Matter and the Limits of Skepticism
The skeptic questions whether we know the external world exists, purporting to provide a proof that we don’t know that it does. The proof takes the form of describing a possible alternative to what we normally assume. Thus it is suggested that a deceiving demon is a possibility, or that we might be dreaming, or that we might be a brain in a vat. Since these are real logical possibilities that we can’t rule out, we must conclude that we don’t know that the world is as we normally take it to be. For instance, I don’t now know that I am sitting at a desk looking at a tree. It might all be one vast illusion or hallucination. It is important to this argument that the skeptical alternative be a real possibility, which must be accepted as such, or else we could simply reply that no such thing is possible, so there is nothing we need to rule out in order to know what we think we know. If the skeptic suggests something impossible, or not clearly possible, his argument is toothless; and the usual suggestions satisfy this condition, since they do describe real logical possibilities, often rooted in familiar facts (people can and do deceive us, we do dream, and we do suffer illusions and hallucinations).
But what about our belief that matter exists? This is not the belief that the external world exists as we customarily think of it, but just the belief that matter of some sort exists. If I am a brain in a vat, then what I take to be the external world is all illusion, but matter still exists in the form of vats and brains. If I am in bed dreaming, then my material bed and body exist even if what I dream about doesn’t. The evil demon can be as material as you like and still deceive me. So the question of matter is very different from the question of the external world as normally conceived. Is it possible to be a skeptic about the existence of matter? Can the skeptic show that we don’t know that matter exists? Can he give a proof of this analogous to his proof that we don’t know the external world exists? Clearly he can’t do this by suggesting his usual logical possibilities, since these all presuppose the existence of matter, so they are not alternatives in which there is no matter. He needs a real possible world in which mind exists but there is no matter of any kind, in order to provide such a proof. He needs to provide a logical possibility that we can’t rule out.
This is a much more difficult thing to do than the usual exercises in skepticism, because there is nothing familiar he can rely on—no actual cases in which we have mind without matter (as there are actual cases of sense impressions without external objects of perception). What has to be claimed is that it is possible to have disembodied minds in a wholly non-material world. And the problem is that this is not clearly possible and may well be quite impossible, so the skeptic has not discharged his obligation to produce a genuinely possible alternative to what we normally take for granted. We do not therefore need to listen to his argument; he has no argument against our belief that our minds exist in a world of matter. Nothing he has to say proves that we don’t know what we take ourselves to know. So this belief about the world beyond the mind is not vulnerable to skeptical challenge of the standard (distressingly convincing) kind.
To clarify the point, let’s consider two other types of skepticism regarding the non-mental world, concerning time and space. Suppose the skeptic says that we don’t know that time exists: we have impressions of time, but there may be no objective time corresponding to these impressions. This, he contends, is a real possibility—that minds can exist without time existing. We would be within our rights to reply that this is not a real possibility: minds exist in time and must do so. For minds change and change requires time—our consciousness consists of temporally successive states. So the skeptic has not provided an indisputable logical possibility that is an alternative to the way we normally takes things to be; at best he has suggested a highly questionable metaphysical theory, namely that minds can exist without time existing. He has certainly not proved that this is a possibility. So he has not undermined our claim to know that time exists by pointing to a logically possible alternative in which we have the same impressions of time but there is no time.
Now consider space: the skeptic claims again that we don’t know that space exists, despite our impressions of space. The reason is that it is logically possible for minds to exist without space, and we can’t rule out the possibility that our minds are like that. But again, we can reply that it is not logically possible to have minds without space—minds necessarily exist in a world of space. Certainly the skeptic has not proved that his supposed alternative is logically possible.  We might argue against him that minds cannot be individuated without space, since space provides the indispensable basis for establishing the numerical distinctness of minds—your mind is not identical to my mind because our minds are in different places. The skeptic might engage in a metaphysical argument with us about this, but he has certainly not suggested an indisputable possibility that we are obliged to accept. So we are not in the same epistemic predicament with respect to our belief in space that we are in with respect to our belief in the external world (as distinct from the world of matter). We are not vulnerable to skeptical doubt in the same way, viz. by exhibiting a clear logical possibility that our evidence fails to rule out.
Similarly with respect to matter: if the skeptic says that there could be minds without matter, we can reply that we don’t agree with that, since minds require brains. These brains may not be as we normally conceive of them, but there has to be some material basis for minds—they cannot be purely immaterial. The skeptic may engage us in metaphysical argument at this point, but what he can’t do is point out that we ourselves accept his alleged possibility as a real possibility—as we do for the brain in a vat possibility. Whether we can prove that mind requires matter is not to the point; the question is whether he can prove that minds can exist without matter. For that is the possibility he needs if he is to show that we don’t know that matter exists. He needs a certain metaphysical possibility to undermine our confidence in what we ordinarily believe, but it is not clear that he has one—or rather, it is clear that he does not have one. So there is a significant asymmetry between this type of belief and the type of belief the usual skeptic questions. The usual skepticism does not then generalize to these further beliefs—in time, space, and matter. Our claim to know of the existence of these things has not been undermined, even granted that our claim to know the existence and nature of the external world has been undermined. 
It may be thought that this is a disappointing result, since we have made no inroads against the skeptic on his favorite territory: for all I have said, we still don’t know we are not dreaming, not a brain in a vat, and not the victim of a deceiving demon. But this is too pessimistic (or perhaps I should say too optimistic) because we have established a definite limit to the corrosive power of skepticism: there are beliefs about the non-mental world that are immune to skeptical challenge (at least of the usual kind). For all that the skeptic has said, we do have knowledge concerning the world beyond the mind—he has said nothing to undermine our confident belief in objective time, space, and matter. His skepticism is thus confined to a certain subset of beliefs about objective reality. I count this a strong anti-skeptical result, even if it falls short of what we might ideally hope for.
 The skeptic can point out that we know of cases in which a sense impression has no corresponding object and then ask how we know this is not always the case, but he cannot likewise point to cases of minds without time, space, and matter and ask how we know our minds are not in this position. There are no such actual cases to point to.
 That is, our belief that we sense external objects and are not subject to massive illusion: this belief isundermined by the skeptic. But he has not undermined our more general belief in things outside the mind.