Williamson thinks that the fact that we have yet to come up with a suitable analysis of knowledge post-Gettier, among other things, should push us to accept that there is no analysis of knowledge.
He thinks that we should treat knowledge as an unanalyzable primitive.
Here’s something I find puzzling, he argues that we should regard knowledge as an unanalyzable primitive even if it turned out that knowledge was co-extensive with some complex analysis. Here’s what he says
Even if some sufficiently complex analysis never succumbed to counterexamples, that would not entail the identity of the analyzing concept with the concept knows. Indeed, the equation of the concepts might well lead to more puzzlement rather than less. For knowing matters, the difference between knowing and not knowing is very important to us. Even unsophisticated curiosity is a desire to know. This importance would be hard to understand if the concept knows were the more or less ad hoc sprawl that analyses have had to become; why should we care so much about that? (Williamson 2000; 31)
I’m actually having a hard time parsing what Williamson says here. My difficulty is that he waffles between a descriptive fact and a normative fact. First, he says that the difference between knowing and not knowing is something that we do care about. Then when he talks about the other property that we might identify with knowledge he simply asks “Why should we care about that?” suggesting, perhaps, that we do not have reasons to care about that.
This switch between a non-normative fact and a normative fact suggests two different arguments Williamson might have in mind.
Non-normative Version of the Argument
- We care about whether or not something is knowledge. (Williamson says this)
- For any complex property/relation P such that that P is coextensive with knowledge, we do not care about whether or not something is P. (Williamson does not say this)
- If (1) and (2), then for any complex property/relation P such that that P is coextensive with knowledge, knowledge is not identical to P.
- Therefore, for any complex property/relation P such that that P is coextensive with knowledge, knowledge is not identical to P.
Normative Version of the Argument
- We should care about whether or not something is knowledge. (Williamson does not say this)
- For any complex property/relation P such that that P is coextensive with knowledge, it’s not true that we should care about whether or not something is P. (Williamson says this…or seems to imply it)
- If (1) and (2), then for any complex property/relation P such that that P is coextensive with knowledge, knowledge is not identical to P.
- Therefore, for any complex property/relation P such that that P is coextensive with knowledge, knowledge is not identical to P.
I’ve bolded the differences between these two arguments. I hope it’s clear why I’ve presented both. In the actual text he says something like premise 1 from the non-normative version of the argument. But then he implies something like premise (2) from the normative version of the argument.
I suspect that he has something like normative version of the argument in mind. I have some things that I think I want to say about this argument, but I’ll stop for now.
Does it look like I have Williamson right?
It seems to me that W isn’t waffling, and is presenting a non-normative version. ‘Should’ has a (non-normative) subjunctive use, though it’s more common in British than in American English. It looks like that’s the use that’s relevant here. To rephrase the argument in American English, you can replace ‘should’ with ‘would’.
That said, I do find the argument puzzling. Church and others have suggested treating the paradox of analysis as involving complicated Frege cases. I don’t see yet why we can’t treat Williamson’s point in the same fashion.
Interesting. Fair enough on the translation.
That’s exactly where I was going to go with an objection…this looks like a Frege puzzle to me.
I find that argument puzzling as well. Here are three comments:
(1) Is your premise (3) really needed?
(2) I agree that probably Williamson has the normative argument in mind. But I don’t think that the actual text requires the descriptive reading. The descriptive/normative is in general hard to apply to statements like Williamson’s. Compare ‘my diet is very important to me’. When asked why, I can’t reply that I only reported my state of mind. In ordinary contexts an utterance like this doesn’t sit either on the descriptive or on the normative side. So it seems strange, I’d say, to interpret Williamson as merely offering a description of what we happen to care about. Interestingly, the presentation of the argument in the Pritchard/Greenough volume (p. 291) doesn’t help to decide the question. Here, Williamson asks why philosophers want to understand knowledge. Again, I’d say, that this question is both descriptive (what are their actual reasons?) and normative (are there indeed good reasons?). Or at least it is not merely descriptive.
(3) Premise 2 is highly implausible, isn’t it? I care about whether my friends smile while I take a picture of them (or whatever). This is obviously complex. So what Williamson probably intends is something like: If P is gerrymandered/’ad hoc sprawl’, we cannot ultimately/intrinsically/etc. care about whether P.
I hope these comments are at least somewhat relevant to your concerns!
Hi Tim,
These are definitely relevant. I have some thoughts about point (1) and (3). I’ll take them in turn.
Regarding (1):
I include the (3) premise to make it explicitly valid. You might think that this is unnecessary because it’s simply an instance of Leibniz Law…but given the Frege Puzzle-y nature of this argument…it seems worth including. Denying Leibniz Law in intensional contexts is a popular response to arguments of the above form. In short, premise (3) is the premise that some would be inclined to reject with respect to this argument, that’s why I include it. (…It’s not the one I would reject)
Regarding (3)
Fair enough. I was thinking that any analysis of knowledge would be a complex property, but that in *this* case with respect to knowledge Williamson would accept premise (2) because in *this* case with respect to knowledge whatever the complex property is would be gerrymandered/ad hoc etc…Your response only works if the support for (2) was some general principle like the one you seem to attack with your case. I wasn’t thinking that Williamson had such a general principle in mind.
You’re right, though, we should probably best formulate the argument by talking about gerrymandered/ad hoc properties.
I took the implicit argument to be normative, but not quite the version you give, with ‘should care’. I take it to be something like this: knowledge matters; the difference between knowing and not knowing is a significant and important one. But it’s very hard to see how the difference between meeting and failing to meet some crazy gerrymandered set of conditions like the ones offered in the post-Gettier literature could matter. So none of those are correct analyses.
I’ll add that I find this argument pretty compelling.