Posted: Dec 17, 2011 11:28 am
Thommo wrote:
jlowder wrote:Consider this analogy. Let E be evidence that I bought lunch today at McDonald's; G be the hypothesis that the earth is the center of the solar system; and H be the hypothesis that the sun is the center of the solar system. H obviously gives no reason at all to expect that I would buy lunch today at McDonald's. In other words, H does not predict E, i.e., Pr(E|H) < 0.5. But so what? It doesn't follow that G is true or even that G is more likely than H. Why? Because G also fails to predict E, i.e., Pr(E|G) < 0.5. So there's no reason at all to think my buying lunch today at McDonald's is evidence favoring geocentrism over heliocentrism, i.e., Pr(E|G) > Pr(E|H).

I'm a little concerned here that you (appear to) suggest that prediction is equivalent to a probability of >0.5. Is that what you meant?

That is what I meant, but maybe I was wrong to write that. I'm sensing you think I was.

Thommo wrote:If you regularly buy lunch at McDonalds 6 days a week (for example), then Pr(E|H) can easily be > 0.5 regardless of any predictions of H.

Not necessarily. I'm using the epistemic interpretation of probability, not the frequency interpretation. If I regularly buy lunch at McDonald's 6 days a week, that could only be relevant IF:

1. We expand the expression Pr(E|H) to Pr(E|H&B), where B represents our background knowledge.
2. We include in B the fact that I regularly buy lunch at McDonald's 6 days a week.

If we do that, then Pr(E|H&B) > 0.5. Of course, H will be explanatorily irrelevant, since it will B, not H, that will make it possible for this value to be > 0.5. In fact, H will be irrelevant precisely because Pr(E|H&B) = Pr(E|B).