The Synthetic View
- A contrasting point of view stems from synthetic philosophy and fields such as cybernetics, electronic engineering and general systems theory. It is little appreciated in analytic philosophy. The synthetic view understands the calculus ratiocinator as referring to a "calculating machine". The cybernetician Norbert Wiener considered Leibniz's calculus ratiocinator a forerunner to the modern day digital computer:
| “ | The history of the modern computing machine goes back to Leibniz and Pascal. Indeed, the general idea of a computing machine is nothing but a mechanization of Leibniz's calculus ratiocinator. (Wiener 1948: 214) | ” |
| “ | ...like his predecessor Pascal, was interested in the construction of computing machines in the Metal. ... just as the calculus of arithmetic lends itself to a mechanization progressing through the abacus and the desk computing machine to the utra-rapid computing machines of the present day, so the calculus ratiocinator of Leibniz contains the germs of the machina ratiocinatrix, the reasoning machine (Wiener 1965: 12) | ” |
Leibniz constructed just such a machine for mathematical calculations which was also called a Stepped Reckoner. As a computing machine, the ideal calculus ratiocinator would perform Leibniz's integral and differential calculus. In this way the meaning of the word, "ratiocinator" is clarified and can be understood as a mechanical instrument that combines and compares ratios.
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Stepped Reckoner
Hartley Rogers saw a link between the two, defining the calculus ratiocinator as "an algorithm which, when applied to the symbols of any formula of the characteristica universalis, would determine whether or not that formula were true as a statement of science" (Hartley Rogers, Jr. 1963; p. 934).
A classic discussion of the calculus ratiocinator is Couturat (1901: chpts. 3,4), who maintained that the characteristica universalis—and thus the calculus ratiocinator—were inseparable from Leibniz's encyclopedic project (chpt. 5). Hence the characteristic, calculus ratiocinator, and encyclopedia form three pillars of Leibniz's project.
Read more about this topic: Calculus Ratiocinator, Two Views
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