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The * calculus ratiocinator* is a theoretical universal logical calculation framework, a concept described in the writings of Gottfried Leibniz, usually paired with his more frequently mentioned

There are two contrasting points of view on what Leibniz meant by *calculus ratiocinator*. The first is associated with computer software, the second is associated with computer hardware.

The received point of view in analytic philosophy and formal logic, is that the *calculus ratiocinator* anticipates mathematical logic—an "algebra of logic".^{[1]} The analytic point of view understands that the *calculus ratiocinator* is a formal inference engine or computer program, which can be designed so as to grant primacy to calculations. That logic began with Frege's 1879 *Begriffsschrift* and C.S. Peirce's writings on logic in the 1880s. Frege intended his "concept script" to be a *calculus ratiocinator* as well as a *universal characteristics*. That part of formal logic relevant to the *calculus* comes under the heading of proof theory. From this perspective the *calculus ratiocinator* is only a part (or a subset) of the *universal characteristics*, and a complete *universal characteristics* includes a "logical calculus".

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, p. 214)

"...like his predecessor Pascal, [Leibniz] 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 ultra-rapid computing machines of the present day, so the

calculus ratiocinatorof Leibniz contains the germs of themachina ratiocinatrix, the reasoning machine."— Wiener (1965, p. 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.

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".^{[2]}

A classic discussion of the *calculus ratiocinator* is that of Louis Couturat,^{[3]} who maintained that the *characteristica universalis* — and thus the *calculus ratiocinator* — were inseparable from Leibniz's encyclopedic project.^{[4]} Hence the *characteristics*, *calculus ratiocinator*, and encyclopedia form three pillars of Leibniz's project.