Archive for November, 2008

A problem for rejecting knowledge of lottery propositions

November 15, 2008

So, lots of people find it plausible to deny knowledge in the following type of case.  Let there be a fair lottery with n tickets (where n is very high, and where one and only one ticket will win).  You receive ticket i, and reason that because 1/n is so small, you believe you will lose.   Lets say you are right, and ticket is in a loser.  Most people find it emminently reasonable to reject that you know that you will lose, for various (seemingly good) reasons.

But if they do, they will also have to deny the following rather plausible principle about the value of knowledge :

Knowledge is Valuable (KIV): A rational person should never prefer to merely truly believe that p, rather than to know that p.* (more…)


Solving the Problem of Old Evidence : Part 2

November 2, 2008

Ok, so we now know how to solve the problem of old evidence as it is traditionally stated : just refuse to allow the probability of our evidence to go to 1.  But, then Earman comes along and points out a quantitative problem of old evidence.  Sure, sure, he says, doing what I just recommended works.  But now consider old evidence for which we are quite certain about, even if we don’t assign it a probability of 1.  Lets say our probability in the evidence is equal to .999.  Then confirmation goes like this, again for a hypothesis that entails the evidence.

Pr(H|E)=Pr(E|H)*Pr(H)/Pr(E)=1*Pr(H)/.999.  This is going to be very nearly Pr(H).  And so we might think that the evidence barely confirms the hypothesis.  This will be bad, because we do have cases of old evidence where we were quite confident in that old evidence, and where that old evidence strongly confirmed the hypothesis (again, this is taken to be the case for Mercury and GTR).  And, on some measures of confirmation – measures that define the degree of confirmation of a hypothesis by some evidence – this will be true.  So now we have a quantitative problem of old evidence : how can old evidence that we are quite sure about strongly confirm a hypothesis?


Solving the Problem of Old Evidence : Part 1

November 2, 2008

Well, I’ve decided to start doing philosophy blogging here again, so here is the first post since I’ve been at Princeton.  I’m splitting this up into two parts, and the posts will show how to solve the problem of old evidence with the log-likelihood ratio measure.  This post shows how I like to solve the traditional problem of old evidence.