I took it that the definitions Swinburne quotes imply that all of a person's
basic beliefs are (privately) rational; Swinburne demurs. It still seems to me that
these definitions have this consequence. Let me briefly explain why. According to
Swinburne, a person's evidence consists of his basic beliefs, weighted by his
confidence in them. So presumably we are to think of S's evidence as the set of the
beliefs he takes in the basic way, together with a sort of index indicating, for each
of those beliefs, his degree of confidence in that belief. Now it is clear, first, that
different basic beliefs can be held with different degrees of confidence. I believe
2+1 = 3 more firmly than there are presently some large trees in my backyard, and
I believe that second proposition more firmly than I played bridge last night.
Nevertheless, I believe all three propositions; I don't just believe them probably.
So, the set of my basic beliefs contains propositions, all of which I believe. Further,
a belief of mine is ‘rendered (evidentially) probable by [my] evidence’, I take it,
just if it is probable with respect to the set of my basic beliefs. But of course
probability of 1 with respect to that set; the degree of confidence with which I hold
those beliefs does not seem to be relevant. Hence my conclusion that on these
definitions all of my basic beliefs are rational.
Swinburne points out that some of my basic beliefs may be improbable with
respect to the rest of my basic beliefs; these beliefs, then, might be thought
irrational, at least if they are not held as firmly as those with respect to which they
are improbable. But this seems to me an uninteresting sense of ‘irrational’. Many
of my basic beliefs are improbable with respect to my other basic beliefs; they are
none the worse for that. I now remember, as it seems to me, that in the second
bridge hand last night I was dealt three aces, three jacks, and three deuces. This is
unlikely on the rest of my basic beliefs. It is, nonetheless, not irrational in any useful
sense; memory is an important and independent source of rational belief, a source
such that its deliverances do not necessarily depend, for warrant or rationality, on
their probability with respect to other basic beliefs. I believe the same goes for
some of my Christian beliefs. They may be improbable with respect to other
beliefs, basic or otherwise, that I hold; but that need be nothing whatever against
them.