The Science of Conjecture: Evidence and Probability Before Pascal.(Review)

James Franklin The Science of Conjecture: Evidence and Probability Before Pascal. Johns Hopkins University Press, 485 pages, $55

What do we know, and how surely do we know it? The general answer was given by Aristotle in the Nicomachean Ethics: certainty can be found only in mathematics, all other knowledge being to some degree doubtful. Much evil has been let loose upon the world by defiance of, or exaggeration of, this simple truth: at the one extreme by the belief that absolute certainty can be found in non-mathematical dogmas, at the other by the vulgar conclusion that since certainty is not possible outside mathematics (nor even inside it, according to a few bold theorists), everything we think we know is really just a set of epiphenomenal delusions arising from our personal and social circumstances. The natural fruit of the first of these errors is obscurantist tyranny; of the second, that mendacious solipsism Americans have come to know so intimately well, according to which, since nothing can be known, language has no content and no purpose but the manipulation of the world for the gratification of our private appetites. We shall eventually find out, since it has colonized a large part of our academic life and seems still to be increasing its hold on the minds of the intelligent young, whether that second folly has any worse mischief to unload on us than the indignities we suffered during the 42nd Presidency.

Aristotle's observation implies that most of what we can hope to know must emerge from the weighing of probabilities. To what branch of human knowledge does this weighing of probabilities, this "science of conjecture" as James Franklin calls it, itself belong? Without thinking very much, most of us moderns would make a paradox of the whole thing by replying: "to mathematics". The fact that we can give this answer at all, and be partly right in giving it, is a wonderful thing in itself, almost a miracle. That mathematics, our only stock of certain knowledge, can be used with great precision to tell us useful things about the uncertain majority of human experience, is astounding. It poses, in fact, deep philosophical questions to which convincing answers are in short supply. In mathematical statistics, for example, there is an entity named the Poisson distribution, used for estimating the occurrence of rare events. It was first derived in 1837 by the French mathematician Simeon-Denis Poisson from a study of deaths by horse kicks in the Prussian army. It turns out that if you list the number of cavalry corps in which there were no deaths, one death, two deaths, three deaths, ... the numbers you have listed follow an elegant mathematical formula. When I first encountered this in my studies, I easily mastered the math but got stuck on the metaphysical question: How did the horses know when to stop kicking? I have still not seen any answer that leaves me entirely satisfied.

The first significant results in the mathematical theory of probability were given to us by Pierre Fermat and Blaise Pascal, who developed the fundamental principles in a sequence of letters in 1654 while discussing two problems posed by the Chevalier de Mere, a professional gambler. (The problems were how to divide the stakes of an unfinished game of chance between two players when one of them is ahead and how to quantify the odds in dice-throwing.) In The Science of Conjecture, James Franklin has set out to provide a full account of all non-mathematical approaches to probabilistic reasoning prior to that annus mirabilis and also, in a brief but very useful epilogue, to summarize subsequent non-mathematical developments. He has embraced a very wide field of inquiry indeed, taking in practically all the major intellectual disciplines and pseudo-disciplines, from medicine to moral theology, from rhetoric to astrology. He begins with Bishop Butler's phrase: "Probability is the very guide of life." He ends with a stirring, and very timely, defense of rational judgment against "the forces of unreason" that are on the loose in our academies.

The author reminds us that premodern thinkers had a keen grasp of the "science of conjecture" long before that science was quantified. Lawyers were specially skillful at weighing, and displaying, probabilities in a convincing way. Charged with having spoken against the supremacy of his king in matters religious, Sir Thomas More was confronted with just one witness, an ...