The Calculus Ratiocinator is a theoretical universal logical calculation framework, a concept described in the writings of Gottfried Leibniz

Gottfried Leibniz

Gottfried Wilhelm Leibniz was a German philosopher and mathematician. He wrote in different languages, primarily in Latin , French and German ....

, usually paired with his more frequently mentioned characteristica universalis

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 the German philosopher Gottfried Leibniz able to express mathematical, scientific, and metaphysical concepts...

, 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

Computer software

Computer software, or just software, is a collection of computer programs and related data that provide the instructions for telling a computer what to do and how to do it....

, the second is associated with computer hardware

Computer hardware

Personal computer hardware are component devices which are typically installed into or peripheral to a computer case to create a personal computer upon which system software is installed including a firmware interface such as a BIOS and an operating system which supports application software that...

.

The analytic view

• The received point of view in analytic philosophy
  Analytic philosophy
  Analytic philosophy is a generic term for a style of philosophy that came to dominate English-speaking countries in the 20th century...
  
   and formal logic
  Logic
  In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
  
  , is that the calculus ratiocinator anticipates mathematical logic
  Mathematical logic
  Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
  
   — an "algebra of logic". The analytic point of view understands that the calculus ratiocinator is a formal inference engine
  Inference engine
  In computer science, and specifically the branches of knowledge engineering and artificial intelligence, an inference engine is a computer program that tries to derive answers from a knowledge base. It is the "brain" that expert systems use to reason about the information in the knowledge base for...
  
    or computer program
  Computer program
  A computer program is a sequence of instructions written to perform a specified task with a computer. A computer requires programs to function, typically executing the program's instructions in a central processor. The program has an executable form that the computer can use directly to execute...
  
   which can be designed so as to grant primacy to calculations. That logic began with Frege's 1879 Begriffsschrift
  Begriffsschrift
  Begriffsschrift is a book on logic by Gottlob Frege, published in 1879, and the formal system set out in that book...
  
  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 lingua characteristica. That part of formal logic relevant to the calculus comes under the heading of proof theory
  Proof theory
  Proof theory is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as plain lists, boxed lists, or trees, which are constructed...
  
  . 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
  Cybernetics
  Cybernetics is the interdisciplinary study of the structure of regulatory systems. Cybernetics is closely related to information theory, control theory and systems theory, at least in its first-order form...
  
  , electronic engineering
  Electronic engineering
  Electronics engineering, also referred to as electronic engineering, is an engineering discipline where non-linear and active electrical components such as electron tubes, and semiconductor devices, especially transistors, diodes and integrated circuits, are utilized to design electronic...
  
   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
  Norbert Wiener
  Norbert Wiener was an American mathematician.A famous child prodigy, Wiener later became an early researcher in stochastic and noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems.Wiener is regarded as the originator of cybernetics, a...
  
   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

Stepped Reckoner

The Step Reckoner was a digital mechanical calculator invented by German mathematician Gottfried Wilhelm Leibniz around 1672 and completed in 1694. The name comes from the translation of the German term for its operating mechanism; staffelwalze meaning 'stepped drum'...

. 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 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.

External links

• Language as Calculus versus Language as Universal Medium