### Evidence and Probability before Pascal

James Franklin, The Science of Conjecture: Evidence and Probability before Pascal, Baltimore: John Hopkins University Press, 2001. Pp. xiii + 497. $55.00, cloth (ISBN 0-8018-6569-7); $22.50, paper (ISBN 0-8018-7109-3).

In The Science of Conjecture, James Franklin, a mathematics lecturer at the University of New South Wales, reviews ancient, medieval, and premodern reasoning about both random and nonrandom events in theology, law, rhetoric, philosophy, science, medicine, and commerce. The subject is not just "probability" in the sense of a gradation of the likelihood of the truth of various propositions, but "mental technologies" (321) for forming beliefs and making decisions about uncertain events or theories. For instance, the varying numbers of witnesses needed to condemn bishops, cardinal priests, and other church officers, according to the medieval False Decretals, is denominated "the world's first quantitative theory of probability" (14). The account of such practices "is a Whig history of mentalities, a story of the Advance of Knowledge as the forces of Reason roll back the frontiers of ignorance.... Generally, a new idea in probability is seen to replace an older one because it is a better idea" (321).

1

There is much detail of interest to lawyers, historians, and many other types of readers in this ambitious survey, but it is not clear that the material demonstrates the truth of the broad thesis of monotonic improvements in "mental technologies." For example, the resort to torture and the veneration of confessions as the "queen of proofs" in medieval Continental law (26) hardly seems like an advance over the deliberations of the Sanhedrin. Franklin sees the resort to torture not as a counterexample to his thesis of progress, but as part of "a darker subplot"—a descent into irrationality induced by demanding certainty when it is not available (360). But this is a subplot that complicates the simple Whiggish claim. And even as to the class of "rational" methods for handling uncertainty, the book makes no effort to explain how one might determine whether an idea is a superior mental technology. Instead, Franklin is content to invoke an inapposite analogy, writing that "[i]n mental technologies, one idea can fly better than another, just as one plan for heavier-than-air aviation can work and one not" (321).

2

Many of the statements about the law and legal systems are difficult to follow. For instance, there is a discussion of "presumptions" in ancient law, but the term is quite protean, ranging from generalizations to the burden of persuasion. In a later chapter, the term "presumption" is used to characterize circumstantial evidence (37). There is historical precedent for such usages, but the failure to distinguish between the archaic and the modern places a special burden on the reader. This burden is increased by a tendency to add conclusions or characterizations elliptically. Thus, many of the connections made are not fully developed. For instance, Franklin describes the Talmudic practice of admonishing witnesses in capital cases that circumstantial evidence and hearsay are unacceptable as "the earliest instance of a requirement similar to the rule in English law that in criminal cases proof must be 'beyond reasonable doubt'" (5).

3

Similarly, we are told that "the inroads of mathematical probability into law have been minimal" (366). By this, Franklin apparently means (a) that "all attempts to quantify the concept [of proof beyond a reasonable doubt] have been resisted" (365) and (b) that the "reasonable man" standard of tort law is no more precise today than it was centuries ago (366–67). This is a narrow notion of what it means for statistics and probability to contribute to legal fact finding and decision making, and one should not take it as a claim that the offerings of these disciplines have been spurned. Modern courts have employed a cardinal scale for probability to describe the differing burdens of persuasions. For instance, the requirement in civil cases of proof by a preponderance of the evidence is widely understood to mean that plaintiffs must prove their cases to a probability exceeding one-half. See, for example, United States v. Fatico, 458 F.Supp. 388 (E. D. N. Y. 1978); D. H. Kaye, "Clarifying the Burden of Persuasion: What Bayesian Decision Rules Do and Do Not Do," International Journal of Evidence and Proof 3 (1999): 1–28. Indeed, some courts in toxic tort cases have translated this numerical criterion into a more-or-less bright-line (and questionable) rule that epidemiological studies must reveal relative risks exceeding two to satisfy this burden with regard to specific causation. See generally Russellyn S. Carruth and Bernard D. Goldstein, "Relative Risk Greater Than Two in Proof of Causation in Toxic Tort Litigation," Jurimetrics: The Journal of Law, Science, and Technology 41 (2001): 195–209. The United States Supreme Court has invoked the ideas of statistical decision theory to explicate the burdens of persuasion, and some judges have described "proof beyond a reasonable doubt" in starkly numerical terms. See Branion v. Gramly, 855 F.2d 1256 (7th Cir.1988) (Easterbrook, J.); cases cited, D. H. Kaye, "Statistical Significance and the Burden of Persuasion," Law and Contemporary Problems 46 (1983): 13–23; cf. Ballew v. Georgia, 435 U.S. 223 (1978) (opinion of Blackmun and Stevens, JJ., discussing probabilities of erroneous convictions as a function of jury size on the "perhaps not unreasonable" assumption that Type I errors are ten times more serious than Type II errors). Beyond these uses of probability in judicial opinions, thousands of cases involve statistical studies and probability calculations as evidence. See generally Modern Scientific Evidence: The Law and Science of Expert Testimony, ed. David Faigman, D. H. Kaye, Michael Saks, and Joseph Sanders, 3d ed. (St. Paul: West Publishing, 2002), vol. 1, 155–330. These may not the kinds of inroads that Franklin has in mind, but they are important nonetheless.

4

In short, the strength of The Science of Conjecture lies in its panoramic exposition of developments across the centuries and across intellectual disciplines and human endeavors. It is, as one reviewer wrote, "a magisterial account of matters as diverse as the Talmud, Justinian's Digest, torture, witch hunts, Tudor treason trials, ancient and medieval astronomy and physics, humanist historiography, scholastic philosophy, speculations in public debt, and 17th century mathematics." James Gordley, "Book Review," International Journal of Evidence and Proof 6 (2002): 191. At the same time, it is "a dense, quite difficult and often very dry account of a large and important subject" (John Derbyshire, "Induction Rules," New Criterion, June 2001, 79).

In The Science of Conjecture, James Franklin, a mathematics lecturer at the University of New South Wales, reviews ancient, medieval, and premodern reasoning about both random and nonrandom events in theology, law, rhetoric, philosophy, science, medicine, and commerce. The subject is not just "probability" in the sense of a gradation of the likelihood of the truth of various propositions, but "mental technologies" (321) for forming beliefs and making decisions about uncertain events or theories. For instance, the varying numbers of witnesses needed to condemn bishops, cardinal priests, and other church officers, according to the medieval False Decretals, is denominated "the world's first quantitative theory of probability" (14). The account of such practices "is a Whig history of mentalities, a story of the Advance of Knowledge as the forces of Reason roll back the frontiers of ignorance.... Generally, a new idea in probability is seen to replace an older one because it is a better idea" (321).

1

There is much detail of interest to lawyers, historians, and many other types of readers in this ambitious survey, but it is not clear that the material demonstrates the truth of the broad thesis of monotonic improvements in "mental technologies." For example, the resort to torture and the veneration of confessions as the "queen of proofs" in medieval Continental law (26) hardly seems like an advance over the deliberations of the Sanhedrin. Franklin sees the resort to torture not as a counterexample to his thesis of progress, but as part of "a darker subplot"—a descent into irrationality induced by demanding certainty when it is not available (360). But this is a subplot that complicates the simple Whiggish claim. And even as to the class of "rational" methods for handling uncertainty, the book makes no effort to explain how one might determine whether an idea is a superior mental technology. Instead, Franklin is content to invoke an inapposite analogy, writing that "[i]n mental technologies, one idea can fly better than another, just as one plan for heavier-than-air aviation can work and one not" (321).

2

Many of the statements about the law and legal systems are difficult to follow. For instance, there is a discussion of "presumptions" in ancient law, but the term is quite protean, ranging from generalizations to the burden of persuasion. In a later chapter, the term "presumption" is used to characterize circumstantial evidence (37). There is historical precedent for such usages, but the failure to distinguish between the archaic and the modern places a special burden on the reader. This burden is increased by a tendency to add conclusions or characterizations elliptically. Thus, many of the connections made are not fully developed. For instance, Franklin describes the Talmudic practice of admonishing witnesses in capital cases that circumstantial evidence and hearsay are unacceptable as "the earliest instance of a requirement similar to the rule in English law that in criminal cases proof must be 'beyond reasonable doubt'" (5).

3

Similarly, we are told that "the inroads of mathematical probability into law have been minimal" (366). By this, Franklin apparently means (a) that "all attempts to quantify the concept [of proof beyond a reasonable doubt] have been resisted" (365) and (b) that the "reasonable man" standard of tort law is no more precise today than it was centuries ago (366–67). This is a narrow notion of what it means for statistics and probability to contribute to legal fact finding and decision making, and one should not take it as a claim that the offerings of these disciplines have been spurned. Modern courts have employed a cardinal scale for probability to describe the differing burdens of persuasions. For instance, the requirement in civil cases of proof by a preponderance of the evidence is widely understood to mean that plaintiffs must prove their cases to a probability exceeding one-half. See, for example, United States v. Fatico, 458 F.Supp. 388 (E. D. N. Y. 1978); D. H. Kaye, "Clarifying the Burden of Persuasion: What Bayesian Decision Rules Do and Do Not Do," International Journal of Evidence and Proof 3 (1999): 1–28. Indeed, some courts in toxic tort cases have translated this numerical criterion into a more-or-less bright-line (and questionable) rule that epidemiological studies must reveal relative risks exceeding two to satisfy this burden with regard to specific causation. See generally Russellyn S. Carruth and Bernard D. Goldstein, "Relative Risk Greater Than Two in Proof of Causation in Toxic Tort Litigation," Jurimetrics: The Journal of Law, Science, and Technology 41 (2001): 195–209. The United States Supreme Court has invoked the ideas of statistical decision theory to explicate the burdens of persuasion, and some judges have described "proof beyond a reasonable doubt" in starkly numerical terms. See Branion v. Gramly, 855 F.2d 1256 (7th Cir.1988) (Easterbrook, J.); cases cited, D. H. Kaye, "Statistical Significance and the Burden of Persuasion," Law and Contemporary Problems 46 (1983): 13–23; cf. Ballew v. Georgia, 435 U.S. 223 (1978) (opinion of Blackmun and Stevens, JJ., discussing probabilities of erroneous convictions as a function of jury size on the "perhaps not unreasonable" assumption that Type I errors are ten times more serious than Type II errors). Beyond these uses of probability in judicial opinions, thousands of cases involve statistical studies and probability calculations as evidence. See generally Modern Scientific Evidence: The Law and Science of Expert Testimony, ed. David Faigman, D. H. Kaye, Michael Saks, and Joseph Sanders, 3d ed. (St. Paul: West Publishing, 2002), vol. 1, 155–330. These may not the kinds of inroads that Franklin has in mind, but they are important nonetheless.

4

In short, the strength of The Science of Conjecture lies in its panoramic exposition of developments across the centuries and across intellectual disciplines and human endeavors. It is, as one reviewer wrote, "a magisterial account of matters as diverse as the Talmud, Justinian's Digest, torture, witch hunts, Tudor treason trials, ancient and medieval astronomy and physics, humanist historiography, scholastic philosophy, speculations in public debt, and 17th century mathematics." James Gordley, "Book Review," International Journal of Evidence and Proof 6 (2002): 191. At the same time, it is "a dense, quite difficult and often very dry account of a large and important subject" (John Derbyshire, "Induction Rules," New Criterion, June 2001, 79).

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