We do ten experiments. A scientist observes the results, constructs a
theory consistent with them, and uses it to predict the results of the
next ten. We do them and the results fit his predictions. A second
scientist now constructs a theory consistent with the results of all
twenty experiments.
The two theories give different predictions for the next experiment. Which do we believe? Why?
One of the commenters links to Overcoming Bias, but as of 11PM on Sep 28th, David's blog's time, no one has given the exact answer that I would have given. It's interesting that a question so basic has received so many answers.
The first theorist had multiple theories to choose from that would have been consistent with the first 10 data points - some of them better than others. Later evidence indicates that he chose well, that he apparently has some kind of skill in choosing good theories. No such evidence is available regarding the skill of the second theorist.
David D. Friedman asks:
One of the commenters links to Overcoming Bias, but as of 11PM on Sep 28th, David's blog's time, no one has given the exact answer that I would have given. It's interesting that a question so basic has received so many answers.