Boole's Logic and Probability
A Critical Exposition from the Standpoint of Contemporary Algebra, Logic and Probability TheoryBy
- T. Hailperin
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.
Studies in Logic and the Foundations of Mathematics
Published: October 1986
...those speaking knowledgeably of Boole have supported their comments by invoking the authority of Hailperin with increasing frequency. The first edition merited that status; the second deserves it even more ...a truly exceptional volume.
J.W. van Evra, History and Philosophy of Logic
This was an important and useful book in its first edition. It has now become even more important, since it now addresses a large class of contemporary problems in the handling and propagation of uncertainty.
H.E. Kyburg, Zentralblatt für Mathematik
- 0. Requisites from Algebra, Logic and Probability. Part I: Logic. 1. Boole's Logic of Class Terms. 2. Formalization of Boole's Logic. 3. Boole's Propositional Logic. Part II: Probability. 4. Probability from Boole's Viewpoint. 5. Boole's Probability Made Rigorous. 6. Applications. Probability Logic. Bibliography. Index.