## An Investigation of the Laws of Thought, on which are founded the Mathematical Theories of Logic and Probabilities.

London, and Cambridge: Walton and Maberly; Macmillan & Co., 1854.

First edition, first issue (see below). In this main work of Boole’s he gave the first proper presentation of Boolean algebra – “Boole 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. Boole’s 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 master’s thesis of Claude Shannon, who recognized that the true/false values in Boole’s two-valued logic were analogous to the open and closed states of electric circuits.” (Hook & Norman, *Origins of Cyberspace*, no. 224).

❧OOC 224 (1st issue, re-backed); Erwin Tomasch B198 (2nd issue); Haskell Norman 266 (3rd issue).

“Since Boole showed that logics can be reduced to very simple algebraic systems - known today as Boolean Algebras - it was possible for Babbage and his successors to design organs for a computer that could preform the necessary logical tasks. Thus our debt to this simple, quit man, George Boole, is extraordinarily great. ... His remark about a ‘special law to which the symbols of quantity are not subject’ is very important: this law in effect is that *x ^{2}=x* for every

*x*in his system. Now in numerical terms this equation or law has as its only solution 0 and 1. This is why the binary system plays so vital a role in modern computers: their logical parts in effect carrying out binary operations... In Boole’s system 1 denotes the entire realm of discourse, the set of all objects being discussed, and 0 the empty set. There are two operations in this system which we may call + and &infty; or we may say

*or*and

*and*. It is most fortunate for us that all logics can be comprehended in so simple a system, since otherwise the automation of computation would probably not have occurred - or at least not when it did” (Goldstine:

*The Computer from Pascal to von Neumann*, pp.37-38).

This is the rare first issue. “The probable first issue of Boole’s

*Laws of Thought*, of which the

*Origins of Cyberspace*copy is an example, has the errata leaf bound in the back, and a binding of black zigzag cloth with blindstamped border, panel, lozenge, and corner- and side-ornaments. The probable second issue has the errata leaf following the last numbered leaf of preliminaries, an additional printed ‘Note’ leaf following page 424 concerning a complex error, an eight-page Walton and Maberly publisher’s catalogue, and a binding of black blindpaneled zigzag cloth without the central lozenge. Both issues have an integral title-leaf with imprint reading ‘London: Walton and Maberly, Upper Gower-Street, and Ivy Lane, Paternoster Row. Cambridge: Macmillan and Co.’ A later issue has been noted in a green pebble-cloth binding, with a cancel title-leaf and imprint reading ‘London: Macmillan and Co.’”(Hook & Norman).

8vo (225 x 143 mm), uncut. Original publishers black blind-paneled cloth with gilt spine lettering (bound by Edmonds & Remnants, London), top of hinges with a very small tear, covers with some very light discoloration, in all a very fine copy of this fragile binding, entirely unrested. Pp [10], 424 [2:errata], text fresh and clean. Rare in such fine condition.

Item #3906

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Price:
$28,500.00
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