Friday, October 19, 2007

New e-Discussion Group on Contextualism & Relativism

In addition to the regular LOGOS Reading Groups, we are planning to run an informal e-discussion group on contextualism and relativism.

Following the format of last year e-RG on meta-metaphysics, the idea would be to have the discussion every two or three weeks here at The bLOGOS, so everybody is welcome to participate, regardless of whether you are sited near Barcelona.

We would be mainly discussing papers by ourselves. It is my pleasure to announce that the first paper to get this started will be Dan Zeman's 'Knowledge Attributions and Relevant Contexts'. New posts discussing this paper are to be expected around 2 November, with titles starting with ‘C&R Zeman.’

As for further e-sessions, I’d like to suggest López de Sa 2007 and Kölbel 2007 exchange (on Kölbel 2004, to which Dan Z also refers). Any other suggestions? Please give them in comments, and add links if available.

Thursday, October 11, 2007

DT RG: Carcel Confusion

This pertains to the reading group on decision theory, but any comments are welcome.
It's my version of the Three Prisoners Paradox. I read about the original paradox years ago in a book about the Monty Hall Problem, and I always assumed that it was created as a variant of this problem. However, Wikipedia recently taught me that it's much older than the MHP, and that it's due to Martin Gardner.
Here goes the story (I assume you know about the Monty Hall Problem; otherwise, read the wikipedia entry first):
Three prisoners, A, B and C, are awaiting their execution. It's known to them that one of them will be pardoned, but part of their punishment is that they may not know who prior to the day of the execution. They are kept in separate cells in different buildings.
One day, as the prison guard comes to check on prisoner A, A begs him to give him a hint concerning his fate. Of course the guard declines, but A keeps begging. At least, A suggests, the guard could tell him the name of only one of the others who will be executed for sure. That way A would still not know whether he will die or live, and the guard wouldn't have disobeyed his orders.
The guard thinks it through and mercifully agrees to give the required information: B will die. A thanks the guard and thinks to himself: "Well, at least I know that my chances to get out alive are 50% now."
So far, so good. Anyone familiar with Monty Hall will see that A is wrong. His chances are still 33%, the guard's revelation has gained him nothing. To draw the analogy to Monty Hall, he should switch fates with C if only he could. If we, the audience, were the type of people who bet on people's lives and deaths, we should put our money on C's staying alive.
That's the Three Prisoners Paradox as I remember reading it in the book. Now my appendix:
The guard passes by the cell of poor B, who is sound asleep, and finally comes to C. Here, a similar scene as before unfolds. C implores the guard to tell him something about his situation. The guard recalls his talk with A, goes through the reasoning once again to make sure he's not disobeying his orders, and tells C that B is going to die. "Whoopy!", thinks C, "So my chances to survive are 50%!!" But of course we know that this is false, his chances are 33%.
To sum up, we have A at a survival-chance of 33%, doomed B at 0% and C at 33% as well. But that seems a bit odd...
I've been puzzled by this for a long time, and I've asked a bunch of people and received a bunch of interesting and interestingly different answers. I think I know what's wrong, but I'm never quite sure (about 66% most of the time), so I await clarification(s)!