Probability-related terminology played an important role in medieval and Renaissance philosophy. Terms such as ‘probable’ (probabilis), ‘credible’ (credibilis) or ‘truth-like’ (verisimilis) were used to assess philosophical claims, qualify uncertain conclusions, gauge the force of arguments and temper academic disagreement. Beyond that, they had a significant impact on the regulation of legal proceedings, moral action and everyday life. The probability-related terminology of the Middle Ages descended from ancient sources such as Aristotle, Cicero and Boethius. There is no precedent, however, for many medieval ways of connecting these terms to rules and principles for legal and practical decision-making.
Medieval scholastic uses of probability evolved into the significantly different probability discourses of early modern scholasticism and humanism, which both were finally eclipsed by modern quantitative notions of probability in the eighteenth century. Much is still unknown concerning these processes, but a fuller understanding can only be approached by accounting for their medieval origins. This background is also important for charting the shifting borders of certainty and uncertainty, or knowledge and opinion, in European philosophy.3. Scholastic Concepts of Probability
3.1 Endoxic (or topical) probability
3.2 Proto-frequentist probability
3.3 Testimonial and juridical probability
3.4 Semantic probability
4. Further aspects of medieval probability
4.1 The dialectical syllogism
4.2 Order relations between probabilities
4.3 Both-sided probability
4.4 Subjectivity and objectivity
5. Probability in the Renaissance
6. Preview of early modern and modern probability
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[size=30]1. Probability: Now and then
Modern notions of probability are quantitative (Hájek 2011). They underlie the representation of probabilities by real (initially: fractional) numbers from the interval between 0 and 1. On this basis, a probability calculus with its own mathematical rules (the Kolmogorov axioms) has arisen.
[1] The present mathematics of probability marks the end-point of a development which began in the middle of the seventeenth century with the calculation of chances in games of fortune by Pascal, Fermat, and Huygens. These early calculations were considerably refined in the eighteenth century by the Bernoullis, Montmort, De Moivre, Laplace, Bayes, and others (Daston 1988; Hacking 2006; Hald 2003). Modern conceptualizations of probability emerged at the same time. They evolved around the ideas of a ratio of possibilities, a relative frequency of events, a degree of belief, or a degree of confirmation.
Pre-modern notions of probability were very different.
No pre-modern notion of probability was numerical. A calculus of probabilities simply did not exist before the seventeenth century.
[2] Pre-modern probability was a qualitative predicate mainly applied to propositions (e.g., by calling an opinion probable), but extending to other subject matters as well. The use of the word ‘probable’ in ordinary language still resembles this older usage to some extent (Franklin 2001, 126; Hacking 2006, 18). Yet, whereas the mathematics of probability was invented in the early modern era, some continuities in the meaning(s) of probability exist. These continuities will be discussed in Section 6. Until that point, it is best to forget the connotations of modern notions of probability and to approach medieval probability-related terms without modern preconceptions. For their vocabulary, medieval and Renaissance authors could draw on a well-stocked ancient Greek and Roman store of probability-related terms. In consequence, a variety of Latin terms were in use, which are today translated as ‘probable’, ‘plausible’, ‘reputable’ (
probabilis); ‘truth-like’, ‘apparently true’ (
verisimilis); ‘credible’, ‘worthy of belief’ (
credibilis,
opinabilis); or ‘most often’, ‘frequently’ (
ut frequenter). Modern readers may not always find it obvious that these terms relate to probability; but, in fact, they are highly relevant for its conceptual evolution. Up to the nineteenth century, when philosophers spoke about probability their claims were still often rooted in medieval notions of probability.
Medieval and Renaissance philosophers used probability-related vocabulary; but they did not analyze the underlying concepts in depth, at least in comparison with the thoroughness of their investigations into the notions of knowledge or science (
scientia). Probability-related terms were usually introduced in passing, and the most differentiated treatments extended to a folio page at best. Nevertheless, issues of probability were not peripheral to medieval thought. Probability-related terms and concepts played an enormous role in the regulation of everyday conduct and in many arts and sciences. Rhetoric and dialectic were by definition concerned with persuasion, credibility, and probability. Yet medieval thinkers were also highly aware that many claims in jurisprudence, theology, and medicine could not be derived with certainty from indubitable premises. Hence, arguments in these fields had to rely more often than not on probable reasoning. The notorious disagreements between scholastic academics in their fields of inquiry, nourished and represented by the practice of scholastic disputation, further increased the demand for probable reasoning. Wherever disagreement was licit and impossible to extirpate by argument, the claims of all sides counted as merely probable. Since medieval theologians and lawyers were no more in agreement concerning the ascription of sins (or of moral actions) than on other matters, the guidance of human conduct by confessors was also a matter of probability. In this domain, the regulation of decisions of conscience relied on a systematic framework of probable reasoning and decision in conditions of uncertainty. In short, for a satisfactory understanding of the medieval intellectual edifice, inspection of the uses of probability seems indispensable.
This is true for the medieval period, the Renaissance, and in different ways for early modern scholasticism until the eighteenth century. We should not assume, however, that the uses and understanding of probability remained unchanged throughout this long span of time. For this reason, the period from roughly 1200–1500 is singled out here for discussion. It is the period of mature medieval scholasticism and covers much of the Renaissance. In the sixteenth century, the discourse on probability underwent significant changes, on the scholastic as well as the humanist side. This early modern discourse needs to be clearly differentiated from its medieval precursor and is therefore excluded from consideration here.
Within the period under consideration, a distinction between scholastic and humanist uses of probability can be made. This is not to say that there was a big divide between them. The same terms were used by scholastics and humanists with similar meanings. The normative and regulatory uses of probability, however, were anchored in scholastic theology and jurisprudence; therefore, they are in the foreground here. At least some Renaissance humanists used probability-related terms differently from the scholastic mainstream; and these differences will be addressed in Section 5.
That the conceptualization of probability was not exclusively a European affair also deserves attention. Many cultures around the world tilled the conceptual field of probability, in antiquity and not least in the medieval era. The question of the extent to which non-Western notions and uses of probability shaped the treatment of probability in the Latin Middle Ages (or vice versa) cannot be answered here; however, some of the scholastic authors discussed below explicitly referred to Islamic sources in their accounts of probability.[/size]
Probability in Medieval and Renaissance Philosophy
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