Annals of Science 36 (6):593-610 (1979)

Abstract
In Descartes, the concept of a ‘universal science’ differs from that of a ‘mathesis universalis’, in that the latter is simply a general theory of quantities and proportions. Mathesis universalis is closely linked with mathematical analysis; the theorem to be proved is taken as given, and the analyst seeks to discover that from which the theorem follows. Though the analytic method is followed in the Meditations, Descartes is not concerned with a mathematisation of method; mathematics merely provides him with examples. Leibniz, on the other hand, stressed the importance of a calculus as a way of representing and adding to what is known, and tried to construct a ‘universal calculus’ as part of his proposed universal symbolism, his ‘characteristica universalis’. The characteristica universalis was never completed—it proved impossible, for example, to list its basic terms, the ‘alphabet of human thoughts’—but parts of it did come to fruition, in the shape of Leibniz's infinitesimal calculus and his various logical calculi. By his construction of these calculi, Leibniz proved that it is possible to operate with concepts in a purely formal way
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DOI 10.1080/00033797900200401
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References found in this work BETA

Cogito, Ergo Sum: Inference or Performance?Jaakko Hintikka - 1962 - Philosophical Review 71 (1):3-32.
Über Das cogito, ergo sum.Heinrich Scholz - 1931 - Kant-Studien 36 (1-2):126-147.
Der anfang der vernunft bei Descartes - autobiographisch und historisch.Wilhelm Kamlah - 1961 - Archiv für Geschichte der Philosophie 43 (1):70-84.

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Descartes' Logic of Magnitudes.Gisela Loeck - 1989 - Dialectica 43 (4):339-372.

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