The Science of Conjecture: Evidence and Probability Before Pascal

by James Franklin

Churches other than the Roman did not develop casuistry to the same degree but could hardly avoid altogether the giving of moral advice to their flocks. The point of view that sees moral choice in terms of cases of conscience was fundamental to Elizabethan thought and evident in its literature.

So English casuistry avoided probabilism in the sense of reliance on the opinions of doctors and gave greater weight to the reasons for and against opinions.

Trust neither me, nor the adverse part, but the Reasons,” says John Donne.)

The Anglicans tended toward probabiliorism, the position between probabilism and tutiorism that holds that the more probable opinion must be followed. Donne complained that probabilism indulges the human propensity to intellectual laziness: “To which indisposition of ours the casuists are so indulgent, as that they allow a conscience to adhere to any probable opinion against a more probable, and do never bind him to seek out whi...

The uncompromising biblicism of the more extreme Puritans left no place for the subtle jugglings of casuistry. Francis Bacon criticized the Calvinists for hollow exhortation in generalities in place of real moral direction. “The word,” he says, “[the bread of life] they toss up and down, they break it not. They draw not their distinctions down ad casus conscientiae; that a man may be warranted in his particular actions whether they be lawful or not.”

On the issue of the doubting conscience, Taylor is firmly for probabiliorism, laying down the rule, The greater probability destroys the less. His argument against probabilism is that “the safety [of an opinion] must increase consequently to the probability, it is against charity to omit that, which is safer, and to choose that, which is less safe.”

The story of probability in moral theology concludes with two opposed figures, Caramuel and Pascal. They were opponents and in many ways exact opposites, though, as is the way with these things, in certain respects identical. Since Caramuel is as obscure as Pascal is famous, some basic facts on his biography will be helpful.

The author of a book called Anticaramuel wrote, “Caramuel has the ability of eight, the eloquence of five, the judgement of two,” the relative ordering of which seems reasonably accurate.

Almost any proposition is probable, he says. “Since we are not angels, but men, we have evident knowledge of scarcely four things, so we are required to act according to probable opinions.” While intrinsic probability is relevant to judges in law, who are not versed in theology, it is not a useful criterion in general, as it is possessed by any proposition that is not against faith and has enough reasons in its favor to confuse objectors; in fact the only really improbable opinions are self-contradictory ones.

extrinsic probability is better known, and “morally speaking” superior. So how many doctors suffice to give an opinion (extrinsic) probability?

As Leibniz does later, he regards the flaw in Aristotle as his dealing only in strictly universal propositions. His logic is thus inapplicable to matters of fact in law and ethics, in which universal propositions, like “All men tell the truth,” or “Caramuel never hallucinates,” are not to be had. So he proposes a logic with more quantifiers that treats such propositions as morally universal, or most vehement: for example, “Almost all mothers love their sons”; and ones of usual force: “Around half of mothers love their sons.”

The story of the Jansenists and their struggle with the Jesuits is well known. It is surely one of history’s best remembered storms in a teacup. The Thirty Years’ War, with casualties running into millions, has left less impression on the collective memory, at least outside Germany, than the entirely bloodless harassment of two French convents. Its renown is almost solely due to Pascal, whose Provincial Letters and Pensées are deservedly acknowledged as classics of French literature. The publication of modern accounts of the affair with high literary merit, notably Sainte-Beuve’s Port Royal, Bremond’s Histoire littéraire du sentiment religieux en France, and Ronald Knox’s Enthusiasm, has only added to the fame of this rather peripheral episode.

It may be conjectured that, though great serious literature survives, humor and propaganda are cumulative arts, like mathematics, in which each age improves on the techniques of its predecessors. Hence the indulgence needed when reading Shakespeare’s or Dickens’ humor. If this is so, then the Provincial Letters are some centuries ahead of their time. The brevity, the timing, the always potent combination of irony and moral indignation are as effective as on the day of printing.

The real source of the disagreement is that Pascal believes there are no experts in morals and that anyone (or at least the saved) can work out his opinions in morals for himself. The modern world has followed Pascal in this—in morals, though not in science; no one would deny that if a noted scientist asserts a scientific opinion, that would be a reason for the layman to believe it, since the scientist can be expected to know the sufficient reasons for the opinion. The casuists’ assumption that the same can be done in morals renders them fossils indeed. We, like Pascal, are shocked even when the casuist is dealing with genuinely disputable cases in which reasoning and experience with similar cases might seem to have some relevance. Pascal has the father say, “Now the authority of a learned and pious man is entitled to very great consideration; because (mark the reason), if the testimony of such a man has great influence in convincing us that such and such an event occurred, say at Rome, for example, why should it not have the same weight in a question of morals?” Pascal’s answer is, “An odd comparison this . . . between the concerns of the world and those of conscience!”120 It marks a sudden break between medieval and modern thought. Before, one supports one’s opinion by adducing the doctors and their reasonings in its support. Afterward, one claims one’s opinion is supported by one’s bare conscience. Which method is likely to lead, in practice, to greater laxity of behavi...

Whose business is it to explain the theory of probability? What discipline owns the theory and the right to evaluate applications of it in other fields? The modern answer has been mathematics. It is an answer that has brought a great deal of clarity into obscure matters and has, for example, saved millions of lives by finding accurate methods of testing drugs for their curative powers. Yet it biases the theory toward aspects of probability that can be given precise numbers. Dice are studied intensively; how to take into account context and background information is neglected. The ancient answer to the same question was that the theory of probability belonged to rhetoric. There are some advantages in that answer too, especially in directing attention to a wide body of data—all the arguments that are found to be persuasive in practice. The concomitant disadvantage is a persistent tendency to blur the distinction between what ought to persuade, because it is probable, and what can be made to persuade by giving it a color of plausibility. That is, the logical and the psychological are easily confused. It is true that the distinction is clearly stated by Aristotle and others and also that the ancient sense of “rhetorical” did not emphasize the merely persuasive as much as the modern sense does, but the focus on what actually persuades was enough to prevent an autonomous theory of nondemonstrative argument from being seriously developed in logic.

the present chapter, potentially the most exciting because it concerns the theory of probability most directly, is in fact something of a disappointment. It is for this reason that the material on rhetoric is placed after that on the law of evidence, although much of it is older. Very little of the rhetorical tradition fed into law, even though ancient rhetoric was especially designed for use in legal contexts. While it might seem natural to have discussed Greek rhetoric before Roman law, the truth is that the rhetorical and juristic attitudes to evidence are so different that the traditions are almost independent. The purpose of rhetoric, in the view of the ancient masters, is the construction of persuasive arguments in, especially, courts of law.

The speeches produced by Greek rhetoricians were intended to be heard by assemblies of ordinary citizens and were usually designed to be delivered by ordinary citizens in the course of defending themselves in lawsuits. So what was said about probability in rhetoric is continuous with ordinary language usage,

The resources of the Greek language included two words, pithanon and eikos, which had some probabilistic content, at least potentially. Pithanon means persuasive, or plausible; it can be used of both speakers and what they say. It can have the suggestion of mere persuasiveness.

The word eikos, literally “like,” is often used in exactly the sense of its English descendant “likely.”4

A second essential piece of the Greek cultural background is the explicit idea of the conflict of opinion and its resolution. The saying, “Hear both sides,” is quoted by choruses in Greek plays as if it is part of ancient wisdom; Aeschylus mentions it at the same time as doubting whether oaths are reliable, thus marking the transition to deliberately rational thought, which the Greeks made in this area as in so many others.

A conscious awareness of probability or of anything like the grading of evidence apparently begins with the treatment of plausibility by the Sophists, who were paid precisely for teaching how to make conclusions plausible. The invention of rhetoric was traditionally ascribed to Corax and Tisias, Greeks of Syracuse about 460 B.C.

Aristotle explains the nature of such arguments and expresses the general disapproval later felt for the whole immoral business. “It is of this line of argument that Corax’s Art of Rhetoric is composed,” he says. “If the accused is not open to the charge, for instance if a weakling is being tried for assault, the defence is that he was not likely (eikos) to do such a thing. But if he is open to the charge—if he is a strong man— the defence is still that he was not likely to do such a thing, since he could be sure that people would think he was likely to do it. And so with any other charge: the accused must be either open or not open to it: there is in either case an appearance of likely innocence, but whereas in the latter case the likelihood is genuine, in the former it is only in the special sense mentioned. This sort of argument illustrates what is meant by making the worse argument seem the better. Hence people were right in objecting to the training Protagoras undertook to give them. It was a fraud; its likelihood was not genuine but an appearance, and has a place in no art except rhetoric and eristic.”

Sicily and Athens in the fifth century B.C. shared, in addition to a rationalist spirit and a love of disputation—entities intangible in the small but undeniable in the mass16—a long period of democracy. Legal as well as political decisions were generally entrusted to popular assemblies, leading to a demand for skill in public speaking.

Plato in particular hoped to raise the intellectual and moral tone of discussion by contrasting his true logic with the Sophists’ immoral use of mere persuasiveness; the English meaning of sophistry is a sign of his success.

The question arises as to whether the picture of the Sophists in Plato and Aristotle is fair. No more than fragments of the Sophists have survived, and men of genius are not known in general for giving fair treatments of their opponents’ views. The distinction between the Socratic school with its high-minded devotion to the truth and the word-chopping Sophists, clear enough no doubt to Plato, was less so in the popular mind, as is apparent from the satire in Aristophanes’ play The Clouds. There was, then, every motive to exaggerate the differences. The arguments of Gorgias and Antiphon above are not unreasonable, though they do leave the impression that the authors are fundamentally not interested in the truth. The idea of dismissing arguments as merely plausible is a trick of the Sophists themselves, parallel with the rhetorical trick of dismissing one’s opponent’s arguments as mere rhetoric.

Until well into the nineteenth century it was almost possible to regard logic as a subject that had sprung fully formed from the head of Aristotle. By this was meant, of course, deductive logic, and it would be too much to expect him to have given birth to nondeductive logic as well. If anything, one would expect the founder of deductive logic to have spent his time emphasizing the distinction between deductive arguments and all “mere persuasions.” The case is almost the exact opposite.

Aristotle’s Rhetoric is the most intrinsically important work on probability before Pascal.

While it is true that Aristotle presents rhetoric as primarily an art of persuasion—an argument “is persuasive (pithanon) because there is someone whom it persuades”31—the whole tenor of the book is to distinguish sharply between arguments that ought to persuade (studi...

Deductive arguments, he says, are rarely useful, since deliberation about actions concerns the contingent; hardly anything is determined with necessity. One must use likelihoods (eikoton) and signs, the likely (eikos) being what usually happens.

The ones relevant to the topic of probability are induction (epagoge), or argument from example, argument from signs, and analogy.

Induction covers arguments from the particular to the general, the argument from observing that a number of As are Bs to the conclusion that all As are Bs. “When we base a proof on a number of similar cases, this is induction in dialectic, example in rhetoric.”

Signs, though at first said to correspond to what is necessarily true, are then divided into fallible and infallible signs.

Arguments from the past to the future also rely on examples: “Examples are most suitable to deliberative speeches [ones recommending future actions], for we judge of future events by divination from past events.”

Other modes of argument to past fact use common knowledge of what things succeed others: “If a man was ‘going to do something,’ he has done it, for it is likely that the intention was carried out. . . . Of all these sequences some are inevitable and some merely usual.”

Aristotle is not entirely explicit at first about whether he understands these arguments to be rationally persuasive or merely ones that happen to persuade. That rationally persuasive is what he means becomes clear in his discussion of how such arguments may be refuted:

If later ages had been familiar with Aristotle’s Rhetoric, they would have had a sound basis for developing a theory of probable argument. That was not the case. While in most centuries Aristotle’s eminence was agreed on and his authority respected, he was not read from beginning to end. For one thing, his total work is enormous and is not understood without great effort. Second, some of the works considered less important were more or less lost for long periods of time. A few of the details of what was known at what times are mentioned later as appropriate, but in general it can be said that while something of Aristotle’s logical works, especially the Prior Analytics and the Topics, were known to the learned of almost all times, the Rhetoric was hardly known in Western Europe between the time of Quintilian and the thirteenth or fourteenth century.

The account of induction, in particular, is much less probabilistic than that in the Rhetoric; it never really becomes clear whether these arguments are supposed to be deductive or not. Sometimes such inductions appear to be inconclusive, and it is said that if someone refuses to admit the conclusion, one is justified in asking what objection he has.48 On the other hand the Prior Analytics suggests that induction must be complete, that is, all the instances must be surveyed.

These passages on induction give substance to the Enlightenment picture of Aristotle as the father of the old order and the prime obstacle in the way of the rise of experimental science. In life Aristotle was a genuine experimenter and observer, especially in biology. In fact he notices that the ideas of rhetorical probability can apply to argument in biology: he remarks on the reasons for thinking that semen comes from all parts of the body: “These opinions are made probable by the witness of such facts as that children are born with a likeness to their parents, not only in congenital but also in acquired characteristics.”52 But the Aristotle of the logical works, as taught in the schools and universities of medieval Europe, was indeed a supporter of the view that pure thought is the method of science, not “argument from examples.”

The Topics is said to be about dialectic; it opens with a division of arguments into three kinds: the demonstrative, the dialectical, and the eristic (fallacious). In demonstration, necessary truths follow from necessarily true premises, as in geometry.

Then “reasoning is dialectical which reasons from generally accepted opinions (endoxon). . . . Endoxa are those which are agreed to by all or most or the wise, that is, to all of the wise or most or the most notable and distinguished of them. Reasoning is eristic if it is based on opinions which appear to be endoxa but are really not so.”55 This passage produced an important result when translated. In the standard Latin translation of Boethius, endoxa appeared as probabilia,56 the same word standardly used to translate pithana. As a result, the formula “Agreed to by all or most or the wise, that is, to all the wise or most or the most notable and distinguished of them” became the standard medieval definition of probable.

It turned out to fit in all too well with the already excessive medieval habit of evaluating propositions in accordance with the weight of the authorities who approved them. The wide knowledge of this dictum was a factor in causing the plague of probabilism that swept the courts and confessionals of Europe in the seventeenth century (described in the previous chapter).

Probability, in this sense, belongs to premises, not arguments, and there is not much in the body of the Topics about probable arguments. Almost the only arguments discussed are from analogy, or similarities: “It is an accepted principle that what holds good of one of several similars, holds good for the rest.”

The argument about the young man is a clearer example than anything in Aristotle of the proportional syllogism, that is, the argument from a proportion in a reference class to a particular case: Young men generally act thus, so this particular young man probably acts thus. The author helpfully adds something on how to reply to such arguments. “If you have never done anything of the kind, but some of your friends do happen to have done such things, you must say that it is not just that you should be discredited because of them, and must show that others of your associates are honest men; you will thus throw doubt on the accusation. If they show that other people who resemble you have done the same things, declare it to be absurd if the fact that certain others can be shown to have done wrong is to be a proof that you too have committed the offences alleged against you. That is how you must make your defence from likelihood (eikoton) if you are denying that you have done the thing alleged, because this will make the charge improbable (apithanon).”

Then there is argument from signs. “A sign of a thing is what usually precedes or accompanies or follows it. . . . A sign may produce either belief or full knowledge; the latter is the best kind of sign, while one that produces a very probable (pithanotaten) opinion is second best.”

Cicero’s expertise was principally as a legal orator, expert in persuasion on matters of fact. Here he is on home ground and is prepared to classify the reasons that make probable arguments persuasive:

Cicero keeps Aristotle’s connection between probabilistic reasoning from what happens for the most part and persuasion using the opinions of the audience. But he introduces a confusion by conflating these with the kind of argument now found mostly under the name of jurisprudential analogy.

“To be sure, some one or two things can by chance have happened in such a way as to throw suspicion on him, but for all the things to agree among themselves from first to last, it is necessary that he committed the crime; this cannot have happened by chance.”

But Quintilian does at least transmit some of the basics of Greek thinking on the combination of evidence. “There are other non-necessary signs, called eikota in Greek. Even if these are not sufficient by themselves to remove doubt, they may be of the greatest value when taken together with others. . . . But bloodstains on a garment may be the result of the slaying of a victim at a sacrifice or of a bleeding nose. . . . Hermagoras would include among such non-necessary signs an argument such as, ‘Atalanta is not a virgin, since she has been roaming in the woods with young men.’ If we accepted this view, I fear we should make all inferences from a fact into signs.”

The diversion of serious thinking into these tedious moralizings, so much admired by the Elizabethans, to us shows the decay of the Silver Age. Let us draw a veil.

From the purely historical point of view, the works of Boethius assume a significance quite out of proportion to their intrinsic merits. For many medieval authors, Boethius was the first, and often the only, point of contact with the more abstract levels of ancient thought.