In his Quadratura, Paul of Venice considers a sophism involving time and tense which appears to show that there is a valid inference which is also invalid. His argument runs as follows: consider this inference concerning some proposition A: A will signify only that everything true will be false, so A will be false. Call this inference B. Then B is valid because the opposite of its conclusion is incompatible with its premise. In accordance with the standard doctrine of ampliation, (...) Paul takes A to be equivalent to 'Everything that is or will be true will be false'. But he proceeds to argue that it is possible that B's premise ('A will signify only that everything true will be false') could be true and its conclusion false, so B is not only valid but also invalid. Thus A and B are the basis of an insoluble. In his Logica Parva, a self-confessedly elementary text aimed at students and not necessarily representing his own view, and in the Quadratura, Paul follows the solution found in the Logica Oxoniensis, which posits an implicit assertion of its own truth in insolubles like B. However, in the treatise on insolubles in his Logica Magna, Paul develops and endorses Swyneshed's solution, which stood out against this ''multiple-meanings'' approach in offering a solution that took insolubles at face value, meaning no more than is explicit in what they say. On this account, insolubles imply their own falsity, and that is why, in so falsifying themselves, they are false. We consider how both types of solution apply to B and how they complement each other. On both, B is valid. But on one (following Swyneshed), B has true premises and false conclusion, and contradictories can be false together; on the other (following the Logica Oxoniensis), the counterexample is rejected. (shrink)

Commentators have not said much regarding Berkeley and Stoicism. Even when they do, they generally limit their remarks to Berkeley’s Siris (1744) where he invokes characteristically Stoic themes about the World Soul, “seminal reasons,” and the animating fire of the universe. The Stoic heritage of other Berkeleian doctrines (e.g., about mind or the semiotic character of nature) is seldom recognized, and when it is, little is made of it in explaining his other doctrines (e.g., immaterialism). None of this is surprising, (...) considering how Stoics are considered arch-materialists and determinists. My aim is to suggest that our understanding of Berkeley’s philosophy is improved significantly by acknowledging its underlying Stoic character. I argue that Berkeley proposes not only a semantic ontology based on assumptions of Stoic logic but also a doctrine in which perceptions or ideas are intelligible precisely because they are always embedded in the propositions of a discourse or language. (shrink)

This paper argues for two principal conclusions about natural language semantics based on John Buridan's considerations concerning the notion of formal consequence, that is, formally valid inference. (1) Natural languages are essentially semantically closed, yet they do not have to be on that account inconsistent. (2) Natural language semantics has to be token based, as a matter of principle. The paper investigates the Buridanian considerations leading to these conclusions, and considers some obviously emerging objections to the Buridanian approach.

This book collects six unpublished and published academic studies on the thought of Francisco Suárez, which is addressed through accurate textual analyses and meticulous contextualization of his doctrines in the Scholastic debate. The present essays aim to portray two complementary aspects coexisting in the work of the Uncommon Doctor: his innovative approach and his adherence to the tradition. To this scope, they focus on some pivotal, but often neglected, topics in Suárez’s metaphysics and psychology – such as his theories of (...) cognition and truth, angelology, continuous quantity – thereby developing an original inquiry into a crucial moment in the development of Western philosophy. (shrink)

From a general semantic point of view, Thomas Bricot and John Mair are proponents of the solution to semantic paradoxes based on appreciation of the contextuality of truth, who differ in their approach to the relations of logical consequence and contradiction. The core of the study is the analysis of Mair's criticism of Bricot presented in the sixth quaestio of his Tractatus insolubilium where the consequences of non-compositional semantics for the concepts of synonymy and logical form are addressed. The polemic (...) between John Mair and Thomas Bricot is construed as having immediate consequences for research in the area of non-compositional semantics. (shrink)

To understand pre-Fregean theories of judgment and proposition, such as those found in Locke and the Port-Royal logic, it is important to distinguish between propositions in the modern sense and propositions in the pre-Fregean sense. By making this distinction it becomes clear that these pre-Fregean theories cannot be meant to solve the propositional attitude problem. Notwithstanding this fact, Locke and Arnauld are able to make a distinction between asserted and unasserted propositions (in their sense). The way Locke makes this distinction (...) turns out to be very different from the way it is made by Arnauld. (shrink)

I examine a sixteenth-century development of the anti-realist propositional semantics which is based on the notion of ‘mode’. Pardo uses this notion to offer a personal interpretation of the Buridanian criticism of complexe significabilia. He develops a middle way between the reduction of the significate of propositions to particular things and the postulation of non-standard entities which are only complexly signifiable. The key to this middle way is Pardo's understanding of the notion of ‘mode’ as connoting a relation between individual (...) things. He offers a new interpretation of the signification of syncategorematic terms, and a definition of ‘comparative’ notions, by which something is known ‘relatively’ with respect to some other thing. And a real relational correlate is postulated for these relational ways of knowing. Relations are thus used to grant a specific significate of propositions, without renouncing the strict Buridanian rejection of any extra-categorial complexe significabilia. The role of r... (shrink)

The meaning of a declarative sentence and that of an interrogative sentence differ in their aspect of mood. A semantics of mood has to account for the differences in meaning between these sentences, and it also has to explain that sentences in different moods may have a common core. The meaning of the declarative mood is to be explained not in terms of actual force (contra Dummett), but in terms of potential force. The meaning of the declarative sentence (including its (...) mood) is called the assertion-candidate, which is explained by what one must know in order to be entitled to utter the declarative with assertive force. Both a cognitive notion (knowledge) and a pragmatic notion (assertive force) are thus part of the explanation of the assertion-candidate. Davidson’s criticism that such a theory is in need of an account of the distinction between standard and non-standard uses of the declarative is answered: without counter-indications an utterance of a declarative sentence is understood as having assertive force. The meaning of an interrogative sentence, the question-candidate, and that of the other sentence types can ultimately be explained in terms of their specific relations to the assertion-candidate. Martin-Löf’s constructive type theory is used to show the philosophical relevance of a semantics of mood. The constructivist notion of proposition needs to be embedded in a theory of the assertion-candidate, which fulfils the offices of being the meaning of the declarative sentence, the content of judgement and assertion and the bearer of epistemic truth. (shrink)

Loci personarum, ‘topics for persons’ were used in Latin rhetoric for the description of persons, their external circumstances, physical attributes, or qualities of character. They stood in the way of fusing rhetoric and dialectic, the goal of sixteenth-century ‘humanistic’ logic: the project of a unified theory of invention depends on the exclusion of loci personarum from the domain of dialectic proper. But still they cannot easily be replaced in the class room. Bartholomaeus Keckermann resolved these difficulties: he proposed to abandon (...) the notion that loci personarum could play a role in finding new arguments concerning persons. So they pose no risks for a unified theory of invention, because they can only be used for the exposition of information that we already have. Since loci personarum are concerned with individuals, the knowledge about individuals that is available to us is inescapably circumstantial and contingent, defying the claim of generality or necessity of dialectic made by Keckermann’s sixteenth-century predecessors. However, our thinking about persons is primarily interested in those aspects that we do not share with other members of our species. For Keckermann, persons are therefore logically different from most individuals belonging to other species. (shrink)

Leibniz's overall view of the relationship between reasoning and computation is discussed on the basis of two broad claims that one finds in his writings, concerning respectively the nature of human reasoning and the possibility of replacing human thinking by a mechanical procedure. A joint examination of these claims enables one to appreciate the wide scope of Leibniz's interests for mechanical procedures, concerning a variety of philosophical themes further developed both in later logical investigations and in methodological contributions to cognitive (...) psychology. (shrink)

This paper explores Simon Stevin’s l’Arithmétique of 1585, where we find a novel understanding of the concept of number. I will discuss the dynamics between his practice and philosophy of mathematics, and put it in the context of his general epistemological attitude. Subsequently, I will take a close look at his justificational concerns, and at how these are reflected in his inductive, a postiori and structuralist approach to investigating the numerical field. I will argue that Stevin’s renewed conceptualisation of the (...) notion of number is a sort of “existential closure” of the numerical domain, founded upon the practice of his predecessors and contemporaries. Accordingly, I want to make clear that l’Aritmetique have to be read not as an ontological analysis or exploration of the numerical field, but as an explication of a mathematical ethos. In this sense, this article also intends to make a specific contribution to the broader issue of the “ethics of geometry.”. (shrink)

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)