The recovery of Aristotle’s logic during the twelfth century was a great stimulus to medieval thinkers. Among their own theories developed to explain Aristotle’s theories of valid and invalid reasoning was a theory of consequence, of what arguments were valid, and why. By the fourteenth century, two main lines of thought had developed, one at Oxford, the other at Paris. Both schools distinguished formal from material consequence, but in very different ways. In Buridan and his followers in Paris, formal consequence (...) was that preserved under uniform substitution. In Oxford, in contrast, formal consequence included analytic consequences such as ‘If it’s a man, then it’s an animal’. Aristotle’s notion of syllogistic consequence was subsumed under the treatment of formal consequence. Buridan developed a general theory embracing the assertoric syllogism, the modal syllogism and syllogisms with oblique terms. The result was a thoroughly systematic and extensive treatment of logical theory and logical consequence which repays investigation. (shrink)

The paper explores the existential import of universal affirmative in Descartes, Arnauld and Malebranche. Descartes holds, inconsistently, that eternal truths are true even if the subject term is empty but that a proposition with a false idea as subject is false. Malebranche extends Descartes? truth-conditions for eternal truths, which lack existential import, to all knowledge, allowing only for non-propositional knowledge of contingent existence. Malebranche's rather implausible Neoplatonic semantics is detailed as consisting of three key semantic relations: illumination by which God's (...) ideas cause mental terms, creation by which God's ideas cause material substances by a kind of ?ontic privation?, and sensation in which brain events occasion states of mental awareness. In contrast, Arnauld distinguishes two types of propositions ? necessary and contingent ? with distinct truth-conditions, one with and one without existential import. Arnauld's more modern semantics is laid out as a theory of reference that substitutes earlier causal accounts with one that adapts the medieval notion of objective being. His version anticipates modern notions of intentional content and appeals in its ontology only to substances and their modes. (shrink)

Two periods in the history of logic and philosophy are characterized notably by vivid interest in self-referential paradoxical sentences in general, and Liar sentences in particular: the later medieval period (roughly from the 12th to the 15th century) and the last 100 years. In this paper, I undertake a comparative taxonomy of these two traditions. I outline and discuss eight main approaches to Liar sentences in the medieval tradition, and compare them to the most influential modern approaches to such sentences. (...) I also emphasize the aspects of each tradition that find no counterpart in the other one. It is expected that such a comparison may point in new directions for future research on the paradoxes; indeed, the present analysis allows me to draw a few conclusions about the general nature of Liar sentences, and to identify aspects that would require further investigation. (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)

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.

Intentional verbs create three different problems: problems of non-existence, of indeterminacy, and of failure of substitutivity. Meinongians tackle the first problem by recognizing non-existent objects; so too did many medieval logicians. Meinongians and the medievals approach the problem of indeterminacy differently, the former diagnosing an ellipsis for a propositional complement, the latter applying their theory directly to non-propositional complements. The evidence seems to favour the Meinongian approach. Faced with the third problem, Ockham argued bluntly for substitutivity when the intentional complement (...) is non-propositional; Buridan developed a novel way of resisting substitutivity. Ockham's approach is closer to the Meinongian analysis of these cases; Buridan's seems to raise difficulties for a referential semantics. The comparision between the Meinongian and medieval approaches helps to bring out merits and potential pitfalls of each. (shrink)

It may come as a surprise to readers familiar with the life and work of the Arts Master that he discusses the Eucharist at all. As he likes to remind us, theological topics are generally out of his wheelhouse. Even so, in his Questions on the “Metaphysics” of Aristotle (QM) 4.6, Buridan takes the sacrament of the Eucharist as a key data point in his discussion of Aristotle’s Categories. In the Eucharist, the accidents of the bread and wine—their color, texture, (...) and so on—remain intact, but the underlying substance is transubstantiated into the body and blood of Christ. Accordingly, God can preserve accidents independent of their underlying substance. Therefore, for our part we can use accidental terms, like whiteness, without connoting any substances, like communion bread. Moreover, it follows that, contrary to Aristotle, substance and the accidental categories are not the most general genera. Instead, being (ens) is, as Buridan concludes. Here, I trace Buridan’s thought on the metaphysical and semantic matters of substance in light of the Eucharist. The Eucharist is for him not only a theological truth, but a metaphysical and semantic datum as well. I conclude by asking why Buridan did not take any and all questions about the Eucharist to be out of his ken. What does this tell us about his attitude toward theology? This paper also includes, as an appendix, the first ever English translation of the question under discussion (QM 4.6): “Does the term being (ens) signify substances and accidents by one single concept or notion?”. (shrink)

Formalizing categorical propositions of traditional logic in the language of quantifiers and propositional functions is no straightforward matter, especially when modalities get involved. Starting...

Universalist and nihilist answers to philosophical questions may be extreme, but they are clear enough. Aliquidist answers, by contrast, are typically caught between the Scylla of vagueness and indeterminacy and the Charybdis of ungroundedness and arbitrariness, and steering a proper middle course—saying exactly where in the middle one is going to settle—demands exceptional navigating powers. I myself tend to favor extreme answers precisely for this reason. Here, however, I consider one sense in which Something may claim superiority over its polar (...) competitors, Everything and Nothing, when it comes to answerting the ontological question, “What is there?”. (shrink)

La lógica de la Edad Media se presenta a los lógicos contemporáneos, filósofos medievalistas, historiadores y filósofos de la lógica, como un campo tan fascinante como de difícil acceso. Parece demasiado intrincado para casi cualquier investigador de estas áreas encontrar la punta del ovillo que lo conduzca a transitar una presentación ordenada e inteligible de la lógica medieval. Este libro pretende solucionar este problema. Para ello, presenta de manera ordenada y autocontenida los desarrollos lógicos de la parte técnicamente más evolucionada (...) de la lógica de la Edad Media: el siglo XIV. A diferencia de otras presentaciones no evade los hechos históricos y culturales que conforman el panorama de la época ni las cuestiones filosóficas detrás de los desarrollos lógicos, a fin de entender cabalmente las cuestiones técnicas y no desnaturalizar la propuesta medieval. Los primeros tres capítulos se abocan a cuestiones introductorias, históricas y a la genealogía de los tópicos más importantes. El cuarto capítulo está dedicado a la presentación sintáctica del lenguaje de la lógica medieval. El quinto y el sexto a la metateoría de esta lógica. El séptimo explora y presenta la semántica. Los dos últimos nos brindan una reconstrucción racional, en términos del lenguaje simbólico contemporáneo, de la lógica de finales del siglo XIV. (shrink)

Although the theory of the assertoric syllogism was Aristotle's great invention, one which dominated logical theory for the succeeding two millenia, accounts of the syllogism evolved and changed over that time. Indeed, in the twentieth century, doctrines were attributed to Aristotle which lost sight of what Aristotle intended. One of these mistaken doctrines was the very form of the syllogism: that a syllogism consists of three propositions containing three terms arranged in four figures. Yet another was that a syllogism is (...) a conditional proposition deduced from a set of axioms. There is even unclarity about what the basis of syllogistic validity consists in. Returning to Aristotle's text, and reading it in the light of commentary from late antiquity and the middle ages, we find a coherent and precise theory which shows all these claims to be based on a misunderstanding and misreading. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

Drawing the complex terrain of the theories of induction and of the various ways to ground inductive knowledge in the middle ages is the aim of this paper. There have already been two excellent attempts to draw this terrain. The first is by Julius R. Weinberg and the second by E. P. Bos. My attempt differs from theirs in two major respects. The first is that it is more detailed in the examination of the various theories and their relations. The (...) second is that I focus on the role of natural necessities in induction. In particular, I try to place the various conceptions of induction within a network of issues that relate to the problem of universals, natural necessities and a power-based approach to activity in nature. Here is the road map. Section 2 explains Aristotle’s views of induction, as this were mainly developed in Posterior Analytics Book II.19 and states what I take it to be the main dilemma of induction, as this was described by Sextus Empiricus: induction is either perfect and impossible or imperfect and unjustified. In section 3, I move to Thomas Aquinas and his own attempt to justify induction and the actuality of general and necessary principles based on experience by an appeal to the natural light of reason. In section 4 I discuss John Duns Scotus’s reliance on a self-evident maxim to bridge the gap between imperfect and perfect induction. Section 5 moves to William of Ockham ’s peculiar attempt to justify single-instance inductions. Then, section 6 offers a detailed account of Jean Buridan’s ground-breaking re-conceptualisation of induction and the role of intellect in it. Section 7 discusses the critique of induction by Nicolaus of Autrecourt. Finally, section 8 offers a brief account of Pseudo-Scotus’s move from knowledge to opinion. (shrink)

In this paper we explain our pretense account of truth-talk and apply it in a diagnosis and treatment of the Liar Paradox. We begin by assuming that some form of deflationism is the correct approach to the topic of truth. We then briefly motivate the idea that all T-deflationists should endorse a fictionalist view of truth-talk, and, after distinguishing pretense-involving fictionalism (PIF) from error- theoretic fictionalism (ETF), explain the merits of the former over the latter. After presenting the basic framework (...) of our PIF account of truth-talk, we demonstrate a few advantages it offers over T-deflationist accounts that do not explicitly acknowledge pretense at work in the discourse. In turning to the Liar Paradox, we explain how the quasi-anaphoric functioning that our account attributes to truth-talk provides a diagnosis of the Liar Paradox (and other instances of semantic pathology) as having no content—in the sense of not specifying any of what we call M-conditions. At the same time, however, we vindicate the intuition that we can understand liar sentences, thereby avoiding one standard objection to “meaningless strategy” responses to the Liar Paradox. With this diagnosis in place, we then, by way of treatment, introduce a new predicate, ‘semantically defective’, and show how the explanation we give for its application allows for a consistent, yet revenge-immune, (dis)solution of the Liar Paradox, and semantic pathology generally. (shrink)

This paper argues that Malebranche’s semantics sheds light on his metaphysics and epistemology, and is of interest in its own right. By recasting issues linguistically, it shows that Malebranche assumes a Neoplatonic semantic structure within Descartes’ dualism and Augustine’s theory of illumination, and employs linguistic devices from the Neoplatonic tradition. Viewed semantically, mental states of illumination stand to God and his ideas as predicates stand in Neoplatonic semantics to ideas ordered by a privative relation on “being.” The framework sheds light (...) on interpretive puzzles in Malebranche studies such as the way ideas reside in God’s mind, the notion of resemblance by which bodies imitate their exemplar causes, and the issue of direct vs. indirect perception through a mechanism by which agents can see bodies by “seeing” ideas. Malebranche’s semantics is of interest in its own right because it gives a full account of the mediating relations that determine indirect reference; lays out a correspondence theory of truth for necessary judgments; defines contingent truth as based on an indirect reference relation that is both descriptive and causal but that does not appeal to body-mind causation; and within his theory of perception, works out an account of singular reference in which singular terms carry existential import, refer indirectly via causal relations, but describe their referents only in a general way. (shrink)

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)

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)

I offer a novel reading in this dissertation of René Descartes’s (1596–1650) skepticism in his work Meditations on First Philosophy (1641–1642). I specifically aim to answer the following problem: How is Descartes’s skepticism to be read in accordance with the rest of his philosophy? This problem can be divided into two more general questions in Descartes scholarship: How is skepticism utilized in the Meditations, and what are its intentions and relation to the preceding philosophical tradition? -/- I approach the topic (...) from both a historical and a text-based analysis, combining textual and contextual research. I examine Descartes’s skepticism against two main traditions in the historical analysis: philosophical skepticism and Aristotelian Scholasticism. I argue that skepticism in the Meditations is intended to oppose and upheave both Scholasticism and skepticism. The intended results of the work are not merely epistemological but also metaphysical and even ethical. Furthermore, these ambitions cannot be neatly distinguished but merge into each other. -/- The third historical context against which the skeptical meditations are examined is the literary genre of meditative exercises, particularly from the 1500–1600’s, which, while religiously and spiritually oriented, likewise provided the practitioner with an enlightened understanding of self-knowledge and their cognitive place in the world on the way to closer spiritual proximity to God. I argue by this reading that the skepticism of the Meditations is an attentive, meditational cognitive exercise that is not merely instrumental and methodological but is to have a genuine and serious (psychologically real) effect on our thinking. The skeptical meditation is not simply a theoretical thought experiment but is to be seriously practiced as a transformative process of reorienting one’s cognitive framework to discover truth, certainty, and a way to a happy, tranquil, and virtuous life. -/- I offer a close reading in the textual analysis of the first three meditations of the Meditations. I argue that the meditative skepticism employed in the work does not reject the previous beliefs but suspends judgment on them, withdrawing assent until further evidence can be found. I introduce a new term into Descartes scholarship in this analysis, based on the terminology of ancient skepticism: Cartesian epochē (gr. epochē, suspension, withdrawal). Instead of rejecting previous beliefs or assenting to the probably false, the skeptical procedure of the Meditations is argued to emulate in important ways the suspension of judgment on equally balanced reasons in ancient Pyrrhonian skepticism. Novel interpretations are presented along the way of the will’s freedom, of the First Meditation’s skeptical scenarios, of the cogito, and of the vindication of metaphysical certainty, as well as a clarification of the Cartesian Circle problem. -/- Reinterpreting the relation of Descartes’s skepticism to the preceding historical and literary traditions leads to a new look at the skeptical method itself. Presenting a new interpretation of skepticism in the Meditations leads at the same time to a new look at its relation to the historical context. The two research questions are, then, intrinsically tied together. -/- My focus in the study is on the Meditations, but I also reference and discuss Descartes’s other philosophical works, as well as his correspondence, when necessary. (shrink)

Sceptics vis-à-vis introspection often base their scepticism on ‘phenomenological disputes’, ‘introspective disagreement’, or ‘introspective disputes’ (Kriegel, 2007; Bayne and Spener, 2010; Schwitzgebel, 2011): introspectors massively diverge in their opinions about experiences, and there seems to be no method to resolve these issues. Sceptics take this to show that introspection lacks any epistemic merit. Here, I provide a list of paradigmatic examples, distill necessary and sufficient conditions for IDs, present the sceptical argument encouraged by IDs, and review the two main strategies (...) to reject such a scepticism. However, both types of strategies are unsatisfactory. In order to save introspection from the looming sceptical threat, I advocate a deflationary strategy, based on either an ‘Argument from Perceptual Kinship’ or an ‘Argument from Ownership’. In the end, there cannot be any genuine IDs, for nothing can fulfil the reasonable conditions for IDs. What looks like IDs may instead be indicators of phenomenal variation. Debates that look like IDs may then arise even if introspection were a perfect method to know one’s mind. Thus, scepticism vis-à-vis introspection based on IDs rests on shaky grounds. (shrink)

The study of the medieval reception of Aristotle’s Topics has largely been oriented toward debates on dialectical argumentation. And this is surely right. Nonetheless, I wish to approach John Buridan’s commentary on the Topics from another perspective, which highlights some semantic features of the set of predicates around which the work is organized. Thus, in my paper I will first reconstruct Buridan’s account of the identification of the predicates discussed in the Topics. I will argue that, for him, they are (...) different in that they reflect one or more features of the way in which definiens and definiendum relate. By doing this, I will shed light on the role the notion of definition plays in Buridan’s commentary, so that an interpretation of it as a work on definition becomes promising. In the second part of the paper, I will offer an analysis of Buridan’s first move in his commentary toward a theory of definition. It concerns the problem of whether there is a definition of definition. In examining Buridan’s answer, I will argue for the close connection between his treatment of definitions and his theory of supposition, so that distinctions among the different modes of supposition help him to disambiguate statements in their possible meanings, and thus to clarify the difficulty related to the definability of definition. (shrink)

Duality in Logic and Language [draft--do not cite this article] Duality phenomena occur in nearly all mathematically formalized disciplines, such as algebra, geometry, logic and natural language semantics. However, many of these disciplines use the term ‘duality’ in vastly different senses, and while some of these senses are intimately connected to each other, others seem to be entirely … Continue reading Duality in Logic and Language →.

In this paper, we provide a historical exposition of John Buridan's theory of divided modal propositions. We then develop a semantic interpretation of Buridan's theory which pays particular attention to Buridan's ampliation of modal terms. We show that these semantics correctly capture his syllogistic reasoning.

Hartry Field's revised logic for the theory of truth in his new book, Saving Truth from Paradox , seeking to preserve Tarski's T-scheme, does not admit a full theory of negation. In response, Crispin Wright proposed that the negation of a proposition is the proposition saying that some proposition inconsistent with the first is true. For this to work, we have to show that this proposition is entailed by any proposition incompatible with the first, that is, that it is the (...) weakest proposition incompatible with the proposition whose negation it should be. To show that his proposal gave a full intuitionist theory of negation, Wright appealed to two principles, about incompatibility and entailment, and using them Field formulated a paradox of validity (or more precisely, of inconsistency). The medieval mathematician, theologian and logician, Thomas Bradwardine, writing in the fourteenth century, proposed a solution to the paradoxes of truth which does not require any revision of logic. The key principle behind Bradwardine's solution is a pluralist doctrine of meaning, or signification, that propositions can mean more than they explicitly say. In particular, he proposed that signification is closed under entailment. In light of this, Bradwardine revised the truth-rules, in particular, refining the T-scheme, so that a proposition is true only if everything that it signifies obtains. Thereby, he was able to show that any proposition which signifies that it itself is false, also signifies that it is true, and consequently is false and not true. I show that Bradwardine's solution is also able to deal with Field's paradox and others of a similar nature. Hence Field's logical revisions are unnecessary to save truth from paradox. (shrink)

Una de las características de la transmisión manuscrita de los _Tractatus _ _de Pedro Hispano es el hecho de que el tratado sobre las _Categorías _no siempre ocupa el mismo lugar al interior de la obra. En algunos manuscritos se encuentra en tercer lugar, después del tratado acerca de la _Isagoge _de Porfirio, siguiendo el orden tradicional de la _logica vetus. _Pero en algunos otros, se encuentra en quinto lugar, después del tratado sobre los _Tópicos _y antes del tratado sobre (...) la suposición. En los dos casos, el lugar de las _Categorías _de Aristóteles en la lógica es definido por la noción de “término”. El propósito de este artículo es entender por qué ocurre esta variación, ya que no es teóricamente neutral. Por tanto, para atender al problema del orden de aparición del tratado sobre las _Categorías _dentro de la lógica, se presentarán tres de los más destacados comentaristas de los _Tractatus_: Juan Buridan, Juan Versor y Pedro Tartaret. Este ejercicio proporcionará algunas conclusiones sobre la relación entre las categorías y la teoría de la suposición, y también sobre la _vexata quaestio _acerca del sujeto de las categorías. (shrink)

This article presents an empirical examination of the consequences of the virtual entailment principle proposed by Jean Buridan to resolve the Liar paradox. This principle states that every sentence in natural language implicitly asserts its own truth. Adopting this principle means that the Liar sentence is not paradoxical but false, because its content is contradictory to what is virtually implied. As a result, humans should perceive the Liar sentence the same way as any other false sentence. This solution to the (...) Liar paradox received criticism for making ad hoc claims about the natural language. However, thanks to modern advancements in psychophysiology, it became possible to empirically investigate if the human brain really perceives the Liar sentence like a false sentence. We designed and conducted an experiment to examine brain activity in response to true sentences, false sentences and self-referential sentences. Our results provide support for the Buridan’s hypothesis and show that the Liar sentence is processed by the human brain identically to false sentences, while the Truthteller sentence is perceived identically to true sentences. This agrees with predictions derived from the virtual entailment principle and supports the idea that humans think with the logic of truth—a logic for which the truth is a designated value of its adequate semantics. (shrink)

In a recent paper Johan van Benthem reviews earlier work done by himself and colleagues on ‘natural logic’. His paper makes a number of challenging comments on the relationships between traditional logic, modern logic and natural logic. I respond to his challenge, by drawing what I think are the most significant lines dividing traditional logic from modern. The leading difference is in the way logic is expected to be used for checking arguments. For traditionals the checking is local, i.e. separately (...) for each inference step. Between inference steps, several kinds of paraphrasing are allowed. Today we formalise globally: we choose a symbolisation that works for the entire argument, and thus we eliminate intuitive steps and changes of viewpoint during the argument. Frege and Peano recast the logical rules so as to make this possible. I comment also on the traditional assumption that logical processing takes place at the top syntactic level, and I question Johan’s view that natural logic is ‘natural’. (shrink)

The ?no???no? paradox (so-called by Sorensen) consists of a pair of propositions each of which says of the other that it is false. It is not immediately paradoxical, since it has a solution in which one proposition is true, the other false. However, that is itself paradoxical, since there is no clear ground for determining which is which. The two propositions should have the same truth-value. The paper shows how a proposal by the medieval thinker Thomas Bradwardine solves not only (...) the Liar paradox, but also symmetric paradoxes like the ?no???no?, the descending ?no???no?, and the Truth-teller paradoxes. (shrink)

I extend theories of nonmonotonic reasoning to account for reasons allowing free choice. My approach works with a wide variety of approaches to nonmonotonic reasoning and explains the connection between reasons for kinds of action and reasons for actions or subkinds falling under them. I use an Anderson–Kanger reduction of reason statements, identifying key principles in the logic of reasons.

Jean Buridan has offered a solution to the Liar Paradox, i.e. to the problem of assigning a truth-value to the sentence ‘What I am saying is false’. It has been argued that either this solution is ad hoc since it would only apply to self-referencing sentences [Read, S. 2002. ‘The Liar Paradox from John Buridan back to Thomas Bradwardine’, Vivarium, 40 , 189–218] or else it weakens his theory of truth, making his ‘a logic without truth’ [Klima, G. 2008. ‘Logic (...) without truth: Buridan on the Liar’, in S. Rahman, T. Tulenheimo and E. Genot, Unity, Truth and the Liar: The Modern Relevance of Medieval Solutions to the Liar Paradox, Berlin: Springer, 87–112 ; Dutilh Novaes, C. 2011. ‘Lessons on truth from mediaeval solutions to the Liar Paradox’, The Philosophical Quarterly, 61 , 58–78]. Against , I will argue that Buridan's solution by means of truth by supposition does not involve new principles. Self-referential sentences force us to handle supposition more carefully, which does not warrant the accusation of adhoccery. I will also argue, against (2), that it is exaggerated to assert that this solution leads to a ‘weakened’ theory of truth, since it is consistent with other passages of the Sophismata, which only gives necessary conditions for the truth of affirmative propositions, but sufficient conditions for falsity. (shrink)

In this paper I will attempt a unified analysis of the various examples of the fallacy of accident given by Aristotle in the Sophistical Refutations. In many cases the examples underdetermine the fallacy and it is not trivial to identify the fallacy committed. To make this identification we have to find some error common to all the examples and to show that this error would still be committed even if those other fallacies that the examples exemplify were not. Aristotle says (...) that there is only one solution “against the argument” as opposed to “against the man”, and it is this solution the paper attempts to find. It is a characteristic mark of my analysis that some arguments that we might normally be inclined to say are fallacious turn out to be valid and that some arguments that we would normally be inclined to say are valid turn out to be fallacious. This is (in part) because what we call validity in modern logic is not the same as the apodicticity that Aristotelian syllogisms require in order to be used in science. The fallacies of accident, uniquely among the fallacies, are failures of apodicticity rather than failures of, in particular, semantic entailment. This makes sense in a tensed and token-based logic such as Aristotle’s. I conclude that the closest analogue to the fallacy of accident that we can point to is a fallacy in modal logic, viz., the fallacy of necessity. (shrink)

Proponents of physical intentionality argue that the classic hallmarks of intentionality highlighted by Brentano are also found in purely physical powers. Critics worry that this idea is metaphysically obscure at best, and at worst leads to panpsychism or animism. I examine the debate in detail, finding both confusion and illumination in the physical intentionalist thesis. Analysing a number of the canonical features of intentionality, I show that they all point to one overarching phenomenon of which both the mental and the (...) physical are kinds, namely finality. This is the finality of ‘final causes’, the long-discarded idea of universal action for an end to which recent proponents of physical intentionality are in fact pointing whether or not they realise it. I explain finality in terms of the concept of specific indifference, arguing that in the case of the mental, specific indifference is realised by the process of abstraction, which has no correlate in the case of physical powers. This analysis, I conclude, reveals both the strength and weakness of rational creatures such as us, as well as demystifying the way in which powers work. (shrink)

This paper explores a currently unnoticed argument used by John Buridan to defend his analysis of modal propositions and to reject the analysis of modal propositions of necessity put forward by William of Ockham. First, I explore this argument and, by considering possible responses of Ockham to Buridan, show some of the ways in which Ockham seems to be keeping closer to Aristotle's remarks about modal propositions in Prior Analytics, 18.

Desde que Tarski publicó su estudio sobreel concepto de verdad en los años 30, hasido una práctica ortodoxa el considerarque t oda i nst anci a del esquema T esverdadera. Sin embargo, algunas instanciasdel esquema son falsas. Éstas incluyen lasi nst anci as paradój i cas ej empl i f i cadaspor la oración del mentiroso. Aquí sedemuestra que un esquema mejor permiteun tratamiento uniforme de la verdad enel que las paradojas semánticas resultanser simplemente falsas.Si nc e Ta r s (...) ki publ i s he d hi s s t udy ofthe concept of truth in the 1930s, it hasbeen orthodox practice to suppose thatevery instance of the T-schema is true.However, some instances of the schemaare false. These include the paradoxicalinstances exemplified by the Liar sentence.It is shown that a better schema allows auniform treatment of truth in which thesemantic paradoxes turn out to be simplyfalse. (shrink)

As a discipline, logic is arguably constituted of two main sub-projects: formal theories of argument validity on the basis of a small number of patterns, and theories of how to reduce the multiplicity of arguments in non-logical, informal contexts to the small number of patterns whose validity is systematically studied . Regrettably, we now tend to view logic 'proper' exclusively as what falls under the first sub-project, to the neglect of the second, equally important sub-project. In this paper, I discuss (...) two historical theories of argument formalization: Aristotle's syllogistic theory as presented in the "Prior Analytics", and medieval theories of supposition. They both illustrate this two-fold nature of logic, containing in particular illuminating reflections on how to formalize arguments . In both cases, the formal methods employed differ from the usual modern technique of translating an argument in ordinary language into a specially designed symbolism, a formal language. The upshot is thus a plea for a broader conceptualization of what it means to formalize. Pode-se dizer que, enquanto disciplina, a lógica é caracterizada por dois subprojetos: teorias formais da validade de argumentos, baseadas em um número reduzido de esquemas e padrões formais, e teorias de como reduzir a multiplicidade de argumentos em contextos informais, não lógicos, ao pequeno número de padrões formais cuja validade é estudada de maneira sistemática no âmbito do primeiro subprojeto. O segundo subprojeto corresponde à noção de formalização de argumentos. Infelizmente, a tendência atual é de considerar como sendo a lógica propriamente dita exclusivamente o que se encaixa no primeiro subprojeto, em detrimento do segundo subprojeto, igualmente importante. Neste artigo, duas teorias históricas sobre a formalização de argumentos são analisadas: a teoria da silogística apresentada por Aristóteles nos "Primeiros Analíticos" e teorias medievais da suposição. Ambas ilustram o caráter duplo da lógica, que envolve dois subprojetos distintos, e contêm reflexões sofisticadas sobre como formalizar argumentos. Em ambos os casos, os métodos formais utilizados se diferenciam dos métodos atuais de tradução de um argumento em linguagem vernacular para um simbolismo especialmente formulado, ou seja, uma linguagem formal. Em conclusão, o artigo pode ser visto como a defesa de uma conceitualização mais abrangente do que significa 'formalizar' um argumento. (shrink)

The paper shows that in the Art of Thinking (The Port Royal Logic) Arnauld and Nicole introduce a new way to state the truth-conditions for categorical propositions. The definition uses two new ideas: the notion of distributive or, as they call it, universal term, which they abstract from distributive supposition in medieval logic, and their own version of what is now called a conservative quantifier in general quantification theory. Contrary to the interpretation of Jean-Claude Parienté and others, the truth-conditions do (...) not require the introduction of a new concept of ‘indefinite’ term restriction because the notion of conservative quantifier is formulated in terms of the standard notion of term intersection. The discussion shows the following. Distributive supposition could not be used in an analysis of truth because it is explained in terms of entailment, and entailment in terms of truth. By abstracting from semantic identities that underlie distribution, the new concept of distributive term is definitionally prior to truth and can, therefore, be used in a non-circular way to state truth-conditions. Using only standard restriction, the Logic’s truth-conditions for the categorical propositions are stated solely in terms of (1) universal (distributive) term, (2) conservative quantifier, and (3) affirmative and negative proposition. It is explained why the Cartesian notion of extension as a set of ideas is in this context equivalent to medieval and modern notions of extension. (shrink)

In his Tractatus de Consequentiis, the 14th century logician John Buridan states a theorem, which reads like a refutation of Aristotelian Syllogistics. Syllogistics in its usual form, indeed, faces problems when propositions about the divine persons are involved, and, in some cases, when past- or future-tense propositions occur. Buridan offers different ways of overcoming some of these obstacles. The first aim of this paper is to analyse these ways, the second aim is to draw some conclusions concerning Buridan’s understanding of (...) logic and its relation to theology. (shrink)