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.