Jack comments on Open Thread: May 2010 - Less Wrong
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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.