Logic and Mathematics in the Seventeenth Century

Usually logic is considered very poor in the period comprised from the beginning of the seventeenth till the first half of the nineteenth Century. The Autor attempt to mild this judgement showing that the main concern of several logicans of this period was that of establishing a link According to the received view (Bochenski, 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 Bochenski 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.