Descartes Mathesis Universalis

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In this presentation we want to elaborate on the meaning of the concept mathesis universalis in the work of Descartes. The concept was not coined by Descartes himself. It was a generally used notion during the sixteenth century by Descartes's contemporaries, and so Descartes refers to this concept as a familiar one. In fact, the idea of the concept goes back even to Aristotle's philosophy (Sasaki 2003).

The specific meaning of the concept in Descartes's work is discussed in secondary literature (Cajori [1894] 1926, Mittelstrass 1979, Sasaki 2003, Van de Pitte 1979). Looking at the history of the meaning of the concept mathesis universalis, it seems at least to be twofold. The first meaning of the concept refers to the set of all mathematical sciences (as historically understood) like geometry, algebra, astronomy, music, optics, mechanics, ... This meaning refers merely to a collective name for all different mathematical (sub)sciences.
The second meaning refers to an epistemological dogma in the philosophy of Descartes. Here, the concept refers to a kind of universal and unifying science by which all problems can (and have to) be solved. For Descartes, the unifying factor of all problems is the fact that they can be characterized by quantity (be it discrete or continuous). Central notions in the methodological prescriptions of Descartes are ordo and mensura (Dijksterhuis 1950). This means that only those problems which are quantifiable can be the subject of human epistemological activity. Descartes's dream of the universal and unifying science appears already in his first writings from 1619 (Bos 2001). He elaborated the idea further in his Regulae ad directionem ingenii, written in 1628 and posthumously published in 1684.

The discussion on the two meanings of the concept mathesis universalis in the work of Descartes focuses more specifically on the fourth rule of the Regulae ad directionem ingenii. This rule consists of two parts (indicated in literature as IVA and IVB) were the first part refers to the general and unifying meaning of the concept, i.e., the second meaning above, and the second part refers to the set of particular mathematical sciences, i.e., the first meaning above.

In this presentation we firstly want to go through the different arguments pro and contra the diverse interpretations in the secondary literature. Secondly, we will bring some new arguments into the discussion based on the later works of Descartes e.g. Discours de la méthode (1637), Méditations (1641), Les principes de la philosophie (1644). Finally we present the implication of Descartes's meaning of mathesis universalis to human epistemological activity in general.
Vertaalde titel van de bijdrageDescartes Mathesis Universalis
Originele taal-2English
TitelIn Proceedings of the International Conference on Philosophical Aspects of Symbolic Reasoning in Early Modern Science and Mathematics (PASR) August 27-29, Ghent.
StatusPublished - 2009
EvenementUnknown - Stockholm, Sweden
Duur: 21 sep 200925 sep 2009




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