Fitch’s paradox and self locating beliefFebruary 21, 2009
It’s been a while since I last posted here – which is bad seeing as I’ve had much less going on recently. I hope to return to regular blogging soon!
For now just a little note on something I’ve been thinking about to do with a version of the knowabality principle for rational belief. Back in this post I considered a version of Fitch’s paradox for rational belief, which shows the following believability principle cannot hold in full generality (C stands for rational certainty)
Here’s another route to that conclusion if you accept something like Adam Elga’s indifference principle. Suppose p is the proposition that you are in a Dr. Evil like scenario: that (a) you are Dr. Evil and (b) you have just received a message from entirely reliable people on Earth saying they have created an exact duplicate of Dr. Evil, whose situation is epistemically indistinguishable from Dr. Evils (including having him receive a duplicate message like this one) who will be tortured unless Dr. Evil deactivates his super laser. Notice that p includes self locating information.
If you accept Elga’s version of the indifference principle, once you’ve become certain of (b) you’re rationally required to lower your credence that you’re Dr. Evil to 1/2 and give credence 1/2 to the hypothesis that you’re the clone. So suppose for reductio that you could be certain that p. Since p is the conjunction of (a) and (b) you must be certain in both (a) and (b). But this is impossible, since indifference requires anyone who is certain in (b) to give credence 1/2 (or less) to (a).
It is impossible to be certain in p (p is probably unknowable too.) And since p is clearly possibly true, the principle given above is at best contingently true.