A logical abacus is a mechanical digital computer. William Stanley Jevons Logic Piano

Also referred to as a "logical machine", the logical abacus is analogous to the ordinary (mathematical)

abacus The abacus (''plural'' abaci or abacuses), also called a counting frame, is a calculating tool which has been used since ancient times. It was used in the ancient Near East, Europe, China, and Russia, centuries before the adoption of the Hi ...

. It is based on the principle of

truth table A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional argumen ...

s. It is constructed to show all the possible combinations of a set of logical terms with their negatives, and, further, the way in which these combinations are affected by the addition of attributes or other limiting words, i.e., to simplify mechanically the solution of logical problems. These instruments are all more or less elaborate developments of the "logical slate", on which were written in vertical columns all the combinations of symbols or letters which could be made logically out of a definite number of terms. These were compared with any given premises, and those which were incompatible were crossed off. In the abacus the combinations are inscribed each on a single slip of wood or similar substance, which is moved by a key; incompatible combinations can thus be mechanically removed at will, in accordance with any given series of premises. The principal examples of such machines are those of

William Stanley Jevons William Stanley Jevons (; 1 September 183513 August 1882) was an English economist and logician. Irving Fisher described Jevons's book ''A General Mathematical Theory of Political Economy'' (1862) as the start of the mathematical method in ec ...

(''logic piano''),

John Venn John Venn, Fellow of the Royal Society, FRS, Fellow of the Society of Antiquaries of London, FSA (4 August 1834 – 4 April 1923) was an English mathematician, logician and philosopher noted for introducing Venn diagrams, which are used in l ...

, and

Allan Marquand Allan Marquand (; December 10, 1853 – September 24, 1924) was an art historian at Princeton University and a curator of the Princeton University Art Museum. Early life Marquand was born on December 10, 1853 in New York City. He was a son of ...

References

* — On p.55f, Jevons gives a description of his logical abacus. {{EB1911, wstitle=Abacus, volume=1, pages=5–6 Abacus Logic Mechanical computers