Marquand's Logic


Most of our critical thinking can be attributed to logical argument. An old and well-established logical rule is the syllogism: (1) All humans are mortal, (2) All Greeks are humans, (1) and (2) conclude via syllogism that (3) All Greeks are mortal. This form (AAA), with A indicating "All," is referred to as Barbara, a mnemonic. In the 1883 text Studies in Logic (John Hopkins University) edited by C.S Peirce, Allan Marquand designed a machine to produce syllogisms with the design illustrated in the above diagram. Marquand's paper was entitled "A Machine for Producing Syllogistic Variations." The design is interesting and appears to serve as a mechanical aid to combinatorics. The hand crank is attached to d. There are "sectors" for each of the d,e, and f wheels causing friction against a, b, and c. Variations are achieved by wheels d, e, and f having diameters of powers of 2: 1, 2, and 4 inches respectively. Mechanical counters are similar except that finger protrusions are used on identically sized wheels to create combinations.