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

Gottfried Leibniz Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathem ...

, usually paired with his more frequently mentioned ''

characteristica universalis The Latin term ''characteristica universalis'', commonly interpreted as ''universal characteristic'', or ''universal character'' in English, is a universal and formal language imagined by Gottfried Leibniz able to express mathematical, scienti ...

'', a universal conceptual language.

Two views

There are two contrasting points of view on what Leibniz meant by ''calculus ratiocinator''. The first is associated with

computer software Software is a set of computer programs and associated documentation and data. This is in contrast to hardware, from which the system is built and which actually performs the work. At the lowest programming level, executable code consist ...

, the second is associated with

computer hardware Computer hardware includes the physical parts of a computer, such as the case, central processing unit (CPU), random access memory (RAM), monitor, mouse, keyboard, computer data storage, graphics card, sound card, speakers and motherboard. ...

Analytic view

The received point of view in

analytic philosophy Analytic philosophy is a branch and tradition of philosophy using analysis, popular in the Western world and particularly the Anglosphere, which began around the turn of the 20th century in the contemporary era in the United Kingdom, United ...

and formal

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from prem ...

, is that the ''calculus ratiocinator'' anticipates

mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of forma ...

—an "algebra of logic". The analytic point of view understands that the ''calculus ratiocinator'' is a formal inference engine or

computer program A computer program is a sequence or set of instructions in a programming language for a computer to Execution (computing), execute. Computer programs are one component of software, which also includes software documentation, documentation and oth ...

, which can be designed so as to grant primacy to calculations. That logic began with

Frege Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic p ...

's 1879 ''

Begriffsschrift ''Begriffsschrift'' (German for, roughly, "concept-script") is a book on logic by Gottlob Frege, published in 1879, and the formal system set out in that book. ''Begriffsschrift'' is usually translated as ''concept writing'' or ''concept nota ...

'' and

C.S. Peirce Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician and scientist who is sometimes known as "the father of pragmatism". Educated as a chemist and employed as a scientist for t ...

's writings on logic in the 1880s.

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 Proof theory is a major branchAccording to Wang (1981), pp. 3–4, proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. Barwise (1978) consists of four corresponding part ...

. 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".

Synthetic view

A contrasting point of view stems from synthetic philosophy and fields such as

cybernetics Cybernetics is a wide-ranging field concerned with circular causality, such as feedback, in regulatory and purposive systems. Cybernetics is named after an example of circular causal feedback, that of steering a ship, where the helmsperson ma ...

electronic engineering Electronics engineering is a sub-discipline of electrical engineering which emerged in the early 20th century and is distinguished by the additional use of active components such as semiconductor devices to amplify and control electric current ...

, and

general systems theory Systems theory is the interdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or human-made. Every system has causal boundaries, is influenced by its context, defined by its structu ...

. It is little appreciated in analytic philosophy. The synthetic view understands the ''calculus ratiocinator'' as referring to a "calculating machine". The cybernetician

Norbert Wiener Norbert Wiener (November 26, 1894 – March 18, 1964) was an American mathematician and philosopher. He was a professor of mathematics at the Massachusetts Institute of Technology (MIT). A child prodigy, Wiener later became an early researcher ...

considered Leibniz's ''calculus ratiocinator'' a forerunner to the modern day digital computer: 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 In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

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". A classic discussion of the ''calculus ratiocinator'' is that of

Louis Couturat Louis Couturat (; 17 January 1868 – 3 August 1914) was a French logician, mathematician, philosopher, and linguist. Couturat was a pioneer of the constructed language Ido. Life and education Born in Ris-Orangis, Essonne, France. In 1887 he ...

, who maintained that the ''characteristica universalis'' — and thus the ''calculus ratiocinator'' — were inseparable from Leibniz's encyclopedic project. Hence the ''characteristics'', ''calculus ratiocinator'', and encyclopedia form three pillars of Leibniz's project.

References

Bibliography

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External links