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. (shrink)

In this paper, I want to make two main points. The first point is methodological: Instead of attempting to give a classical analysis or reductive definition of the term “expertise”, we should attempt an explication and look for what may be called symptoms of expertise. What this comes to will be explained in due course. My second point is substantial: I want to recommend understanding as an important symptom of expertise. In order to give this suggestion content, I begin to (...) develop an account of understanding. Finally, I will draw attention to some consequences of this approach. (shrink)

Greek antiquity saw the development of two distinct systems of logic: Aristotle’s theory of the categorical syllogism and the Stoic theory of the hypothetical syllogism. Some ancient logicians argued that hypothetical syllogistic is more fundamental than categorical syllogistic on the grounds that the latter relies on modes of propositional reasoning such asreductio ad absurdum. Peripatetic logicians, by contrast, sought to establish the priority of categorical over hypothetical syllogistic by reducing various modes of propositional reasoning to categorical form. In the 17th (...) century, this Peripatetic program of reducing hypothetical to categorical logic was championed by Gottfried Wilhelm Leibniz. In an essay titledSpecimina calculi rationalis, Leibniz develops a theory of propositional terms that allows him to derive the rule ofreductio ad absurdumin a purely categorical calculus in which every proposition is of the formA is B. We reconstruct Leibniz’s categorical calculus and show that it is strong enough to establish not only the rule ofreductio ad absurdum, but all the laws of classical propositional logic. Moreover, we show that the propositional logic generated by the nonmonotonic variant of Leibniz’s categorical calculus is a natural system of relevance logic known as RMI$_{{}_ \to ^\neg }$. (shrink)

ABSTRACTHow did the traditional doctrine of parts and wholes evolve into contemporary formal mereology? This paper argues that a crucial missing link may lie in the early modern and especially Wolf...

As denominadas filosofias do _hen kai pan_tiveram um papel determinante no pensamento alemão do século XVIII e XIX, em boa parte devido ao tratamento que lhes foi dado por F. H. Jacobi em _Sobre a doutrina de Espinosa em cartas ao senhor Moses Mendelssohn _. Espinosa e Giordano Bruno são os grandes representantes desse modo de pensar, e suas filosofias inauguram uma nova articulação entre causa e razão, mundo e Deus. Jacobi identifica em ambos o modelo da máxima coerência intelectual (...) que uma filosofia pode alcançar, um monismo imanente cuja consistência lógica não pode ser combatida no interior do sistema com as armas da metafísica pura. Por outro lado, é no princípio indeterminado, comum a essas doutrinas, que Jacobi verá a confirmação de uma danosa tendência da história da filosofia que culmina no idealismo de Fichte e na filosofia do jovem Schelling, isto é, na união entre natureza naturada e naturante no eu. (shrink)

The aim of this paper is to assess the central role the imagination acquires in Pierre Gassendi’s logic. I trace the structuring scheme of the three acts of the mind—common to a good number of late scholastic and early modern logics—to the Thomistic notion of the movement of reasoning in knowledge and argue that Gassendi revisits this notion in his logic. The three acts scheme is from the beginning a bridge between logic and the natural philosophical treatment of the soul. (...) I show how Gassendi’s take on the three acts is similarly poised between his Logic and his Physics and I discuss the rationale, sources and consequences of his attribution of the three acts to the imagination. I argue for the following points: Gassendi’s conception of the logical role of the imagination answers to his empiricist epistemology, his naturalized view of the mind and his notion of a natural logic; it is also operative in his pairing of the formal mechanism of logical operations with a progressive mechanism of the operations of the mind; and it serves as a counterpart to his experimental understanding of the progress of knowledge.1. (shrink)