Book review - The Science of Conjecture Evidence and Probability before Pascal

by James Franklin, 497 pp, ISBN 0-8018-6569-7, Baltimore, Md,
The Johns Hopkins University Press, 2001
Reviewer Frederick Butzen.

In The Science of Conjecture, James Franklin, associate professor in mathematics at the University of New South Wales, tells the story of how people thought about evidence and likelihood in the years before Pascal and Fermat discovered how to compute probability. Because there are few areas of life in which people do not weigh likelihood and ponder evidence, The Science of Conjecture explores many out-of-the-way places from astronomy to witch trials, from religious redemption to maritime insurance. Through them all, Franklin shows how thought sharpened over the centuries, to the point where Pascal and Fermat could raise the measurement of likelihood from an art to a science.

Franklin calls this book a "Whig history of mentalities, a story of the Advance of Knowledge as the forces of Reason roll back the frontiers of ignorance." The author shows how one model succeeded another because it better describes reality, as proved by the test of functionality: as he puts it, "one idea can fly better than another, just as one plan for heavier-than-air aviation can work and one not." This idea is not fashionable among scholars, particularly those in the humanities; yet, like Dr Johnson kicking the stone, Franklin shows it to be true.

The Science of Conjecture begins with several chapters on the law. Case law, after all, largely consists of evaluating incomplete and contradictory evidence. Over the centuries, jurists refined the rules both for evaluating evidence and for concluding that a case was proved, leading to the "reasonable man" metaphor that is used to this day in English jurisprudence. Other topics include examination of wills for veracity, the measurement of consanguinity for purposes of divorce or annulment of marriage, and (perhaps the grimmest episode in the book) the Renaissance craze for witch trials.

Another chapter explores theology and ethics or, as Franklin calls them, "the rules for the deliberations of the internal forum of conscience." A person must judge both how licit his actions are and the state his mind was in when he performed the act. Both judgments are difficult under the best of circumstances, and both admit of doubt. Although this appears at first glance to be an abstruse topic, it is in fact the cornerstone of any discussion of ethical behavior. After all, behaving ethically requires judging both the act and one's own mind in evaluating the acta degree of self-knowledge that is not always in evidence. The theologians argued about how to evaluate self-knowledge, a topic that a number of recent murder trials have shown to be vitally important, yet still unsettled.

A chapter on the hard sciences, particularly astronomy, shows that these were rich grounds for thought about probability. In one of the book's most interesting sections, Franklin retells the development of the heliocentric model of the solar system. Unlike popular history, which pits a "bad" Ptolemy against a "good" Copernicus, Franklin describes how both worked to find the model that best describes the motions of the planets. The contributions of all were needed to discover the truth.

Another chapter explores how the science of conjecture developed among the "soft sciences," a class that includes physiognomics, divination, astrologyand medicine. "It is in medicine," Franklin notes, "that there is most pressure to find correct methods of learning from experience. And there is always money available for it. The subject matter, unfortunately, is recalcitrant; though there are true generalizations to be found, in contrast to divination or astrology, it is much harder than in astronomy to find simple hypotheses that are true universally."

As Franklin describes it, writers on medicine fell into two schools: Dogmatists, who held that theory should be paramount in devising treatment, and Empiricists, who rejected theory altogether in favor of a catalogue of treatments and outcomes. Both Dogmatists and Empiricists asserted a certainty that is destructive of knowledge: the Dogmatists edited experience to suit their theory; while the Empiricists catalogued phenomena but rejected any attempt to develop a model within which data can be organized.

Between them ran a pragmatic approach, which recognized the need for theory to organize data, but which also recognized the limits of theory. This approach seeks patterns and is satisfied with likelihood rather than certainty. This school, Franklin notes, is marked by "its choice of a middle path in finding the correct reference class for a generalization, still one of the hardest problems to solve in probabilistic reasoning."

One of the many topics Franklin discusses in passing is drug testing, which was as important in ancient times as it is now. The medieval Arab physician Avicenna noted that the following variables must be taken into account when determining a drug's effectiveness in treating a disease: purity of the drug, proper diagnosis of the disease, dosage, the disease stage at which the drug is administered, consistency of effect in multiple patients, and effectiveness in humans as opposed to animals. Protocols were devised to study drugs. For example, Bernard of Gordon proposed that drugs be tested first "on birds, then on dumb animals, then in hospitals, then on Franciscans." (It is not noted whether Bernard was a Dominican.)

A later chapter presents a fascinating study of aleatory contractsthat is, annuities, insurance, and lotteries. Franklin notes that the Catholic Church's ban on usury forced merchants to be creative in devising licit ways to raise capital. They discovered that they could sell risk in the form of an insurance policy. The Church held such policies to be licit because both insurer and policy holder shared risk, unlike usury, in which the lender is guaranteed a profit but the borrower performs all the work and bears all the risk. As early as the 13th century, Venetian insurers were underwriting merchant voyages. They adjusted their rates based on season, destination, and cargo which suggests that they had some rough-and-ready way to measure risk, centuries before Pascal.

In the book's final chapter, Franklin describes how Pascal and Fermat invented the mathematics of probability. They did so in order to solve an old problem, that of fairly dividing the stake in an interrupted game of dice. Those who are not familiar with the Pascal-Fermat letters will find Franklin's retelling both fascinating and enlightening.

The Science of Conjecture tells a fascinating story and tells it superbly. Its author is broadly and deeply learned, yet he wears his learning lightly. He writes densely but with clarity and wit. This reader found something of interest on nearly every page, to judge from my copy, which is heavy with marginal notes and underlining. I believe that it will be enjoyed by all who are interested in statistics or the history of thought, or who simply like a stimulating read. "Of that," in W. S. Gilbert's words,

. . . there is no manner of doubt
No probable, possible shadow of doubt
No possible doubt whatever.

*Frederick Butzen
Chicago, Ill

*Books, Journals, New Media Section Editor: Harriet S. Meyer, MD, Contributing Editor, JAMA; David H. Morse, MS, University of Southern California, Norris Medical Library, Journal Review Editor; adviser for new media, Robert Hogan, MD, San Diego.

Updated: 14 Dec 2007