Posts on: Knowledge
Last week, I gave a talk in Manchester at a
(very nice) workshop on "David Lewis and His Place in the History of Analytic
Philosophy". My talk was on "Lewis's empiricism". I've now written it up as a
paper, since it got too long for a blog post.
The paper is really about hyperintensional epistemology. The question is how we
can make sense of the kind of metaphysical enquiry Lewis was engaged in if we
accept his models of knowledge and belief, which leave no room for substantive
investigations into non-contingent matters.
Mostly, when we don't believe something, we don't know it either. But arguably not always. The timid student thinks she's merely guessing, while in fact she knows. She knows, but she lacks the confidence required for belief. It would be nice to have an analysis of knowledge that allowed for such cases, but also explained why they are rare.
Lewis's analysis tries to do that. On Lewis's account, you know p iff your evidence rules out any relevant situation where ~p. Among the rules for what counts as 'relevant', the 'rule of belief' tells us that any possibility with non-negligible subjective probability counts as relevant. Now suppose you don't believe p. Then you give non-negligible probability to ~p situations. So you know p only if your evidence rules out all those ~p situations. Moreover, your present evidence 'rules out' a situation iff you have different evidence in that situation than you actually have. So if you have knowledge without belief, you must assign positive probability to situations where you have different evidence than you actually have. On a suitable understanding of evidence, those cases will be rare, because we are normally confident that we have the evidence that we have.
Here is Lewis's 1996 analysis of knowledge:
S knows proposition P iff P holds in every possibility left uneliminated by S's evidence. ("Elusive Knowledge", p.422 in Papers)
By evidence, Lewis explains, he means perceptual experiences and memories; a possibility W counts as eliminated iff the subject does not have the same evidence in W: "When perceptual experience E (or memory) eliminates a possibility W [...], W is a possibility in which the subject is not having experience E" (424). It follows that everyone trivially knows what perceptual experiences they have: In every possibility W in which I have experience E, I obviously have experience E.
Searching. Mary is in the park, looking for Fred. She recognizes Fred's friend Ted some distance away on the left. Knowing that Fred is often in the park with Ted, she turns that way.
Waiting. Alexandre is waiting for Veronique in a cafe. He's been waiting for several hours now, and is doubtful that Veronique will ever show up. Nevertheless, he thinks it is worth waiting some more.
Mary and Alexandre are acting rationally here, even though Mary does not know that Fred is to the left, and Alexandre does not know that Veronique will ever show up. Even if it turns out that both were wrong, I wouldn't blame them for their decisions.
Lots of interesting stuff came up at the Summer School and the GAP and the A Priori workshop. Here's just two quick notes on something Jason Stanley mentioned in his talk on "Knowledge and Certainty".
Jason argued that knowledge does not entail certainty. He pointed out that in Unger's arguments to the opposite conclusion, "know" is always emphasized, as in:
In July, I tried to show that Williamson's argument against luminosity fails
for states that satisfy a certain infallibility condition. I now think that (for basically the same reason) Williamson's argument fails for any state whatsoever, including knowing something and being such that it's raining outside. (The latter of course isn't luminous, but this is not established by
Williamson's argument.)
Tim Williamson argues that no interesting conditions are such that if they obtain, then one is in a position to know that they obtain. I'll try to show that his argument fails for all conditions for which one can only non-inferentially believe that they obtain if they really do obtain. It seems to me that many interesting conditions -- probably including feeling cold and knowing that one feels cold -- are of this kind. I haven't checked the secondary literature, so what I'm going to say is probably old. Anyway, here goes.
For some reason, I find Moore's refutation of idealism ("here is a hand; therefore there is an external world") much more convincing than his refutation of skepticism ("I know that here is a hand; therefore I know that I am not a brain in a vat".) Why is that?
In both cases, Moore's argument would not convince his opponent who would obviously reject Moore's premise. So that's not the difference. I think the difference also isn't that skepticism is a philosophically stronger position than idealism. Rather, it seems to me that the premise against idealism is much more certain than the anti-skeptical premise. That here is a hand (or at least that there are hands) is about as certain as non-logical truths get, that I know that here is a hand is not. If I were to compile a list of Moorean facts -- of facts that are at least as certain as any philosophical argument against them --, I would include all kinds of facts about material objects, other people, experiences, mathematics and modality, but knowledge claims probably wouldn't make the list.
I once believed that in non-contingent matters, knowledge is true,
justified belief. I guess my reasoning went like this:
How do we come to know, say, metaphysical truths? Not by direct
insight, usually. Nor by simple reflection on meanings, sometimes.
Rather, we evaluate arguments for and against the available
options, and we opt for the least costly position. If that's how
we arrive at a metaphysical belief, the belief is clearly justified
-- we have arguments to back it up. But it may not be knowledge:
it may still be false. Metaphysical arguments are hardly ever
conclusive. But suppose we're lucky and our belief is true. Then it's knowledge: what more could we ask for? Surely not any causal connection to the non-contingent matters.
But now that Antimeta has asked for Gettier cases in mathematics, it seems
to me that there are perfectly clear examples (I've posted a comment over there, but it seems to have gone lost):
Jonathan Schaffer argues (in Analysis 2001) that Relevant Alternatives Theories of knowledge (RATs) such as Lewis's fail because of Missed Clues cases:
Professor A is testing a student, S, on ornithology. Professor A shows S a goldfinch and asks, 'Goldfinch or canary?' Professor A thought this would be an easy first question: goldfinches have black wings while canaries have yellow wings. S sees that the wings are black (this is the clue) but S does not appreciate that black wings indicate a goldfinch (S misses the clue). So S answers, 'I don't know'.
We want to say that S doesn't know that the bird is a goldfinch. Yet it seems that S's evidence rules out all relevant alternatives. For situations with goldfinch-perceptions but no goldfinches are skeptical scenarios and usually regarded as irrelevant.
Sometimes people say that for logical reasons there can be no examples of unknown or unknowable truths. The logical reason is this: to know that p is an unknown truth requires knowing that p is true, which contradicts the requirement of p being unknown.
Before I give examples of unknown and unknowable truths let me give examples of philosophers who died more than 100 years ago: Hume, Leibniz, Kant, and the philosopher first born in the 16th century. One might have thought that it is impossible for physical reasons to give such examples. After all, a philosopher who died more than 100 years ago just isn't there any more, so he can't be given as an example. But not so. In order to give an example of a dead philosopher it suffices to name or describe one; it is not necessary to dig him out.
John Hawthorne has some
nice arguments for the view that knowledge is closed under known
implication. I don't know much about knowledge, but it seems to me that
there is a good reason to believe that at least justification -- and hence
presumably also justified true believe -- is not so closed. The reason
is this:
E is some evidence, H and S are alternative and incompatible hypotheses.
(Obvious examples are skeptical scenarios, like E = visual evidence of
a zebra, H = there is a zebra, S = there is a mule disguised as a zebra.) E
strongly supports H: It raises its probability of truth from about 0.3 to
about 0.9. And H implies Not-S. Yet E does not raise the probability of
Not-S. On the contrary, it raises the probability of S.
Let "S(p)" abbreviate "p is strongly supported by the availble evidence".
The picture shows that
S(p) and S(p -> q) does not imply S(q);
S(p & q) does not imply S(p); (let p=-S, q=H)
S(p) does not imply S(p v q); (let p=H, q=-S).
