Spring 2016, NYU Abu Dhabi

Stroud's Chapter 1

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?

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:

These are called Closure Principles for knowledge. The second closure principle is more plausible than the first.

If you're curious why we say "knowledge is closed...," here's the explanation. In general, we say that a set S is closed under a relation R just in case for every object x which belongs to S, if there's an object y such that x stands in R to y, then y also belongs to S. For example, the set of descendents of Thomas Jefferson is closed under the child relation: for any x who is a descendent of Jefferson, if there's a y that's a child of x, then y is also a descendent of Jefferson. A closure principle about knowledge says that the set of things you know is closed under a relation like logical entailment. That is, for any x in the set of things you know, if there's a y that's logically entailed by x, then y will also be in the set of things you know.

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.

Different Skeptical Hypotheses

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.