The Science of Conjecture: Evidence and Probability Before Pascal

by James Franklin

This is the earliest instance of a requirement similar to the rule in English law that in criminal cases proof must be “beyond reasonable doubt.”

An unusual feature of Jewish law was that it always refused to admit confessions as evidence in criminal law.

A happy result of this prohibition is that Jewish legal procedure was always free of torture.

There is also in the Talmud a good deal of reasoning from presumption (hazakah), that is, something that is taken as true unless there is reason to think otherwise.

Another kind of presumption arises from “what happens mostly” (a kind of reasoning that we see also in Aristotle, Cicero, and the Greek medical writers). Decisions can be based on such well-known generalizations as “One does not ordinarily pay a debt before term” (though exceptions are recognized as common enough), “Most women’s pregnancies last nine months,” “Most children will turn out to be fertile.”19 Such presumptions may conflict, in which case a distinction needs to be drawn to see which is applicable.

Roman law too was rather explicit about its rules of evidence, though, as in other areas, in a rather haphazard way.23 The concept of “onus of proof,” though not itself probabilistic, was basic to further developments. The fundamental rule in Roman law, and since, was that “proof is incumbent on the party who affirms a fact, not on him who denies it.”24 This was developed into the rule that is the ancestor of modern “proof beyond reasonable doubt” laws.

The tendency of Roman law was always to keep very close to the cases rather than to generalize; this causes some of the rules to be, to our eyes, overspecialized

A rescript of Hadrian says that “it is impossible to define strictly the amount and mode of proof needed on each issue. The truth can often but not always be found without recourse to public records. Sometimes the number of witnesses, sometimes their dignity and authority, at others common knowledge settles the truth of the matter in issue. In short, all I can reply to you is that a judicial inquiry should not be tied at once to a single mode of proof. You must judge from your own conviction what you believe and what you find not proved.”

An emphasis on the inner conviction of the judge is characteristic of such later absolutist regimes as those of Robespierre and Stalin.

The connection between torture and the sufficiency of evidence is especially clear in the requirement that judges investigating public crimes should not begin with torture but should use whatever “likely and probable arguments” (argumentis verisimilibus probabilibusque) were already available.

That these words really do mean “probable” is confirmed by the fact that such arguments can be overcome by proofs to the contrary: “It is likely (verisimile), however, that in this instance also the party who gave the dowry had a view to his own interest; for he who made the gift on account of the marriage can, if the marriage is not performed, bring an action for recovery as if on the ground of want of consideration, unless the woman should be able to show by the most evident proofs that he did this rather for her benefit than for his own advantage.”

An explicit link appeared between probability and presumptions. Sometimes presumptions were, as in Jewish law and the modern presumption of innocence, methods of reaching decisions under uncertainty, irrespective of whether the decision was probable or not.

if there was a doubt as to whether a child was in fact the issue of someone who had left money in a will, the presumption was in favor of the child.43 That is, the question was settled for moral reasons, without considering how probable the outcome was. But at other times, a presumption clearly does mean what is probable:

Here and elsewhere the essential idea of a presumption is seen to consist in what is now called default reasoning: A presumption is what is to be taken as true, unless and until there are reasons to the contrary.45 That there can be grades of presumption is never explicitly stated but is suggested by the mention at one point of a “not light” presumption.46

“a [Roman] jurisconsult would immediately feel at home in running over these briefly formulated definitions and precepts [in the Narada].”49 The similarity in method with Roman law is clear. Internal laws of development of law codes generally could explain the common outcome but hardly the simultaneity.

MEDIEVAL LAW IS BUILT on ancient law. Continental medieval law actually claims to be the same as ancient (Roman) law, with a few minor changes. It is not. The difference is that the medievals and their successors are always explaining principles, comparing texts, arguing about the conflict of one text or principle with another. In the course of doing so, they are forever drawing distinctions. Among them are distinctions among the grades of proof.

The resulting theory is a coherent one. It is not numerical, and there is no reason to think that it would have been improved if it had been numerical.

since modern (English) law has a similar theory, and insists on keeping it nonnumerical,1 there is every reason to believe the medievals were correct in avoiding numbers.

when a seventeenth-century writer evaluates scientific evidence, or discusses conflicting claims in religion, he turns to the language of the law of evidence. Consequently, this is the central chapter in the book.

The story of anything intellectual in the centuries between the time of Justinian and the Gregorian Reform amounts to occasional survivals, at the most minimal level, of what was done in antiquity. Nevertheless, the common picture of the monks blindly copying ancient manuscripts they did not understand is something of a caricature of the way ancient thought survived. Among advanced concepts that survived in actual use, legal ones were among the most successful.

The legal system of the tribal world was not as irrational as it seems at first. The more picturesquely irrational methods seem to have been largely reserved for doubtful cases, as proofs of last resort, when the common knowledge of the neighborhood failed to produce an agreed outcome.

There is certainly a case for saying that if evidence really is balanced, any method of breaking the deadlock is as rational as any other.

It is the world’s first quantitative theory of probability. Which shows why being quantitative about probability is not necessarily a good thing.

The periods immediately following the Dark Ages are known as the Gregorian Reform and the twelfth-century “Renaissance.” These weak terms entirely fail to express the magnitude of what happened.

If developments in probability suddenly appear in fifth-century B.C. Athens or seventeenth-century France, no one is surprised, since the general outline of events in those times and places is well known, and it is generally understood why those were periods of rapid intellectual change. It may be less expected that twelfth-century France and Italy should be a hotbed of probability theories, since modern perceptions of that epoch have been distorted by propaganda connected with the myth of the Renaissance, which requires the Renaissance to contrast with an earlier period of darkness and slow change. A series of books in recent decades has convinced the majority of medieval historians that the period 1050–1200 was the real turning point in Western history that created modern Europe.

The central individual of the eleventh century was the monk Hildebrand, later Pope Gregory VII; the Catholic Church as a centralized bureaucracy of educated celibate clergy, independent of local political control, is largely his creation.

For the story of this book, it is important that the Gregorian revolution was led on the intellectual front by logic and law, the fields in which probability had been developed in antiquity. These two subjects achieved a relative importance that they have never had before or since.

Law was the means by which all the other advances were put securely into place.

Though all the major ancient thinkers—Aristotle, Ptolemy, Euclid, Plato—had been rediscovered and translated by 1200, the first great find was Justinian’s Digest, discovered in an Italian library about 1070, possibly by agents of Gregory VII looking for texts to support papal claims.

On such matters of evidence, the Lombard commentators already show the characteristic medieval tendency to generalize much more than the Roman lawyers and to inquire into abstract principles. How can a law legislate against those who plot against the king’s life, when only God can know anyone’s thought? “[The question] is solved in this way: it is known through indications, for example if someone is discovered in the king’s chambers after hours having a naked sword under his cloak, or with a knife in his sleeve, or if the cupbearer of the king while near him is seen to prepare poison.”

The theme of proof by indications, later called circumstantial evidence, has been one of the most vexed themes in the law of evidence.18 It is not essentially a legal question but one involving judgments of probability from facts to facts.

Whereas understanding the Digest itself is like interpreting fossil remains, reading the Glossators is not unlike reading a modern legal judgment. The reason is simply that modern law, both English and Continental, descends from the Glossators in an unbroken tradition.

The Glossators were at once faced with a problem. Their initially reverent and literal approach to the text had to coexist with a number of inconsistencies in the text. Of this dilemma was born the Scholastic method characteristic of the whole of medieval thought. A topic is discussed by collecting authoritative texts and arguments that are or seem to be contradictory and then resolving the apparent contradiction by looking for suitable general principles and distinctions. It is the principles, vocabulary, maxims, and concepts of great generality produced by this method that constitute the most lasting contribution of medieval thinking to later thought.

Since the Corpus almost wholly lacks any explanation of general principles, a certain amount of creative interpretation was necessary. The originality of a medieval juristic proposal may often be judged by the irrelevance of the texts cited to support it. This greatly incensed the Renaissance humanists, who complained at length about the medieval jurists’ barbaric accretions on the original Roman law (“nothing but filth and villainy,” says Rabelais),21 but from the point of view of developing concepts, as opposed to preserving the purity of a more primitive era, one’s sympathies may well lie with the Glossators.

Presumption is said to be “not properly proof but standing in place of proof” and “standing until the contrary be proved.”

“The law presumes her a slave, who has been a slave, unless by some supervening circumstance the contrary is proved.”26 The last example illustrates reasoning by presumption from the past to the present, in which legal reasoning comes close to induction.

presumptiones iuris et de iure.

the most significant and original idea of the Glossators for probabilistic argument: half-proof (semiplena probatio). In the 1190s, this word was invented for the class of items of evidence that were neither null nor full proof.31 The word expresses the natural thought that, if two witnesses are in theory full proof, then one witness must be half. Azo writes: “It would seem this does not hold, because either the plaintiff proves, or not. If he proves, the defendant should be condemned. If not, he is acquitted, according to the rule. . . . I reply that although according to Aristotle it would seem to be an exhaustive division, it is not so according to the laws. There is a medium, namely, half-proof. Say therefore that in such a case proof has been less than full. Then the judge gives the right to complete the case by oath to the plaintiff. Otherwise if he has not proved at all, the defendant is acquitted, and an oath is not allowed, except in cases where the law gives the defendant the right to clear himself by oath. . . . The right to an oath is therefore given to the plaintiff if he half proves, either by private documents, or by the flight of the defendant . . . or by one witness. . . . Full proof is by two witnesses, therefore half proof by one.”

The importance of this text is the statement in the abstract that there are degrees of rational belief. The division is close to the Glossators’ divisions of proofs. It is not unlike some remarks of Quintilian (see chapter 5), but the relevant book of Quintilian was apparently unknown in the Middle Ages.

The threefold division of presumptions into rash, probable, and violent was repeated by all standard legal authors for centuries.

The man most responsible for making the intellectual apparatus of canon law part of everyday practice is Innocent III, pope from 1198 to 1216 and the most powerful pope in history. His rule marks a dividing line in medieval history. Medievalists divide into two camps according to their attitudes to the times before and after this date. Thomists and others see the age before 1200 as essentially a prelude to the building of great structures, Aquinas’s Summa theologiae, the high Gothic cathedrals, and the Divine Comedy. The opposite view is that a bright new dawn was hijacked by careerist bureaucrats, lawyers, dry Scholastics, and inquisitors. These views agree at least that the world became more organized, and writings even of the time reflect a recognition that everything from then on was controlled by and for “the system,” that is, the Papal Curia.

The reader will suspect that I am not choosing examples at random but am acting like filmmakers who view the Middle Ages as a setting in which one may be particularly free with examples of sex and violence. That is not true.

The Roman law studied at Bologna was not at first in force anywhere. In southern Europe, a much simplified system of Roman law had partly survived, but in most of Europe the law up to about 1200 remained largely the customary law of the Germanic tribes. The methods of proof by ordeal did not survive the rationalist mood of the twelfth century. Popular belief waned as ordeal by battle was sometimes replaced by contests of hired champions,63 a procedure whose faults are especially evident, though the concept is not entirely unknown to modern law.

He expresses the new mood using the language of reason and probability: “No one ought to tempt God when he has rational courses of action. . . . If the miracles the Lord promised in the Gospel . . . are not guaranteed (nec sunt in necessitate) how can these ordeal miracles be guaranteed to happen or have their result? . . . In doubtful cases sentence should be withheld, especially in capital cases, where there should be no proceeding merely conjecturally or probably but only judging with reasons transparent and clearer than light.”

Compurgation is not strictly irrational, provided the sanctity of oaths retains its meaning. Though it was retained in some places as a useful second line of defense after some rationalization,67 it was clearly unsuited as a main method of deciding criminal cases.

There were two choices available, and the different choice made by English and Continental law remains the most prominent difference between the two to the present day. The English option stemmed from the fact that Henry II instituted a working system of evidence evaluation. This was the jury, in the form later known as the grand jury, or jury of presentment. Its original purpose was to decide whether the evidence was strong enough to proceed to the ordeal. The evidence was to be evaluated more or less freely, not by the judge but by a panel of men to whom the accused could not reasonably object, namely his peers (“who would understand”).

When the ordeals were forbidden, England thus had a working system of evaluating evidence capable of replacing them. By 1220 a system of juries (petty juries, distinct from grand juries) was enforced for final verdicts in cases in which guilt was neither manifest nor only lightly suspected.72 Since the evaluation of the evidence was still effectively free, however, there was little call for rules concerning it, so English law has not contributed as much to the discussion of probability as has Continental law. Another effect was that English law never accepted torture to obtain evidence.

The solution adopted on the Continent was that the judge evaluated the evidence but was bound by strict rules that were publicly known and seen to be fair. The two-witness rule was a beginning. Actually reducing the evaluation of evidence completely to rules was not contemplated, however; the possibility was denied in the Roman law texts, and it has not proved possible since.

The desire for certainty, the wish not to condemn anyone “solely on account of suspicion, however vehement,” as Innocent put it, pushed the legal system toward a policy of trying and trying again until a confession was achieved. Torture was used more and more as time went on.

been remarked that the English jury could convict on less evidence than the Glossators required for torture,76 and it can hardly be doubted that the jury system avoided torture at a high cost in unjust sentences of death. The most serious problems with the European system arose for those suspected of particularly heinous crimes that left no traces—like rape, treason, heresy, and witchcraft.