|Missing Shade of Blue
Joined: Dec. 2008
So to my two conditions you would have to add a third:
3. You possess no background information whereby certain non-falsifying observations would actually weaken the hypothesis more than they strengthen it.
And with that third condition, you and I (and Jaynes) are in agreement. That's all I was trying to say really, that for instance confirmation to work, the background information (or, as I put it, auxiliary assumptions) need to cooperate.
Of course, once you have a condition as broad as 3, I begin to wonder whether you're not approaching triviality. Isn't 3 pretty close to "Observations of this type strengthen your hypothesis unless they don't"?
I think the way to go is to abandon Hempelian instance confirmation entirely and just be a straight-up Bayesian. With Bayes' rule you're guaranteed to be updating your beliefs rationally without having to make all sorts of caveats.
BTW, to anyone interested in this sort of stuff I highly recommend Jaynes' "Probability Theory: The Logic of Science". Not easy going, but the most subtle and enlightening text on probability/statistics I've ever read. I recommend it especially to Fisherians. Hypothesis testing, like instance confirmation, works well enough for most of the purposes to which it's applied, but conceptually it's a mess.