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Unformatted text preview: Williamsons Argument Against KK 10/11/06 (B.F.) Before moving on to this weeks material, I want to begin by returning to Conees argument against E = K . We decided last week that his argument, as stated, is not compelling. But, his example already contains a clear counterexample to E = K , just not the one he focused on. In his example, the expert testifies that ( E ) there is a distinction between how things appear (to S ) to be experienced by S , and how they really are experienced by S . And, E served to defeat ( E ) the evidence provided by S s being appeared to -ly for the claim that S is having a -ish experience. We agreed last time that it was controversial as to whether E was still evidence for S even though it had been defeated by E . No problem. Just take E to be the evidence in question. And, assume that E is false (Conee explicitly allows this). Then, E will be something that is evidence for S , but is not known by S . OK, now onto the argument against KK presented by Williamson in chapter 5. It seems to me that the strategy here is largely driven by formal arguments in modal logic that Williamson gave in a 1992 paper. 1 In that paper, Williamson was concerned not with the operator ( K ) S knows that, but with the operator it is clearly (or determinately) the case that. [That paper is largely about the logic of vague predicates.] These operators (both being read as a sort of necessity operator in this context) are significantly different (intuitively). And, I think some of the things Williamson assumes about the K operator in this chapter are pretty implausible (although, they might be more plausible for the determinately true operator). This threatens to undermine his argument against KK . The argument itself is actually very simple (the presentation in the chapter is unnecessarily complex, I think). In a nutshell, it can be condensed down to the following line of reasoning. S looks at a tree but cannot tell how tall it is. The idea is to represent S s self-klnowledge of their own ignorance by the following claim (in schematic form, where i is a positive natural number): (I i ) S knows that if the tree is i + 1 inches tall then S doesnt now that it isnt i inches tall. Here, the conditional is allowed to be a material implication. Let K stand for the proposition that S knows that the tree is inches tall. Then, (I i ) can be written more perspicuously as follows: (I i ) K[(i + 1 ) K i] This principle is just one of the premises of the argument. But, I dont find it at all plausible. Think about it in terms of the contraposition of the embedded conditional: (I i ) K[K i (i + 1 )] This says that S knows that if he knows that the tree is not i inches tall, then it is not i + 1 inches tall. That seems like an awful lot of knowledge for someone so shortsighted! But, putting these intuitions (of mine) to one side, we can already see that (I i ) is problematic by making a few simple...
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- Fall '06