It's unsurprising, then, that Lady Mary Shepherd devotes special attention to the subject. Her basic answer is that we do not, in fact, dream of things that we regard as continuous, external, and independent; the dreaming world lacks essential features necessary for something to be the external world, or part of the external world. Objects in the dreaming world are incomplete, and their incompleteness crucially affects what we can conclude about them. The way Shepherd puts this is that they are "not capable of fulfilling their definitions" (EPEU 87). Further, in the waking world we recognize that our judgment in the dream-world was impaired, and that it was not taking into account the full set of relations constituting the thing. For instance, we recognize in the waking world that dream-world bread did not fill or nourish, that injuries did not actually harm, that things acted in ways that were not consistent with their supposed natures. Now, this does not in and of itself capture everything that is needed to handle the problem. But it does show quite clearly that, however it might seem like real bread when we are dreaming, dream-bread is not the same, nor is it bread in the same sense, as the bread of waking life, and we can say this for everything in the dream except our own minds. Even if we assumed that dream-bread continuously and independently existed outside our minds, it is still not real bread. For it to be real, it would have to "fulfill its definition", but it fails to exhibit any qualities of bread beyond the most basic appearances.
Nonetheless, it is important to say yet again that this does not wholly eliminate the dream-world from the realm of the external universe. And one reason for this is that Shepherd is quite clear that part of the reasoning we looked at in the previous posts does apply to the dream-world. The dream-world is full of things that are not really what they seem to be; but this does not mean that it is wholly severed from the external world. In particular, the dream-world, just like the waking world, requires causes independent of our minds. First of all, there are the background causes: there has to be a capability for sensation in general (a mind) and, because differences are introduced into this capability in a dream-state just as much as they are in the waking-state, dreams are in a general way also expressions of the external world. Where the dream-world differs from the waking world is not in its general causes but in the particular causes of the particular objects in it. We establish that particular objects continually and independently exist outside our minds by irregularly calling upon them with the senses and discovering that they are regularly ready to appear; this readiness to appear is an effect that needs explanation by an adequate cause, namely, one that continually and independently exists outside the mind. With dreams, some of the same arguments show that there must be some causes of the sensible qualities in our dreams that are independent of the mind (understood, again, as the capability for sensation in general). And the same is true for externality:
Nay, the real, plain, matter of fact is, that objects external to mind are needed even for illusory ideas for all ideas whatever, and their causes, are external to, (i.e., not included in,) any particular given state of sensation and its cause. (EPEU 98)
The crucial difference between the dream-world and the waking world, then, is that in the waking world we can conclude that the causes of our perceptions continue to exist even when unperceived, whereas we cannot do so for the dream-world. In dreams we do not get the same readiness to appear in response to irregular calls of the senses, and therefore cannot conclude that there is anything ready to appear. One thinks of the well-known phenomenon that in dreams things that are complicated (writing, faces) can look different every time you look at them. On the basis of this we can recognize them as illusory. When we talk about 'bread' we mean something that on irregular calls of the senses returns such-and-such effects regularly. But what seems like bread in a dream does not do this, and is shown therefore to be something different from what 'bread' means. It does not fulfill its definition, and thus is not real bread.
More than that, in dreams we generally don't have proper calls of the senses at all. In waking life we actually use our sensory organs, and, as we have seen, the use of those sensory organs is a crucial part of our sense of the world around us. But it is rare if at all that we have the sense of using our sensory organs in dreams. What we are generally getting in dreams is a collection of sensible qualities that would, in waking life, require the use of the sense organs to get; but in dreams we get them without anything clearly identifiable as the use of those organs. We see things without the concomitant sensations connected with using your eyeballs; we hear things without the directional differences involved in using our ears; we move (remember that Shepherd treats motion as a sort of sixth sense) without clear use of legs, arms, and so forth. Even when we have something like the sensation of using our sensory organs in dreams, it does not have the coherence and order that such use does in waking life, and therefore cannot be given the same explanation.
The appearance of close similarity between dreaming and waking experience is due almost entirely to the fact that, when we have incomplete information about an object, we cannot be certain of what to expect. If all we have of a thing is its superficial sensible qualities, it may well surprise us. The causal reasoning remains the same, and it remains as rigorous. but because we start with only partial information, we can only get partial or merely probable conclusions. Objects in dreams have all the same "present qualities" as objects in waking life. But they fail to meet the test of active observation the way waking-world objects do, and while our information can be as defective in the waking-world case (optical illusions, for instance), this occurs within a framework of objects that meet the test and show themselves ready to appear. That is, we can and do have illusions in the waking world, but they occur within the framework of a continually existing external world independent of us. In the dream-world we lack the basis to get this complete framework up and running; we can conclude that there is some kind of cause, external to and independent of the mind, affecting us, but we can't get its continual existence. The lack of such continually existing causes associated with our objects is associated with the fact that the dream-world seems massively less coherent than the waking world.
Shepherd herself admits that dreams are a difficult case, and is more tentative about her answers here than elsewhere. This is not, I think, so much because she has doubts about her arguments as that they get a fairly weak conclusion: they do not guarantee, for instance, that there is no dream-world continually existing on its own external to and independent of us. Rather, they simply show that, given common behavior of dreams, we are not able to draw this conclusion, and that even if we did we could not conflate dream-objects with the objects of waking life, however similar they seemed, because they do not exhibit the same order. This is weaker than what one might expect; one might want to have a proof that the dream-world is not a real world. But this would be a tall order. On Shepherd's account even in waking life we do not have direct experience of objects except insofar as they cause effects on us in experience and we are used to taking those effects as signs of their causes. But no adequate account of dreams can avoid saying that there are causes for our experiences in dreams, and thus that in dreaming we really are experiencing something outside our minds, understood as the capability for sensory experience in general. Even in dreams we are in, and are affected by, a world outside our minds. The only difference is how much dream-experiences, as opposed to waking-experiences, tell us about that world.
I think I will have one more post in this series, on some further applications and implications of Shepherd's account of our perception of the external universe.