These all come up in the introduction of Knowledge and Its Limits.1 Here is my best attempt to extract these arguments. The labels are my own.
The Argument from Non-reflexive Entailment
- Knowledge entails belief
- Belief does not entail knowledge.
- If concept A entails concept B, but concept B doesn’t entail concept A, then B is conceptually prior to A.
- Therefore, belief is conceptually prior to knowledge.
Williamson’s Objection: It’s actually not clear to me what the objection is. I’m going to post something separately about this later. For now, I’d like to simply present all three arguments.
The Argument from Analysis
- There is a true, informative analysis of knowledge in terms of belief.
- If there is a true, informative analysis of knowledge in terms of belief, then belief is conceptually prior to knowledge.
- Therefore, belief is conceptually prior to knowledge.
The Argument from Good Approximate Analysis
- There is a candidate conceptual analysis of knowledge that is a good approximation of a true analysis in terms of belief.
- If there is a candidate conceptual analysis of knowledge that is a good approximation of a true analysis in terms of belief, then belief is conceptually prior to knowledge.
- Therefore, belief is conceptually prior to knowledge.
All I’ll do for now is get these arguments up so I have something to link back to if I ever discuss them in more detail in the future. If you’ve got any thoughts/objections to the arguments, fire away.
notes
1 Williamson, T. (2000). Knowledge and its Limits. Oxford University Press, USA.
2 Before you get mad at Williamson here, he does note that for the purposes of his book will assume this. He also acknowledges that this is controversial. (Williamson 2000: 4)
3 He has an example with a ballpark/close approximation of analyzing parent in terms of ancestor that he thinks helps establish this point. (Williamson 2000:4)
Premise 3 of the first argument seems mistaken. entails , and not vice versa. But that tells us nothing about the relative priority of those two concepts.
My symbols got interpreted as html….I meant to write “the concept of DESK entails the concepts BEING SUCH THAT 1+1=2, and not vice versa”.
I agree with Dennis; the first argument is completely nuts, and Williamson will say the obvious thing: premise (3) is hopeless. (That’s one of the points of RED and COLORED.)
I don’t know if I’d say that (3) is completely nuts. Dennis’ counterexample has me persuaded that, as stated, it’s false.
I suspect we could Chisholm away at it. One thing striking about Dennis’ counterexample is that being-such-that-1+1=2 is a concept that all existing things have as a matter of necessity. We might be able to restrict the principle to contingent concepts.
We also might restrict it so that it was an epistemic principle (e.g. non-reflexive entailment in the case of contingent concepts is strong evidence of priority such that barring strong evidence to the contrary you should think that one concept is conceptually prior to the other)
How about this: DESK entails DESK OR CHAIR, but not vice versa. Yet this is no reason to think DESK OR CHAIR is prior to DESK!
That desk example is great, but it works as an obvious counterexample because of the identity relation between DESK and DESK. So…
OPTION ONE: If you were trying to Chisholm away, you could add a “and B is not identical to some part of A” clause. That doesn’t sound terribly ad hoc.
OPTION TWO: If you were going to frame the principle epistemically, so that non-reflexive entailment was merely strong evidence of priority that could be defeated…a case involving this kind of identity would simply qualify as a defeater.
I am not sure how strong the non-identity clause is supposed to be. But, I think there are probably counterexamples to such a Chisholmed principle. Consider -being-a-fork and -being-a-piece-of-silverware. The first entails the second, but not vice versa. But it doesn’t seem that -being-a-piece-of-silverware is not conceptually prior to -being-a-fork. Or perhaps, -being-a-cat entails -being-concrete and not vice versa. but, I don’t think that being-concrete is conceptually prior to -being-a-cat (at least if conceptual priority is supposed to have something to do with conceptual analysis).
I am not sure what to think of the second option you suggest. I wonder if we can show that the strong evidence principle is mistaken by coming up with a bunch of examples of non-reflexive entailment that do not involve the appropriate kind of conceptual priority. Here are some more potential examples: SHOE and EXTENDED THING, WOMAN and GREAT GREAT GREAT GRANDDAUGHTER, CRY and ACTIVITY INVOLVING HYDROGEN, ICE and IS BELOW A TEMP AT WHICH WATER FREEZES, WIKIPEDIA and CAUSES LOSS OF PRODUCTIVITY. I’m not sure if these are really cases of non-reflexive entailment without the appropriate priority. I’m also not sure how many such cases (if any) are enough to show that the epistemic principle is mistaken.
I just don’t see why we should expect anything in the neighborhood of the relevant premise to be true. Why are we trying to defend it?
Because something in the ballpark seems to me like it might be true. Here’s one reason to think that something like it might be true…maybe…
Here’s a standard (sensible) procedure for doing conceptual analysis. You have some concept A that you’re interested in analyzing, so you generate a list of paradigmatic As. Then you start to look for similarities and you come to realize that all of the As on your list are Bs. Upon further reflection you find that you can generate lots of cases where a B is not an A.
Philosophers often seem to assume that awareness of this makes it sensible to try and construct an analysis of A in terms of B. I think that’s a sensible starting point to.
But I don’t think this would seem sensible to me if coming to realize that all As are Bs and some Bs are not As didn’t give us some prima facie reason to think that B is conceptually prior to A.
I guess that’s why I’m thinking that some version, at least an epistemic version, of the principle may well be true.