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 way science is currently done, experimental data that the formulator of the hypothesis did not know about is much stronger evidence for a hypothesis than experimental data he did know about.
A hypothesis formulated by a perfect Bayesian reasoner would not have that property, but hypotheses from human scientists do, and I know of no cost-effective way to stop human scientists from generating the effect. Part of the reason human scientists do it is because the originator of a hypothesis is too optimistic about the hypothesis (and this optimism stems in part from the fact that being known as the originator of a successful hypothesis is very career-enhancing), and part of the reason is because a scientist tends to stop searching for hypotheses once he has one that fits the data (and I believe this has been called motivated stopping on this blog).
Most of the time, these human biases will swamp the other considerations (except that consideration mentioned below) mentioned so far in these comments. Consequently, the hypothesis advanced by Scientist 1 is more probable.
Someone made a very good comment to the effect that Scientist 1 is probably making better use of prior information. It might be the case that that is another way of describing the effect I have described.