Mathematicians tend to identify "probabilistic reasoning" with the mathematical theory of probability. James Franklin's The Science of Conjecture reminds us that there is much more to it than that. The book is a history and analysis of qualitative probabilistic reasoning before the time of Pascal. Thus, though the author is a mathematician, this is not primarily a book about mathematics. Nevertheless, it should be useful to historians of mathematics because it studies the context and tradition from which our quantitative version of probability emerged.
Franklin observes that qualitative probabilistic reasoning still is quite common, particularly in the law. (Think of "beyond a reasonable doubt" or "a preponderance of the evidence.") Much of his book deals with legal reasoning, though it also discusses philosophy, theology, "aleatory contracts" (insurance, annuities, bets), and even some pre-Pascal quantitative analysis of games of chance.
The book is well-written and pleasant (though not easy) to read, and the ideas are provocative. Franklin has an axe to grind: he is out to defend our ability to make rational decisions about truth when the evidence only allows conclusions that are probable or likely. Since this includes essentially all such decisions outside of mathematics, his argument should be of interest to philosophers and others who want to understand how we think and make decisions.
Fernando Q. Gouvêa (firstname.lastname@example.org) is the editor of FOCUS and MAA Online.