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date: 28 May 2020

Summary and Keywords

Mathesis universalis is perhaps the ultimate formal system. The fact that the concept ties together truth, possibility, and formalism marks it as one of the most important concepts in Western modernity. “Mathesis” is Greek (μάθησις) for “learning” or “science.” The term is sometimes used to simply mean “mathematics”; the planet Mathesis, for instance, is named after the discipline of mathematics. It is philosophically significant when rendered as “mathesis universalis,” combining a Latinized version of the Greek μάθησις (learning) with the Latin universalis (universal). The most significant modern philosophers to develop the term were René Descartes (1596–1650) and Gottfried Leibniz (1646–1716), who used it to name a formal system that could support a project of scientia generalis (Descartes) or the ars combinatoria (Leibniz). In each case, mathesis universalis is a universal method. In this sense it does not constitute the content of the sciences but provides the formal system that undergirds no less than the acquisition and veracity of knowledge itself. Although mathesis universalis is only rarely mentioned in the literature of Descartes and Leibniz, philosophers including Edmund Husserl, Ernst Cassirer, and Martin Heidegger considered it one of the key traits of modernity, breaking with the era of substance (Rabouin) or resemblance (Foucault) to signal a new period defined by formalism and quantification. Thus, in the 20th century, the scant and often contradictory literature on mathesis actually produced by the great philosophers of the Enlightenment comes to take on an importance that far exceeds the term’s original level of systematic elaboration.

The term mathesis universalis was rarely used by either Descartes or Leibniz, and the latter used many different terms to refer to the same concept. The complexity and subtlety of the term, combined with difficulties in establishing a rigorous systematic interpretation, has meant that mathesis universalis is often used vaguely or to encompass all scientific method. It is a difficult concept to account for, because although many philosophers and literary theorists will casually refer to it, often in its abbreviated form (Lacan references mathesis in opposition to poesis to contrast the procedures of the sciences and the arts, for instance), there is not a great deal of consistent theoretical elaboration of the term in literary and cultural theory.

Although mathesis universalis is not simply an avatar of mathematics, it is difficult to establish exactly where maths ends and mathesis begins, so to speak. The distinction is murky in both Descartes’s and Leibniz’s work, and this ambiguity would become a key controversy surrounding the term in the 20th century, with Bertrand Russell arguing that the significance of symbolic logic to mathesis universalis prevented it from being a “premier” science. Along with Russell, Ernst Cassirer and Louis Couturat would contest the relation between symbolic logic and the symbolic algebra of mathesis universalis, providing the terms of the debate for 20th-century philosophical work on ontology.

Mathesis universalis was also a source of debate and controversy in the 20th century because it provided a node from which to examine the status of scientific truth. It is the work of 20th-century philosophers that expanded the significance of the term, using it to exemplify aspects of Enlightenment thought that many philosophers wished to react against, namely the aspiration to a universal science and the privileging of formal systems as avenues to truth. In this respect, the term is associated with Edmund Husserl, Martin Heidegger, and especially Michel Foucault, whose extensive work on the “classical episteme” provided a popular method of characterizing the development and enduring features of Enlightenment science. Although Foucault’s rendering of mathesis universalis as a “science of calculation” in The Order of Things (1970) is the most commonly used definition in literary and cultural studies, debates centering on Leibniz’s work in the early 20th century suggest that critics still took divergent approaches to the definition and significance of the term. It is Foucault who has popularized the contraction of the term to “mathesis.”

Keywords: mathematics, Enlightenment, philosophy, truth, science

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