Probability theory

April 30, 2009

In a silly, condescending sort of way, Trevor Stone (Letters, 23 April) tries to tell us how any "right-thinking, honest intellectual" should think about religion. He says that its basic hypothesis is "highly improbable". This is untenable in an academic context.

The term "probability" has two sorts of precise scientific meaning. In neither sense can we claim to know that the existence of God is probable or improbable. In the logical, statistical sense of the word, we can calculate, for instance, the probability that any particular number will come up in a lottery draw if we know the number of digits contained and assume that the draw is random. We cannot talk about the probability of God's existence in this sense.

In the empirical sense of the term, we can know from experience the probability that, for instance, someone or other will have blood belonging to a specified blood group. However, we do not know from experience the probability that the universe in which we live is one that has or does not have a God. We do not know from experience that, if God exists, there would be evidence of Him. We do not know from experience what would count as evidence. We are not able to isolate a random sample of universes and discover how many of them have and do not have a God.

Probability in both senses is not the polar opposite of uncertainty. One can be justifiably certain about the precise probability that a number will win the lottery, just as one can be justifiably certain about the precise specifiable probability that a person, chosen at random, will belong to a particular blood group.

Of course, improbable things can and do happen, and the improbability of the existence of something should not be mistaken for evidence that it does not exist. Thereby, miscarriages of justice are readily spawned and fallacious conclusions hospitably entertained.

Hugh V. McLachlan, School of Law and Social Sciences, Glasgow Caledonian University.

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