|Missing Shade of Blue
Joined: Dec. 2008
The dissertation is nearing completion, thank god. Hopefully just another few months, and I'll be the proud (and probably unemployed) holder of a doctoral degree.
I mostly agree with what you're saying here, Keith. The example I gave was merely in response to your claim that it is absurd to think that an instance of a hypothesis does not in general confirm the hypothesis. Under certain auxiliary assumptions, an instance can disconfirm the generalization.
As for the rest, I'm with you. It is in fact a straightforward consequence of Bayes' theorem that a yellow banana confirms the hypothesis "All ravens are black" given natural assumptions about sampling. And you're right, I shouldn't have said the sampling procedure has to be completely random. But there are constraints on sampling, and this is partly what I meant by auxiliary assumptions being essential. Here's another example: Suppose my lab assistant is collecting samples for me, and I know she's a bit scientifically dishonest. She will never collect a sample which falsifies the hypothesis. Out of all the samples that don't falsify the hypothesis she picks randomly. Suppose she goes into a room that I know contains a million ravens and two bananas, in order to pick a sample for me. She comes out carrying a yellow banana. Given my auxiliary assumptions about her sampling procedure, I should actually drastically reduce my credence in the hypothesis. She probably would not have brought me a banana unless almost all the ravens in the room were not black. So yeah, while the assumption of random sampling is unnecessarily, some constraint on sampling is necessary in order for any evidence to count as genuinely confirmatory.