While his highly technical lectures may not net Christianity many fresh converts, Mr. Swinburne's efforts to bring inductive logic to bear on questions of faith have earned him a considerable reputation in the small but vibrant world of Christian academic philosophy. Thanks to the efforts of Mr. Swinburne and a handful of other nimble scholarly minds -- including Alvin Plantinga at the University of Notre Dame and Nicholas Wolterstorff at Yale -- religious belief no longer languishes in a state of philosophical disrepute. Deploying a range of sophisticated logical arguments developed over the last 25 years, Christian philosophers have revived faith as a subject of rigorous academic debate, steadily chipping away at the assumption -- all but axiomatic in philosophy since the Enlightenment -- that belief in God is logically indefensible.

''They are the first group within 20th-century Anglo-American philosophy to tackle questions of religious faith using the tools of philosophy,'' said Brian Leiter, a professor of law and philosophy at the University of Texas at Austin and editor of the Philosophical Gourmet Report, which ranks academic philosophy departments. ''It would be accurate to say that it's a growth movement.''

Mr. Wolterstorff, who retired from Yale in December and in whose honor the conference was organized, agreed. ''And it's not just graybeards,'' he added, referring to the dozens of younger scholars and graduate students in attendance. ''Within the general discipline, this development of the philosophy of religion has been extraordinary.''

To be sure, not all of the movement's philosophers agree with one another, use the same tactics or even hold the same religious beliefs. Some, including Mr. Swinburne, for example, are what's known as evidentialists: they accept the Enlightenment doctrine that a belief is justified only when evidence can be found for it outside the believer's own mind. According to the classic evidentialist argument, for faith to be considered rational it has to be supported by independent proof, and there simply isn't any. (Asked what he would say if God appeared to him after his death and demanded to know why he had failed to believe, the British philosopher and staunch evidentialist Bertrand Russell replied that he would say, ''Not enough evidence, God! Not enough evidence.'')

In ''The Existence of God'' (Oxford University Press, 1979), Mr. Swinburne, a Greek Orthodox Christian, tried to meet the evidentialist challenge using Bayes's theorem. Supplying pages of intricate, technical argumentation to back up his claims, he wrote that many natural phenomena -- including the universe itself -- are, well, if not incontrovertible proof of God's handiwork, at least ''more probable if there is a God than if there is not.'' (Mr. Swinburne, it turns out, is not the first to enlist Bayes's theorem in defense of religion. In a 1763 paper presented to the British Royal Society, the minister Richard Price used it to show there was good evidence in favor of the miracles described in the New Testament.)