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doi: 10.1007/s11787-015-0121-0pmid: N/A
The goal of this article is to call attention to different ways in which logic was understood in the thirteenth century. Thus, it will recall some relevant historical facts related to the problem of classifying logic among scientific disciplines. This problem involved methodological questions linked to the form of presenting both the scientific disciplines and the books by which they were transmitted. Next, it will stress the contexts that led Medievals to raise questions about the nature of logic and why these issues were necessarily accompanied by considerations on the relation of logic to the disciplines dealing with language. Finally, it will analyze a change in perspective with respect to the status of logic, which moves from a science of human discourse to a science of mental acts.
doi: 10.1007/s11787-015-0122-zpmid: N/A
Peter Abelard and William of Ockham represent the two main figures of the nominalism of the Middle Ages. Both share the fundamental thesis of that doctrine, according to which only individual entities exist. The repercussions of nominalism are quite evident in relation to the question of universals, which constitutes a subject that, until now, won the attention of the majority of contemporary studies on the two most important logicians of their time. Nevertheless the nominalism of each of these two protagonists apparently diverges in a significant manner, especially in respect to the role exercised by the mind in the semantic process. Ockham seems to distance himself definitely from his predecessors, including Abelard, when he transfers grammar and semantic functions of conventional language to the level of mental language. In the present article, the chief intention is to expound the theory of sign and signification of each of the authors under consideration. The ultimate objective is to compare their respective semantic positions and indicate the principal points of agreement and disagreement, keeping in mind the hypothesis according to which these two medieval nominalists should have more theoretical elements in common than not.
doi: 10.1007/s11787-014-0114-4pmid: N/A
In his main work Summa Logicae written around 1323, William of Ockham developed a system of propositional modal logic which contains almost all theorems of a modern calculus of strict implication. This calculus is formally reconstructed here with the help of modern symbols for the operators of conjunction, disjunction, implication, negation, possibility, and necessity.
doi: 10.1007/s11787-014-0112-6pmid: N/A
In this article I present the analysis of the syncategorematic term ‘omnis’ in the commentaries on the Topics by the Parisian masters of Arts Boethius of Dacia and Radulphus Brito. I shall focus on the different relations between subject, predicate and particular instances that obtain in universally quantified statements, and in particular on the relations that obtain in universally quantified statements with an empty subject. I also attempt to highlight some continuities and ruptures with respect to this problem in its 13th-century treatments, by comparing Boethius and Brito’s analyses with the earlier (first half of the century) analyses put forth by Peter of Spain and William of Sherwood.
Goubier, Frédéric; Perini-Santos, Ernesto
doi: 10.1007/s11787-014-0113-5pmid: N/A
According to several late medieval logicians, the use the universal quantifier ‘omnis’ creates the requirement that the sentence refers to at least three items—the principle of sufficientia appellatorum. The commitment is such that, when the quota is not fulfilled, one has to import the missing items from the realm of the nonexistent. While the central argument for this principle, whose origin is Aristotle’s De Caelo, stems from the contrast between unrestricted universal quantifiers and binary quantifiers, the discussion is often mixed with another issue, concerning the requirement of a plurality of referents for universals. In this paper, we try to distinguish those different issues and map the reactions of xiii th authors to the principle of sufficientia appellatorum.
doi: 10.1007/s11787-014-0115-3pmid: N/A
Bradwardine’s solution to the the logical paradoxes depends on the idea that every sentence signifies many things, and its truth depends on things’ being wholly as it signifies. This idea is underpinned by his claim that a sentence signifies everything that follows from what it signifies. But the idea that signification is closed under entailment appears too strong, just as logical omniscience is unacceptable in the logic of knowledge. What is needed is a more restricted closure principle. A clue can be found in speech act pluralism, whereby indirect speech reports are closed under intersubstitutivity of co-referential terms. The conclusion is that solving the semantic paradoxes does not require revision of logic, thus saving logic from paradox.
doi: 10.1007/s11787-015-0123-ypmid: N/A
The rediscovery of Aristotle’s works on syllogisms in the Latin world, especially the Sophistici Elenchi and then the Prior Analytics, gave rise to sophisticated views on the nature of syllogistic form and syllogistic matter in the thirteenth century. It led to debates on the ontology of the syllogism as studied in the Prior Analytics, i.e. the syllogism made of letters and the four logical constants a/e/i/o, with deep consequences on the definition of logic as a universal method for all sciences and as a science itself.
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