Friday, August 31, 2007
So this is the new year.....
I always find Summer the toughest time to keep the blog going. I know a lot of bloggers who just go on hiatus, but I've tried to avoid that when possible - it makes it all the harder to build up any momentum. On the other hand, hardly anyone reads what you write over summer, and there's always other things one could be doing than writing posts noone will read. Anyways, I'm going to endeavor to post much more now term's underway, starting with my twin posts on knowability earlier this week.
On a different topic, I'm intrigued by this new OUP collection of philosophers discussing atheism. There are some names which will already be familiar to readers of this blog, but mostly for other reasons: my teacher at St Andrews, Stewart Shapiro, contributes the opening piece, and Jamie Tappenden, Ken Taylor, Simon Blackburn and David Lewis show up, amongst others. (HT: Logic Matters)
Stewart also seems to have a new paper coming out with William Taschek in JPHIL called 'Cognitive Command and Excluded Middle', which sounds right up my street. Sadly, there doesn't seem to be an online version up anywhere.
Monday, August 27, 2007
Knowability and Actuality
KP: P only if it is possible that P is known.
They've understood this principle such that it's constrained by the actual distribution of truth-values; the actual distribution of truth-values over statements determines what is knowable. Why?
In my post, I took it to be because otherwise knowability isn't nearly demanding enough. Suppose that P is false. Still, P might be knowable in the sense that there is some world in which P is knowable - it might only have to be a world in which P is true. But the anti-realist was looking for a more substantial sense of knowability, one according to which falsehoods are not knowable. So anti-realists understand knowability in such a manner so as P is knowable if and only if P.
In the Analysis note I discussed in the previous post, Jesper Kallestrup clearly sees things quite differently. He writes:
'It would be too easy to refute anti-realism if [KP] failed in cases where P is actually true, but not known in worlds in which P is false.'
The suggestion is that having what's knowable determined by the actual distribution of truth-values blocks putative counterexamples to KP. But I'm not seeing how the point is supposed to go. Suppose that P is actually true, but not known in worlds in which P is false. I'm not seeing any danger from such cases, though they refute the following thesis:
KP!!: P only if it is necessary that P is known.
Since KP doesn't require that P is known in all possible worlds, it's not clear to me how the observation that P is not knowable in worlds in which P is false is meant to provide the material for an even prima facie counterexample to KP. So it's quite unclear to me how consideration of such cases could motivate adopting the thesis that what is knowable is fixed by the actual distribution of truth-values. Unless I'm missing something, I think the motivation has to stem from the worry about diluting the notion of knowability too much.
(Andreas blogged about related issues a while back).
Knowability and Dialetheism
S: No omniscient being knows that which the sentence S expresses.
S is clearly self-referential, but it doesn't trip itself up; it's simply true if there aren't any omniscient beings. Now, suppose that ~S, i.e.,
1. Some omniscient being knows that which S expresses.
Then, given what S expresses,
2. Some omniscient being knows that no omniscient being knows that which the sentence S expresses.
But then by the factivity of knowledge,
3. No omniscient being knows that which the sentence S expresses.
But that's just S. So S is true.
Now suppose that X is an omniscient being. Then X knows all, including what we've just shown, namely (3). So,
4. X knows that no omniscient being knows that which the sentence S expresses,
which, given what S expresses, yields,
5. X knows that which S expresses.
But X is omniscient. So,
6. Some omniscient being knows that which S expresses.
But (6) is just ~S. So, on the assumption that an omniscient being exists, S & ~S.
Milne leaves the reader to draw their own conclusions from his proof. Jesper Kallestrup has picked up the baton, and adapted Milne's proof to show that the knowability principle (KP) entails a contradiction. Again, rather than treating this as a reductio, we might accept that the contradiction is true. A final application of (KP) yields that this contradiction is knowable. Anti-realists are committed to dialetheism.
It can hardly have escaped the attention of readers of this blog that I'm more sympathetic than most to anti-realism, and (unlike Jon Cogburn), I'm not in the market for the conclusion that it entails committment to dialetheism. There's a lot that might be said in order to dodge this conclusion. Jesper notes that so-called restriction strategies that have been offered by Dummett and Tennant in response to the knowability paradox also work here, but he points out they are associated with a whole bunch of problems. Crispin Wright's endorsement of KP as a local thesis also blocks Jesper's reasoning, which requires an assumption that KP holds globally.
Here I just want to suggest that there's a further restriction to KP the anti-realist can make, one that's independently motivated and yet which blocks the proof. Let's begin by examining Jesper's argument that KP entails a contradiction.
Consider the following variant of S:
S*: Nobody possibly knows that which the sentence S expresses.
Again, this is self-referential but does not simply implode. But now suppose that we adopt the following:
KP: P expresses a truth only if it is possible that somebody knows that P expresses a truth.
Actuality Assumption (AA): It is possible that somebody knows that P expresses a truth only if there is some actual person who, perhaps which finite extensions to her capacities, possibly knows that P expresses a truth.
Factivity Assumption (FA): It is possible that somebody knows that P expresses a truth only if P expresses a truth.
AA and FA are usually taken as being part of a package with KP (though, always the exception, Jon Cogburn seems to reject FA here, p238).
Now, suppose the following:
1. That which S* expresses is true.
Then by KP we have,
2. It is possible that somebody knows that which S* expresses.
By AA, we get,
3. Somebody possibly knows that which S* expresses.
But (3) is simply ~S*.
4. That which S* expresses is false.
Then, by the contrapositive of FA, we arrive at,
5. It is not possible that somebody knows that which S* expresses.
Hence by AA,
6. Nobody possibly knows that which S* expresses.
But this is just S*! So, given KP, AA, and FA (the standard anti-realist package), we get ((S* -> ~S*) & (~S* -> S*)), which intuitionistically yields (~S* & ~~S*), and classically (~S* & S*). Hence the standard package entails a contradiction.
I think the main issue here is how to understand the constraint on KP that FA imposes. We don't want KP to be trivially true or false; surely every party in this debate wants to be affirming a doctrine with some substance. But there's some trickiness here: adopting FA is meant to block trivializing KP by allowing it to be satisfied in cases where P is false in @ and yet it is possible to know that P since there is a world w such that w is not @, and P expresses a truth and thus something knowable in w. The motivating idea behind FA is that KP is supposed to be constrained by the distribution of truth-values at the actual world, since otherwise even falsehoods are knowable - not the interpretation of knowability the anti-realist wants.
Unfortunately, adopting FA threatens to make KP come out trivially false. KP is supposed to be a necessary truth by the anti-realist's lights. So it's supposed to be impossible that P express a truth and yet it be impossible for some suitably pimped-out subject to come to know that P expresses a truth. But now suppose that it happens not to be known that Q expresses a truth, even though it in fact does. Given the requirement that we've attempted to capture in FA, that KP be sensitive to the actual distribution of truth-values, the question is whether it's possible that someone might come to know that Q expresses a truth, given the actual distribution of truth-values. But this obviously isn't possible, since the actual distribution of truth-values determines that nobody knows that Q expresses a truth. So, contrary to KP taken as a necessary truth, it is possible that Q express a truth and yet it be impossible that a suitably pimped-out subject to come to know that Q expresses a truth. That's a possibility just because of the simple fact that sometimes truths aren't in fact known by any subject in the actual world. (This line of thought is Sven Rosenkranz's, from p354 of his 2003).
So the anti-realist has a balancing act to do. (S)he wants to hold on to the thought that P expresses a truth if and only if it is possible that somebody knows that P expresses a truth. The right-to-left direction of this is AA, and it constrains the notion of knowability so that what is knowable is determined by the actual distribution of truth-values. But if we allow that what is knowable is determined by the actual distribution of truth-values over sentences expressing our current state of ignorance (or knowledge), we're in trouble, for then KP is clearly false. That was the upshot of Sven's argument. A principled way of avoiding this difficulty is needed, and Sven offers a proposal in his paper.
This has all been pretty torturous, but I've still to show how this all might bear on Kallestrup's proof. We need to look again at the move from line (4) to line (5):
4. That which S* expresses is false.
Then, by the contrapositive of FA, we arrive at,
5. It is not possible that somebody knows that which S* expresses.
But S* is clearly a sentence expressing something about our current state of ignorance, and we resolved, in the light of Sven's point, to understand KP and FA in such a way that the truth-values of such sentences did not go towards determining what is knowable (for example, Sven's suggestion may be put (I hope!) as follows: KP and FA only hold when the truth-value of P isn't alterable by any (perhaps idealized) subject). My suggestion, then, is that once we take Sven's point seriously, and change our understanding of KP and FA accordingly, the move from (4) to (5) will be invalidated. So the upshot, if I'm right, is that an already necessary restriction on the standard anti-realist package serves to invalid Kallestrup's proof of a contradiction.
Homework: What's the bearing of this, if any, on the knowability paradox?
Kallestrup, J. 2007. If omniscient beings are dialetheists, then so are anti-realists. Analysis 67: 252-4.
Milne, P. 2007. Omniscient beings are dialetheists. Analysis 67: 250-1.
Rosenkranz, S. 2003. Realism and Understanding. Erkenntnis 58: 353-78.
Thursday, August 23, 2007
Stanley's Knowledge and Practical Interests
Hat-tips: Kvanvig and Leiter.
Labels: Jason Stanley
Friday, August 17, 2007
Bleg: Epistemic Closure and Testimony
(There are, of course, a number of general discussions of closure, and of other specific closure puzzles such as other sceptical arguments and the lottery paradox. But I'm hoping specifically for references on the problem for testimony).
Saturday, August 11, 2007
CFP: Knowledge and Understanding
The keynote is Ernest Sosa of Rutgers, so it should be a wonderful conference - get submitting!
Friday, August 03, 2007
Is Knowledge-How Gettier-Susceptible?
Pettit's target is epistemic accounts of linguistic understanding, whereby understanding an expression just is, or at least requires, knowledge of some proposition stating that expression's meaning. Pettit's first attack on the epistemic view proceeds by offering a case in which a subject's belief in the proposition that 'Krankenschwester' means 'Nurse' is Gettierized, and yet we are strongly drawn to judge that the subject nonetheless understands 'Krankenschwester'. The natural reading of Pettit takes his argument to proceed as follows. The moral to draw from the case described is that understanding language, in stark contrast to propositional knowledge as it is usually understood by epistemologists, is unGettierizable. Hence the identification of linguistic understanding with propositional knowledge is untenable, and Gettier cases like the one Pettit offers will be examples of understanding without the relevant piece of propositional knowledge.
But it seems clear that Pettit does not need to make the really strong claim that understanding is unGettierizable. All he needs, and all his case strictly speaking shows, is that there are Gettier cases in which we are prone to judge that a subject understands some expression, and yet that subject's belief in the proposition knowledge of which - according to the epistemic view - constitutes or necessarily accompanies understanding of that expression is Gettierized. That's enough to defeat the epistemic view.
(I should stress, I don't buy Pettit's conclusion. I've been convinced by Stanley in his reply to Hornsby that there's a lot still to be said in favor of the epistemic view. Here I'm simply pointing out that the argument need not rely on drawing the moral that understanding is immune to Gettierization.)
Pettit and others have suggested that his argument against the epistemic view can also be wielded against Stanley and Williamson's proposal that it is true that one knows how to x (in a given context) if and only if for some contextually relevant way w, one stands in the knowledge-that relation to the (Russellian) proposition that w is a way for one to x (and one entertains this proposition under a practical mode of presentation). The basic suggestion is that while propositional knowledge is usually taken to be vulnerable in Gettier cases, knowledge-how - like linguistic understanding - is unGettierizable.
Stanley and Williamson offer two replies to this (435). Firstly, they doubt that propositional knowledge in general is Gettier-susceptible. Secondly, they describe what they take to be a Gettier case for knowledge-how, undermining the claim that knowledge-how is unGettierizable.
But, as with the epistemic view of understanding, it would suffice to object to their proposal if it could be shown that there are Gettier cases in which Stanley and Williamson's biconditional fails: so cases in which we would on reflection attribute the subject knowledge-how to x, and yet we'd hold that the subject fails to stand in the knowledge-that relation to the proposition that w (for some appropriate w) is a way for her to x because her belief has been Gettierized. On a first pass, Stanley and Williamson's responses don't seem to address this point; once we refrain from making the strong claim that knowledge-how is unGettierizable, their purported Gettier case for know-how is besides the point, and unless we have good reason to think that beliefs in propositions of the form 'w is a way for me to x' are amongst the ones that it might be plausible to regard as Gettier-immune, it's hard to see how it helps to point out that some knowledge-that might enjoy such immunity.
The upshot is it seems that there's still room to explore a version of the Pettit objection against the Stanley-Williamson proposal. Mark Sainsbury has suggested to me that if one accepts their account, it will be quite plausible that there could not be Gettier cases in which their biconditional fails (so their first reply, that not all knowledge-that is Gettier-susceptible, is very much to the point after all). As I've blogged before, Stanley and Williamson see themselves in part as trying to challenge the Rylean account of the nature of the knowledge-that relation, and Mark's suggestion is that once we take that challenge seriously, it's very difficult indeed to come up with Gettier cases in which it's intuitively the case that the subject knows how to x, and yet fails to possess the knowledge-that which the right-hand side of the Stanley-Williamson biconditional would have us attribute. So the suggestion is that once we understand the kind of view of the nature of knowledge-that which Stanley and Williamson favor, their proposal is not vulnerable to a Pettit-style objection, even as I've reconstrued it here. I think Mark's probably right about this, and there's no counterexample to Stanley and Williamson in the offing here, but it seems worth thinking more about, and I don't know of any discussion in the literature.
CFP: 2007 Yale/UConn Conference