Concurrently with the great strides being made with mechanical computers that could handle mathematics, much work was also being done with the formalizing of the logic. As hinted vaguely in the syllogisms of the early philosophers, thinking did seem amenable to being diagrammed, much like grammar. Augustus De Morgan devised numerical logic systems, and George Boole set up the logic system that has come to be known as Boolean algebra in which reasoning becomes positive or negative terms that can be manipulated algebraically to give valid answers.
John Venn put the idea of logic into pictures, and simple pictures at that. His symbology looks for all the world like the three interlocking rings of a well-known ale. These rings stand for the subject, midterm, and predicate of the older Aristotelian syllogism. By shading the various circles according to the major and minor premises, the user of Venn circles can see the logical result by inspection. Implicit in the scheme is the possibility of a mechanical or electrical analogy to this visual method, and it was not long until mathematicians began at least on the mechanical kind. Among these early logic mechanizers, surprisingly, was Lewis Carroll who of course was mathematician Charles L. Dodgson before he became a writer.
Carroll, who was a far busier man than most of us ever guess, marketed a “Game of Logic,” with a board and colored cardboard counters that handled problems like the following:
All teetotalers like sugar.
No nightingale drinks wine.
By arranging the counters on Carroll’s game board so that: All M are X, and No Y is not-M, we learn that No Y is not-X! This tells the initiate logician that no nightingale dislikes sugar; a handy piece of information for bird-fancier and sugar-broker alike.
Lewis Carroll’s “Symbolic Logic.”
Charles, the third Earl Stanhope, was only slightly less controversial than his prime minister, William Pitt. Scientifically he was far out too, writing books on electrical theory, inventing steamboats, microscopes, and printing presses among an odd variety of projects; he also became interested in mechanical logic and designed the “Stanhope Demonstrator,” a contrivance like a checkerboard with sliding panels. By properly manipulating the demonstrator he could solve such problems as:
Eight of ten children are bright.