Annette: "And the only cases of representation we should recognize are when someone can compare the representation with the represented, to see how well it represents."

Nicely put.  I was making a similar point a couple of posts back when I noted that a real bowl of flowers is different from an image of a bowl of flowers and the mental image of a bowl of flowers is more like a "sprite" and not really like an image.

On Hume's implied problem of whether or not we can extrapolate from the state of signals to the physical state of the sources of these signals, obviously we can. Thats what we do all the time and it is the entire project of science.   So we can indeed know the relationships between the states of things but we cannot be the substance of things that are not our minds.

Even when I am dreaming my mind is a small part of the world, albeit in my brain, how could I doubt this or the possibility that this small part might be derived from and connected by signals to the whole?

Incidently, does anyone know how philosophers have got into such a mess when defining "physicalism"?  As a scientist I study the relations between states (forms), scientific physicalism is simply the observation that these states are interrelated.  On this definition the "mind" is the most pre-eminently physical geometric form that exists because it contains our observation, the "top level" of states that we interrelate.