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

Gottfried Leibniz Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Isaac Newton, Sir Isaac Newton, with the creation of calculus in ad ...

, 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 consists of computer programs that instruct the Execution (computing), execution of a computer. Software also includes design documents and specifications. The history of software is closely tied to the development of digital comput ...

, the second is associated with

computer hardware Computer hardware includes the physical parts of a computer, such as the central processing unit (CPU), random-access memory (RAM), motherboard, computer data storage, graphics card, sound card, and computer case. It includes external devices ...

Analytic view

The received point of view in

analytic philosophy Analytic philosophy is a broad movement within Western philosophy, especially English-speaking world, anglophone philosophy, focused on analysis as a philosophical method; clarity of prose; rigor in arguments; and making use of formal logic, mat ...

and formal

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...

, is that the ''calculus ratiocinator'' anticipates

mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...

—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. It is one component of software, which also includes software documentation, documentation and other intangibl ...

, which can be designed so as to grant primacy to calculations. That logic began with Frege's 1879 ''

Begriffsschrift ''Begriffsschrift'' (German for, roughly, "concept-writing") 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 notati ...

'' 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 Proof theory is a major branchAccording to , proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. consists of four corresponding parts, with part D being about "Proof The ...

. 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 the transdisciplinary study of circular causal processes such as feedback and recursion, where the effects of a system's actions (its outputs) return as inputs to that system, influencing subsequent action. It is concerned with ...

electronic engineering Electronic engineering is a sub-discipline of electrical engineering that 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 flo ...

, and

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

. 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 computer scientist, mathematician, and philosopher. He became a professor of mathematics at the Massachusetts Institute of Technology ( MIT). A child prodigy, Wiener late ...

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 Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...

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, 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