This book collects six unpublished and published academic studies on the thought of Francisco Suárez, which is addressed through accurate textual analyses and meticulous contextualization of his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)

In this study I compare the work of two scholars who are important for contemporary research into the history of semiotics. The main goal of the study is to describe specific rhetorical/figurative forms and structures of persuasion between two epistemological positions that determine various possibilities in the historiography of semiotics. The main question is this: how do we understand two important metatheoretical forms of descriptions in the historiography of semiotics or the history of sign relations? The first perspective is semiology (...) and its corollary, “structuralism,” as presented in Michel Foucault’sThe Order of Things. This perspective prefers to consider history as a set of ruptures (i). The second position explores the possibility of the historical development of semiotic consciousness as presented in the works of John N. Deely (ii). The main aim of this study lies in the exploration of these two different epistemological bases – divergent bases for developing specific understandings of interconnections that hold between between semiotics, semiosis and historical processes. A goal of this paper is to demonstrate the limits and advantages of these two paradigmatic positions. The positions in question are “meta-theoretical” in the following senses such that: (i) the historical episteme is taken to be ana priorideterminant of all sign-operations in a given era and is also the semiologic grid through which Foucault approaches every mode of scientific knowledge (from “science” to “economy” and beyond); (ii) the quasi-Hegelian development of semiotic consciousness based on a conception of the sign considered as a triadic ontological relation. The latter is Deely’s guiding meta-principle, through which the history of semiotics can be articulated, examined and evaluated. (shrink)

This article reconstructs Kant's view on the existential import of categorical sentences. Kant is widely taken to have held that affirmative sentences (the A and I sentences of the traditional square of opposition) have existential import, whereas negative sentences (E and O) lack existential import. The article challenges this standard interpretation. It is argued that Kant ascribes existential import only to some affirmative synthetic sentences. However, the reasons for this do not fall within the remit of Kant's formal logic. Unlike (...) traditional logic and modern standard quantification theory, Kant's formal logic is free from existential commitments. (shrink)

Peter Geach describes the 'doctrine of distribution' as the view that a term is distributed if it refers to everything that it denotes, and undistributed if it refers to only some of the things that it denotes. He argues that the notion, so explained, is incoherent. He claims that the doctrine of distribution originates from a degenerate use of the notion of ?distributive supposition? in medieval supposition theory sometime in the 16th century. This paper proposes instead that the doctrine of (...) distribution occurs at least as early as the 12th century, and that it originates from a study of Aristotle's notion of a term's being ?taken universally?, and not from the much later theory of distributive supposition. A detailed version of the doctrine found in the Port Royal Logic is articulated, and compared with a slightly different modern version. Finally, Geach's arguments for the incoherence of the doctrine are discussed and rejected. (shrink)

Consider the following argument written on the board in room 227: 1 = 1. So, the argument on the board in room 227 is not valid. This argument generates a paradox. The aim of this paper is to present a resolution of this paradox and related paradoxes of validity, including a version of the Curry paradox. The proposal stresses the close connections between these validity paradoxes and paradoxes of truth and paradoxes of denotation. So a more general aim is to (...) provide a unified response to semantic paradox. The positive proposal is in part inspired by a brief, tantalizing suggestion of Gödel’s, that the paradoxes might appear “as something analogous to dividing by zero”—so that the concept of validity, for example, is everywhere applicable except for certain singular points or singularities. A second central claim is that ‘valid’ is a context-sensitive predicate. The key notions of this contextual-singularity theory are presented and applied to a variety of cases. Any purported solution to paradox must deal with the phenomenon of revenge, and a response to revenge is outlined. The paper closes with remarks about the accommodation of Tarski’s claim that natural languages are universal. (shrink)

This paper arose from an attempt to determine how the very late medieval1 supposition theorists treated anaphoric pronouns, pronouns whose significance is derivative from their antecedents. Modern researches into pronouns were stimulated in part by the problem of "donkey sentences" discussed by Geach 1962 in a section explaining what is wrong with medieval supposition theory. So there is some interest in seeing exactly what the medieval account comes to, especially if it turns out, as I suspect, to work as well (...) as contemporary ones. Besides, finding a good analysis of pronouns has proved to be very difficult, and so we might possibly find some insight in a historically different kind of approach. I discuss a version of supposition theory that aims at producing analyses of sentences containing quantified terms,2 as articulated around 1400 by Paul of Venice, and as further developed by certain logicians such as de Soto and Celaya in the 1400's and early 1500's.3 Much of what I will say also applies indirectly to earlier versions of supposition theory (before 1400). (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)

Abstract Boyle distinguished clearly between the areas which we would call scientific and theological. However, he felt that they overlapped seamlessly, and that the truths we discovered (or which were revealed to us) in one of these areas would be relevant to us in the other. In this paper I outline and discuss Boyle's views on the limitations of human knowing, Boyle's arguments in favour of accepting the revelations of the Christian faith, and his views on the kind of epistomological (...) standing that scientific knowledge claims have. Given this background I then consider the relation between hypotheses, theories and facts in Boyle's work, and consider a particular case, that of Boyle's Law, as an exemplification of the claims made in the rest of the paper. (shrink)

One way to determine the quality and pace of change in a science as it undergoes a major transition is to follow some feature of it which remains relatively stable throughout the process. Following the chosen item as it goes through reinterpretation permits conclusions to be drawn about the nature and scope of the broader change in question. In what follows, this device is applied to the change which took place in logic in the mid-nineteenth century. The feature chosen as (...) the focal point is the categorical syllogism. (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)

History witnesses alternative approaches to “the proposition”. The proposition has been referred to as the object of belief, disbelief, and doubt: generally as the object of propositional attitudes, that which can be said to be believed, disbelieved, understood, etc. It has also been taken to be the object of grasping, judging, assuming, affirming, denying, and inquiring: generally as the object of propositional actions, that which can be said to be grasped, judged true or false, assumed for reasoning purposes, etc. The (...) proposition has also been taken to be the subject of truth and falsity: generally as the subject of propositional properties, that which can be said to be true, false, tautological, informative, inconsistent,etc. It has also been taken as the subject and object of logical relations, e.g. that which can be said to imply, be implied, contradict, be contradicted, etc. Prima facie, such properties and relations are non-mental and objective. It has also been taken to be the resultants or products of propositional operations, usually mental or linguistic; e.g. judging, affirming, and denying have been held to produce propositions called judgments, affirmations, and negations, respectively. Propositions have also been taken to be certain declarative sentences. Finally,propositions have been taken to be meanings of certain declarative sentences. This essay is an informal, selective, and incomplete survey of alternative approaches to “the proposition” with special attention to the views of the late American philosopher Peter Hare (1935–2008)and of those who influenced him. DOI: 10.5007/1808-1711.2011v15n1p51. (shrink)

In the _Meditations_ and related texts from the early 1640s, Descartes argues that the self can be correctly considered as either a mind or a human being, and that the self’s properties vary accordingly. For example, the self is simple considered as a mind, whereas the self is composite considered as a human being. Someone might object that it is unclear how merely considering the self in different ways blocks the conclusion that a single subject of predication—the self—is both simple (...) and composite, which is contradictory. In response to this objection, this paper develops a reading of Descartes’s various ways of considering the self. I argue that the best reading of Descartes’s qualified claims about the self, i.e., about the self _qua_ mind or the self qua human being, presupposes an account of the unqualified self, that is, of the self _simpliciter_. I argue that the self _simpliciter_ is not a mind, and that it is not a human being either. This result might suggest the pessimistic conclusion that Descartes’s view of the self is incoherent. To avoid this result, I introduce a new metaphysical account of the Cartesian self. On my view, the self is individuated by a unified mental life. The self is constituted by the beings that jointly produce this mental life, and derives its unity from it. (shrink)

Supposition is a controversial logical theory. Scholars have investigated many points of this doctrine such as its historical origin, its use in theology, the logical function of the theory, or the relationship between supposition and signification. In the article I focus on this latter aspect by discussing how some Italian, and in particular Florentine, Dominican followers of Aquinas—Francis of Prato, Girolamo Savonarola, and Georgius Rovegnatinus —explained the relation between the linguistic terms’ properties of signifying and suppositing, and hence the division (...) of supposition. After sketching out Thomas Aquinas, Hervaeus Natalis, and William of Ockham’s positions on the relationship between signification and supposition, I closely examine Francis’s criticism of Ockham. Francis follows Walter Burley’s account of supposition and considers the statement that a term has simple supposition when it is taken not significatively and stands for an intention of mind as the weak point of Ockham’s explanation of supposition. According to Francis, if this were the case, there would be no semantic basis for differentiating simple from material supposition. Francis is however hesitant about the full subordination of supposition to signification, especially with regards to material supposition, when a term, suppositing for itself, is taken to signify itself besides its meaning. More than one hundred years later, Girolamo Savonarola and Georgius Rovegnatinus have no doubt about the fact that terms may supposit only for what they signify. (shrink)

Peter Ludlow shows how word meanings are much more dynamic than we might have supposed, and explores how they are modulated even during everyday conversation. The resulting view is radical, and has far-reaching consequences for our political and legal discourse, and for enduring puzzles in the foundations of semantics, epistemology, and logic.

This book presents novel formalizations of three of the most important medieval logical theories: supposition, consequence and obligations. In an additional fourth part, an in-depth analysis of the concept of formalization is presented - a crucial concept in the current logical panorama, which as such receives surprisingly little attention.Although formalizations of medieval logical theories have been proposed earlier in the literature, the formalizations presented here are all based on innovative vantage points: supposition theories as algorithmic hermeneutics, theories of consequence analyzed (...) with tools borrowed from model-theory and two-dimensional semantics, and obligations as logical games. For this reason, this is perhaps the first time that these medieval logical theories are made fully accessible to the modern philosopher and logician who wishes to obtain a better grasp of them, but who has always been held back by the lack of appropriate ‘translations' into modern terms.Moreover, the book offers a reflection on the very nature of logic, a reflection that is prompted by the comparisons between medieval and modern logic, their similarities and dissimilarities. It is thus a contribution not only to the history of logic, but also to the philosophy of logic, the philosophy of language and semantics.The analysis of medieval logic is also relevant for the modern philosopher and logician in that, being the unifying methodology used across all disciplines at that time, logic really provided unity to science. It thus presents a unified model of scientific investigation, where logic plays the aggregating role. (shrink)

“The problem of universals” in general is a historically variable bundle of several closely related, yet in different conceptual frameworks rather differently articulated metaphysical, logical, and epistemological questions, ultimately all connected to the issue of how universal cognition of singular things is possible. How do we know, for example, that the Pythagorean theorem holds universally, for all possible right triangles? Indeed, how can we have any awareness of a potential infinity of all possible right triangles, given that we could only (...) see a finite number of actual ones? How can we universally indicate all possible right triangles with the phrase ‘right triangle’? Is there something common to them all signified by this phrase? If so, what is it, and how is it related to the particular right triangles? The medieval problem of universals is a logical, and historical, continuation of the ancient problem generated by Plato's (428-348 B.C.) theory answering such a bundle of questions, namely, his theory of Ideas or Forms. (shrink)

The purpose of this entry is to provide a systematic introduction to medieval views about the nature and ontological status of relations. Given the current state of our knowledge of medieval philosophy, especially with regard to relations, it is not possible to discuss all the nuances of even the best known medieval philosophers' views. In what follows, therefore, we shall restrict our aim to identifying and describing (a) the main types of position that were developed during the Middle Ages, and (...) (b) the most important considerations that shaped their development. We shall have occasion along the way, however, to examine in detail certain aspects of the views of important representatives of all the main medieval positions, including Peter Abelard (1079 1142), Gilbert of Poitiers (1085 1154), Albert the Great, (1200 1280), Thomas Aquinas (1225 1274), John Duns Scotus (1265 1308), Henry Harclay (1270 1317), Peter Auriol (1280 1322), and William Ockham (1285 1347). (shrink)

For Jizang (549−623), a prominent philosophical exponent of Chinese Madhyamaka, all things are empty of determinate form or nature. Given anything X, no linguistic item can truly and conclusively be applied to X in the sense of positing a determinate form or nature therein. This philosophy of ontic indeterminacy is connected closely with his notion of the Way (dao), which seems to indicate a kind of ineffable principle of reality. However, Jizang also equates the Way with nonacquisition as a conscious (...) state of freedom from any attachment and definite understanding whatsoever. The issue then becomes pressing as to how we are to understand Jizang's notion of the Way. Does it indicate some metaphysical principle or reality? Is it actually a skilful expedient to lead one to the consummate state of complete spiritual freedom? How is this issue related to Jizang's conception of ontic indeterminacy? In this book chapter, I examine Jizang's key writings in an attempt to clarify his ontological position. (shrink)

It is a received view that Kant’s formal logic (or what he calls “pure general logic”) is thoroughly intensional. On this view, even the notion of logical extension must be understood solely in terms of the concepts that are subordinate to a given concept. I grant that the subordination relation among concepts is an important theme in Kant’s logical doctrine of concepts. But I argue that it is both possible and important to ascribe to Kant an objectual notion of logical (...) extension according to which the extension of a concept is the multitude of objects falling under it. I begin by defending this ascription in response to three reasons that are commonly invoked against it. First, I explain that this ascription is compatible with Kant’s philosophical reflections on the nature and boundary of a formal logic. Second, I show that the objectual notion of extension I ascribe to Kant can be traced back to many of the early modern works of logic with which he was more or less familiar. Third, I argue that such a notion of extension makes perfect sense of a pivotal principle in Kant’s logic, namely the principle that the quantity of a concept’s extension is inversely proportional to that of its intension. In the process, I tease out two important features of the Kantian objectual notion of logical extension in terms of which it markedly differs from the modern one. First, on the modern notion the extension of a concept is the sum of the objects actually falling under it; on the Kantian notion, by contrast, the extension of a concept consists of the multitude of possible objects—not in the metaphysical sense of possibility, though—to which a concept applies in virtue of being a general representation. While the quantity of the former extension is finite, that of the latter is infinite—as is reflected in Kant’s use of a plane-geometrical figure (e.g., circle, square), which is continuum as opposed to discretum, to represent the extension in question. Second, on the modern notion of extension, a concept that signifies exactly one object has a one-member extension; on the Kantian notion, however, such a concept has no extension at all—for a concept is taken to have extension only if it signifies a multitude of things. This feature of logical extension is manifested in Kant’s claim that a singular concept (or a concept in its singular use) can, for lack of extension, be figuratively represented only by a point—as opposed to an extended figure like circle, which is reserved for a general concept (or a concept in its general use). Precisely on account of these two features, the Kantian objectual extension proves vital to Kant’s theory of logical quantification (in universal, particular and singular judgments, respectively) and to his view regarding the formal truth of analytic judgments. (shrink)

This thesis is on the history and philosophy of logic and semantics. Logic can be described as the ‘science of reasoning’, as it deals primarily with correct patterns of reasoning. However, logic as a discipline has undergone dramatic changes in the last two centuries: while for ancient and medieval philosophers it belonged essentially to the realm of language studies, it has currently become a sub-branch of mathematics. This thesis attempts to establish a dialogue between the modern and the medieval traditions (...) in logic, by means of ‘translations’ of the medieval logical theories into the modern framework of symbolic logic, i.e. formalizations. One of its conclusions is that, when properly understood within their own framework, the interest of medieval logical theories for modern investigations go beyond mere historical interest, but that a thorough conceptual analysis of such theories must be undertaken in order to avoid conceptual misprojections. While such translations of medieval into modern logic have been attempted before, the approach presented here is innovative in that attention is paid to the similarities as well as to the dissimilarities between the two traditions, and to what can be learned from the medieval masters for modern investigations in logic and semantics. (shrink)