There’ s a sense of “model” according to which models have to be models of something, and a sense of “representation” according to which representations have to be representations of something. But if we rely just on that, there’s a pretty quick argument to the conclusion that no theory of representation can account for the representation of non-existent objects! (All you need to assume is a non-crazy metaphysics.)

The right thing to say, I think, is that some models and representations *purport* to represent things that don’t exist, but they’re representations nonetheless. However, I don’t really care what one decides is the right thing to say. The main thing is to account for the phenomena, which I think the above story does. The main phenomenon is: there are some shareable concepts that lack referents, and which are not complex (and so cannot be explained in terms of concepts that do have referents).

Sorry for the looooong delay, but I’m happy to take this at a snail’s pace if you are.

Your remarks do help clarify things quite a bit, and I like the illustration of the model maker. I worry, though, that you might still not have solved the problem of representing the non-existent. Take, for instance, how you describe the blob that ASM secretes after Trickster Pete has played his tricks: “This blob isn’t a model of anything” (emphasis yours. It sounds to me like you are taking “model of” as a relation here. If something is a model only if it is true in some sense or other that it is a model of something, then the blob isn’t a model.

Is it supposed to be part of the story that at some point the Pete Blobs are models even though there is nothing that they do model? If they just aren’t models, and so-called unicorn representations are supposed to be analogous the the Pete Blobs, then are so-called unicorn representations not really representations?

Here’s an analogy, the Automatic Scale Modeller (ASM): It’s designed to take an object through its input door, make a mould of the object, shrink the mould, fill it with molten plastic, and then spew a model out. The model is a model of the input object (whatever it comes across, maybe this thing zooms around by iself on wheels). The models this thing spits out are supposed to be spatially isomorphic to the input objects that cause them.

Normally things go well, and the ASM produces a nice accurate model (true belief). But sometimes things go wrong, for instance there’s a little lump on its model of my telephone - the model inaccurately represents that my telephone has a lump on it (false belief). And sometimes, Trickster Pete really messes it up, as follows: he triggers its object detecting laser, which makes the machine start on its model-making procedures. While the machine is chugging along, Pete shakes it vigorously, maybe blows some air through its output door, etc., and the machine spits out a misshapen blob. This blob isn’t a model of anything (empty representation).

Now, suppose that Pete publishes his exact procedure for messing up the ASM on the internet, and lots of people begin to follow it with their own ASMs, producing exactly similar misshapen blobs. People start calling it “The Pete Blob”. We can identify this empty representation across individuals by what causes it, and each Pete Blob has the same underlying explanation for why it looks like the other ones (having to do with Pete’s instructions and the internal design of the ASM). Unlike in the normal case, however, this explanation does not involve the referent of the model, because there isn’t one. That’s like fiction, as a replicated cognitive illusion. Now suppose that Pete is forgotten, and the origins of the Pete Blobs get lost in the mysts of time; small variations are introduced, and replicated within different cultures in somewhat different ways. That’s like unicorns.

Our brains are model-making machines, that aim at isomorphism not to spatial structure, but to regularity structure. And our brains can go wrong in just the same sorts of ways that the ASM can go wrong. (Plus some others!)

Re: topic 2, I can see your points and don’t really have much further quibble on this.

Re: topic 3. there’s a problem that it seems (though I’m not sure) you don’t have a satisfactory answer to: What is representation such that it can be the same thing in true, false, and empty contexts? I take it that there’s no difference in what representation is in the true representation of dogs as having hearts and the false representation of dogs as having beaks. I take it as well that there’s no difference of what representation is in the empty representation of unicorns as having hearts.

As I understand referential externalism, it would have to hold that there is no representation in the so-called empty context, since there is no existing thing that is being represented as having hearts.

If you want to hold that the empty context is a genuine case of representation in spite of there being no referent, then it looks like you’ll be forced to give a very different account of representation in the empty case than in the true and false cases. In the true and false cases, representation is a relation. And in these particular cases it is a relation to dogs. In the empty case representation is a relation to nothing at all.

Topic 1 - Here’s an analogy: take a model of a Spitfire, a Spitfire, and a giraffe, and suppose we’re interested in spatial isomorphism. Given natural categories, the model of a Spitfire is more nearly isomorphic to the Spitfire, not the giraffe. But given gerrymandered spatial categories, there’s a perfectly good mapping from the model of the Spitfire to various points internal to the giraffe - a Spitfire-shaped collection of giraffe guts, as it were. (That’s one type of gerrymandering, involving the referent of the representation. Another type is gerrymandering of the isomorphic relations themselves, the relations that are “preserved” across the mapping. If any degree of spatial distortion is permitted, there will be a perfectly good mapping from the model of the Spitfire to the *surface* of the giraffe too.) Analogous problems will infect mappings of inferential roles onto regularity structures (or whatever it is inferential roles are supposed to map onto in the world), if non-natural categories and/or mappings are permitted.

Topic 2 - On your second point - sure! Then how about adding 3) content is that which *explains* TSCs (where applicable). That takes care of non-propositional representations. [On your first point - I disagree that TSCs depend on attitude context - that's the point of talking about "truth or satisfaction". My belief that grass is green and my desire that grass be green have the same propositional contents and the same TSC. No?]

Topic 3 - Well, I do explicate content in terms of relations to extra-mental entities, and in the case of non-propositional representations, those extra-mental entities normally include the referents of those representations. But not in the case of empty representations. They’d better not, since empty representations don’t have referents! I think in the ordinary cases, someone would unhesitatingly classify me as a referential externalist, and the account of empty representations basically falls out of how I treat the ordinary cases. So you decide: am I a referential externalist?

I agree that truth/satisfaction conditions (TSCs) and content are related. I think that it wouldn’t be question begging re internalism/externalism to characterizing content in terms of truth in the way you suggest. However, I’m not particularly happy with the characterization offered for a couple of reasons.

First, I think contents and attitudes are to be distingusihed, but TSCs attach to content-attitutde pairings, e.g., it is my belief that grass is green that is made true by grass being green and it is my desire that the icecream have sprinkles that is satisfied by the icecream having sprinkles.

Second, unless certain combinatorial semantics are going to be ruled out by stipulation, then we need to leave open the possibility that, e.g. the representation of Socrates in flight is acheived by combining separately contentful representations of Socrates and flight. But these latter representations will no more have TSCs than does the name “Socrates” have a truth value.

This helps me understand what you have in mind. I remain to be convinced, though, that there is a problem. I can imagine lots of situations in which increased complexity of structure will actually reduce the number of possible mappings, so I don’t see how complexity per se is the problem (if any) gerrymandering introduces.

Here’s another way of spelling out how gerrymandering doesn’t strike me as introducing a special problem. I assume that an example of the gerrymandered/nongerrymandered distinction would be warm-blooded animal vs. warm-blooded-animal-or-igneous-rock. I’m not seeing why mapping representations onto representeds would be any more difficult in the one case than the other.

I argue that the cerebral cortex is a SINBAD network. “SINBAD” stands for “set of interacting backpropagating dendrites”, and refers to the mechanism by which the network’s activation dispositions come to be isomorphic to regularities in the environment. The key aspect of SINBAD networks is that individual cells tune to what I have called “sources of correlation” and now call “sources of mutual information” (SOMIs): things that are characterized by clusters of properties that tend to co-occur for an underlying reason. (Boyd’s homeostatic property clusters count as SOMIs, for example, but I would extend the notion to purely historical kinds - where there’s no homeostasis per se - and individuals. So SOMIs are more like Millikan’s “substances”.) As SINBAD networks get exposed to an environment via sensory receptors, they gradually come to mirror its deep structure, becoming isomorphic to regularities involving SOMIs in that environment. (The relations among SOMIs that the network can come to mirror can be multivariate and nonlinear - this ain’t no simple Hebbian associative network.) I also argue that the cortex is supposed to mirror regularities involving SOMIs (the teleological element). That’s what it was selected for. That is, the cortex comes to model (= be normatively isomorphic to) the deep structure of the environment it is exposed to. Think of it as mental wax, that represents what comes to be “impressed” upon it.

A wax impression represents the thing that caused it to acquire its structure (or rather the aspects of its structure that are supposed to resemble something - its density structure doesn’t represent anything, for instance, only its spatial structure does). Similarly, to figure out what a particular SINBAD cell represents, you have to identify the SOMI that caused it to adopt its place in the big isomorphism. The details of the SINBAD mechanism, and the history of the cell’s interaction with other cells and (indirectly) the environment, allow you to figure out what SOMI this is. (Often it’s more than one, and the cell is equivocal or ambiguous - thus the typical need for a population code.)

Now for empty representations: sometimes the system can be tricked into “tuning” to something that isn’t there. One set of clear examples involve clustering illusions. In cases like these (possibly the “hot hand” in basketball), there’s a clustering of properties, but there’s no underlying explanation for the clustering - it occurs purely by chance. Nevertheless, a cell will pick up on the clustered properties and “tune” to their nonexistent source. The result is an empty representation. Another way for empty representations to occur is via prior misrepresentation. Consider the scintillating grid illusion, for instance. If you looked at these enough, your cognitive system might introduce a concept for “that kind of spot” - except of course there isn’t any such thing! What’s happened is that early visual processing in the cortex has represented a bunch of properties that cluster, except a subset of those representations are consistently misrepresentations. This leads some SINBAD cells to “tune” to the nonexistent type of object. We can still identify this representation across individuals in terms of its content, though, because the misleading clustering has a similar cause in each case - not a type of object in the environment (though that’s part of it, i.e. the crossed lines etc.), but also the internal structure of the human visual system. I suggest that the concept of Sherlock Holmes is just the same, except that it is a product of cognitive illusion rather than visual illusion. Words on the page (or phosphors on a screen) set up a systematic misrepresentation of the environment in your head, causing you to acquire spurious concepts due to illusory clusterings. (The concept acquisition machinery goes on its merry way, whether or not you believe the fiction is real.) Again, we can still identify this concept across individuals by its content, since the misrepresented clustering has the same explanation for each individual, namely the fiction, understood as a text (or whatever), plus humans’ susceptibility to this particular type of cognitive illusion. The concept of a unicorn would get the same treatment, except the relevant fiction is a more diffuse historical kind than in the case of Sherlock Holmes.

Whether it’s a SINBAD representation of cats or unicorns (or anything else), there is no particular conceptual role that a representation must play in order to realize the concept in question. Your concepts of cats and unicorns may play different conceptual roles from mine, if our SINBAD cells have picked up on different aspects of the rich clustering of features that are related to real cats and the unicorn fiction. This means that both the concept of cats and the concept of unicorns get the same, non-descriptionist treatment, which maintains the theoretical unity between the two types of concepts that we were after in the first place.

I don’t know if that was long-winded or too sketchy. (Probably both!) If it doesn’t make sense, my Mind & Language paper might help. (But ignore the brief and misleading remarks I make about empty concepts and “fictional kinds” there!)

How about adding this to your characterization of content: 3) content is that which has truth-(or-satisfaction)-conditions. This doesn’t deny that truth-(or-satisfaction) conditions could be linked to a particular mental state on the basis of purely intrinsic features of that mental state. (It doesn’t even say that particular truth-(or-satisfaction)-conditions are essential to a particular content!) So I don’t think it begs any questions against internalism. It just makes it clear that the challenge of explaining truth conditions is a challenge to be met by any theory of content.