tag:blogger.com,1999:blog-3891434218564545511.post8801435449577484401..comments2024-03-28T13:23:50.623-05:00Comments on Alexander Pruss's Blog: Carnap's probability measureAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-3891434218564545511.post-54634746397391531092010-02-26T16:20:06.581-06:002010-02-26T16:20:06.581-06:00Looks like Tooley (and I) should have both been th...Looks like Tooley (and I) should have both been thinking about newer Carnapian systems. See the discussion on <a href="http://prosblogion.ektopos.com/archives/2010/02/tooleys-use-of.html" rel="nofollow">prosblogion</a>.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-7624120392370826832010-02-24T14:40:43.152-06:002010-02-24T14:40:43.152-06:00Theorem 3: Let E_1 be any evidence solely about th...Theorem 3: Let E_1 be any evidence solely about the particulars r_1,...,r_n. Let H be a hypothesis solely about r_{n+1}. Let E_2 be the evidence that P(r_1)&...&P(r_n)&~P(r_{n+1}), where P is some predicate. Then, according to PC, E_1 and H are conditionally independent given E_2. <br /><br />Remark: This means that if you're trying to do simple induction, and you also know that there is any property that the particulars involved in the inductive data have and which the particular you are trying to learn about does not have, the inductive data tells you nothing about the particular. But this is always going to be the case--the unobserved particular will be differently located, less accessible, whatever. Minimally, the unobserved particular will be unobserved!Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.com