Theism and Explanation - Appeared-to-Blogly

24 Theism and Explanation
potential explanation only if it is confi rmed in the absolute sense, that is to
say, if the evidence in its favour makes it more probable than not, and if it
has no more probable competitor. 19 More formally, where E is the evidence,
H is a potential explanation of E, and K our background knowledge, then
we can regard H as a successful explanation if
Pr(H|E & K) > 0.5
and there exists no competing hypothesis whose probability given E and K
is higher. 20 The probability of H given E and K (its posterior probability)
can be discovered by estimating the prior probability of H and the likelihood
of E given H and then applying Bayes’s theorem. In its simplest form,
this states that the posterior probability of a hypothesis, given some piece
of evidence (E), is discovered by multiplying the prior probability of H by
the likelihood of E given H, and dividing the result by the prior probability
of E.
Pr(H|E) =
Pr(E|H) × Pr(H)
Pr(E)
As we shall see (6.1.2), this is precisely how Swinburne argues.
There are practical diffi culties with a justifi cationist view, particularly
one that appeals to Bayes’s theorem. There is, fi rst of all, the diffi culty,
which Swinburne readily acknowledges, 21 of assigning precise numerical
values to the probability estimates required. 22 But there are also diffi culties
in spelling out the required conception of probability. Swinburne, for
instance, identifi es three broad categories of probability, which he refers
to as “physical,” “statistical,” and “inductive.” Physical probability has
to do with the propensities that are actually at work in the universe. As
Swinburne puts it, it is “a measure of the extent to which some particular
outcome is predetermined by its causes at some earlier time.” 23 In a fully
deterministic universe, every actual event would have a physical probability
of 1.0. Statistical probability, on the other hand, is a measure of the
proportion of the members of a class who possess a certain property. 24 But
what really interests Swinburne—and what he employs in The Existence
of God—is what he calls “inductive probability.” This is, as Swinburne
writes, “a measure of the extent to which one proposition r makes another
one q likely to be true.” 25
What about explanations? Does it make sense to speak of the probability
of an explanatory hypothesis? Swinburne assumes that since both hypotheses
and bodies of evidence are expressed in propositions, inductive probability
can also be applied to explanations. The inductive probability of a
hypothesis, on this view, is a measure of how likely it is to be true, given