Posted: Dec 17, 2011 6:44 am
Mick wrote:jlowder wrote:Like all inductive or evidential arguments, appeals to possibility do nothing to undermine to the claim about probability.
I'm not too sure if you meant to generalize this entirely. However, I should say that appeals to possibility could indeed undermine the claim about probability. Inductive or evidential arguments from evil could be rendered impotent with appeals to ontological arguments.
1. <>(<>{}(<>G--><>[]G) & <>G)
2.<>{}(<>G--><>[]G) & <>G
Both 1 and 2 are possibility claims which are logically equivalent to []G in some modal logics.
In the interest of brevity, I think I was too brief.
If E is our evidence, H1 and H2 are competing explanatory hypotheses, and the claim is that E is antecedently more likely on H1 than on H2, i.e., Pr(E | H1) > Pr(E | H2), then pointing that it's possible that both E and H2 are true misses the point. So in the sentence you quoted above, I was referring to appeals to the possibility of both E and H2 being true.