Probability and Opinion: A Study in the Medieval Presuppositions of Post-Medieval Theories of Probability

Description

This is a sort of precursor to Franklin's The Science of Conjecture: Evidence and Probability Before Pascal.

First discovered on the Bibliographia Thomistica, which describes this work as follows:

Aquinas's pre-scientific theory of probability compared with early and recent interpretations of calculus of probability is discussed in this book. A quasi-mathematical notion of probability enters into Aquinas's reasonings about decisions under conditions of uncertainty. This approach is, however, but one aspect of a cautious epistemology of "opinion" that compares unfavorably to perfect, or ideal, knowledge what humans learn from tradition, argumentation, or even demonstration. Founders of the calculus of probability, even into the nineteenth century, similarly contrasted probability calculations to the perfection of newtonian science. This critical backdrop to probabilities is systematically disregarded in contemporary mathematical theories, but finds expression in tangential considerations

Modern physics has accustomed us to consider events which cannot give rise to certainty in our knowledge. A scientific knowledge of such events is nevertheless possible. The method which has enabled us to obtain a stable and exact knowledge about uncertain events consists in a kind of changing of plane and in the replacing of the study of indi­ vidual phenomena by the study of statistical aggregates to which those phenomena can give rise. A statistical aggregate is not a collection of real phenomena, among which some would happen more often, others more rarely. It is a set of possibilities relative to a certain object or to a certain type of phenomenon. For example, we could consider the differ­ ent ways in which a die, thrown in given conditions, can fall: they are the possible results of a certain trial, the casting of the die (in the fore­ seen conditions). The set of those results constitutes effectively a set of possibilities, relative to a phenomenon of a certain type, the fall of the die in specified circumstances. Similarly, it is possible to consider the different velocities which can affect a molecule in a volume of gas; the set of those velocities constitutes effectively a set of possible values which a physical property, namely the velocity of a molecule, can have.