The Logic of Aspect-Perception and Perceived Resemblance

Does the relation of seeing something as another really differ from seeing the one as resembling the other? Does seeing a cloud as a camel really differ from seeing a resemblance between the cloud and a camel? It is easy to think not, but I claim that the logic of the relation B sees x as resembling y differs markedly from that of B sees x as y and thus that we have two relations, not one. Aspect-perception is nontransitive, nonsymmetric, (presumably) irreflexive and categorical. Perceived or subjective resemblance is weakly or faintly transitive, symmetric, reflexive and graded. By the ‘ logic ’ of aspect-perception and perceived resemblance respectively, I do not mean the question of formalization per se — involving the syntax and perhaps the semantics of symbols in a formal system — but the logic of certain relations, as when we say that fatherhood is irreflexive. I shall argue that the logic of the relation B sees x as resembling y differs from that of B sees x as y and thus that we have two relations, not one. It is easy to think otherwise. One looks at a passing cloud, and suddenly one sees the cloud as a camel (of course, one is not under the illusion that a camel is in the sky; one thinks ‘ A camel! ’ without ever forgetting that one is looking at a cloud, not a camel). At the same time, one takes the cloud to resemble a camel. Are these not the same thing? Does not the phrase ‘ x looks like y ’ cover both, for the very good reason that these are each other ’ s notational variant? No. The relations differ in their respective formal properties — in particular, they differ or whether they are categorical rather than graded, and over transitivity, symmetry and reflexivity.


Some Preliminaries
I will speak only of visual resemblance and visual aspects.
I will speak only of 'seeing-as', leaving aside the arguably more complicated 'seeing-in' (But I shall sometimes use the more flexible term 'aspect-perception' or 'aspect-seeing', which is indifferent between seeing-as and seeing-in.). For brevity, I will speak of the two places occupied by x and y as taking only noun phrases-terms denoting objects-not as verb phrases or adjective phrases and, more significantly, not as the nominalizations of sentences expressing facts or states of affairs (not that there are no such uses of these constructions; it is connected with 'seeing-in', a connection the importance of which was stressed by Wollheim 1980). In, for example, the construction 'A sees x as y', the terms inserted for 'x' will always be singular; those inserted for 'y' can be general or singular-typically an indefinite description, as in 'an F', for example, 'an ostrich', but they also can be definite descriptions or proper names, for example, 'The Leaning Tower of Pisa' or 'Henry VIII'. I use 'x' and 'y' (and 'F') merely as schematic letters, not as variables.
Sometimes I will speak of the primary object-the immediately perceived object (such as the cloud) in which one sees an aspect or that is seen as resembling some object-as opposed to the secondary object, the object that the primary object is seen as, or which the primary object is seen as resembling, e.g. the camel or a camel.
I am talking about subjective resemblance, experienced or perceived resemblancenot objective resemblance, assuming that there is such a thing. In speaking of perceived resemblance, I am speaking of the subjective counterpart of the objective relation x resembles y, just as one may distinguish A perceives x as blue from x is blue. In the case of resemblance, the direction of explanation-whether from subjective to objective or objective to subjective-is contentious, whereas aspect-perception appears to be without an objective side. In any case, I will ignore the objective side save a remark at the end.
With respect to the position occupied by a term for the secondary object, these forms involving 'sees' create an intensional context (actually the context is hyper-intensional), and thus, differences of scope will obtrude, as in: There are various ways to cope with these phenomena, perhaps from Brentano, Meinong and Husserl but definitely from Frege, Russell and Carnap to modern accounts; for the points I make beginning at Sect. 2, it is more or less indifferent which one is chosen so long as the account delivers the logical behaviour just outlined. The position on the contrary occupied by 'x' in the de dicto forms seems to be fully referential, open to substitution salva veritate by identicals. The second and fourth de re forms are plainly intelligible, with again x fully referential and y not. The first and third de re forms are only dubiously intelligible and are mentioned only for completeness.

Relativity
A minor difference is that perceived resemblance is manifestly relativizable (even if not in every case). Without incurring any protest, we speak of shape-resemblance, colourresemblance, hue-resemblance, build-resemblance, face-resemblance (equally: similarity in various 'respects'), and so on. Indeed almost always-but not always-if we say 'x resembles y', we are understood to be committed to some statement of the form 'x Fresembles y'. I am not going to say that aspects do not ever come relativized to types in these ways, but still they do not as readily admit of such relativization, and some-such as colour-do not seem to appear at all. If one is looking at the clouds and sees a cloud as a polar bear, one naturally says 'A polar bear!', with at least the words appearing quite unrelativized. One does not say that one sees a polar bear in a cloud because of the colour. It very likely comes down to aspect-perception being limited to perceived shape-so that is is (implicitly) relativized, but I will not pursue the matter further.

Gradedness
Perceived resemblance is a matter of degree, forming a continuum of cases with a region of uncertainty in the middle, a region within which it is not clear that resemblance holds or fails to hold. Seeing-as, on the contrary, is discrete, like the throwing a switch, either on or off: just as a shade of red can be more or less close to a given shade of red, but a natural number cannot be more or less a perfect square, one can experience resemblance in various degrees, but on a given occasion one either sees the ubiquitous drawing as a duck or one does not (Levinson 1998, p. 228). The experience of exact resemblance is the asymptote of the experience of degrees of resemblance or similarity. One's experience when looking at an emu might be that its appearance is roughly similar to that of an ostrich, that of a jackdaw closely similar to that of a rook, and that of a crow exactly similar to that of another crow. In contrast, the discreteness of the experience of aspects is evident especially in the case of experiences of puzzle pictures, where suddenly the object 'leaps out' of the lines-the aspect 'dawns', as Wittgenstein famously put it.
In the next three sections, I will confine my remarks to cases where the primary objects and the secondary objects are particular objects, not kinds.

Transitivity
It would be a mistake to claim that perceived resemblance or perceived exact resemblance exhibits full-blooded transitivity. However, it comes close in a way that aspect-perception does not. If one perceives x as exactly resembling y (in outline shape say) and if one perceives y as exactly resembling z (same), then one can perceive x as closely (perhaps exactly) resembling z. If one perceives x as closely resembling y and y as closely or exactly resembling z, then one can perceive x as resembling (perhaps exactly or perhaps closely) z. We are talking about the human mind, so one naturally hesitates to bring in numbers, but in general, let Rxy be the degree of perceived resemblance between x and y (where 0 ≤ Rxy ≤ 1). Then-at least plausibly-if for some values μ and ν, Rab = μ and Rbc = ν, then Rac ≳ μν. The perceived resemblance of a with c is roughly at least the product of the degree of resemblance of a and b and the degree of resemblance of b and c. 1 There is, I take it, no temptation to think that seeing-as exhibits such quasitransitivity or near-transitivity, even though one can find or dream up individual cases where it is plausible to say that x is seen y, y is seen as z and x is seen as z (e.g. a case where one sees a drawing as a certain person and one can see the person as the person's twin and also sees the drawing as the person's twin). Thus the relation of aspectperception is not intransitive.
The point is related to the one about gradedness: One would expect this quasitransitive behaviour only with respect to graded relations.

Symmetry
If one perceives x as resembling y, then one can perceive y as resembling x. Seeing-as exhibits no such symmetry. If one sees a cloud as a certain dog, say Snoopy, it is if not impossible, quite rare that one can see the dog as the cloud. But in the special case of faces, for example, one may see a face as another (one speaks of seeing a 'likeness'), and the other as the one. Aspect-perception is thus nonsymmetric, not asymmetric.

Reflexivity
Irrespective of the general fact that symmetry and transitivity imply reflexivity, I take it that whereas one's natural reaction to a non-metaphorical utterance of 'I see the duck as itself'-understood as wide scope or de dicto-would be incomprehension, one's natural reaction to 'The duck resembles itself', or 'I see the duck as resembling itself', would merely be an eye roll, as if the speaker had advanced a bad-joke tautology. As in 'Yes all right you win there is one thing present that the duck resembles, namely itself'. But the case of the utterance 'I see the duck as the duck' or 'I see the duck as itself', the utterance, if not patent nonsense, stands in need of special explanation.
To sum up, aspect-perception is nontransitive, nonsymmetric, (presumably) irreflexive and categorical. Perceived or subjective resemblance is weakly or faintly transitive, symmetric, reflexive and graded. There is more to say about each of these points, but my purpose is only to establish the logical difference between the two relations, which I assume has been achieved.

Material Difference
The contrast between aspects and resemblance also emerges in the following way, a way that has little to do with points of logic but with their epistemology. That the experience of resemblance or similarity of two objects does not require one of aspectperception involving the two is evident from cases like the similarity of various stones one finds in the shallow of a stream; one does not see one as another, but of course, one may see them as resembling. The other way around does appear to hold: one sees x as y only if one sees x as resembling y. But the experience of aspect-perception does not require that it be backed by or entail an experience of resemblance in any respect in particular; one can see one face in another without being able to specify what it is about the one in virtue of which one sees it in the other.
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