the world - see Latimer (1998) for an elaboration of this point.
3. Opie asserts that, "we give the impression that careful attention to the meanings of 'part' and 'whole' (i.e., a little conceptual analysis) can resolve a significant debate in psychology concerning the mechanism responsible for gestalts." (para. 1). This is overstating our claims. We argue that conceptual analysis of the whole/part relation is a necessary precursor to any empirical investigation of whole/part perception, but we do not believe that conceptual analysis, in and of itself, is sufficient to resolve the significant debate on these issues.
4. Opie suggests that "To say that a whole is more than the sum of its parts is merely to say that a whole is not just a heap; its parts must enter into relations of some kind, and these relations are as much constitutive of the whole as are its parts." (para. 3). Great care is needed in any consideration of the ontological status of relations. Relations are not things, and some of the most venerable theoretical blunders in the history of psychology have come about because of the propensity of theorists to reify relationships. For example, as far back as the fifties, neobehaviourists regarded intervening variables such as "habit strength" or sHr as mere relationships, between stimuli and responses. However, difficulties arose when these supposed relationships were inevitably treated as entities in their own right. As Maze (1954) pointed out, "A relation is not "between" its terms, even in the most neutral way; one should say, rather, that they have or stand in, that relation." (p. 233).
5. Opie further suggests that we fail "to appreciate the real insight at the heart of the Gestalt movement: the idea that relations among the elements of perception - be they part-whole relations, part-part relations, or whatever - might be determined by INHERENT STRUCTURAL PROPERTIES of the brain." We rather thought that our Sections XI through XIV dealing with the Rescher & Oppenheim (1955) notions of Dependence Relations, Structured Wholes, Isomorphism, Invariance, Complexes and Complexial Features demonstrated our appreciation of the importance of relations between parts, as well as the structural properties of wholes.
6. Opie notes that where perception is concerned, we hold the view that "a global perceptual attribute is 'underivable' if it can only be extracted DIRECTLY from stimulus patterns, and not on the basis of computations defined over representations of local elements". (para. 7). We in fact describe a number of possible forms of derivability and underivability (Sect. 6). We do, however, suggest that the sort of holistic attributes proposed by the Gestaltists and, more recently, by global precedence theorists, may be unconditionally underivable from any decomposition of a whole and attributes of that decomposition. Such a conception captures the essence of the Gestaltist assertion that wholes transcend and are not reducible to their parts. Global precedence theorists constantly claim that holistic properties are detected prior to local properties, and while such global properties may well be derivable from the local properties, they are not so derived, but are claimed to exist in their own right and be available for direct extraction. Our question is, of course, what sort of mechanism could effect such direct extraction? Let us now look closely at the one suggested by Opie.
7. Turning now to the major issue raised in Opie's commentary, that being intrinsic representation and its implications for part/whole processing. The brain, by generating representations of parts, immediately represents the relationships among those parts and thereby any wholes of which those parts might be constituents. Thus, rather than analysis of parts necessarily preceding extraction of holistic properties, the perceptual system computes local and global properties simultaneously. At first glance the proposed parallel computation of local and global properties provides a formidable stumbling block for any claims of necessary local precedence, but nonetheless, Opie seems unsure. First, he notes that "The beauty of the scheme is that when one represents the parts, representation of the wholes comes for free." (para. 9) He also notes that "Such a system computes local and global attributes simultaneously." (para. 9). However, he makes the seemingly contradictory claim that "One might rightly call this style of processing HOLISTIC, even though it does not actually bypass the representation of local elements, because representations of global attributes are an inevitable product of representing local elements." (para. 9). It appears from the latter statement that Opie believes, with us, that holistic properties do not exist in their own right, but are derived from the products of prior local processing.
8. Opie may baulk at the suggestion that local processing is necessarily prior in his scheme, but one has only to look at the connectionist examples he cites as possible models for perceptual processing in the brain. Activation in such systems is initiated at the level of the individual units and spreads by way of interconnections. The spread of activation, the relaxation within a network, occurs across time, as units affect the activation of other units. There is nothing even approaching simultaneity in these systems as they settle down to a steady level of activation which requires the cooperation of many units. Even the simplest possible example of a real neural net - a receptor cell connected to an inter-neuron - displays the necessary time lag involved in producing a configuration of activation. Activation in the dendrites of the receptor cell passes to the cell body and may sum temporally to exceed threshold and propagate the neural impulse along the cell axon to terminals, synapses, and thence to the dendrites of the inter-neuron. Backpropagation networks involve pre-specification of parts - input units - that reflect aspects of the stimulus. Hidden units in these multi-layered networks may compress information to enable efficient mapping from input units to some output response but, as highly-dimensional as the hidden unit configuration is, it is still derivable from non-linear combinations of the input parts. Even in self-organising systems there is a sense that global configurations arise from combinations of parts or elements (Mitchell, 1998). There is no doubt that Opie recognises this production or derivation of the whole configuration in a network by way of time-consuming interactions between the processing units. He notes that, "constituent networks all arrive at a stable configuration simultaneously". His concern is with the arrival, and he appears to ignore the necessary journey of derivation wherein the local units interact to produce the holistic configuration.
9. Opie concludes that "What we have here is a quasi-holistic processing mechanism, in which local perceptual elements are made to conform to global constraints, and in which neither local nor global attributes take priority." (para. 10). This is certainly not how artificial neural networks model perceptual processing, and probably not how the brain works. Opie would need to specify exactly which connectionist models of visual perception embody his principles, but generally in such models, stimuli create activation initially in the input units which pass activation to hidden layers and thence to output units. During this process, as for example in the interactive-activation model of McClelland & Rumelhart (1981), units modify activation of other units by way of ascending and descending excitatory and inhibitory connections, but there is nothing simultaneous in this system, and activation must be initiated at the level of local units before being modified in any global sense. Similarly, in the real visual system, the first registration of stimuli is a rich and highly detailed local analysis at the level of the photoreceptors before theoretical processes such as lateral inhibition may arise in the ganglion cells prior to processing in the higher visual areas of the cortex. Where is the simultaneity here? Granted, the global configuration of stimulation, once it has been formed, may feedback to modify activation at the level of local units, but the basis for that global configuration has been laid by prior processing at a local level.
10. In our paper we labour the point that "Only when the context makes clear which specific part relation is intended may we even speak of parts and wholes and until definitions of 'whole' and 'part' are proffered, discussions of these terms cannot proceed." (para. 11). Opie, like so many others, has chosen to ignore this advice and has attempted to argue his case in general terms. If Opie believes, again like so many others, that perceptual wholes can come into existence simultaneously and underived (or even underivable) from analysis of their parts, and that intrinsic representation can provide the mechanism for this process, then he will have to spell out this mechanism in the required detail. First, we will need to know exactly what each whole is, what its decomposition is and what are the attributes of the decomposed parts. Next, he will have to provide a detailed specification of how each whole, parts and attributes function in a mechanism for simultaneous, underived holistic properties. Until he (or someone else) fulfils these requirements, we see no reason to withdraw the central challenge of our target article.
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