Show-Me the Argument

At the APA yesterday Jim Joyce gave an interesting talk on the future for inductive logic. Joyce argued that there is no future for it since there is no correct objective measure of confirmation. The goal of inductive logic is to characterize the inductive strength of arguments from some given evidence to a conclusion. This can be represented as a conditional probability, the probability of a hypothesis on a body of evidence—P(H/E1 & E2 & … & En). Joyce argues that even the clearest cases of inductive probability turn out to rely on a mistaken assumption. Here’s the case:

A ball will be drawn at random from an urn containing 100 balls.
Seventy-five balls are white and twenty-five are black.
—
A white ball will be drawn.

What is the degree of confirmation the premises provide for the conclusion? The intuitive answer is .75. Joyce argues, however, that this is mistaken because it relies on the principle of insufficient reason–treating equipossible outcomes as having an equal probability of occurring. (more…)

For those of you who are better than me at modal logic, logic, or the use of counterfactuals, can you help me prove that this:
(1) (p)(Wp → (Tp→~Ap))
entails (or is logically equivalent to) this:
(2) ~(â—Š(∃p)(Wp&~Tp) → â—Š(∃p)(Wp&Ap))?

(If you’re interested, (1) is Daniel and Francis Howard-Snyder and Neil Feit’s proposal for a necessary condition for warrant that blocks all Gettier counterexamples and (2) is what I deny in Zagzebski’s argument for warrant infallibilism (see my earlier posts on warrant infallibilism) . A = is accidentally true, T = is true, W = is warranted. p is some belief. Given the background philosophy behind this, I know that there is some entailment relationship; I just need to figure out how it works.)