The Science of Conjecture: Evidence and Probability Before Pascal

by James Franklin

During the seventeenth century, English law recovered the autonomy that had been threatened by absolute monarchy, with its unconstrained use of torture and its unconstitutional doctrine of the divine right of kings. The main mover was Sir Edward Coke, who defended the independence of the judiciary against James I, when absolutism was at its height.

Although by and large a jealous guardian of English traditions in law, in matters of evidence Coke tended to adopt Continental concepts, since English law had virtually nothing to say on the subject. His classification of the grades of evidence, much quoted later, is that of medieval Roman law: “Bracton saith, there is a probatio duplex, viz. viva, as by witnesses viva voce, and mortua, as by deeds, writings and instruments. And many times juries, together with other matter, are much induced by presumptions; whereof there be three sorts, viz. violent, probable and light or temerary. Violenta praesumptio is manie times plena probatio; as if one be runne throw the bodie with a sword in a house, whereof he instantly dieth, and a man is seen to come out of that house with a bloody sword, and no other man was at that time in the house. Praesumptio probabilis moveth little but praesumptio levis seu temeraria not at all. So it is in the case of a charter of feoffment, if all the witnesses to the deed be dead (as no man can keep his witnesses alive, and time weareth out all men) then violent presumption which stands for a proof is continuall and quiet possession.”97

Coke takes over the medieval distinction between presumptions which admit proof to the contrary and those which do not: “So if a man be within the four seas, and his wife hath a child, the law presumeth that it is the child of the husband, and against this presumption the law will admit no proof.”

Even Ockham’s Razor gets a mention, in the form, “It is in vain done by more, which can be done by fewer.”

All the old problems about balancing the number and weight of witnesses, and of authorities, recurred with argument from precedents. When one criticizes Scholastics and others for relying on arguments from authority, it is well to remember that there are disciplines, like law and theology, in which such arguments are indeed appropriate.

The resulting misgivings helped concentrate legal minds on questions of evidence, and the question was partly resolved by the Statute of Frauds of 1677, which required a written contract in such cases.

English law has certainly continued to emphasize decided cases over learned treatises on theory, though without its advantage over Continental law with regard to certainty becoming apparent.

But subtle distinctions among grades of presumptions, and fractions of proof, were ill adapted to explanation to juries. Eventually all probabilistic concepts in English law were reduced to one word, reasonable. The common understanding that the standard of proof in criminal trials should lie somewhere between suspicion and complete certainty came to be expressed solely in the formula “proof beyond reasonable doubt.”

The relevant sense of reasonable, and the phrase reasonable doubt, appeared in the sixteenth-century Scholastic, Suarez,110 while the reasonable man has an ancestor in the steady man of medieval canon law: If a man and woman are surprised by her father and compelled to marry, the man’s consent is null and the marriage void if the fear inflicted on him is such as would coerce a “steady man.”

The use of the formula “proof beyond reasonable doubt” to express the standard of proof in criminal cases became established in English law around 1800.

If rules for evaluating evidence in court seem natural to us, the idea that there should be rules for the deliberations of the internal forum of conscience is a very strange one. The modern attitude, at least before the recent widespread formation of ethics committees in medical research and the like, has been that there are no experts in morals. Everyone not warped by an unhappy childhood is presumed to be able to decide on what is right by an immediate intuition. Or if that is too absolutist a view of morals, it is regarded as the right of all to decide their own paths. In either case, experts are not invited to give their views.

the Catholic point of view is different, in a way that is important for the history of probability. There is a greater emphasis on the intention of the individual, leading to rules on what to do when the conscience is in doubt.

The word “probability” in the early seventeenth century mostly refers to the doctrine of probabilism in moral theology, and Pascal’s attacks on probabilism in the Provincial Letters did more than anything else to discredit casuistry and replace it with the modern attitude, in which each is his own judge of morality.

There is the inevitable origin in Aristotle. Perhaps the most read of all Aristotle’s works was the Nicomachean Ethics, and consequently the remarks about probability in the introduction are the most quoted and influential opinions on the subject, without exception: Our discussion will be adequate if it has as much clearness as the subject-matter admits of; for precision is not to be sought for alike in all discussions, any more than in all the products of the crafts.

for it is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits; it is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician demonstrative proofs.

The story resumes, as do so many in the history of ideas, with the twelfth-century Renaissance. The period was one of the discovery of the inner life and the origin of European individualism.2 Antiquity does not have autobiography, in the modern sense, and the meaning of the word “classical” attests to a certain impersonality that everyone can sense in ancient art. The Gospels’ ethical emphasis on the intention of the heart, developed by Augustine’s Confessions, provided the foundation for a new orientation.3 The twelfth century concentrates on the personal in sculpture and stained glass, in the autobiographies of Abelard and others, in the poetry of the troubadours and Chrétien de Troyes, in the piety of confession and devotion to Mary, and in Abelard’s theory that sin is essentially a matter of internal consent to evil.

Now it is no accident that confession is the common name for the sacrament of penance as well as that of the “queen of proofs” in law. In effect, Innocent and the church hierarchy saw the confessional as a miniature, though secret, court of canon law.

The decree requiring confession was soon obeyed almost everywhere, and the effect on the European soul was profound.8 The mere effort to classify a year’s sins was a greater demand for abstract thought than the common man or woman had experienced before. Guilt flourished, though without as much diminution as might have been hoped in things to be guilty about. Sin and conscience became prominent topics of study, and it is here that much of the subsequent discussion of doubts and their resolution occurs.

Evaluation of evidence was thus a moral matter, while conscience had a cognitive role. When evaluating cases of doubt from a moral point of view, there are requirements other than that of simply reaching the most probable conclusion.

Innocent III again had a part to play, in enunciating another of the general maxims so favored by medieval lawyers: “In doubtful matters the safer path is to be chosen” (In dubiis via est tutior eligenda).13 This much-discussed axiom, sane enough on the surface, stands in need of some interpretation. What does safer mean? Does it mean more probable? Or morally safer? Can these two meanings conflict? The more natural interpretation is morally safer, as explained by Peter the Chanter: in doubtful cases in which doctors disagree and no decision can be found in scripture or in papal decrees, “it is safer to incline to that part in which it is certain there is no sin.”

In hard times, there are always demands that academic research should be “relevant.” Political theorists are funded to justify the tyrannies of their patrons, mathematicians to perfect weaponry and devise tax minimization schemes. He who pays the piper calls the tune.

The outcome in theology was the production of manuals for confessors. It was these that eventually produced the theory known as probabilism.

Particularly influential were the various works on morals by Jean Gerson, chancellor of the University of Paris around 1400. Gerson seems to have been the first to introduce the term, occasionally still heard in English, “moral certainty” (certitudo moralis) to mean a very high but not complete degree of persuasion.

In general, one should have moral certainty that a proposed course of action is right before doing it.

Gerson obviously did not mean to suggest by “moral certainty” any more than the content of the Aristotelian remark that less certainty is to be found in morals than in mathematics. It is a dangerous phrase nevertheless, tending to suggest as it does that something that is not certain is certain. Just as a suspected criminal is not a kind of criminal, so moral certainty is not a kind of certainty. But there is an inevitable tendency to think it is. The problem is the same as in some modern philosophies of science that describe a theory against which there is (merely) statistical evidence as “refuted”—it confuses deductive reasons with nondeductive ones.

The entry for probable is, “‘Probable’ is used in two ways. First as the opposite of hidden, that is what is proved by witnesses (see ‘Notorious’). Second, as what pertains to opinion. And this in two ways. First, the object of a believed opinion; thus Aristotle (Topics I) says that the probable is what seems to be to all, or most, or the wise . . . according to the Chancellor [Gerson], what is thus probable is called morally certain . . . it is equally vicious for the mathematician to seek the persuasive as for the moralist the demonstrative.”

While tutiorism in the hands of the medievals had been an instrument for directing the faithful along the paths of approved conduct, Adrian drew a consequence that was certainly logical but not such as to commend itself to the powers that be. This was an age, it will be recalled, when the powers were more than usually powerful. The period of the Renaissance and the Reformation discovered the individual to be worthless in the sight not only of God but also of the state. Western Europe took centuries to recover from the diversion of political development away from medieval constitutionalism to primitive divine right absolutism.

As the historian Tawney remarked, “Sceptical as to the existence of unicorns and salamanders, the age of Machiavelli and Henry VIII found food for its credulity in the worship of that rare monster, the God-fearing Prince.”

Into this un-receptive milieu Adrian dropped his tutiorist corollary: if a soldier has doubts as to the justice of the prince’s war, he must not serve in it, this being the safer course (morally safer, of course, rather than physically).33 This argument was dealt with rather neatly by Francisco de Vitoria, founder of the Thomist School of Salamanca. Before describing his answer, let us look at how he used probability in something more central to his work. According to many, Vitoria was the real founder of international law.34 Professor of theology at the University of Salamanca from 1526...

Nor are the Indians in a particularly good evidential situation: “They are not bound to believe unless the faith has been set before them with persuasive probability. But I have not heard of any miracles or signs, nor of any exemplary saintliness of life sufficient to convert them. On the contrary, I hear only of provocations, savage crimes, and multitudes of unholy acts.”

To Adrian’s argument Vitoria answers with a balancing of risks: “If subjects fail to obey their prince in war from scruples of doubt, they run the risk of betraying the commonwealth into the hands of the enemy, which is much worse than fighting the enemy, doubts notwithstanding.”37 He interestingly compares the case with other standard cases of action under uncertainty: an officer of the law must carry out the judge’s sentence, even if he doubts its justice.

Bartolome de Medina, another student of Vitoria, was celebrated as the author of probabilism, the doctrine that in moral matters one may follow an opinion that is probable, even if the opposite is more probable. This proposition appeared in his commentary on the Summa of Aquinas, published in Salamanca in 1577. It is worth quoting his views at some length, since they summarize everything that has gone before, and they are the classic statement of what probability normally meant in the century before Pascal.

These arguments certainly seem very good, but it seems to me that if an opinion is probable it is licit to follow it, though the opposite be more probable.

Medina is a powerful arguer, but plainly something has gone very wrong. He is trying to think of probable and more probable by analogy with safe and safer and also sees probable as meaning something like approvable—as its etymology might suggest. But the case he is dealing with is that of a probable opinion and, its opposite, which is more probable. This is completely impossible on a usual understanding of probable, since if the opposite of a proposition is more probable than it, then the proposition itself is not probable but improbable. But this is only so if probable is taken to mean, as it should, probable on one’s total evidence, that is, after consideration of all reasons for and against. It is natural not to do this, and to regard probable as meaning “supported by some good reasons” (irrespective of the reasons there may be to the contrary). It is Medina’s conflation of “supported by good reasons” with “supported by the total of all reasons relevant to it” that has led to his assertion of probabilism.

By far the best-known of the School of Salamanca was Francisco Suarez, the most famous philosopher of the sixteenth century and of the Jesuit order. He is regarded by modern followers of Aquinas as the foremost of the “decadent Scholastics,” to whose perversions they attribute the decline of medieval thought. His taste for novelty (as we would say, originality) in opinions, while staying within the Scholastic framework of questions, is expressed in his treatment of obligation and doubt.

Suarez is not so cavalier in allowing dispensations from the law of the state. While obedience to human laws that are contrary to God’s is not permitted, Suarez asks how much certainty one must have of the evil of a law in order to disobey it. The standard he requires is moral certainty. “For if the matter is doubtful, a presumption must be made in favour of the lawgiver . . . otherwise the subjects would assume an excessive licence to disregard the laws, since the latter can hardly be so just that it is impossible for them to be called in doubt by some for apparent reasons.”

Suarez’ main contribution to theory was a clear distinction between negative and positive doubt. Doubt is negative when there are no reasons for either side, positive when there are reasons but there is some balance between them. The distinction is relevant to Suarez’ treatment of the case of common soldiers in doubt whether the war of their prince is just: “If the doubt is purely negative, it is more probable that they can go to war, without examining the fact, and leaving the whole burden to the Prince to whom they are subject; whom however I suppose to be of good reputation among all. This is clearly taught by Vitoria and agreed to by all Thomists. But if the doubt is positive, and there are probable reasons on either side, I believe they are perhaps obliged to inquire into the truth. If they cannot arrive at that, they should follow what is more probable, and aid him who more probably is in the right; for when there is doubt on a matter of fact, and one which concerns the harm of our neighbour or the defence of the innocent, one must follow what appears more probable.”

his distinction between negative and positive doubt points to a much later era. The debates of the time of Laplace on the principle of insufficient reason never satisfactorily resolved whether the probability of a coin’s landing heads is a half because the coin is symmetrical, and hence there is no reason to prefer heads to tails, or because many throws of coins have been observed to produce about half heads and half tails. Keynes’ chapter on the weight of evidence shows that we are still no closer to explaining the difference between the probability of a hypothesis in the two cases in which there is little evidence with a certain probability on balance and in which there is a great deal of evidence with the same probability on balance.46 Are there two dimensions of probability, one giving the total probability and the other the firmness or weight with which that probability can be held?

Suarez made another and more lasting contribution to debate on the just war. Twentieth-century Catholic just war theory has been prepared to consider that some wars might be just if they satisfy certain stringent conditions. The list of these is not fixed but is roughly the following: the war must be fought for a just cause, involving a grave injury to the state; it must be declared by a legitimate authority—in particular only states may declare war; it should be conducted by legitimate means for a limited end, in proportion to the injury; and there must be a reasonable chance of winning.

The initiator of the reasonable chance condition was Suarez, in the following passage, which asserts that there ought to be some reasonable proportion between the probability of victory and the harms involved:

The wreck of Scholastic casuistry in the mid-seventeenth century left among its detritus the theory of international relations. The survival of this fragment owes something to the distributed nature of international power: There is no overarching legislative or legal power, so individual nations are thrown back on their own casuistical resources to justify their positions. It also owes something to the individual success of the last of the Scholastic theorists and first of the moderns, Grotius.

In the era of Rembrandt, Vermeer, Huygens, Snell, Spinoza, and Tasman, the leading contributor from Holland in the area of social science was Hugo Grotius.

Grotius is clear that political affairs are bound by the same moral principles as any other actions. At the opposite extreme was the position of Machiavelli, or at least the one popularly attributed to him, that there is no connection between morality and political action. While Machiavellianism was universally abhorred, there was a school of thought that sought a middle way, holding that actions not normally licit, like lying, might be justified in political affairs by reason of state—”a mean between that which conscience permits and affairs require.”52 The notion was justified in terms of a primitive decision theory involving considerations of risk. It is all very well for the prince to keep to high-minded moral principles like keeping his word, but ought he do so when the safety of his subjects is at stake?

Hobbes’ political theories were, in a sense, entirely founded on the concept of risk, or danger, although he does not exactly express himself in those terms. Or from another point of view, his position can be seen as the just war theory writ small, in which the actors are individual persons instead of states, though he does not use precisely those terms either. The famous phrase in Leviathan about the life of man in a state of nature being “nasty, brutish, and short” occurs in a paragraph that attributes that condition to lack of certainty about the effects of actions. “In such condition, there is no place for industry; because the fruit thereof is uncertain: and consequently no culture of the earth, no navigation . . . no arts, no letters, no society; and, which is worst of all, continual fear, and danger of violent death; and the life of man, solitary, poor, nasty, brutish and short.”

Hobbes’ phrase “just suspicions” alludes to the casuists’ use of this concept. It descends from the fear that the steady man of medieval canon law was to evaluate. The casuists define the just fear that is sufficient to nullify a contract as one that would disturb a steady man.

The connection between cold-blooded calculation with probabilities and lack of moral fiber was beginning to look close.

In the eighty years after Bartolome de Medina proposed it, the doctrine of probabilism had an astonishing success among Catholic theologians, as author after author strove to attenuate the obligation of law in cases of a doubting conscience. Moral theology was the concern of the age, and the print expended on that subject far exceeded that on science, for which the period in question is now chiefly known.

It was not really true, as Pascal’s Provincial Letters claim, that the entire Jesuit order was committed to the thesis that an opinion was probable, and hence permitted, if there was a single doctor who asserted it. But the truth is not so distant as to make the caricature unrecognizable.

Yet another Jesuit advises that one need not be certain of the probability of an opinion one adopts; it is enough that it be “probably probable.”

Escobar, later made famous by the attacks on him in the Provincial Letters, rejoices in the diversity of moral opinions among doctors, by which the yoke of the Lord is made lighter.67 These doctors naturally praise one another extravagantly, giving their opinions even more extrinsic probability. The expression Barockmorale is unavoidable.