Despite the widespread assumption that they are fatally flawed, it’s hard to find a sustained discussion of the problems associated with resemblance theories of content determination. Instead, one finds scattered somewhat haphazardly across the literature brief allusions to the same five objections. The canonical rendering of three of these can be found in the opening paragraphs of Nelson Goodman’s Languages of Art:
The most naive view of representation might perhaps be put somewhat like this: “A represents B if and only if A appreciably resembles B”, or “A represents B to the extent that A resembles B”. Vestiges of this view, with assorted refinements, persist in most writing on representation. Yet more error could hardly be compressed into so short a formula.
Some of the faults are obvious enough. An object resembles itself to the maximum degree but rarely represents itself; resemblance, unlike representation, is reflexive. Again, unlike representation, resemblance is symmetric: B is as much like A as A is like B, but while a painting may represent the Duke of Wellington, the Duke doesn’t represent the painting. Furthermore, in many cases neither one of a pair of very like objects represents the other; none of the automobiles off an assembly line is a picture of any of the rest; and a man is not normally a representation of another man, even his twin brother. Plainly, resemblance in any degree is no sufficient condition for representation. (1969, pp. 3–4)
In short, representation can’t be based on resemblance, since the latter is reflexive (where the former isn’t), symmetric (where the former isn’t), and insufficient (all manner of objects resemble others without representing them). But however influential these three objections might be when applied to a dyadic analysis of representation, they lose all force in the context of a triadic conception. This conception agrees with Goodman that relations between vehicles and their represented objects are insufficient to confer representational status. A representing vehicle must also undergo interpretation, either by triggering thoughts in a cognitive subject or by modifying the subject’s behavioural dispositions. And it is this process of interpretation, according to a resemblance theory, that also enforces the non-reflexivity and asymmetry of representation.
A fourth objection is that resemblance theories of mental content are incompatible with our commitment to physicalism:
If mental representations are physical things, and if representation is grounded in [resemblance], then there must be physical things in the brain that are similar to (i.e., share properties with) the things they represent. This problem could be kept at bay only so long as mind-stuff was conceived as nonphysical. The idea that we could get redness and sphericity in the mind loses its plausibility if this means we have to get it in the brain. (Cummins 1989, p. 31)
But this objection is easily deflected once a proper understanding of the different forms of resemblance is in place. The most straightforward kind of resemblance—the kind that Cummins in the above quotation has in mind, for example—involves the sharing of one or more properties. This relationship can be termed first-order resemblance.[8] It is this kind of resemblance that grounds the content of many public forms of representation, such as paintings, sculptures, and scale models. As Cummins points out, however, first-order resemblance is clearly unsuitable as a ground of mental content, since it is incompatible with what we know about the brain.
There is, nonetheless, a more abstract species of resemblance available. The requirement that representing vehicles share properties with their represented objects can be relaxed in favour of one in which the relations among a system of vehicles mirror the relations among their objects. This relation-preserving mapping between two systems can be called second-order resemblance.[9] And while it is extremely unlikely that first-order resemblance is the general ground of mental content (given what we know about the brain), the same does not apply to second-order resemblance. Two systems can share a pattern of relations without sharing the physical properties upon which those relations depend. Second-order resemblance is actually a very abstract relationship: essentially nothing about the physical form of a system of representing vehicles is implied by the fact that it resembles a set of represented objects at second-order. Contrary to the fourth objection, therefore, a theory of mental content determination that exploits second-order resemblance is compatible with physicalism.[10]
However, this emphasis on second-order resemblance, at least in the eyes of many theorists, takes this approach to content determination out of the frying pan and into the fire. This is because the highly abstract nature of second-order resemblance invites the charge that it entails a massive and intractable indeterminacy of mental content. And it is this fifth objection, perhaps more than any other, that accounts for the current unpopularity of resemblance theories (Sprevak 2011).
The problem here can be illustrated by returning to Dretske’s thermostat. The world–mind relation that does all the heavy lifting here constitutes a second-order resemblance: the relations among the representing vehicles (the set of bi-metallic strip curvatures) systematically mirror the relations among the representing objects (the set of ambient air temperatures).[11] The worry embodied in the fifth objection, however, is that this same set of representing vehicles will second-order resemble not just the temperature surrounding the thermostat but any set of objects, regardless of their nature and location, that shares its relational organisation. This fact is entailed by the abstract nature of second-order resemblance. And this is a problem, of course, because it suggests that second-order resemblance is incapable of delivering determinate content. The most we can say about the thermostat’s bi-metallic strip is that its curvature represents that potentially large and motley collection of objects with which it systematically corresponds. And this would seem to be a long way from saying it represents the temperature of the ambient air.
Fortunately, the triadic analysis again offers a way to surmount this difficulty. On this account, representations aren’t manufactured solely from relations between vehicles and the objects they represent. Rather, the process of interpretation must also be thrown into the mix. We’ve seen that interpretation is discharged ultimately in terms of modifications to a system’s behavioural dispositions. But not any old modifications will do—representing vehicles must modify the system’s dispositions towards their represented objects. Consequently, interpretation plays an important content-limiting role. Specifically, a system’s behavioural dispositions will anchor its representing vehicles to particular represented domains. Once a domain is secured in this way, second-order resemblance relations determine the content of the individual vehicles. In the case of the thermostat, for example, the behavioural dispositions of the system restrict the represented domain to ambient air temperature, and the second-order resemblance relations determine what temperature each vehicle represents.