Both Fodor and Rey (and many others) desire theories of concepts to provide for publicity, or shared concepts. However, explaining how concepts can be public proves difficult for many theories. Furthermore, some examples seem inherently nonpublic and in some cases this may not be a problem. In this paper I will therefore examine the desired benefits of publicity, some of the problems publicity causes for theories of concepts, when publicity can hold, what sorts of publicity exceptions we should make, and how much of it must be maintained.
Both Jerry Fodor and George Rey include publicity in their list of conceptual theory desiradata. Fodor requires that "Concepts are public; they're the sorts of things that lots of people can, and do, share." Rey requires both intrapersonal and interpersonal stability. In the former case, concepts are "the basis for cognitive competence and for comparison of cognitive states within a given agent." In the latter, concepts are "the basis for comparisons of cognitive states across agents." In other words, one person may have the same concept as another person. And, for the intrapersonal case, one person can have the same concept over a significant span of time. The requirement of publicity's place with other major demands on theories of concepts indicates that neither theorist believes that publicity is a minor issue. To meet their requirements, a theory must allow most, if not all, concepts to be public, at least in principle.
Why publicity? What's good about shared concepts? If two people have the same concept car, they can communicate freely and usefully about it. One person can convey useful knowledge, such as "you can buy a car on the corner of 28th and Glenwood." The two can settle disagreements (e.g. "Does Cindy own two cars or just one?"). If, however, the two people did not share the concept car, these communications would be confusing or meaningless at best. If Adam's version of car applies to toy cars as well as drivable cars, the statement about buying a car would be true even if that corner lacked a car dealership but instead housed a toy store. However, if Beth's version of car was restricted to conventional automobiles, the claim would be false in that case. Similarly, if Cindy owns a both Cadillac and a remote-control car, Adam can correctly believe she owns two cars while Beth correctly believes she owns just one and the dispute cannot be resolved (that is, a third person hearing the debate is left to conclude that Cindy owns two cars and owns just one car, which is clearly an undesirable conclusion). While this dispute might be resolved by Adam and Beth clarifying their concepts (Cindy owns one car that a person can sit in and drive and one remote-controlled car), if concepts are in principle unsharable, even this clarification is in trouble, since neither party can have the same refined concept. Thus, without any interpersonal publicity, we cannot share information and without any intrapersonal publicity, a person's conclusions today don't hold tomorrow.
Not all concepts need to be even potentially public. Self-referential concepts seem especially private. While the reference may be the same, it doesn't seem problematic to suppose that my concept me and someone else's concept Trevor Stone are fundamentally different, and it may even differ from my own concept Trevor Stone*. My concept my mother differs in reference from almost everyone else's concept of my mother, even though the two concepts might both be defined as "The woman who gave birth to me." A theory of concepts therefore doesn't suffer if some concepts cannot be shared. The publicity requirement only requires that most concepts or a sufficient set of concepts must be shared. Of course, these concepts aren't necessarily exempt from intrapersonal stability.
Publicity needn't be complete and absolute in all respects. We know from neuropsychology that two people can perform identically on conceptual tasks despite significantly different brain organizations. Publicity clearly doesn't need to hold at the neural level. Furthermore, two people's concepts needn't be identical in all respects at the semantic level to be considered shared. People clearly have different memories associated with car and some people know more about cars (such as how engines work or when the first one was made) than others do. However, these facts shouldn't prevent a concept from being shared.
Unlike ancillary information such as memories, it's not clear that two people can share a concept if they differ in parts of the fundamental representation. For instance, under the classical theory, it's possible for one person's concept bachelor to be defined as "a man who is not married" while another person's concept bachelor might be defined as "a man who does not have a current marriage license on file." Even if these two definitions are coextensive, it seems questionable to claim that these are the same concept, since they differ in extent in some possible worlds and since they lead to different conclusions.
The prototype theory suffers a similar problem -- if one person's prototypical bird is a robin while another's is a finch, should we say they share the concept bird? And for the theory-theory, should we say a concept is shared when the two defining theories differ in small, possibly irrelevant respects? These theories clearly allow for peoples' concepts to differ in these ways, so are they without a hope of significant publicity?
If it can be managed, these examples seem worthy of public status. A first attempt at a solution to this problem might call on reference for help. Concepts could differ subtly in fundamental representation if they share their reference and extent are identical. Thus, if a person's prototypical bird is a robin we can say he has the same concept bird as the finch-holder if they classify the same set of things as birds.
The reference solution is problematic, though. First, we don't want to equate all coreferential concepts, such as triangle and trilateral. This problem may be avoided by stipulating that the concepts need to have a sufficiently similar structure to look to reference. For the theory-theorist, if two people's theories differ only in ancillary detail, publicity might be determined by reference. But if the theories are wildly different and merely happen to be coreferential, we can say they are different concepts. An analogous solution might work for concepts with empty reference if we look for coextension in possible worlds.
However, intuitively we don't want to claim that two people's concepts are not shared at all merely because they differ slightly in extent. Suppose scientists genetically engineer two blue lemons, unbeknownst to Deb and Frank. For whatever reason, Deb's concept lemon allows for blue lemons, but Frank's does not. Deb and Frank clearly maintain a great deal of sharing regarding the concept lemon. Shown a basket with three ordinary lemons, Deb and Frank can both agree on the number of lemons in the basket, they can discuss whether a piece of fish would taste better spritzed with lemon, and so forth. The only lemony situations in which their communication breaks down come when they are confronted with the azure lemons or if Frank makes a claim like "All lemons are yellow." It certainly seems extreme to abandon all claims that Deb and Frank share the concept lemon in this case.
The blue lemon case gets even worse in intrapersonal situations. Suppose concept identity is determined by fundamental structural identity, referential extent, or both. Frank can't be convinced that the new blue fruits are lemons because that would change both his fundamental representation (removing the requirement that lemons be yellow) and add new objects to the extent. Frank would therefore have a new concept, say lemon'. While this might not seem so bad, all of Frank's old lemony beliefs are about lemons, so he could still claim he was correct in claiming that "all lemons are yellow." He just means something different by "lemon" now.
This problem seems inherent to the learning process. We rarely learn of all of the important features of a concept when we first encounter it. A child might be only familiar with four-door cars, and hence encode that element as part of his concept car1. When people use the word "car," the child's linguistic processing would then bring the concept car1 into his mind. Upon first seeing a two-door sports car, he might ask what it is. After being told it's a "car," he might drop the four-door requirement, forming concept car2, which is henceforth activated by the word "car." If the child then sees a pickup, he might point to it and say "car," only to be told that it's not a "car" but a "truck," since it has a cab and a bed. The child then has a concept car3 which excludes trucks. The child presumably retains all three concepts for at least a while -- he can still think about car1 and car2. When he utters "car," we should presumably take him to mean car3, so can he still talk about his old concepts car1 and car2? In most theories, the lexical concept car1 has a very different fundamental structure than the compositional concept car3s with four doors and different reference too, since it applies to four-doored trucks. However, immediately upon refining car2 into car3, he can correctly apply all of his knowledge about car1s to trucks and car3s with four doors. Furthermore, a year later the child's memories formed while riding in what he believed at the time to be car1s, car2s, and car3s will be linked, suggesting a temporal identity of concepts. We can, of course, still maintain that car1 and car2 are not identical concepts in the same way that we claim that first and second drafts of a book are different, but both are part of a single book's lifetime. This touches on long-standing problems in the nature of identity, and it shouldn't fall to a theory of concepts to resolve them.
The requirement of publicity may not be as restrictive as some people think. One of the motivations for requiring publicity is to allow people to share information, engage in debate about the world, and so forth. But if there's another way to satisfy this ability, concept publicity loses importance.
In communication between computers, the participating machines or programs rarely need to share the same internal structure. All they must do is implement a shared communications protocol. To communicate, a sender converts its internal representation into a format understandable by both parties and sends that message. The receiver then converts the message from the shared format into its own internal representation. The designer of each program is therefore free to encode information in whatever way she sees fit, so long as enough information is retained to allow communication. In principle, researchers could build a simulation of human interaction in which some simulated people's concepts are implemented according to the classical theory and while others were built with prototypes, so long as they had a shared communication protocol. This arrangement maintains referential publicity while discarding almost entirely structural publicity.
By analogy, then, people could posses concepts wildly different in structure so long as they can use language (or some other means, such as body language) to establish a shared symbol system into which concepts can be mapped. This doesn't do away with shared concepts entirely, of course. There must be some concept sharing to establish a communications protocol. In the computer realm, the protocol designers specify what the terms in the protocol mean. This is metapublicity -- the outside interpretation of the protocol is shared, even though the internal representations aren't. In the human realm, we'd need some sort of shared concept to know that saying "cat" and pointing to Garfield indicates that "cat" applies to all cats, not just to orange cats and not to all furry animals. However, with a small set of (possibly innate) public concepts, a large language could be built which allowed for the majority of concepts to differ in structure.
In many scientific and technical disciplines handle conceptual variance by defining key terms. In math logic and theoretical linguistics, the term "language" is defined as a set of symbol strings. Strings inside the set are considered "grammatical" or "in the language" while those not in the set are "ungrammatical" or "outside the language." Based on that definition, scholars can develop new concepts and terms. This technique of bootstrapping allows technical and precise discourse about this concept language, even though most people's internal concepts language' are different. Thus, to discuss formal language, participants need not come to the table with shared concepts. It's sufficient that they can build a satisfactory shared concept. Therefore, a theory need not provide for publicity in the private brain for the majority of cases if it can give an account of how shared concepts can be constructed in a shared medium.
Public meaning can occur even when reference differs. This happens in cases like Frank and the blue lemons above, but more strikingly it occurs in some cases where overlapping reference is essentially nil. Consider the concept beautiful. Unlike the syntactically similar concept red, people vary significantly in the objects and people they classify as beautiful. To shift to a noun-like concept where most concept theorists feel comfortable, the compositional concept beautiful person can be narrowed into the lexical concept hottie. Since the requirements for hottie status vary from person to person, most theorists' first instinct is to say that hottie is a nonpublic concept. We can, however, engage in public discussion about hotties, even though the particulars of each person's version of hottie differ. For instance, someone could claim "There aren't enough hotties in the world," "Most people prefer to have sex with a hottie," and "Hotties get paid more than non-hotties." Despite a lack of public reference, these statements are all understandable. One explanation is to say that we interpret the word "hottie" as referring to those people who fall under the concept hottie for the speaker or the subject of the sentence. But this implies that we have a concept that person's concept hottie. This latter concept might encode, say, the role hottie might play in a theory of people, it might indicate the sorts of features that constitute a definition, it might be a picture of the person's prototypical hottie, and so on. In principle, a sufficiently introspective person could share his concept hottie by giving examples, listing features, and so forth. Each person's concept hottie is thus in principle public, even though not all concepts hottie are identical.
To summarize, the requirement of publicity isn't as strong as one might think. Not all concepts must be public; self-referential concepts, for instance, are not. Concept identity is not required for significant discourse to take place, as shown by the blue lemons case. Actual publicity isn't necessary so long as concepts are potentially public. Not all public concepts must share structure, as illustrated by the communication and technical definition analogy. Not all public concepts must share reference, as demonstrated in the hottie example. So where does this leave the requirement of publicity?
But a theory of concepts must still allow at least some concepts to be shared. If publicity is completely impossible, so is meaningful communication, but people clearly communicate. Even if most publicity is potential, a theorist must hold that some basic concepts are structurally identical or give a very good explanation of how shared concepts are bootstrapped otherwise. A fully-developed theory needs to explain how concepts explained by one person are converted into concepts in another person's mind, though much conceptual progress may be made even if this is left as a black box. Finally, since the conditions in which a concept may be shared are not clear cut, a theory of concepts should be able to determine whether two concepts are shared.