Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!mnetor!seismo!ut-sally!ghostwheel!milano!wex From: wex@milano.UUCP Newsgroups: sci.philosophy.tech Subject: Re: The nature of knowledge Message-ID: <4865@milano.UUCP> Date: Wed, 8-Jul-87 12:24:57 EDT Article-I.D.: milano.4865 Posted: Wed Jul 8 12:24:57 1987 Date-Received: Sat, 11-Jul-87 07:05:30 EDT References: <3587e521.44e6@apollo.uucp> <680@gargoyle.UChicago.EDU> <121@cavell.UUCP> Sender: wex@milano.UUCP Distribution: world Organization: MCC, Austin, TX Lines: 47 Keywords: knowledge belief truth certainty Summary: beliefs in conjunction In article <121@cavell.UUCP>, jiml@alberta.UUCP (Jim Laycock) writes: > Consider a much smaller scenario--one in which I have but three beliefs: > > 1. Bel(p) > 2. Bel(q) > 3. Bel(~(p^q)) > > Surely if such a situation were to come about, you'd have no trouble > considering me to be inconsistent. Perhaps this is alright for small cases, but in the real world, people knowingly hold inconsistent beliefs. My favorite example is the one of the proofreader. He has just finished proofreading a 350-page book and seen all the typos corrected. If we ask him "Do you believe there is a typo on pageof this book?" for all 350 possible values of , he will say "no" each time. However, if we ask "Do you believe there is a typo somewhere in the 350 pages of this book?" he will answer "yes." Inconsistent? Yes. So why does he hold this set of beliefs? The best answer I could give him was that his beliefs were not a matter of simple truth/falsity, but were a matter of degree. Thus, the correct questions should have been "Do you believe that there is a one-in-three-hundred-fifty chance that there is a typo on page of this book?" To this, I claimed, he would have answered "yes." This makes consistent his reply of "yes" to the final question. That is, given that he understands probability, and that there is a 1/n chance of a typo per page in an n-page book, it is reasonable to say that there is a typo in the book. [Side note: he was not satisfied with this answer. He remarked that he did not actively consider such probabilities in his answers and, in fact, he really had no grasp of what a one-in-three-hundred-fifty chance meant for proofreading. His counter-claim was that my answer was not an explanation, simply a way to rationalize a set of beliefs that he, the belief-holder, considered inconsistent.] -- Alan Wexelblat ARPA: WEX@MCC.COM UUCP: {seismo, harvard, gatech, pyramid, &c.}!sally!im4u!milano!wex "Oh well, a touch of grey, Kinda suits you anyway."