Mathematical Analysis of Logic by BOOLE, George - 1847

First Edition of Boole's First Book, and the Introduction to Mathematical Logic BOOLE, George. The Mathematical Analysis of Logic. Being an Essay Towards a Calculus of Deductive Reasoning. Cambridge: Macmillan, Barclay, & Macmillan, 1847. First edition of Boole's first book. Octavo (8 x 5 1/8 inches; 205 x 130 mm). [2], [1]-82 pp. With errata slip bound after title-page. Aside from this copy, we could only find three other copies at auction in the past 50 years. The Honeyman Copy at Sotheby's in 1978, the OOC copy at Christie's in 2005 and a copy at Bonhams in 2013. Modern full brick red morocco. Boards double ruled in gilt with tiny flower corner devices. Spine lettered and tooled in gilt. All edges speckled red. Marbled endpapers. Overall a very clean, near fine copy. "This was Boole's first work of logic, in the introduction to which he first refuted W. Hamilton's claim that logic was a part of philosophy and that no mathematician could possibly contribute anything to this field. It was this volume that began the revolution that led to the development of mathematical logic. In recent times, Boolean logic has found widespread use in the design of digital computers and communications systems" (Tomash & Williams). ìBoole invented the first practical system of logic in algebraic form, which enabled more advances in logic to be made in the decades of the nineteenth century than in the twenty-two centuries preceding. Booleís work led to the creation of set theory and probability theory in mathematics, to the philosophical work of Peirce, Russell, Whitehead and Wittgenstein, and to computer technology via the masterís thesis of C.E. Shannon (1937), who recognized that the true/false values in Booleís two-valued algebra were analogous to the open and closed states of electric circuits. This invention of the binary digit or ëbití made possible the development of the digital computerî (Norman Library). "Booleís path to logic fame started in a curious way. In early 1847 he was stimulated to launch his investigations into logic by a trivial but very public dispute between De Morgan and the Scottish philosopher Sir William Hamilton (1788ñ1856)ónot to be confused with his contemporary the Irish mathematician Sir William Rowan Hamilton (1805ñ1865). This dispute revolved around who deserved credit for the idea of quantifying the predicate (e.g., ìAll A is all B,î ìAll A is some B,î etc.). Within a few months Boole had written his 82 page monograph, Mathematical Analysis of Logic, giving an algebraic approach to Aristotelian logic, then looking briefly at the general theory. (Some say that this monograph and De Morganís book Formal Logic appeared on the same day in November 1847.)" (Stanford Encyclopedia of Philosophy). "Boole's The Mathematical Analysis of Logic was distinguished from the logics that preceded it in that it derived its theorems not from ordinary language (e.g, the Aristotelian syllogism), but from a purely formal system. Boole's work also contains what Bertrand Russell called the greatest discovery of the nineteenth century: the nature of pure mathematics. Objecting to the then-current view of mathematics as the science of magnitude or number, Boole adopted a far more general view: 'We might justly assign it as the definitive character of a true Calculus, that it is a method resting upon the employment of Symbols, whose laws of combination are known and general, and whose results admit of a consistent interpretation ... It is upon the foundation of this general principle, that I propose to establish the Calculus of Logic, and that I claim for it a place among the acknowledged forms of mathematical analysis' (p. 4). Boole further developed these ideas in his Investigation of the Laws of Thought. That work contained the first proper presentation of Boolean algebra, although earlier incomplete attempts had been made by others, including Leibnitz and De Morgan. (Christie's Origins of Cyber Space 2/23/2005, Lot 68). Origins of Cyberspace, 223. Tomash & Williams, B199. Norman Library. HBS 68111. $20,000