Theism and Explanation - Appeared-to-Blogly

106 Theism and Explanation
In terms of confi rmation theory, the gremlin hypothesis has a low posterior
probability because it has a low prior probability. What is it about the
gremlin hypothesis that gives it a low prior probability? Well, one reason
is that it enjoys little support from our background knowledge: it bears
little relationship to those other things which we know to be true. So, as
Swinburne is well aware, a key issue is the prior probability of the theistic
hypothesis, and a key issue in determining this is the role of background
knowledge. I shall come back to these questions shortly (7.2).
We can approach the same question more formally, by way of the Bayesian
reasoning that forms so important a part of Swinburne’s argumentation. As
we have seen (2.1.3.1), the relationship I have been discussing—that between
likelihood and posterior probability—is formalised by Bayes’s theorem:
Pr(H|E) =
Pr(E|H) × Pr(H)
Pr(E).
If, with Swinburne, we assume that a hypothesis is confi rmed to the degree
that it is rendered probable—and I have already hinted at an alternative
account (2.1.3.2)—then Bayes’s theorem also gives us the degree to which
a hypothesis is confi rmed. Let’s see how this works by assigning some fi gures,
more or less at random. Let’s say that the prior probability of E is 0.2.
(It is a surprising fact that we’re trying to explain.) And let’s say the likelihood
of E, given H, is 0.9. (H has a high degree of explanatory force.) Can
we say that E confi rms H? Yes, in the weak sense of “confi rm” we can. It
renders it more likely than it would be otherwise. But by how much? Well,
it depends on the prior probability of H. If the prior probability of H is low,
let’s say 0.1, then its probability is raised to 0.45. This is impressive, but it
falls short of demonstrating that H is probably true (if that is what you are
interested in doing). 23
6.1.2.2 The Probability of Theism
So the second step in Swinburne’s reasoning is to turn these various
C-inductive arguments, as he calls them, into a P-inductive argument. 24
A P-inductive argument is one that makes the conclusion more probable
than not. Swinburne argues that the prior (or “intrinsic”) probability of
theism is high, at least “relative to other hypotheses about what there
is.” 25 For prior probability, he claims, will be directly proportional to the
simplicity of a hypothesis, its narrowness of scope, and its conformity to
background knowledge. 26 Swinburne argues that background knowledge
need not be taken into account when assessing the theistic hypothesis, since
theism “purports to explain everything logically contingent (apart from
itself).” 27 But this means that the theistic hypothesis leaves nothing in the