Boole's logic and probability : a critical exposition from the standpoint of contemporary algebra, logic, and probability theory

Hailperin demonstrates how Boole's very difficult technique for solving problems in probability logic can be easily solved by using a linear programming approach , such as parametric and integer-mixed integer techniques.This approach makes the computation of Boolean probabilistic intervals straightforward.An additional benefit of Hailperin's solutions repertoire is that Keynes's improved technique for solving probabilistic interval estimate problems ,formally discussed by Keynes in chapters 15 and 17 of his A Treatise on Probablity in 1921(the actual work in this area was done by Keynes in 1907 and 1908,respectively,in two Cambridge University fellowship theses)and applied in chapters 20 and 22 of the TP on pp.234-237 and pp.255-257,respectively,can also be solved using Hailperin's approach although Hailperin himself appears not to realize this. Unfortunately,Hailperin's work on probability interval estimate techniques,as well as Boole's and Keynes's earlier contributions,have been completely overlooked by contemporary economists and philosophers still laboring under the misbelief that all probabilities used by rational decision makers must be unique,single number answers that add to one. Since the publication of the first edition in 1976, there has been a notable increase of interest in the development of logic. This is evidenced by the several conferences on the history of logic, by a journal devoted to the subject, and by an accumulation of new results. This increased activity and the new results - the chief one being that Boole's work in probability is best viewed as a probability logic - were influential circumstances conducive to a new edition.

Chapter 1, presenting Boole's ideas on a mathematical treatment of logic, from their emergence in his early 1847 work on through to his immediate successors, has been considerably enlarged. Chapter 2 includes additional discussion of the ``uninterpretable'' notion, both semantically and syntactically. Chapter 3 now includes a revival of Boole's abandoned propositional logic and, also, a discussion of his hitherto unnoticed brush with ancient formal logic. Chapter 5 has an improved explanation of why Boole's probability method works. Chapter 6, Applications and Probability Logic, is a new addition. Changes from the first edition have brought about a three-fold increase in the bibliography.

Since the publication of the first edition in 1976, there has been a notable increase of interest in the development of logic. This is evidenced by the several conferences on the history of logic, by a journal devoted to the subject, and by an accumulation of new results. This increased activity and the new results - the chief one being that Boole's work in probability is best viewed as a probability logic - were influential circumstances conducive to a new edition. Chapter 1, presenting Boole's ideas on a mathematical treatment of logic, from their emergence in his early 1847 work on through to his immediate successors, has been considerably enlarged. Chapter 2 includes additional discussion of the ``uninterpretable'' notion, both semantically and syntactically. Chapter 3 now includes a revival of Boole's abandoned propositional logic and, also, a discussion of his hitherto unnoticed brush with ancient formal logic. Chapter 5 has an improved explanation of why Boole's probability method works. Chapter 6, Applications and Probability Logic, is a new addition. Changes from the first edition have brought about a three-fold increase in the bibliography Content: Edited by Pages ii-iii Copyright page Page iv Dedication Page v Preface to the First Edition Pages vii-viii Th. Hailperin Preface to the Second Edition Page ix Theodore Hailperin Introduction Pages 1-7 Chapter 0 Requisites from Algebra, Logic and Probability Pages 9-59 Part I. Logic Page 61 Chapter 1 Boole's Logic of Class Terms Pages 63-134 Chapter 2 Formalization of Boole's Logic Pages 135-172 Chapter 3 Booles's Propositional Logic Pages 173-211 Part II. Probability Page 213 Chapter 4 Probability from Boole's Viewpoint Pages 215-284 Chapter 5 Boole's Probability Made Rigorous Pages 285-353 Chapter 6 Applications. Probability Logic Pages 355-410 Bibliography Review Article Pages 411-424 Index Pages 425-428