Calculus ratiocinator

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The calculus ratiocinator is a theoretical universal logical calculation framework, a concept described in the writings of

"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 ratiocinator of Leibniz contains the germs of the machina 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.

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.

See also

• Algebraic logic § Calculus of relations
• Mathesis universalis

References

Bibliography