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notes_7

# notes_7 - Fall 2006 Williamson Knowledge and its Limits...

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Fall 2006 Sherri Roush 1 Williamson, Knowledge and its Limits , Chapters 5 and 6 1. When you consider Ii (Mr. Magoo knows that if the tree is i +1 inches tall, then he does not know that the tree is not i inches tall) in its contrapositive form, as Branden did, it seems to me the intuition is overwhelmingly against it. For, it seems, Magoo’s knowing that the tree is not i inches tall says nothing at all about whether what it is instead is i + 1 , i-1 or i + n for any other n. It’s not being i doesn’t say it’s not i + 1, and how could Magoo’s knowledge have any implications about how the world is? Yet, in the positive form TW stokes the intuition for Ii well when he says (115, top): … even if he so judges [that it is i inches tall] and in fact it is i inches tall, he is merely guessing: for all he knows it is really i–1 or i+1 … This is because Magoo can’t discriminate visually between i inches and i+1 inches, etc. So he merely happened to get it right so far as the value is distinct from i+1 (so he doesn’t know it is i inches tall, says TW). Thus, if it is i inches tall, then he does not know it isn’t i+1 inches tall. Similarly, if it is i+1 inches tall, then he does not know it isn’t i inches tall. And there we have Ii. Why the two conflicting intuitions, about the positive and contrapositive forms of the claim? For me it was easier to start with the contrapositive and try to figure out why it’s supposed to be true. Then that tells you exactly what underpins Ii. So: Ii = K (i+ 1 -K-i) Consider just the thing claimed to be known: i + 1 -K-i Contrapose: K-i -(i + 1) What could Magoo’s knowledge that it’s not i have to say about it’s not being a particular other value? Well, we know it’s not coming from its being true that it’s not i, so it must be coming from his knowing it. In other words, there’s a requirement for knowledge which Magoo must have fulfilled if we count him as knowing, and this requirement implies that in the actual world the value is not i+1. The requirement is safety . A belief is safe if in worlds 1) nearby to the one he actually believes it in and 2) such that he would still form the belief that he actually does, it’s also true. Supposing Magoo knows it’s not i, that belief must be safe on the assumption TW must be making here. That means it must be true in the worlds that are nearby to the actual world and in which he believes it. Given that Magoo can’t discriminate between i and i+1, the actual- world tree must be, like, i+100 inches tall, so as to insure that the worlds nearby the actual world are also worlds in which his way of tending to form the belief that it’s not i (i.e. using a faculty with imperfect discrimination) won’t lead him to a false belief. If the actual world were i+1 then he’d form the false belief that it wasn’t i in the close world in which it was i. That’s not allowed because the antecedent says Magoo knows it’s not i, and safety is required for knowledge. Safety is the precise counterpart of the intuition TW is pumping with his comment about “merely guessing”.

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• Fall '06
• FITELSON
• Hope That We Can Be Together Soon, actual world, surprise examination, Mr. Magoo, surprise examination paradox

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notes_7 - Fall 2006 Williamson Knowledge and its Limits...

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