Logic and Mathematics in the Seventeenth Century

History and Philosophy of Logic 31 (4):297-314 (2010)
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Abstract

According to the received view (Bocheński, Kneale), from the end of the fourteenth to the second half of nineteenth century, logic enters a period of decadence. If one looks at this period, the richness of the topics and the complexity of the discussions that characterized medieval logic seem to belong to a completely different world: a simplified theory of the syllogism is the only surviving relic of a glorious past. Even though this negative appraisal is grounded on good reasons, it overlooks, however, a remarkable innovation that imposes itself at the beginning of the sixteenth century: the attempt to connect the two previously separated disciplines of logic and mathematics. This happens along two opposite directions: the one aiming to base mathematical proofs on traditional (Aristotelian) logic; the other attempting to reduce logic to a mathematical (algebraical) calculus. This second trend was reinforced by the claim, mainly propagated by Hobbes, that the activity of thinking was the same as that of performing an arithmetical calculus. Thus, in the period of what Bocheński characterizes as ‘classical logic’, one may find the seeds of a process which was completed by Boole and Frege and opened the door to the contemporary, mathematical form of logic.

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References found in this work

The development of logic.W. C. Kneale - 1962 - New York: Oxford University Press. Edited by Martha Kneale.
New Essays on Human Understanding.Gottfried Wilhelm Leibniz - 1981 - New York: Cambridge University Press. Edited by Peter Remnant & Jonathan Bennett.
Sämtliche Schriften und Briefe.Gottfried Wilhelm Leibniz - 1967 - Revista Portuguesa de Filosofia 23 (4):500-501.
A Survey of Symbolic Logic.C. I. Lewis - 1918 - Journal of Philosophy, Psychology and Scientific Methods 17 (3):78-79.

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