Mathesis universalis
Encyclopedia
Mathesis universalis is a hypothetical universal science modeled on mathematics
envisaged by Leibniz and Descartes, among a number of more minor 16th and 17th century philosophers and mathematicians. John Wallis invokes the name as the title to a textbook on Cartesian geometry. For Leibniz, it would be supported by a Calculus ratiocinator
.
Descartes' clearest description of the mathesis universalis occurs in Rule IV of the Rules for the Direction of the Mind
, written before 1628. The desire for a language more perfect than any natural language
had been expressed before Leibniz by John Wilkins
in his An Essay towards a Real Character and a Philosophical Language
in 1668. Leibniz attempts to work out the possible connections between algebra, infinitesimal calculus, and universal character in an incomplete treatise titled 'Mathesis Universalis' in 1695.
Predicate logic
could be seen as a modern system with some of these universal characteristics, at least as far as mathematics and computer science
are concerned. More generally, mathesis universalis, along with perhaps François Viète
's algebra
, represents one of the earliest attempts to construct a formal system
.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
envisaged by Leibniz and Descartes, among a number of more minor 16th and 17th century philosophers and mathematicians. John Wallis invokes the name as the title to a textbook on Cartesian geometry. For Leibniz, it would be supported by a Calculus ratiocinator
Calculus ratiocinator
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, a universal conceptual language....
.
Descartes' clearest description of the mathesis universalis occurs in Rule IV of the Rules for the Direction of the Mind
Rules for the Direction of the Mind
In 1619, René Descartes began work on an unfinished treatise regarding the proper method for scientific and philosophical thinking entitled Regulae ad directionem ingenii, or Rules for the Direction of the Mind. This work outlined the basis for his later work on complex problems of mathematics,...
, written before 1628. The desire for a language more perfect than any natural language
Natural language
In the philosophy of language, a natural language is any language which arises in an unpremeditated fashion as the result of the innate facility for language possessed by the human intellect. A natural language is typically used for communication, and may be spoken, signed, or written...
had been expressed before Leibniz by John Wilkins
John Wilkins
John Wilkins FRS was an English clergyman, natural philosopher and author, as well as a founder of the Invisible College and one of the founders of the Royal Society, and Bishop of Chester from 1668 until his death....
in his An Essay towards a Real Character and a Philosophical Language
An Essay towards a Real Character and a Philosophical Language
An Essay towards a Real Character, and a Philosophical Language is the best-remembered of the numerous works of John Wilkins, in which he expounds a new universal language, meant primarily to facilitate international communication among scholars, but envisioned for use by diplomats, travelers, and...
in 1668. Leibniz attempts to work out the possible connections between algebra, infinitesimal calculus, and universal character in an incomplete treatise titled 'Mathesis Universalis' in 1695.
Predicate logic
Predicate logic
In mathematical logic, predicate logic is the generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic or infinitary logic. This formal system is distinguished from other systems in that its formulae contain variables which can be quantified...
could be seen as a modern system with some of these universal characteristics, at least as far as mathematics and computer science
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
are concerned. More generally, mathesis universalis, along with perhaps François Viète
François Viète
François Viète , Seigneur de la Bigotière, was a French mathematician whose work on new algebra was an important step towards modern algebra, due to its innovative use of letters as parameters in equations...
's algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
, represents one of the earliest attempts to construct a formal system
Formal system
In formal logic, a formal system consists of a formal language and a set of inference rules, used to derive an expression from one or more other premises that are antecedently supposed or derived . The axioms and rules may be called a deductive apparatus...
.
External links
- Raul Corazzon's Ontology web page: Mathesis Universalis: a bibliography