On p. 14, Stroud distinguishes three questions.
Q1. If you are dreaming that P, does it follow that you don't know that P? (Compare step 1 in our earlier formulation of the skeptic's argument.)
Stroud argues that this does follow. Or, more cautiously, if you're dreaming that P, it follows that you don't thereby know that P. Perhaps while you're dreaming you still know things like "Dogs bark," because those are things you learned when you were awake, and you haven't forgotten them. But, Stroud says, if you dream that things are a certain way in your environment, that can't be the way you first acquired knowledge that things are that way.
Q2. If you're to know something about the external world on the basis of perception, is it required that you also know you're not dreaming?
Stroud devotes most of his attention to this question (pp. 23-31); we will take up his discussion in just a moment.
Q3. Can you know that you're not dreaming?
Some philosophers believe that it is just obvious that you can't know you're not dreaming. Robert Nozick wrote:
The skeptic asserts that we do not know his possibilities don't obtain, and he is right. Attempts to avoid skepticism by claiming we do know these things are bound to fail. The skeptic's possibilities make us uneasy because, as we deeply realize, we do not know they don't obtain; it is not surprising that attempts to show we do know these things leave us suspicious, strike us even as bad faith. (Philosophical Explanations, p. 201)
Other philosophers say that you can't know you're not dreaming because it'd be possible to have the experiences you have and yet be dreaming. In other words, your experiences don't guarantee that you're not dreaming.
We've already noted that some philosophers are fallibilists about knowledge. Those philosophers think that it's possible to know that P even if your evidence doesn't guarantee that P is true.
What Stroud says here is a bit more complicated. He talks about what he calls a "straightforward response" to the skeptic (pp. 18-23). This response accepts (i) that knowing things about the external world requires you to know you're not dreaming, but it says (ii) that you can know you're not dreaming. Stroud argues that this straightforward response fails. At this point in his discussion, he doesn't want to come flat out and say that you can't know you're not dreaming. But he thinks that if you accept (i), then you have to say you can't know you're not dreaming. In other words:
If Descartes is right that:
Knowing you're not dreaming is a requirement for knowing anything about the external world
Then Descartes is also right that:
We can never know we're not dreaming.
See Stroud's argument for this on pp. 20-23.
Hence, Stroud thinks if we want to resist Descartes' argument, a better strategy would be to argue that Descartes is wrong to say that:
Knowing you're not dreaming is a requirement for knowing anything about the external world.
In the end, Stroud will say that Descartes is right about that claim, too. But he thinks that matters are much trickier there, and it takes more argument.
Some philosophers say you can know you're not dreaming, on the following grounds: the best explanation of your having the experiences you do is that there's an external world which you're perceiving. That fact gives you good reason to believe that you're not dreaming. (Naturally, anyone who adopts this response to the skeptic owes us an account of why the hypothesis of an external world is the best explanation of your experiences. We will discuss these issues in later classes.)
Other philosophers argue that you can know you're not dreaming like this: "Of course I can know I'm not dreaming! I know on the basis of perception that I'm not in bed, I'm standing up, and so on, and from that I can conclude that I'm not dreaming." The skeptic, of course, will say that this begs the question.
Let's set aside the question whether you can know you're not dreaming, and turn to the question whether knowing things about the external world requires you to know you're not dreaming.
Is it really true that you have to rule out the possibility that you're dreaming, if you're to know anything on the basis of perception? This is Stroud's Q2. He discusses it on pp. 23-31.
Stroud tries to persuade us that we do have to rule that possibility out. He thinks that the standards we rely on when making knowledge-claims in ordinary life include this requirement. In all sorts of ordinary situations, Stroud says, we think:
We can't know P unless we've ruled out the possibilities we recognize to be incompatible with P.
The following principles play a large role in contemporary discussions of skepticism:
When a philosopher says that "knowledge is closed under logical entailment," that means that if you know that P, and P logically entails that Q, then you know Q too. (Well, perhaps you won't believe Q; but at least you'll be in a position to know Q.)
When a philosopher says that "knowledge is closed under known logical entailment," that means that if you know that P, and you know that P logically entails that Q, then you know Q too (or at least, you'll be in a position to know Q).
These are called Closure Principles for knowledge. The second closure principle is more plausible than the first.
Stroud argues that in ordinary life, we do usually treat knowledge as being closed under known logical entailment. If there's some possibility D we know to be incompatible with P, then we do ordinarily expect someone to be able to rule D out, if he's to know that P.
At this point a complication arises.
If the skeptic's hypothesis is "You're dreaming," this hypothesis is not logically incompatible with most of the propositions you purport to know on the basis of perception. You might purport to know that you're sitting in a theater, and really be in a theater, even though you're dreaming. So dreaming isn't an alternative to your sitting in a theater. At best, it's just an alternative to your knowing that you're sitting in a theater. It undercuts your ability to know that. As Stroud argues, if you're dreaming that P, you can't thereby know that P.
Let's call skeptical hypotheses of this sort "alternatives-to-your-knowing."
Other skeptical hypotheses are alternatives both to what you purport to know and to your knowing it. For instance, consider the hypothesis that you're a brain in a vat. This is incompatible with your sitting in a theater. (Brains in vats can't sit.) So it's also incompatible with your knowing that you're sitting in a theater. (Remember, knowing that p requires that p be true. So anything which is incompatible with p is also incompatible with your knowing that p.) Call alternatives of this sort "simple alternatives."
If we're dealing with a skeptical hypothesis like dreaming, which is not a simple alternative to what we purport to know, then we can't just rely on Closure Principles to show that we need to rule that skeptical hypothesis out. Closure Principles only tell us that, if we're to know that P, we have to rule out the things we know to be logically incompatible with P. Dreaming that P is not logically incompatible with P. As we said, it is possible to dream you are sitting in a theater, and at the same time to be sitting in a theater.
So if we're dealing with skeptical hypothesis like dreaming, we need to appeal to a stronger principle. Consider the following:
Stroud's Principle. If you know that P, and you recognize that Q is incompatible with your knowing that P, then you have to know not-Q (or at least, you have to be in a position to know not-Q).
Stroud appeals to this principle at several places in his discussion (see esp. pp. 24 and 29). He doesn't give it any special name; "Stroud's Principle" is my name for it, not his.
Stroud's Principle is equivalent to the claim that knowledge is closed under known logical entailment, combined with the claim that if you know something, then you know that you know it. This latter claim is called the KK Principle. The KK Principle is very controversial. We will come back to it later in the term.
Stroud thinks that Stroud's Principle is true, and that we implicitly rely on it in the way we make and assess ordinary knowledge-claims. He calls it a "familiar commonplace" about knowledge; and he argues that insofar as we find Descartes' reasoning at all plausible, it's because something like Stroud's Principle strikes us as very compelling.