The Science of Conjecture review

The Science of Conjecture is James Franklin's history of probable reasoning from classical antiquity through the seventeenth century, the period traditionally treated as the starting point for mathematical probability. Franklin's argument is that the focus on mathematical probability has obscured a rich pre-mathematical tradition of qualitative reasoning about evidence, risk, and degrees of belief — a tradition that includes Roman law, medieval theology, Renaissance merchants, and the first insurance markets. Mathematical probability did not invent reasoning under uncertainty; it formalized a practice already centuries old.

The book is a work of intellectual history rather than mathematics or philosophy. Franklin traces how Greek and Roman lawyers developed concepts like "half-proof" and "violent presumption" to reason about testimony and circumstantial evidence. He shows how medieval scholastics grappled with moral uncertainty — when is a person permitted to act on a belief that might be wrong? — and developed casuistry as a system for reasoning about probable obligation. He traces the development of life tables and annuity pricing in medieval and Renaissance Europe, which required actuarial reasoning about risk long before Bernoulli formalized it.