Monthly Archives: September 2007

Followup to:  The Bottom Line, What Evidence Filtered Evidence?

In "The Bottom Line", I presented the dilemma of two boxes only one of which contains a diamond, with various signs and portents as evidence.  I dichotomized the curious inquirer and the clever arguer.  The curious inquirer writes down all the signs and portents, and processes them, and finally writes down "Therefore, I estimate an 85% probability that box B contains the diamond."  The clever arguer works for the highest bidder, and begins by writing, "Therefore, box B contains the diamond", and then selects favorable signs and portents to list on the lines above.

The first procedure is rationality.  The second procedure is generally known as "rationalization".

"Rationalization."  What a curious term.  I would call it a wrong word.  You cannot "rationalize" what is not already rational.  It is as if "lying" were called "truthization".

Continue reading "Rationalization" »

 Yesterday I discussed the dilemma of the clever arguer, hired to sell you a box that may or may not contain a diamond.  The clever arguer points out to you that the box has a blue stamp, and it is a valid known fact that diamond-containing boxes are more likely than empty boxes to bear a blue stamp.  What happens at this point, from a Bayesian perspective?  Must you helplessly update your probabilities, as the clever arguer wishes?

If you can look at the box yourself, you can add up all the signs yourself.  What if you can’t look?  What if the only evidence you have is the word of the clever arguer, who is legally constrained to make only true statements, but does not tell you everything he knows?  Each statement that he makes is valid evidence – how could you not update your probabilities?  Has it ceased to be true that, in such-and-such a proportion of Everett branches or Tegmark duplicates in which box B has a blue stamp, box B contains a diamond?  According to Jaynes, a Bayesian must always condition on all known evidence, on pain of paradox.  But then the clever arguer can make you believe anything he chooses, if there is a sufficient variety of signs to selectively report.  That doesn’t sound right.

Continue reading "What Evidence Filtered Evidence?" »

There are two sealed boxes up for auction, box A and box B.  One and only one of these boxes contains a valuable diamond.  There are all manner of signs and portents indicating whether a box contains a diamond; but I have no sign which I know to be perfectly reliable.  There is a blue stamp on one box, for example, and I know that boxes which contain diamonds are more likely than empty boxes to show a blue stamp.  Or one box has a shiny surface, and I have a suspicious – I am not sure – that no diamond-containing box is ever shiny.

Now suppose there is a clever arguer, holding a sheet of paper, and he says to the owners of box A and box B:  "Bid for my services, and whoever wins my services, I shall argue that their box contains the diamond, so that the box will receive a higher price."  So the box-owners bid, and box B’s owner bids higher, winning the services of the clever arguer.

The clever arguer begins to organize his thoughts.  First, he writes, "And therefore, box B contains the diamond!" at the bottom of his sheet of paper.  Then, at the top of the paper, he writes, "Box B shows a blue stamp," and beneath it, "Box A is shiny", and then, "Box B is lighter than box A", and so on through many signs and portents; yet the clever arguer neglects all those signs which might argue in favor of box A.  And then the clever arguer comes to me and recites from his sheet of paper:  "Box B shows a blue stamp, and box A is shiny," and so on, until he reaches:  "And therefore, box B contains the diamond."

Continue reading "The Bottom Line" »