One of the aims of “Equi-Probabability Prior to 1500” was to instigate interest in empirical and statistical research concerning the use of probability-related terms like “equally probable.” Therefore, I am pleased that Mark Thakkar has added significantly to our knowledge concerning this issue, even if he refutes one of my main empirical claims (on which, however, I was careful enough not to rely very much in The Debate on Probable Opinions). As more and more medieval texts become available in digitalized, machine-readable form, further changes of our picture of the historical usage of probability-related terms are possible, and even likely to occur.
Given Thakkar’s findings, it cannot be upheld that references to equal probability were “virtually absent from medieval thought,” as I had claimed. The number of prominent scholastic authors listed in his note speaks for itself and documents that the concept of equal probability was available and used in the period under consideration. Nevertheless, some central props of my thesis remain in place. The apparent total absence of references to “equal probability” in Aquinas’s and apparently also Duns Scotus’s vast corpus of writings is still surprising. More importantly, significant differences between the period immediately before the invention of modern mathematical probability (ca. 1500–1650) and the period ca. 1200–1500 can still be identified. In the early modern period, equal probability became a frequently used term in treatises De iustitia et iure, handbooks of casuistry, and the debate on probable opinions. In these contexts, equal probability became an explicit condition for the legitimate choice between opinions. The discussion of such regulations became one of the main venues for scholastic contributions to the rise of modern probability. Hence, the thesis can still be upheld that increased usage of the term “equally probable” in contexts of the normative regulation of opinions paved the way to modern mathematical probability. I did not find any instances of “equally probable” in medieval regulations and discussions of choices of opinion under moral uncertainty, although this moral theological context was an explicit locus of scholastic discussion at least since the thirteenth century. Thakkar indirectly confirms this part of my thesis by not offering any medieval counter-examples from the field of the theological regulation of probability or doubt. He lists two cases in which equal probability and doubt are connected, but none of these pertains to the normative regulation of doubt, e.g., through the rule “in doubt the safer side is to be preferred.”
Apparently, a significant shift occurred ca. 1500 in the literature on moral agency under conditions of probability and doubt, offering an explicit role to the condition of equal probability. However, as Thakkar shows, this shift should not be understood as the spread of a new concept which had been virtually absent in the medieval period. If near absence of the concept in medieval thought was not the reason for the absence of equiprobability from medieval regulations on the use of probable opinions, some other reason needs to be found for why it was not there. Moreover, an explanation is lacking as to why a shift occurred ca. 1500. Thakkar offers an explanation for why references to equal probability were much rarer ca. 1200–1500 than references to greater probability. Most authors were eager to pass off their own preferred opinions as more probable than their alternatives. This explanation appears convincing, and Thakkar also applies it to differences in the frequency of “greater probability” and “equal probability” in texts from the nineteenth and twentieth centuries. However, the very general validity of Thakkar’s explanation prevents it from accounting for the shift in medieval and early modern practices with respect to equiprobability and the regulation of probable opinions. Even if we recognize that “more probable” is generally more likely to occur than “equally probable,” it still remains unexplained why the latter became a frequently used term in the regulation of opinions ca. 1500–1650 but was not used in this role before.
Of course, this rejoinder depends on my claim that the respective shift occurred in the regulation of probable opinions, and this claim might also be challenged. However, Thakkar at least does not challenge it since none of his findings come from the field of the moral theological regulation of opinions. Moreover, I am still confident that this part of the picture will not fundamentally change, because I know many of the moral theological sources on the usage of probability firsthand and need not rely on automated searches in this respect. This is not to say that I am now willing to bet on the general absence of equiprobability from moral theological sources ca. 1200–1500. Many of the respective texts are not yet machine-readable. Equiprobability may lurk in some corners of thick handbooks which are difficult to survey as a whole before they have become machine-readable. However, it is not to be found in core passages which proved central for the evolution of regulations for the usage of probable opinions and were referenced as such by early moral theologians. This result suffices to create an explanatory puzzle with respect to a significant shift in the normative role of equiprobability in the period leading up to the discovery of modern mathematical probability.
Candidates for explaining a shift ca. 1500 are, of course, not difficult to find. The new technology of print, for instance, may have instigated broader surveys of opinions because of a larger number of circulating texts. New postal and traveling opportunities may have increased and sped up knowledge about the handling of cases of conscience in different locations. Moral theologians (and their principals) may therefore increasingly have come to rely on surveys of opinions rather than only advertising their own most preferred views.1 It seems natural that equiprobability in the sense of a rough balance of opinions pro and contra is a more likely outcome in a survey of opinions than as a result of a single person’s reasoning. An explanation via an ‘information revolution’ which occurred at the outset of the early modern era (and, in fact, largely constituted the new era) thus appears plausible. It is nevertheless difficult to prove this explanation in the way Thakkar statistically corroborated his explanation of differing frequencies for “more probable” and “equally probable.”
The differentiation of moral theology as a branch of theology in the sixteenth century may also help to explain why the normative regulation of opinions became more complex. I have called medieval endeavors moral theological if they were classified as moral theological after the said differentiation had occurred. The same is usually accepted with respect to calling medieval philosophers and theologians “scholastic,” although a clear concept of scholastic philosophy and theology only emerged in the early modern era; see Riccardo Quinto, Scholastica. Storia di un concetto (Padua, 2001).