Probable miracles or impossible gods?

Probability is the very guide of life," was apparently first said by Cicero some 18 centuries before Bishop Joseph Butler, to whom it is usually attributed. Just as cobblers think there is nothing like leather, so statisticians think that there is nothing like probabilities and likelihoods. David Bartholomew was not only professor of statistics at the London School of Economics, but he has already written one interesting book reflecting on theological themes, God of Chance (1984), which drew some justified appreciation for its discussion of divine relationship to a contingent world. He now brings his professional expertise to bear on the question of the rational justification of religious belief.

To some degree, the result is disappointing. The method centres on the approach pioneered by the 18th-century clergyman, Thomas Bayes. His formula equates (the prior probability of A) x (the probability of B given A) to the same expression with A and B interchanged. As it stands, this equation is a tautology, for the two sides represent two different ways of calculating the same thing, the probability of both A and B together. Suppose A is the probability that a miracle has happened and B is the probability that God exists. We can use the formula to estimate the evidential effect of the miracle (that is to say, we calculate the probability that God exists given that the miracle happened). Wonderful! one might think, but the problem is that the answer comes out proportional to the prior probability that God exists. The atheistic sceptic who puts this at zero will never allow the calculation of a likelihood of divine existence arising from any event, whatever its nature.

Bartholomew is well aware of this problem of prior probabilities and a good deal of his book is spent discussing what to do about it. One gets involved in the question of the role of background beliefs and collateral considerations. I think this indicates the limitations of a quantitative approach to such matters, based solely on "the logic of uncertainty" (in Bartholomew's phrase). Acts of judgement of a qualitative kind are also involved. That is why many of us who have been concerned with the contemporary revival of natural theology have wished to speak of it in a modest insightful mode, rather than as an attempt to produce demonstration.

The style of the book is careful and much of its detailed considerations conduct the reader over well-trodden ground. There are also some interesting side excursions. A chapter is devoted to discussing evidence for paranormal phenomena, not produced as direct evidence for theism but as an exercise to see whether horizons of possibility can be widened beyond the range defined by scientific expectation and everyday convention. It concludes with a discussion of near-death experiences. Bartholomew rejects Susan Blackmore's purely physiological explanation, asking why in that case experience of the self would persist when the rest of the world is disintegrating. He believes, with Brian Pippard, that the subjective experience of the self lies outside the grasp of objective science.

The least satisfactory chapter is that discussing the Bible, where quantitative methods seem to have only a limited field of application. Bartholomew makes a strong assertion of their value and necessity but one of his commended examples - the "conclusions" of the so-called Jesus seminar, where a self-appointed coterie of scholars settled questions of the authenticity of words attributed to Christ by majority vote - seems particularly unhappy. In such matters more subtle and nuanced judgements, calling on tacit skills which cannot be reduced to algorithmic procedures, appear to be called for. Bartholomew acknowledges gladly that one of the most significant arguments for the value of the Bible is the effect that its writings have produced in many lives.

Although probabilistic analysis of a mathematical kind has only a limited role to play in the discussion of great metaphysical questions such as the existence of God, it is of interest to see how a professional in statistical science approaches the matter. One of the most effective aspects of his analysis is to reveal the corresponding problems relating to atheistic belief. "We have moved far enough, I believe to show that the simple certainties of the atheist are no less vulnerable than is the unthinking dogmatism of the believer". Bartholomew's conclusion is not agnosticism, for he believes that commitment to a fruitful way of life can properly go beyond the rationally certain. "Believers I can confidently explore the new world in which human reason is not the ultimate arbiter of truth".

John Polkinghorne is president, Queens' College, Cambridge.