So I’m working on a Bayesian approach to the Duhem-Quine problem. Basically, the problem is that any experiment never tests a hypothesis directly but only the conjunction of the hypothesis and other auxiliary assumption. The standard method for dealing with this is to make
P(h|e)=P(h & a|e) + P(h & -a|e) (so if e falsifies h&a you just use the h&-a)
So if e falsifies h&a you end up with:
P(h|e) = P(e|h&-a) * P(h&-a) / P(e)
This guy Strevens objects on the grounds that e can impact h without impacting a. His example:
Newstein, a brilliant but controversial scientist, has asserted both that h is true and that e will be observed. You do not know Newstein’s reasons for either assertion, but if one of her claims turns out to be correct, that will greatly increase your confidence that Newstein is putting her brilliance to good use and thus your confidence that the other claim will also turn out to be correct. Because of your knowledge of Newstein’s predictions, then, your P(h|e) will be higher than it would be otherwise.
Am I crazy or shouldn’t that information already be contained in the above formula? Specifically, the term P(e|h&-a) should be higher than it would otherwise.
HELP NEEDED Today if at all possible.
So I’m working on a Bayesian approach to the Duhem-Quine problem. Basically, the problem is that any experiment never tests a hypothesis directly but only the conjunction of the hypothesis and other auxiliary assumption. The standard method for dealing with this is to make
P(h|e)=P(h & a|e) + P(h & -a|e) (so if e falsifies h&a you just use the h&-a)
So if e falsifies h&a you end up with:
P(h|e) = P(e|h&-a) * P(h&-a) / P(e)
This guy Strevens objects on the grounds that e can impact h without impacting a. His example:
Am I crazy or shouldn’t that information already be contained in the above formula? Specifically, the term P(e|h&-a) should be higher than it would otherwise.