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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 ''[[Characteristica universalis|characteristica universalis]]'', 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, the second is associated with [[Computer hardware|computer hardware]].

=== Analytic view ===
The received point of view in [[Philosophy:Analytic philosophy|analytic philosophy]] and formal [[Logic|logic]], is that the ''calculus ratiocinator'' anticipates [[Mathematical logic|mathematical logic]]&mdash;an "algebra of logic".{{sfnp|Fearnley-Sander|1982|p=164}} The analytic point of view understands that the ''calculus ratiocinator'' is a formal [[Philosophy:Inference engine|inference engine]]<!--what makes an inference engine formal or informal?--> or [[Computer program|computer program]], which can be designed so as to grant primacy to calculations. That logic began with Frege's 1879 ''[[Begriffsschrift]]'' and [[Biography:Charles Sanders Peirce|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]]. 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 [[Biography:Herbert Spencer#Synthetic philosophy|synthetic philosophy]] and fields such as [[Cybernetics|cybernetics]], [[Electronic engineering|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 [[Biography:Norbert Wiener|Norbert Wiener]] considered Leibniz's ''calculus ratiocinator'' a forerunner to the modern day digital computer:

{{quote|"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''."|{{harvtxt|Wiener|1948|p=214}}}}

{{quote|"...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."|{{harvtxt|Wiener|1965|p=12}}}}

Leibniz constructed just such a machine for mathematical calculations, which was also called a "[[Stepped reckoner|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.

{{gallery|align=center|mode=packed
|File:Leibniz Stepped Reckoner mechanism.png|Internal mechanism of the [[Stepped reckoner|stepped reckoner]]
|File:Leibnitzrechenmaschine.jpg|Contemporary replica of the stepped reckoner 
}}

Hartley Rogers saw a link between the two, defining the ''calculus ratiocinator'' as "an [[Algorithm|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".{{sfnp|Rogers|1963|p=934}}

A classic discussion of the ''calculus ratiocinator'' is that of [[Biography:Louis Couturat|Louis Couturat]],{{sfnp|Couturat|1901|loc=chapters 3, 4}} who maintained that the ''characteristica universalis'' — and thus the ''calculus ratiocinator'' — were inseparable from Leibniz's encyclopedic project.{{sfnp|Couturat|1901|loc=chapter 5}} Hence the ''characteristics'', ''calculus ratiocinator'', and encyclopedia form three pillars of Leibniz's project.

== See also ==
* {{section link|Algebraic logic|Calculus of relations}}
* ''[[Mathesis universalis]]''

== References ==
{{reflist|15em}}

== Bibliography ==
{{refbegin|2}}
* {{cite book |last1=Couturat |first1=Louis |year=1901 |title=La Logique de Leibniz |location=Paris |publisher=Felix Alcan |translator1-last=Rutherford |translator1-first=Donald |url=http://philosophyfaculty.ucsd.edu/faculty/rutherford/Leibniz/contents.htm|archive-url=https://web.archive.org/web/20120814062611/http://philosophyfaculty.ucsd.edu/faculty/rutherford/Leibniz/contents.htm |archive-date=2012-08-14 }}
* {{cite journal |last1=Rogers |first1=Hartley Jr. |year=1963 |title=An Example in Mathematical Logic |journal=[[The American Mathematical Monthly]] |volume=70 |issue=9 |pages=929–945|doi=10.1080/00029890.1963.11992146 }}
* {{cite journal |last1=Wiener |first1=Norbert |year=1948 |title=Time, communication, and the nervous system |journal=Annals of the New York Academy of Sciences |volume=50 |issue=4 |pages=197–219|doi=10.1111/j.1749-6632.1948.tb39853.x |pmid=18886381 |bibcode=1948NYASA..50..197W |s2cid=28452205 }}
* {{cite book |last1=Wiener |first1=Norbert |year=1965 |title=Cybernetics or the Control and Communication in the Animal and the Machine |edition=2, paperback |publisher=The MIT Press}}
* {{cite journal |last1=Fearnley-Sander |first1=Desmond |year=1982 |title=Hermann Grassmann and the Prehistory of Universal Algebra |journal=[[The American Mathematical Monthly]] |volume=89 |issue=3 |pages=161–166|doi=10.1080/00029890.1982.11995404 }}
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== External links ==
* [http://www.ontology.co/two-views-language.htm Language as Calculus ''versus'' Language as Universal Medium]

{{Gottfried Wilhelm Leibniz}}
{{DEFAULTSORT:Calculus Ratiocinator}}
[[Category:Concepts in logic]]
[[Category:History of computing]]
[[Category:Mechanical calculators]]

{{Sourceattribution|Calculus ratiocinator}}