Latimer & Stevens (1997) make a persuasive case that attending to the conceptual analysis of the part-whole relation clarifies some of the issues surrounding perceptual gestalts. Several disagreements are registered here. Their account of the part-whole relation is stronger than they need to make their points work.
2. On the other hand, L&S, following R&O, stipulate only a restricted class of wholes. A whole must possess some attribute peculiar to it in virtue of its status as a whole, and characteristic of it as a whole; the parts must stand in some relation of dependence with one another; and the whole must have some structure which supports the attribution of distinctively structural characteristics to it (para 10). Calling these "structural wholes" marks their distinctiveness from wholes in general.
3. L&S note that any whole has an indefinite number of decompositions. Here, we can define a decomposition of a whole W as: a property F such that the sum of all parts of W which are F, is W. Note: (i) F may be a disjunction of properties, e.g., F is (G or H). (ii) Not every property of parts of a whole is a decomposition of that whole, e.g., being a carbon atom is a property of some of your body parts; but your body is not the sum of the carbon atoms in it, since there are other atoms in your body. (iii) Some wholes do have decompositions, e.g., being a carbon atom is a decomposition of a molecule of Buckminsterfullerene C60 (buckyballs); or being a (vertex or an edge or a face) is a decomposition of any polyhedron (iv) W may have more than one decomposition, e.g., C60 is decomposed by the property of being a carbon atom, but also decomposed by the disjunctive property of being a proton or a neutron or an electron. (v) The property of being C60 is emergent and unshared relative to a decomposition, in the sense that it is a property not possessed by any of the (proper) parts of the decomposition. (vi) That W is decomposed by a certain property F is not necessarily all there is to be known about W, since the relation between the parts, its structure, is not necessarily determined by the fact that its parts are F. This is a stronger kind of emergence, "underivability." For example, though C60 is decomposed by being a carbon atom, not just any collection of 60 carbon atoms is C60, since they have to be arranged (related) in a certain way. In this (harmless) sense, although C60 can be decomposed into nothing but carbon atoms, being C60 is underivable from being a carbon atom. Wholes which have a decomposition we can call "decomposed wholes," and these clearly involve a relation to a decomposition F.
4. In these terms, it is evident that any whole has an indefinite number of decompositions, and hence there are an indefinite number of ways in which properties of wholes can be derivable or underivable from properties of their decomposed parts. L&S overstate this as the claim that the meaning or definition (para 8) of "whole" should be relativised to the decomposition F. But this would be appropriate at most if one held that only structural wholes are wholes. At any rate, as Popper and Quine both emphasised, one should have as little as possible to do with claims as to meaning.
5. Even so, this is no criticism of L&S's call for clarity in respect of the way in which part-whole theory enters into various holist and gestaltist claims about perception. But these claims are best addressed simply by considering the role of those parts of the whole which are F, for some specified partition F, since it is decomposed wholes which are relevant to their discussion. Thus, in answer to L&S's request in their Rationale for "arguments to the effect that wholes and parts can exist in some absolute sense," it can be replied that the initial insight that some things are parts of some other things, supported by classical part-whole theory, gives all the unrelativised wholes one wants. Nor should one be overly concerned about the question of "the conditions under which an object x is to be considered as a part or a whole of object y" or "which specific part relation is intended" (para 11), since the classical part-whole relation is invariant with respect to decomposition.
6. L&S's treatment of the colour wheel gets it a bit wrong too. They say that the whole wheel when spun has the phenomenal attribute "white," which is not a phenomenal attribute of any of the "components" (para 13). This seems to be comparing unlike things. After all, the parts of the spun wheel look white too; and if we stop the wheel to see the colours of the parts, we cease to see the phenomenal attribute white. Later (para 19), L&S say that the trichromatic theory of colour perception renders the phenomenon non-emergent, whereas hue-cancellation conceives of the whiteness of the wheel as emergent. They don't exactly tell us with respect to what we are to judge emergence here, though it seems that the problem is to account for how the spinning wheel looks white, in terms of a decomposition of the properties of the stationary wheel, together with the fact that it is moving and what that does to our perceptual mechanisms. This supports L&S's general thesis that holists must pay attention to which decomposition is to bear the theoretical weight. However, it does not support their contention that unless and until the definition of part-whole is relativised to a decomposition, "it is difficult to see how any empirical evidence could ever be brought to bear on the issue" (Para 8). On the contrary, empirical evidence will always have a bearing on whether a given property F is a decomposition of a whole W, and what attributes are emergent relative to a fixed F, since it is an empirical issue which properties are decompositions of which wholes.
7. L&S's discussion of the cork example (para 25) is a little infelicitous for the same reason. If anything is a local phenomenon, it is how a magnetised needle will orient itself in a magnetic field. That is solely a function of local field strength and direction. Of course, local field strength is a function of the contributions of many sources, but it is a vector summation of forces. The latter aspect is surely the sort of theoretical background which L&S stipulate should be allowed in assessing emergence (e.g., additivity of mass).
8. Finally, we can consider L&S's general challenge to any holist theory, to give an account of a suitable holist processing mechanism. This is a powerful challenge, if only because the parts of a decomposition are obviously at least relevant to the behaviour of any processing mechanism which takes that decomposition into account. Here we can distinguish between holist processing (right from transduction) and holist representation. The latter would seem to be in principle easier to achieve. PDP models use both at some level, but L&S's general advice to be clear about the decomposition is relevant here. Relativised to a decomposition F, there will be the theoretical primitives which go to make up F. If an account of processing at this level is successful (PDP or not), and if recognition of the theoretical primitives of F is a primitive operation in the processing, then the explanation is in that sense holist about those theoretical primitives. They are not seen as deriving from the behaviours of any of their own decompositions in turn. This is not what holists seem to have in mind, of course. There the project has to be to specify the theoretical primitives, claim that the behaviour of the whole cannot be derived from the behaviour of the parts of the decomposition, and finally claim that this explanation is superior to any rival decompositions wherein it can be so derived. That, as L&S say, is a task demanding considerable exactitude.
Latimer, C. & Stevens, C. (1997). Some remarks on wholes, parts and their perception. PSYCOLOQUY 8(13) part-whole-perception.1.latimer.
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