Calculus ratiocinator
calculus ratiocinator, leibniz calculus ratiocinatorThe 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, a universal conceptual language
Contents
 1 Two views
 11 The analytic view
 12 The synthetic view
 2 Notes
 3 See also
 4 References
 5 External links
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
The analytic view
 The received point of view in analytic philosophy and formal logic, is that the calculus ratiocinator anticipates mathematical logic — an "algebra of logic" 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 CS Peirce's writings on logic in the 1880s Frege intended his "concept script" to be a calculus ratiocinator as well as a lingua characteristica 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 characteristic, and a complete universal characteristic includes a "logical calculus"
The synthetic view
 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: 214  ” 
“  like his predecessor Pascal, 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 utrarapid computing machines of the present day, so the calculus ratiocinator of Leibniz contains the germs of the machina ratiocinatrix, the reasoning machine Wiener 1965: 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

Stepped Reckoner
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" Hartley Rogers, Jr 1963; p 934
A classic discussion of the calculus ratiocinator is Couturat 1901: chpts 3,4, who maintained that the characteristica universalis—and thus the calculus ratiocinator—were inseparable from Leibniz's encyclopedic project chpt 5 Hence the characteristic, calculus ratiocinator, and encyclopedia form three pillars of Leibniz's project
Notes
 ^ FearnleySander 1982: p164
See also
 Gottfried Leibniz
 Characteristica universalis
References
 Louis Couturat, 1901 La Logique de Leibniz Paris: Felix Alcan Donald Rutherford's English translation of some chapters
 Hartley Rogers, Jr 1963, An Example in Mathematical Logic, The American Mathematical Monthly, Vol 70, No 9, pp 929–945
 Norbert Wiener, 1948, "Time, communication, and the nervous system," Teleological mechanisms Annals of the NY Acad Sci 50 4: pp 197–219
  1965, Cybernetics, Second Edition: or the Control and Communication in the Animal and the Machine, The MIT Press
 Desmond FearnleySander, 1982 Hermann Grassmann and the Prehistory of Universal Algebra, The American Mathematical Monthly, Vol 89, No 3, pp 161–166
External links
 Language as Calculus versus Language as Universal Medium



Mathematics and philosophy 

Works 

Other 




Topics and concepts 

Proposals and implementations 

In fiction 
See also: Logic machines in fiction and List of fictional computers 
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29.10.2014
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