The Stanhope Demonstrator: An Instrument for Performing Logical Operations. Separately-paginated offprint from: Mind, Vol. IV.
Aberdeen: A. King & Co., 1879. First edition, extremely rare separately-paginated offprint, inscribed by the author, of the first published description of “the world’s first logic machine” (Martin Gardner), designed by Charles Stanhope, third Earl Stanhope, in the 1770s. “His system consisted essentially in the reduction of both positive and negative propositions to a single form, that of the identity of two things or classes of things, and in the employment of symbols to represent the quantities of things involved in such propositions. In his general use of logical symbols and his manipulation of them he introduced a new rigour into the science and looked ahead towards Boole’s virtual reduction of logic to a branch of pure mathematics” (Beatty, p. 206). Stanhope “succeed[s] in demonstrating that the consequences of two logical statements are capable of solution by mechanical means. Although earlier logicians had proposed mechanical contrivances (e.g., Euler’s circles), Stanhope was the first to construct an instrument to deal with this kind of problem” (ibid., p. 208). “The first model was constructed in 1775. It consisted of two slides coloured red and gray mounted in a square brass frame. This could be used to demonstrate the solution to a syllogistic type of problem in which objects might have two different properties and the question was how many would have both properties. Scales marked zero to ten were used to set the numbers or proportions of objects with the two properties. This form of inference anticipated the numerically definite syllogism which Augustus De Morgan laid out in his book, Formal Logic, in 1847 … At least four of the devices with this square style were built. In 1879, Robert Harley wrote that he had one which he had been given by Stanhope’s great-grandson, Arthur, who had kept one. The other two were owned by General Babbage – the son of Charles Babbage, who continued his work on the Analytical Engine. One of the devices was donated to the Science Museum, London by the last Earl in 1953. Other styles, such as circular models, were constructed, but these were less convenient” (Wikipedia). “Stanhope’s speculations on logic covered a period of some thirty years, but he published nothing about his logical views beyond printing on his own hand press several early chapters of an unfinished work, titled The Science of Reasoning Clearly Explained upon New Principles. These chapters were circulated only among a few acquaintances. In a letter written shortly before his death, he advises a friend not to discuss his logical methods with others lest ‘some bastard imitation’ of his views appear before the publication of his projected work [which was, in fact, never completed or published]. It was not until 60 years later that one of the earl’s contrivances, together with relevant letters and notes, came into the hands of Rev. Robert Harley, who then published an account of the demonstrator and the logic on which it was based” (Gardner, pp. 80-81). Harley notes that “Earl Stanhope’s Demonstrator is much less powerful as a logical instrument than Professor Jevons’ machine, but the former is undoubtedly a distinct anticipation of the latter. It is probably the first attempt ever made to solve logical problems by mechanical methods.” OCLC lists 5 copies worldwide (Trinity College, Cambridge; National Library of Wales; Glasgow; Chicago; Huntington); not in BL. Not on RBH. Provenance: Inscribed on upper wrapper, ‘George Wooding Esqre. / With the Writer’s kind regards.’ “Although Ramon Llull made use of rotating discs to facilitate the working of his eccentric system of reasoning, his devices are not logic machines in the sense that they can be used to solving problems in formal logic. The inventor of the world’s first logic machine in the strict sense of the term was a colorful eighteenth-century British statesman and scientist, Charles Stanhope, third Earl Stanhope (1753-1816). His curious device, which he called a ‘demonstrator,’ is interesting in more ways than one. Not only could it be used for solving traditional syllogisms by a method closely linked to the Venn circles; it also took care of numerical syllogisms (anticipating De Morgan’s analysis of such forms) as well as elementary problems of probability. In addition, it was based on a system of logical notation which clearly foreshadowed Hamilton’s technique of reducing syllogisms to statements of identity by making use of negative terms and quantify products … “In his day, Stanhope was better known throughout England for his fiery political opinions and confused domestic affairs than for his many scientific inventions. His first wife was the sister of England’s young and controversial prime minister, William Pitt. For a time the earl was a supporter of Pitt, but he later broke with the ministry to become a vigorous opponent of most of its measures. As a member of the Revolution Society, formed to honor the revolution of 1688, his political views were strongly liberal and democratic. His impetuous proposals in the House of Lords were so often and so soundly defeated that he was widely known as ‘the minority of one’, and his thin figure was prominent in the political cartoons of the period. He was an ardent supporter of the French republicans in the early days of the French Revolution. It is said that even went so far as to discard all the external trappings of his peerage. “At the early age of 19 he was elected a fellow of the Royal Society and for the rest of his life he devoted a large segment of his time and income to scientific pursuits … In addition to his logic machine, he also devised an arithmetical calculating machine employing geared wheels” (Gardner, pp. 80-81). “Stanhope’s Demonstrator was designed as a device able to solve mechanically traditional syllogisms, numerical syllogisms, and elementary probability problems. The rectangular version of the device consists of a brass plate (size 10 x 12 x 2 cm), affixed to a thin mahogany block. On the brass face, along three sides of the window, integer calibrations from zero to ten were marked. In the center, there is a depression (4 cm in area and 2.5 cm deep), called the holon. Across the holon two slides can be pushed; one, set in a slender mahogany frame, is of red transparent glass and works through an aperture on the right. The other is of wood and is called the gray slider. In working the ‘Rule for the Logic of Certainty’ this slide is passed through an aperture to the left; but in working the ‘Rule for the Logic of Probability’, it is drawn out and inserted in an aperture at the top, when it works at right angles to the red slide. “To solve a numerical syllogism, for example: Eight of ten A’s are B’s; Four of ten A’s are C’s; Therefore, at least two B’s are C’s Stanhope would push the red slide (representing B) eight units across the window (representing A) and the gray slide (representing C) four units from the opposite direction. The two units that the slides overlapped represented the minimum number of B’s that were also C’s. “To solve a probability problem like: Prob (A) = 1/2; Prob (B) = 1/5; Therefore, Prob (A and B) = 1/10 Stanhope would push the red slide (representing A) from the north side five units (representing five-tenths) and the gray slide from the east two units (representing two-tenths). The portion of the window (5/10 x 2/10 = 1/10) over which the two slides overlapped represents the probability of A and B. “In a similar way, the Demonstrator could be used to solve a traditional syllogism like: No M is A. All B is M. Therefore, No B is A. “The Demonstrator had obvious limitations. It could not be extended to syllogisms involving more than two premises or to probability problems with more than two events (always assumed to be independent of one another) … “Stanhope bases his system on what De Morgan will call later the arithmetical view of the proposition; and this view determines the form of his method of mediate inference and leads to an extension of the common doctrine. He proposed a rule “for discovering consequences in logic”, which is a remarkable anticipation of that given by De Morgan from the numerically definite syllogism” (http://www.computer-timeline.com/timeline/charles-stanhope/). Beatty, ‘The Scientific Work of the Third Earl Stanhope,’ Notes and Records of the Royal Society of London 11 (1955), pp. 202-221. Gardner, Logic Machines and Diagrams, 1958.
8vo (220 x 137 mm), pp. [3], 4-21, [1, blank] (journal pagination 192–210). Original printed wrappers (foxing, mainly to the wrappers, lower inner margin of wrappers chipped, light vertical crease for posting).
Item #6353
Price: $1,500.00
