The Demonstrator of Charles Stanhope
The name of British statesman and versatile scientist Charles Stanhope (1753-1816) (see biography of Charles Stanhope), 3rd Earl Stanhope and Viscount Mahon, was mentioned several times in this site, concerning his mechanical calculators (see calculating machines of Charles Stanhope). Now it is time to pay attention to his pioneering work in the world of logic machines.
Stanhope’s Circle Demonstrator versions
Stanhope worked on his logic machines some 30 years, creating several versions. On the upper image is shown a circular version of his Demonstrator, created in the late 18th century. The most effective version of the device was the rectangular one (see the lower image), created in the beginning of the 19th century.
Stanhope's Demonstrator is 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 (10x12x2 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 centre there is a depression (4 cm in area and 2.5 cm deep), called the holon. Across the holon 2 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.
The face of Lord Stanhope’s Demonstrator
To solve a numerical syllogism, for example:
Eight of ten A’s are B’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.
Four of ten A’s are C’s;
Therefore, at least two B’s are C’s.
To solve a probability problem like:
Prob (A) = 1/2;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.
Prob (B) = 1/5;
Therefore, Prob (A andB ) = 1/10.
In a similar way the Demonstrator could be used to solve a traditional syllogism like:
No M is A.Therefore, No B is A.
All B is M.
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). Any of the problems it could handle were solved easily and quickly without the aid of the machine. Actually Stanhope designed his devices for demonstration purposes, as it can be seen by the name Demonstrator, not for solving real-life problems. He wrote "As the instrument is so constructed as to assist us in making demonstrations. I have termed it Demonstrator. It is so peculiarly contrived as likewise to exhibit symbolically those proportions or degrees of probability which it is the object of the Logic of Probability to discover".
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.
Nonetheless, Stanhope believed he had made a fundamental invention. The few friends and relatives who received his privately distributed account of the Demonstrator, The Science of Reasoning Clearly Explained Upon New Principles, were advised to remain silent lest "some bastard imitation" precede his intended publication on the subject. This publication never appeared and the Demonstrator remained unknown until the Reverend Robert Harley described it in the Philosophical Transactions in 1879.
The Demonstrator was important mainly because it demonstrated to others, most notably to William Jevons, that problems of logic could be solved by mechanical means.