## Pure Logic or the Logic of Quality apart from Quantity: with remarks on Boole's System and on the Relation of Logic and Mathematics.

London: Edward Stanford, 1864.

First edition of Jevons's first work on logic, and a fine copy in original condition. “Jevons’ logical system was regarded by him as being to a large extent founded on the work of Boole. ‘The forms of my system,’ he says (*Pure Logic*, p. 3), may in fact be reached by divesting his (i.e., Boole’s) system of a mathematical dress, which, to say the least, is not essential to it’” (Mays & Henry, p. 485). “Jevons actually improved on Boole in some important details, as, for instance, in showing that the Boolean operations of subtraction and division were superfluous” (DSB 7:105). Jevons had already consulted Boole before sending him a copy of the present work; in a letter of 1863 he recorded, ‘I have written on the subject to Professor Boole, on whose logical system mine is an improvement. In his answer he does not explain away an objection I had raised against his system. He seems to think that my paper viz. *Pure Logic* probably does not contain more than he himself knows, this being a common failing of philosophers and others; but still he tells me very civilly that if I think still that there is anything new in my paper I ought to publish, which of course I shall do one way or another before long.’ Jevons’s principal advance was to reduce the operations of the Boolean calculus to a mechanical procedure. He here stood at the start of a road that led to the modern application of logic in computer-programming; he himself designed a ‘logical abacus’ and ‘logical piano’, which “solved problems with superhuman speed and accuracy, and some of its features can be traced in modern computer designs” (*ibid*.).

*Provenance*: Charles J. Poynting (bookplate on front paste-down and signature on initial blank dated 30 April [18]75). Erwin Tomash (book label on front paste-down). Tomash & Williams suggest that Poynting may be the son of the physicist John Henry Poynting, known for the ‘Poynting vector’ which describes the direction and magnitude of electromagnetic energy flow: “Both had a close association with Owens College, Manchester, where Jevons was at the time of this publication” (Tomash Library Catalogue, p. 681).

“There is a need for a revaluation of the logical work of Jevons, especially as he was a pioneer in the mechanisation of logic. His achievements in this direction have been overlooked and remain relatively unknown. Jevons seriously believed that he was the discoverer of a new kind of logic, and records in his Journal an illumination resembling that of Descartes when he discovered coordinate geometry. He tells us: ‘As I awoke in the morning, the sun was shining brightly into my room. There was a consciousness on my mind that I was the discoverer of the true logic of the future. For a few minutes I felt a delight such as one can seldom hope to feel.’ If Jevons were alive today it is unlikely that he would be surprised by modern digital computers and the arithmetical marvels which they perform” (Mays & Henry, p. 484).

“Jevons’ Logic Piano anticipates contemporary computing in an oblique fashion. Computers as we know run on 1s and 0s. Indeed the logical aspect of a computer sits at the bottom of its structure and is embodied in the circuitry (presuming it is electronic of course). Jevons system of logic uses the same basic logic operations, and indeed, in 1940 a young American engineer called Claude Shannon showed in his Masters thesis, ‘A symbolic analysis of relay switching circuits’, that Boolean algebra could be used to describe switching circuits. The architecture of the contemporary computer has subsequently proceeded from this point. However, the system that we presently understand as Boolean Algebra is quite different to that originally developed by Boole in the 1840s and 1850s. According to Nathan Houser and Ivor Grattan–Guinness, Boole’s system has been much modified in order to become the Boolean Algebra we now know, and that this is a process of modification begun by Jevons. Although he was not interested in what we call truth-value calculus—1s and 0s—Jevons’ logic machine was actually performing a function provided today by a truth table. Indeed, Wolf Mays defines Jevons as the first user of matrix analysis. In essence Jevons’ primary legacy in the history of computing is his mechanization of Boolean logic, a key aspect of contemporary computing. It is also reasonable to assert that Jevons was of the key figures in the reformulation of Boolean logic into Boolean algebra, such that it could be employed by Claude Shannon to describe the switching of circuits” (Barrett & Connell).

“Jevons’s fame as the inventor of a logic machine has tended to obscure the important role he played in the history of both deductive and inductive logic … At a time when most British logicians ignored or damned with faint praise the remarkable achievements of George Boole, Jevons was quick to see the importance of Boole’s work as well as many of its defects. He regarded Boole’s algebraic logic as the greatest advance in the history of the subject since Aristotle. He deplored the fact that Boole’s two revolutionary books, published as early as 1847 [*The Mathematical Analysis of Logic*] and 1854 [*The Laws of Thought*], had virtually no effect on the speculations of leading logicians of the time.

“On the other hand, Jevons believed (and modern logicians agree with him) that Boole had been led astray by efforts to make his logical notation resemble algebraic notation. ‘I am quite convinced,’ Jevons stated in a letter, ‘that Boole’s forms . . . have no real analogy to the similar mathematical expressions.’ He also saw clearly the weakness in Boole’s preference for the exclusive rather than the inclusive interpretation of ‘or.’

“It was to overcome what he regarded as unnecessary obscurity and awkwardness in Boole’s notation that Jevons devised a method of his own that he called the ‘method of indirect inference.’ ‘I have been able to arrive at exactly the same results as Dr. Boole,’ he wrote, ‘without the use of any mathematics; and though the very simple process which I am about to describe can hardly be said to be strictly Dr. Boole’s logic, it is yet very similar to it and can prove everything that Dr. Boole proved.’ Jevons’s system is also very similar to Venn’s diagrammatic method as well as a primitive form of the familiar matrix or truth-table technique …

“[Jevons’] method … correspond[s] closely to a truth-table analysis. The logical alphabet is simply another way of symbolizing all the possible combinations of truth-values. Each premise forces us to eliminate certain lines of this ‘truth table.’ What remain are of course the lines that are consistent with the premises. If the premises contain a contradiction, then all the lines will be eliminated just as all the compartments will become shaded if contradictory truth-value premises are diagramed on Venn circles. Jevons likes to call his system a ‘combinatorial logic,’ and although he did not apply it to propositional functions, he clearly grasped the principles of matrix analysis that had eluded Boole …

“To increase the efficiency of his combinatorial method, Jevons devised a number of laborsaving devices, culminating in the construction of his logic machine … As early as 1863 Jevons was using a ‘logical slate.’ This was a slate on which a logical alphabet was permanently engraved so that problems could be solved by chalking out the inconsistent lines. Still another device, suggested to Jevons by a correspondent, is to pencil the alphabet along the extreme edge of a sheet of paper, then cut the sheet between each pair of adjacent combinations. When a combination is to be eliminated, it is simply folded back out of sight” (Gardner, pp. 92-100).

Jevons was the ninth child of Thomas Jevons, a Liverpool iron merchant, and Mary Arm, daughter of William Roscoe, a noted banker, historian and art collector of the same city. The family were Unitarians and Stanley's background was thus that of a cultured and well-to-do Nonconformist family; but his childhood was shadowed by the death of his mother in 1845, the illness of his eldest brother, which began in 1847, and the failure of the family business in 1848. Jevons’s schooling, begun at the Mechanics Institute High School in Liverpool, was continued at University College School, London, and in 1851 he entered University College London itself to study chemistry and mathematics. At this stage Jevons apparently intended to enter a business career without completing his degree but when a post as assayer to the newly established Mint in Sydney, Australia, was offered to him in 1853 he decided to take it, encouraged by his father, whose finances had never been restored after the family bankruptcy in 1848. Jevons spent the years from 1854 to 1859 in Australia, applying his knowledge of chemistry at the Sydney Mint and studying, mainly botany and meteorology, in his spare time. From 1857 onwards his interest turned towards social and economic questions; he began to see his life-work as lying in ‘the study of Man’ and decided that this involved returning to England to improve his academic qualifications. Arriving home in September 1859 he re-enrolled at University College London, completing his BA in 1860 and then the MA course in 1862. Jevons's attempts to make a career as a journalist in London met with little success and he followed up a suggestion made by his cousin, Henry Enfield Roscoe, who was already Professor of Chemistry at Owens College, Manchester, that he should apply for a vacancy there as a general tutor. When Jevons took up this very junior post in 1863 he was quite unknown even in academic circles, but he had already produced two works which were to prove of seminal importance in economics - his ‘Brief Account of a General Mathematical Theory of Political Economy’, first read before the British Association in 1862, and his outstanding applied research into changes in the value of gold. In the following year, 1864, his first published contribution to the study of logic (*Pure Logic*) also appeared, and during the next ten years he produced a series of works which established his standing as one of the leading thinkers of his time in both political economy and logic.

Tomash J-20 (this copy). Barrett & Connell, ‘Jevons and the Logic ‘Piano’,’ *The Rutherford Journal*, vol. 1 (2005); Gardner, *Logic Machines and Diagrams*, 1958. *Mays* & *Henry**, *‘*Jevons and Logic**,*’ *Mind*, vol. 62 (1953), pp. 484-505.

Small 8vo, pp. [vi], 87, [1]. Original pebble-grained blue cloth, printed paper label to spine and front cover, boards panelled in blind, brown coated endpapers (very minor rubbing to extremities). A fine copy.

Item #4640

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Price:
$2,850.00
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