(from , "science or learning", and "universal") is a hypothetical universal science modelled on

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

envisaged by Descartes and

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 Sir Isaac Newton, with the creation of calculus in addition to many ...

, among a number of other 16th- and 17th-century philosophers and mathematicians. For Leibniz, it would be supported by a ''

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 conc ...

''.

John Wallis John Wallis (; ; ) was an English clergyman and mathematician, who is given partial credit for the development of infinitesimal calculus. Between 1643 and 1689 Wallis served as chief cryptographer for Parliament and, later, the royal court. ...

invokes the name as title in his ''Opera Mathematica'', a textbook on

arithmetic Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. ...

algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

, and

Cartesian geometry In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and als ...

History

Descartes' most explicit description of ''mathesis universalis'' occurs in ''Rule Four'' of the '' Rules for the Direction of the Mind'', written before 1628. Leibniz attempted to work out the possible connections between

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 ...

infinitesimal calculus Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of ...

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

, and universal characteristics in an incomplete treatise titled "''Mathesis Universalis''" in 1695.

Predicate logic First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables ove ...

could be seen as a modern system with some of these ''universal'' qualities, at least as far as mathematics and

computer science Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...

are concerned. More generally, ''mathesis universalis'', along with perhaps

François Viète François Viète (; 1540 – 23 February 1603), known in Latin as Franciscus Vieta, was a French people, French mathematician whose work on new algebra was an important step towards modern algebra, due to his innovative use of letters as par ...

, represents one of the earliest attempts to construct a

formal system A formal system is an abstract structure and formalization of an axiomatic system used for deducing, using rules of inference, theorems from axioms. In 1921, David Hilbert proposed to use formal systems as the foundation of knowledge in ma ...

. One of the perhaps most prominent critics of the idea of ''mathesis universalis'' was Ludwig Wittgenstein and his philosophy of mathematics. As Anthropologist Emily Martin notes:

René Descartes

In Descartes' corpus the term ''mathesis universalis'' appears only in the '' Rules for the Direction of the Mind''. In the discussion of ''Rule Four'', Descartes' provides his clearest description of ''mathesis universalis'':

Gottfried Leibniz

In his account of ''mathesis universalis'', Leibniz proposed a dual method of universal synthesis and analysis for the ascertaining

truth Truth or verity is the Property (philosophy), property of being in accord with fact or reality.Merriam-Webster's Online Dictionarytruth, 2005 In everyday language, it is typically ascribed to things that aim to represent reality or otherwise cor ...

, described in ''De Synthesi et Analysi universale seu Arte inveniendi et judicandi'' (1890).

''Ars inveniendi''

''Ars inveniendi'' (

Latin Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...

for "art of invention") is the constituent part of ''mathesis universalis'' corresponding to the method of synthesis.

''Ars combinatoria''

Leibniz also identified synthesis with the '' ars combinatoria'', viewing it in terms of the recombination of symbols or human thoughts.

''Ars judicandi''

''Ars judicandi'' (

for "art of judgement") is the constituent part of ''mathesis universalis'' corresponding to the method of analysis.

References

Bibliography

* * * * * *

External links

* Raul Corazzon's Ontology web page
''Mathesis Universalis'' with a bibliography
{{History of science Mathematical logic Gottfried Wilhelm Leibniz René Descartes Philosophy of science Latin words and phrases