This book has been extensively reviewed since its first appearance in 2001, with a reprint in 2012, so this current (2015) review will be in the context of the new preface and by reordering the sequence of chapters to bring out some less obvious features. Having said that, and having read the book when it first appeared, I can assert that the material in it is stimulating, interesting and informative—but challenging: One has to go to and fro with its many cross-references, and extensive list (one hundred pages) of notes which are themselves an illuminating insight into the depth and breadth of the erudition of Professor Franklin (and his dry, sometimes sardonic, wit). Part, but only part, of the importance of the book, and hence its revival, is the neglect of conjecture and probability in the philosophy of mathematics. For instance, Shapiro (2005) has no mention of them in the index and only fleeting references to Fermat and Pascal, two of the stars in the slowly evolving development of these ideas as Franklin unravels their historical meanings in law, philosophy and science in general. Another part of the importance of the book in my rereading of it was to see how public opinion is changed to accept what was once unacceptable (or vice versa) within increasingly shorter time frames. This is picked up too in Hazareesingh (2015) who in his study of the elements of French thinking from the times of Descartes reflects on the way history is used to structure reasoning, through concepts such as rupture, revolution and progress. Not quite in this context but it is worth noting here that Franklin elaborates in different places on the spectrum of opinion, conjecture, probability and certainty in Descartes’ writings, particularly as influenced by the Scholastics.
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