Apropos Williamson. The following question came up last year when
we discussed The Philosophy of Philosophy in Canberra. I
thought it had a sensible answer that we just couldn't figure out, but
then Dorothy Edgington raised the same question at the recent
phloxshop workshop in Berlin, and even though there were quite a few
Williamsonians present, there was no agreement on what the answer is,
and the proposals didn't sound very convincing.
The question is simply how, on Williamson's account, we can have
knowledge of substantial metaphysical necessities, e.g. of the fact
that gold necessarily has atomic number 79. Williamson explains that
when we counterfactually imagine gold having atomic number 78 (knowing
that it has number 79), we will "generate a contradiction", because we
hold "such constitutive facts [as atomic number] fixed" (p.164). But
the distinction between constitutive and not-constitutive facts can
hardly be analysed as the distinction between whatever we happen to
hold fixed and the rest, given Williamson's commitment to strong
mind-independence of metaphysical modality. So what justifies our
holding fixed the atomic number?
Suppose we want to follow Frege and distinguish an expression's
denotation from its sense. Suppose also we take the
denotation of a predicate to be its extension: the set of its instances. The following argument
appears to show that this leads to trouble.
- All humans are featherless bipeds, and all featherless bipeds are
human, but there could have been featherless bipeds that are not
human. In short, (Ax)(Hx <-> FBx) & <> (Ex)(~Hx & FBx)).
- By existential generalisation over the predicate positions, it
follows that (EX)(EY)((Ax)(Xx <-> Yx) & <> (Ex)(~Xx &
Yx)).
- If things in predicate position denote sets of individuals, this
can be read as: there is a set X and a set Y such that X and Y have
the same members and it is possible for something to be a member of Y
and not of X.
- But if X and Y have the same members, then they are identical; and then
nothing could belong to "one of them" without also belonging to "the
other".
- Hence things in predicate position do not denote sets of
individuals.
The argument is modeled on a brief passage (p.13) in Tim
Williamson's latest
paper on the Barcan Formula. Williamson there argues against the
plural interpretation of second-order quantifiers. On this
interpretation, the sentence in (2) can be read as "there are things
xx and things yy such that all xx's are yy's and all yy's are xx's and
it is possible for something to be one of the yy's but not of the
xx's". Williamson objects that if the xx's just are the yy's,
then it is not possible for something to belong to "the ones" without
also belonging to "the others".
Okay. Here are some thoughts on a talk Frank Jackson gave last week on Williamson on thought experiments.
The question is what Gettier discovered in his famous article. According to Frank, he revealed a fact about our concept 'knowledge': that it is not the same as our concept of justified true belief. According to Williamson, Gettier has revealed a fact about knowledge itself: that it is not justified true belief. A discovery merely about our concepts, Williamson says, "would show little of philosophical interest"; it would be "of significance primarily to theorists of concepts, not to epistemologists". For "the primary concern of epistemology is with the nature of knowledge, not with the nature of our concept of knowledge". (All of these are from p.206 of The Philosophy of Philosophy.) Frank disagrees. He thinks that results about the key concepts of a discipline are quite important to that discipline.
Carrie, Joe and Brit have recently commented on Williamson's proposal that modal knowledge is based on counterfactual knowledge. I share their suspicion, partly for the reasons Carrie mentions: the mere fact that statements about necessity and possibility are equivalent to counterfactuals doesn't tell us that the route to knowing the former proceeds via the latter. In fact, the assumption that we have a special cognitive faculty for knowing counterfactuals already seems odd to me. After all, we don't have special faculties for knowing indicatives or negations or conjunctions.
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.
Some people intuit that
- the subject in a Gettier case has knowledge;
- Saul Kripke has his parents essentially;
- "Necessarily, P and Q" entails "Necessarily, P";
- whenever all Fs are Gs and all Gs are Fs, the set of Fs equals the
set of Gs;
- the liar sentence is both true and not true;
- the conditional probability P(A|B) is the probability of the
conditional "if B then A";
- it is rational to open only one box in Newcomb's problem;
- switching the door makes no difference in the
Monty Hall problem;
- propositions are not classes;
- people are not swarms of little particles;
- a closed box containing a duck weighs less when the duck inside
the box flies;
- spacetime is Euclidean;
- there is a God constantly interfering with our world.
They are wrong. All that is false.