The Problem of Certainty and the Changing Status of Probable Proofs

Abstract

This essay offers a preliminary survey of the development of probabilistic proofs in the early modern period.  It examines several disciplines and their adoption of a mode of proof which embraced a scale of probability  and whose high point was variously labeled “satisfied conscience,” “mind,” and “understanding,” “moral” as opposed to “mathematical certainty” or “demonstration,” and  proof “beyond reasonable doubt.“ Although my focus is on England, I view this essay as part of a broader account that would include French, Italian and Spanish developments and earlier and later periods.  I emphasize the long-lived ancient distinction between probability and certain knowledge, and between rhetoric and “science,” arguing that these distinctions played a crucial role in shaping thinking about proof. My account highlights the role of witnessing, the criteria for evaluating testimony, and the possibility of reaching moral certainty, that is, belief beyond reasonable doubt.
The first discipline to be examined is history, a discipline characterized by tension between the humanist desire for a rhetorically persuasive narrative on the one hand and truth telling norm on the other. The next to be examined are the probabilistic proofs adopted in several religious contexts.  There follows a comparison of continental and English approaches to legal proof.  The most challenging intellectual area to be examined is the natural sciences. There I examine efforts to find a probabilistic alternative to “science,” “demonstration” and  “mathematical certainty.  Scientists sought to adopt “hypothesis” as a means of linking “matters of fact” with generalizations, principles and theory.   A brief treatment of Locke and his philosophical successors suggests how probabilistic proofs penetrated English thinking. The concluding section includes a discussion of disciplinary differences and suggestions for a more complete treatment of probable but believable proof.