I'm a dispositionalist. By this I mean that to believe some particular proposition, such as that your daughter is at school, is nothing more or less than to be disposed toward certain patterns of behavior, conscious experience, and cognition, under a range of hypothetical conditions -- for example, to be disposed to go to your daughter's school if you decide you want to meet her, to be disposed to feel surprise should you head home for lunch and find her waiting there, and to be disposed, if the question arises, to infer that her favorite backpack is also probably at the school (since she usually takes it with her). All of these dispositions hold only "ceteris paribus" or "all else being equal" and one needn't have all of them to count as believing. (For more details about my version of dispositionalism in particular, see here.) Crucial to the dispositionalist approach (but not unique to it) is the idea that the implementational details don't matter -- or rather, they matter only derivatively. It doesn't matter if you've got a connectionist net in your head, or representations in the language of thought, or a billion little homonuculi whispering in thieves' cant, or an immaterial soul. As long as you have the right clusters of behavioral, experiential, and cognitive dispositions, robustly, across a suitably broad range of hypothetical circumstances, you believe.
On a representationalist view, implementation does matter. On a suitably modest view of what a "representation" is (I like Dretske's account), the human mind uses representations. For example, it's very plausible that neural activity in primary visual cortex is representational, if representations are states of a system that function to track or convey information about something else. (In primary visual cortex, patterns of excitation in groups of neurons function to indicate geometrical features in various parts of the visual field.) The representationalist about belief commits to a general picture of the mind as a manipulator of representations, and then characterizes believing as a matter of having the right sort of representations (e.g., one with the content "my daughter it school") stored or activated in the right type of functional role in the mind (for example, stored in memory and poised (if all goes well) to be activated in cognitive processing when you are asked, "where is your daughter now?").
I interpreted some of the pushback from Block, Mandelbaum, and their students as follows: "Look, the best cognitive science employs a representational model of the mind. So representations are real. Even you don't deny that. So if you want a truly scientific model of the mind instead of some vague dispositionalism that looks only at the effects or manifestations of real cognitive states, you should be a representationalist."
How is a dispositionalist to reply to this concern? I have three broad responses.
The Implementational Response. The most concessive response (short of saying, "oops, you're right!") is to deny that there is any serious conflict between the two positions by allowing that the way one gets to have the dispositional profile constitutive of belief might be by manipulating representations in just the manner that the representationalist supposes. The views can be happily married! You don't get to have the dispositional profile of a believer unless you already have right sort of representational architecture underneath; and once you have the right sort of representational architecture underneath, you thereby acquire the relevant dispositional profile. The views only diverge in marginal or hypothetical cases where representational architecture and dispositional profile come apart -- but maybe those cases don't matter too much.
However, I think that answer is too concessive, for a couple of reasons.
The Messiness Response. Here's a too-simple hypothetical representationalist architecture for belief. To believe that P (e.g., that my daughter is at school today) is to just to have a representation with the content P ("my daughter is at school today") stored somewhere in the mind, ready to be activated when it becomes relevant whether P is the case (e.g., I'm asked "where is your daughter now?"). One problem with this view is the problem of specifying the exact content. I believe that the my daughter is at school today. I also believe that my daughter is at JFK Elementary today. I also believe that my daughter is at JFK Elementary now. I also believe that Kate is at JFK Elementary now. I also believe that Kate is in Ms. Salinas' class today. This list could obviously be expanded considerably. Do I literally have all of these representations stored separately? Or is there only one representation stored, from which the others are swiftly derivable? If so, which one? How could we know? This puzzle invites us to reject the simplistic picture that believing P is a matter of having a stored representation with exactly the content P. But once we make this move, we open ourselves up to a certain kind of implementational messiness -- which is plausible anyway. As we have seen in the two best-developed areas of cognitive science -- the cognitive science of memory and the cognitive science of vision -- the underlying architectural stories tend to be highly complex and tend not to map neatly onto our folk psychological categories. Furthermore, viewed from an appropriately broad temporal perspective, scientific fashions come and go: We have this many memory systems, no we have this many; early visual processing is not much influenced by later processing, wait yes it is influenced, wait no it's not after all. Dynamical systems, connectionist networks, patterns of looping activation can all be understood in terms of language-like representations, or no they can't, or maybe map-like representations or sensorimotor representations are better. Given the messiness and uncertainty of cognitive science, it is premature to commit to a thoroughly representationalist picture. Maybe someday we'll have all this figured out well enough so that we can say "this architectural structure, this one, is what you have if you believe that your daughter is at school, we found it!" That would be exciting! That day, I abandon dispositionalism. Until then, I prefer to think of belief dispositionally rather than relying upon any particular architectural story, even as general an architectural story as representationalism.
The What-We-Care-About Response. Why, as philosophers, do we want an account of belief? Presumably, it's because we care about predicting and explaining our behavior and our patterns of experience. So let's suppose as much divergence as it's reasonable to suppose between patterns of experience and behavior and patterns of internal architecture. Maybe we discover an alien species that has outward behavior and inner experiences virtually identical to our own but implemented very differently in the underlying architecture. Or maybe we can imagine a human being whose actions and experiences, not only in her actual circumstances but also in a wide range of hypothetical circumstances, are just like that of someone who believes that P, but who lacks the usual underlying architecture. On an architecture-driven account, it seems that we have to deny that these aliens or this person believes what they seem to believe; on a dispositional account, we get to say that they do believe what they seem to believe. The latter seems preferable: If what we care about in an account of belief is patterns of behavior and experience, then it makes sense to build an account of belief that prioritizes those patterns of behavior and experience as the primary thing, and treats purely architectural considerations as secondary.
Some related posts and papers:
A Phenomenal, Dispositional Account of Belief (Nous 2002).
Belief (Stanford Encyclopedia of Philosophy, 2006 revised 2015).
Mad Belief? (blog post, Nov. 5, 2008).
A Dispositional Approach to Attitudes: Thinking Outside of the Belief Box (in Nottelmann, ed., New Essays on Belief, 2013).
Against Intellectualism About Belief (blog post, July 31, 2015)
The Pragmatic Metaphysics of Belief (essay in draft, October 2016).