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A Boole anthology. Recent and classical studies in the logic of George Boole. Including papers from the international Boole conference, Lausanne, Switzerland, September 26–27, 1997. (English) Zbl 0972.01024

Synthese Library. 291. Dordrecht: Kluwer Academic Publishers. xii, 336 p. (2000).

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This anthology combines papers delivered at an international conference (Lausanne, September 1997) on the occasion of the sesquicentennial anniversary of the publication of G. Boole’s “The mathematical analysis of logic” (MAL) [Cambridge, Macmillan, Barclay and Macmillan (1847)] with classic texts on Boole and his algebra of logic.
The section with classic texts is opened by two contemporary, but almost unknown pieces written in the year of Boole’s death: S. Neil, “The late George Boole, LL.D., D.C.L.” (1865, pp. 1-25), and G. P. Young, “Remarks on Professor Boole’s mathematical theory of the laws of thought” (1865, pp. 27-43).
The other classic texts include: L. M. Laita, “The influence of Boole’s search for a universal method in analysis on the creation of his logic” (pp. 45-59) [Ann. Sci. 34, 163-176 (1977; Zbl 0362.01005)] setting Boole’s logical work into the context of his earlier mathematical work on differential equations; T. Hailperin, “Boole’s algebra isn’t Boolean Algebra” (pp. 61-77) [Math. Mag. 54, 173-184 (1981; Zbl 0473.03003)] comparing Boole’s logic of class terms with contemporary symbolical algebra and modern Boolean Algebra; M. Dummett, “Review of Boole” (1959, pp. 79-85), dealing especially with G. Boole’s “Studies in logic and probability” [R. Rhees (ed.), London, Watts & Co. (1952; Zbl 0049.00802)], and showing “how ill-constructed this theory actually was and how confused his explanation of it” (p. 79); J. W. van Evra, “A reassessment of George Boole’s theory of logic” (pp. 87-99) [Notre Dame J. Formal Logic 18, 363-377 (1977; Zbl 0348.02004)], demanding systematical and historical justice for Boole against his recent critics arguing with the specific character of Boole’s method; J. Corcoran and S. Wood, “Boole’s criteria for validity and invalidity” (pp. 101-128) [ibid. 21, 609-638 (1980; Zbl 0438.03009)], critically examining Boole’s early criteria of what follows, or does not follow in the system MAL, comparing Boole’s approach with that of Aristotle.
The recent studies are presented in four sections dealing with the background, mathematical aspects, philosophical aspects and consequences. T. Hailperin, in his paper “Algebraical logic: Leibniz and Boole” (pp. 129-138), discusses similarities and differences of Leibniz’s algebraical calculi to the system of MAL. In “Logic versus algebra: English debates and Boole’s mediation” (pp. 139-166), M.-J. Durand-Richard is concerned with the historical question “how Boole’s work is included in a social and cultural context where logic and mathematics are increasingly cross-examined about their foundations” (p. 139).
In the section on mathematical aspects, M. Panteki compares in “The mathematical background of George Boole’s Mathematical analysis of logic (1847)” (pp. 167-212) MAL with Boole’s first mathematical masterpiece “On a general method in analysis” (1844), determines the concept of mathematics represented by these works and puts them into the context of contemporary British symbolical algebra. I. Grattan-Guinness examines in “On Boole’s algebraic logic after The mathematical analysis of logic” (pp. 213-216) the further development of Boole’s logical theory.
In the section on philosophical aspects S. Nambiar shows in “The influence of Aristotelian logic on Boole’s philosophy of logic: the reduction of hypotheticals to categoricals” (pp. 217-239) that Boole’s work was in many respects a step backward from Aristotle’s logic (p. 237). In her paper “The conceptualization of time in Boole’s algebraic logic” (pp. 241-255) B. Godard-Wendling discusses Boole’s temporal interpretation of secondary propositions. In “George Boole and the science of logic” (pp. 257-270) G. Bornet deals with Boole’s position concerning the role of logic in a philosophy of science.
In the final section on consequences, V. Peckhaus determines in “Was George Boole really the ‘father’ of modern logic” (pp. 271-285) Boole’s place in the history of logic, arguing that in any case speaking of fatherhood in modern logic makes no sense. Shahid Rahman in “Hugh MacColl and George Boole on hypotheticals” (pp. 287-310) deals with Boole’s position towards hypotheticals relating it to his precursors and especially to MacColl’s later reformulation. In the final paper on “Psychologism in logic: some similarities between Boole and Frege” (pp. 311-325) N. Vasallo challenges the common view of Boole as a psychologistic philosopher.
The book is closed by indices of names and subjects. It offers a broad view on G. Boole’s algebra of logic in its context.

MSC:

01A55 History of mathematics in the 19th century
03-03 History of mathematical logic and foundations
03-06 Proceedings, conferences, collections, etc. pertaining to mathematical logic and foundations
00B15 Collections of articles of miscellaneous specific interest
03A05 Philosophical and critical aspects of logic and foundations
01-06 Proceedings, conferences, collections, etc. pertaining to history and biography
01A75 Collected or selected works; reprintings or translations of classics
01A70 Biographies, obituaries, personalia, bibliographies
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