I argue that the medieval form of dialectical disputation known as obligationes can be viewed as a logical game of consistency maintenance. The game has two participants, Opponent and Respondent. Opponent puts forward a proposition P; Respondent must concede, deny or doubt, on the basis of inferential relations between P and previously accepted or denied propositions, or, in case there is none, on the basis of the common set of beliefs. Respondent loses the game if he concedes a contradictory set (...) of propositions. Opponent loses the game if Respondent is able to maintain consistency during the stipulated period of time. The obligational rules are here formalised by means of familiar notational devices, and the application of some game-theoretical concepts, such as (winning) strategy, moves, motivation, allows for an analysis of some crucial properties of the game. In particular, the primacy of inferential (syntactic) relations over semantic aspects and the dynamic character of obligations are outlined. (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)

11We thank Rohan French for a detailed discussion of this review. We also wish to reciprocally thank Shawn Standefer for detailed discussions about the book.Logical pluralism is the view according...

A distinction often drawn is one between conservative versus revisionary conceptions of philosophical analysis with respect to commonsensical beliefs and intuitions. This paper offers a comparative investigation of two revisionary methods: Carnapian explication and ameliorative analysis as developed by S. Haslanger. It is argued that they have a number of common features, and in particular that they share a crucial political dimension: they both have the potential to serve as instrument for social reform. Indeed, they may produce improved versions of (...) key concepts of everyday life, for example those pertaining to social categories such as gender and race, which in turn may lead to social change. The systematic comparison of these two frameworks offered here, where similarities as well as differences are discussed, is likely to provide useful guidance to practitioners of both approaches, as it will highlight important aspects of each of them that tend to remain implicit and under-theorized in existing applications of these methodologies to specific questions. (shrink)

The paper argues that much of the difficulty with making progress on the issue of the normativity of logic for thought, as discussed in the literature, stems from a misapprehension of what logic is normative for. The claim is that, rather than mono-agent mental processes, logic in fact comprises norms for quite specific situations of multi-agent dialogical interactions, in particular special forms of debates. This reconceptualization is inspired by historical developments in logic and mathematics, in particular the pervasiveness of such (...) dialogical conceptions in the early days of logic in ancient Greece. The multi-agent, dialogical perspective then allows for the formulation of compelling 'bridge principles’ between the relation of logical consequence and dialogical normative principles, something that is notoriously difficult to achieve in a mono-agent setting pertaining exclusively to thought and belief. The upshot is also that the truth-preserving rules of logic generally do not have a primary normative bearing on mono-agent mental processes, and in this sense the paper sides with Harman's critique of the idea that logic has a normative import for thought and belief. (shrink)

This comprehensive account of the concept and practices of deduction is the first to bring together perspectives from philosophy, history, psychology and cognitive science, and mathematical practice. Catarina Dutilh Novaes draws on all of these perspectives to argue for an overarching conceptualization of deduction as a dialogical practice: deduction has dialogical roots, and these dialogical roots are still largely present both in theories and in practices of deduction. Dutilh Novaes' account also highlights the deeply human and (...) in fact social nature of deduction, as embedded in actual human practices; as such, it presents a highly innovative account of deduction. The book will be of interest to a wide range of readers, from advanced students to senior scholars, and from philosophers to mathematicians and cognitive scientists. (shrink)

Formal languages are widely regarded as being above all mathematical objects and as producing a greater level of precision and technical complexity in logical investigations because of this. Yet defining formal languages exclusively in this way offers only a partial and limited explanation of the impact which their use actually has. In this book, Catarina Dutilh Novaes adopts a much wider conception of formal languages so as to investigate more broadly what exactly is going on when theorists put (...) these tools to use. She looks at the history and philosophy of formal languages and focuses on the cognitive impact of formal languages on human reasoning, drawing on their historical development, psychology, cognitive science and philosophy. Her wide-ranging study will be valuable for both students and researchers in philosophy, logic, psychology and cognitive and computer science. (shrink)

In describing numerosity as “a kind of ersatz number,” Clarke and Beck fail to consider a familiar and compelling definition of numerosity, which conceptualizes numerosity as the cognitive counterpart of the mathematical concept of cardinality; numerosity is the magnitude, whereas number is a scale through which numerosity/cardinality is measured. We argue that these distinctions should be considered.

This volume, the first dedicated and comprehensive companion to medieval logic, covers both the Latin and the Arabic traditions, and shows that they were in fact sister traditions, which both arose against the background of a Hellenistic heritage and which influenced one another over the centuries. A series of chapters by both established and younger scholars covers the whole period including early and late developments, and offers new insights into this extremely rich period in the history of logic. The volume (...) is divided into two parts, 'Periods and Traditions' and 'Themes', allowing readers to engage with the subject from both historical and more systematic perspectives. It will be a must-read for students and scholars of medieval philosophy, the history of logic, and the history of ideas. (shrink)

Although not entirely mainstream, uses of formal methods for the study of the history of philosophy, the history of logic in particular, represent an important trend in recent philosophical historiography. In this chapter, I discuss what can be achieved by the application of formal methods to the history of philosophy, addressing both motivations and potential pitfalls. The first section focuses on methodological aspects, and the second section presents three case studies of historical theories which have been investigated with formal tools: (...) Aristotle’s syllogistic, Anselm’s ontological argument, and medieval theories of supposition. (shrink)

The paper investigates the propriety of applying the form versus matter distinction to arguments and to logic in general. Its main point is that many of the currently pervasive views on form and matter with respect to logic rest on several substantive and even contentious assumptions which are nevertheless uncritically accepted. Indeed, many of the issues raised by the application of this distinction to arguments seem to be related to a questionable combination of different presuppositions and expectations; this holds in (...) particular of the vexed issue of demarcating the class of logical constants. I begin with a characterization of currently widespread views on form and matter in logic, which I refer to as 'logical hylomorphism as we know it'—LHAWKI, for short—and argue that the hylomorphism underlying LHAWKI is mereological. Next, I sketch an overview of the historical developments leading from Aristotelian, non-mereological metaphysical hylomorphism to mereological logical hylomorphism (LHAWKI). I conclude with a reassessment of the prospects for the combination of hylomorphism and logic, arguing in particular that LHAWKI is not the only and certainly not the most suitable version of logical hylomorphism. In particular, this implies that the project of demarcating the class of logical constants as a means to define the scope and nature of logic rests on highly problematic assumptions. (shrink)

On the basis of passages from John Buridan's Summula Suppositionibus and Sophismata, E. Karger has reconstructed what could be called the 'Buridanian theory of inferential relations between doubly quantified propositions', presented in her 1993 article 'A theory of immediate inference contained in Buridan's logic'. In the reconstruction, she focused on the syntactical elements of Buridan's theory of modes of personal supposition to extract patterns of formally valid inferences between members of a certain class of basic categorical propositions. The present study (...) aims at offering semantic corroboration 'a proof of soundness' to the inferential relations syntactically identified by E. Karger, by means of the analysis of Buridan's semantic definitions of the modes of personal supposition. The semantic analysis is done with the help of some modern logical concepts, in particular that of the model. In effect, the relations of inference syntactically established are shown to hold also from a semantic point of view, which means thus that this fragment of Buridan's logic can be said to be sound. (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)

We can’t simply teach our way out of anti-science sentiment. Building public trust is as much about power as about knowledge.

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)

What does it mean to say that logic is formal? The short answer is: it means (or can mean) several different things. In this paper, I argue that there are (at least) eight main variations of the notion of the formal that are relevant for current discussions in philosophy and logic, and that they are structured in two main clusters, namely the formal as pertaining to forms, and the formal as pertaining to rules. To the first cluster belong the formal (...) as schematic; the formal as indifference to particulars; the formal as topic-neutrality; the formal as abstraction from intentional content; the formal as de-semantification. To the second cluster belong the formal as computable; the formal as pertaining to regulative rules; the formal as pertaining to constitutive rules. I analyze each of these eight variations, providing their historical background and raising related philosophical questions. The significance of this work of ?conceptual archeology? is that it may enhance clarity in debates where the notion of the formal plays a prominent role (such as debates where it is expected to play a demarcating role), but where it is oftentimes used equivocally and/or imprecisely. (shrink)

A range of formal models of human reasoning have been proposed in a number of fields such as philosophy, logic, artificial intelligence, computer science, psychology, cognitive science, etc.: various logics, probabilistic systems, belief revision systems, neural networks, among others. Now, it seems reasonable to require that formal models of human reasoning be empirically adequate if they are to be viewed as models of the phenomena in question. How are formal models of human reasoning typically put to empirical test? One way (...) to do so is to isolate a number of key principles of the system, and design experiments to gauge the extent to which participants do or do not follow them in reasoning tasks. Another way is to take relevant existing results and check whether a particular formal model predicts these results. The present investigation provides an illustration of the second kind of empirical testing by comparing two formal models for reasoning – namely the non-monotonic logic known as preferential logic; and a particular version of belief revision theories, screened belief revision – against the reasoning phenomenon known as belief bias in the psychology of reasoning literature: human reasoners typically seek to maintain the beliefs they already hold, and conversely to reject contradicting incoming information. The conclusion of our analysis will be that screened belief revision is more empirically adequate with respect to belief bias than preferential logic and non-monotonic logics in general, as what participants seem to be doing is above all a form of belief management on the basis of background knowledge. The upshot is thus that, while it may offer valuable insights into the nature of human reasoning, preferential logic is ultimately inadequate as a formal model of the phenomena in question. (shrink)

Can arguments change minds? Philosophers like to think that they can. However, a wealth of empirical evidence suggests that arguments are not very efficient tools to change minds. What to make of the different assessments of the mind-changing potential of arguments? To address this issue, we must take into account the broader contexts in which arguments occur, in particular the propagation of messages across networks of attention, and the choices that epistemic agents must make between alternative potential sources of content (...) and information, which are very much influenced by perceptions of reliability and trustworthiness. Arguments can change minds, but only under conducive, favourable socio-epistemic conditions. (shrink)

We investigate the philosophical significance of the existence of different semantic systems with respect to which a given deductive system is sound and complete. Our case study will be Corcoran's deductive system D for Aristotelian syllogistic and some of the different semantic systems for syllogistic that have been proposed in the literature. We shall prove that they are not equivalent, in spite of D being sound and complete with respect to each of them. Beyond the specific case of syllogistic, the (...) goal is to offer a general discussion of the relations between informal notions—in this case, an informal notion of deductive validity—and logical apparatuses such as deductive systems and (model-theoretic or other) semantic systems that aim at offering technical, formal accounts of informal notions. Specifically, we will be interested in Kreisel's famous 'squeezing argument'; we shall ask ourselves what a plurality of semantic systems (understood as classes of mathematical structures) may entail for the cogency of specific applications of the squeezing argument. More generally, the analysis brings to the fore the need for criteria of adequacy for semantic systems based on mathematical structures. Without such criteria, the idea that the gap between informal and technical accounts of validity can be bridged is put under pressure. (shrink)

Genealogical anxiety is the worry that the origins of beliefs, once revealed to be influenced by “irrelevant” factors such as personal histories and circumstances of upbringing, will undermine or cast doubt on those beliefs. Discussions on these irrelevant influences in the epistemological literature have so far primarily focused on their contingency. But there is another issue that merits further examination: the fact that epistemic environments condition beliefs suggests that epistemic agency is significantly curtailed. I present a model of belief-forming processes (...) that highlights how networks of attention and trust/distrust influence these processes. The model suggests that, while there is a lot happening beyond our control that shapes what we come to believe, we still retain some degree of agency to the extent that we can rewire our networks of attention and trust/distrust. I conclude that, surprisingly, genealogical anxiety may in fact increase agency insofar as it may encourage critical resistance. (shrink)

In this paper, I highlight the significance of practices of _refutation_ in philosophical inquiry, that is, practices of showing that a claim, person or theory is wrong. I present and contrast two prominent approaches to philosophical refutation: refutation in ancient Greek dialectic (_elenchus_), in its Socratic variant as described in Plato’s dialogues, and as described in Aristotle’s logical texts; and the practice of providing counterexamples to putative definitions familiar from twentieth century analytic philosophy, focusing on the so-called Gettier problem. Moreover, (...) I discuss Lakatos’ method of proofs and refutations, as it offers insightful observations on the dynamics between arguments, refutations, and counterexamples. Overall, I argue that dialectic, in particular in its Socratic variant, is especially suitable for the philosophical purpose of questioning the obvious, as it invites reflection on one’s own doxastic commitments and on the tensions and inconsistencies within one’s set of beliefs. By contrast, the counterexample-based approach to philosophical refutation can give rise to philosophical theorizing that is overly focused on hairsplitting disputes, thus becoming alienated from the relevant human experiences. Insofar as philosophical inquiry treads the fine line between questioning the obvious while still seeking to say something significant about human experiences, perhaps a certain amount of what Lakatos describes as ‘monster-barring’—a rejection of overly fanciful, artificial putative counterexamples—has its place in philosophical argumentation. (shrink)

Public engagement is one of the fundamental pillars of the European programme for research and innovation _Horizon 2020_. The programme encourages engagement that not only fosters science education and dissemination, but also promotes two-way dialogues between scientists and the public at various stages of research. Establishing such dialogues between different groups of societal actors is seen as crucial in order to attain epistemic as well as social desiderata at the intersection between science and society. However, whether these dialogues can actually (...) help attaining these desiderata is far from obvious. This paper discusses some of the costs, risks, and benefits of dialogical public engagement practices, and proposes a strategy to analyse these argumentative practices based on a three-tiered model of epistemic exchange. As a case study, we discuss the phenomenon of vaccine hesitancy, arguably a result of suboptimal public engagement, and show how the proposed model can shed new light on the problem. (shrink)

Overdoing Democracy is an important contribution to the literature on (deliberative) democracy, as it offers a sobering diagnosis of the risks and pitfalls of (overdoing) democracy in the form of internal critique. But the book does not go far enough in its diagnosis because it is not sufficiently critical towards some of the basic assumptions of deliberative conceptions of democracy. In particular, Talisse does not sufficiently attend to the inevitable power struggles in a society, where different groups and individuals must (...) protect their own (often conflicting) interests instead of working towards a ‘common good.’ In this essay, I contrast two different visions of democracy and politics, one based on ideals of consensus and cooperation, and another on the inevitability of perennial conflict. I then briefly present an alternative to deliberative conceptions of democracy that has gained traction in recent decades, known as agonism. Next, I offer a short reconstruction of Talisse’s proposal, and finally I sketch a critical assessment of some of his main claims and assumptions from an agonistic perspective. (shrink)

In the scholarship on medieval logic and semantics of the last decades, Ockham’s theory of supposition is probably the most extensively studied version of such theories; yet, it seems that we still do not fully understand all its intricacies. In this paper, I focus on a phrase that occurs countless times throughout Ockham’s writings, but in particular in the sections dedicated to supposition in the Summa logicae: the phrase ‘denotatur’. I claim that an adequate understanding of the role of the (...) concept of denotatur within Ockham’s supposition theory shall yield a deeper understanding of the theory as a whole. Here, I first examine a few uses of the term ‘denotatur’ and its variants by other authors. I then turn to Ockham: first I briefly mention some uses of the term in contexts other than his theory of supposition. Following that, I focus on his supposition theory, in particular on how ‘denotatur’ allows him to deal with two crucial puzzles, namely the supposition of empty terms and the supposition of terms in false affirmative propositions. The treatment of these two puzzles suggests that Ockham’s theory of supposition must be understood as a theory chiefly intended for the generation of the meanings of propositions. (shrink)

It is often remarked that first-order Peano Arithmetic is non-categorical but deductively well-behaved, while second-order Peano Arithmetic is categorical but deductively ill-behaved. This suggests that, when it comes to axiomatizations of mathematical theories, expressive power and deductive power may be orthogonal, mutually exclusive desiderata. In this paper, I turn to Hintikka’s :69–90, 1989) distinction between descriptive and deductive approaches in the foundations of mathematics to discuss the implications of this observation for the first-order logic versus second-order logic divide. The descriptive (...) approach is illustrated by Dedekind’s ‘discovery’ of the need for second-order concepts to ensure categoricity in his axiomatization of arithmetic; the deductive approach is illustrated by Frege’s Begriffsschrift project. I argue that, rather than suggesting that any use of logic in the foundations of mathematics is doomed to failure given the impossibility of combining the descriptive approach with the deductive approach, what this apparent predicament in fact indicates is that the first-order versus second-order divide may be too crude to investigate what an adequate axiomatization of arithmetic should look like. I also conclude that, insofar as there are different, equally legitimate projects one may engage in when working on the foundations of mathematics, there is no such thing as the One True Logic for this purpose; different logical systems may be adequate for different projects. (shrink)

We investigate the relations among Brandom’s three dimensions of semantic inferential articulation, namely, incompatibility entailments, committive consequences, and permissive consequences. In his unpublished manuscript “Conceptual Content and Discursive Practice” Brandom argues that (1) incompatibility entailment implies committive consequence, and that (2) committive consequence in turn implies permissive consequence. We criticize this hierarchy both on internal and external grounds. Firstly, we prove that, using Brandom’s own definitions, the reverse of (1) also holds, and that the reverse of (2) may hold (but (...) the proof relies on substantive assumptions). This suggests that there are no three different notions of inference emerging from Brandom’s definitions, but at most two, and perhaps even just one. Secondly, this result puts into question the connections between the three inferential relations and the familiar notions of deduction and induction. (shrink)

A fundamental fact about human minds is that they are never truly alone: all minds are steeped in situated interaction. That social interaction matters is recognized by any experimentalist who seeks to exclude its influence by studying individuals in isolation. On this view, interaction complicates cognition. Here, we explore the more radical stance that interaction co-constitutes cognition: that we benefit from looking beyond single minds toward cognition as a process involving interacting minds. All around the cognitive sciences, there are approaches (...) that put interaction center stage. Their diverse and pluralistic origins may obscure the fact that collectively, they harbor insights and methods that can respecify foundational assumptions and fuel novel interdisciplinary work. What might the cognitive sciences gain from stronger interactional foundations? This represents, we believe, one of the key questions for the future. Writing as a transdisciplinary collective assembled from across the classic cognitive science hexagon and beyond, we highlight the opportunity for a figure-ground reversal that puts interaction at the heart of cognition. The interactive stance is a way of seeing that deserves to be a key part of the conceptual toolkit of cognitive scientists. (shrink)

Since at least the 1980s, the role of adversariality in argumentation has been extensively discussed within different domains. Prima facie, there seem to be two extreme positions on this issue: argumentation should never be adversarial, as we should always aim for cooperative argumentative engagement; argumentation should be and in fact is always adversarial, given that adversariality is an intrinsic property of argumentation. I here defend the view that specific instances of argumentation are adversarial or cooperative to different degrees. What determines (...) whether an argumentative situation should be primarily adversarial or primarily cooperative are contextual features and background conditions external to the argumentative situation itself, in particular the extent to which the parties involved have prior conflicting or else convergent interests. To further develop this claim, I consider three teloi that are frequently associated with argumentation: the epistemic telos, the consensus-building telos, and the conflict management telos. I start with a brief discussion of the concepts of adversariality, cooperation, and conflict in general. I then sketch the main lines of the debates in the recent literature on adversariality in argumentation. Next, I discuss the three teloi of argumentation listed above in turn, emphasizing the roles of adversariality and cooperation for each of them. (shrink)

Argumentation is important for sharing knowledge and information. Given that the receiver of an argument purportedly engages first and foremost with its content, one might expect trust to play a negligible epistemic role, as opposed to its crucial role in testimony. I argue on the contrary that trust plays a fundamental role in argumentative engagement. I present a realistic social epistemological account of argumentation inspired by social exchange theory. Here, argumentation is a form of epistemic exchange. I illustrate my argument (...) with two real-life examples: vaccination hesitancy, and the undermining of the credibility of traditional sources of information by authoritarian politicians. (shrink)

I examine the theory of consequentia of the medieval logician, John Buridan. Buridan advocates a strict commitment to what we now call proposition-tokens as the bearers of truth-value. The analysis of Buridan's theory shows that, within a token-based semantics, amendments to the usual notions of inference and consequence are made necessary, since pragmatic elements disrupt the semantic behaviour of propositions. In my reconstruction of Buridan's theory, I use some of the apparatus of modern two-dimensional semantics, such as two-dimensional matrices and (...) the distinction between the context of formation and the context of evaluation of utterances. (shrink)

Catarina Dutilh Novaes on why we should dig into the cosmopolitan roots of logic.

Explication is the conceptual cornerstone of Carnap’s approach to the methodology of scientific analysis. From a philosophical point of view, it gives rise to a number of questions that need to be addressed, but which do not seem to have been fully addressed by Carnap himself. This paper reconsiders Carnapian explication by comparing it to a different approach: the ‘formalisms as cognitive tools’ conception. The comparison allows us to discuss a number of aspects of the Carnapian methodology, as well as (...) issues pertaining to formalization in general. We start by introducing Carnap’s conception of explication, arguing that there is a tension between his proposed criteria of fruitfulness and similarity; we also argue that his further desideratum of exactness is less crucial than might appear at first. We then bring in the general idea of formalisms as cognitive tools, mainly by discussing the reliability of so-called statistical prediction rules, i.e. simple algorithms used to make predictions across a range of areas. SPRs allow for a concrete instantiation of Carnap’s fruitfulness desideratum, which is arguably the most important desideratum for him. Finally, we elaborate on what we call the ‘paradox of adequate formalization’, which for the Carnapian corresponds to the tension between similarity and fruitfulness. We conclude by noting that formalization is an inherently paradoxical enterprise in general, but one worth engaging in given the ‘cognitive boost’ it affords as a tool for discovery. (shrink)

In [Dutilh Novaes, Medieval-obligations as logical Games of Consistency maintenance, synthese, (2004)], I proposed a reconstruction of Walter Burley’s theory of obligationes, based on the idea that Burley’s theory of obligationes could be seen as a logical game of consistency maintenance. In the present paper, I intend to test the game hypothesis on another important theory of obligationes, namely Roger Swyneshed’s theory. In his treatise on obligationes [edited by P.V. Spade, cf. Spade History and philosophy of Logic 3(1982) (...) 1-32], Swyneshed introduced significant modifications to the general framework of obligationes. To compare the two theories, I apply the same formal apparatus used in the previous paper. It will become patent that Swyneshed’s theory is considerably different from Burley’s, among other reasons because the dynamic aspects that play a major role in the latter are simply not present in the former. My conclusion is that Swyneshed’s version of obligationes is not directed towards consistency maintenance, but rather towards inference recognition, and that it is, from a game-theoretical perspective, less interesting a theory than Burley’s. (shrink)

It is well known that reductio ad absurdum arguments raise a number of interesting philosophical questions. What does it mean to assert something with the precise goal of then showing it to be false, i.e. because it leads to absurd conclusions? What kind of absurdity do we obtain? Moreover, in the mathematics education literature number of studies have shown that students find it difficult to truly comprehend the idea of reductio proofs, which indicates the cognitive complexity of these constructions. In (...) this paper, I start by discussing four philosophical issues pertaining to reductio arguments. I then briefly present a dialogical conceptualization of deductive arguments, according to which such arguments are best understood as a dialogue between two participants—Prover and Skeptic. Finally, I argue that many of the philosophical and cognitive difficulties surrounding reductio arguments are dispelled or at least further clarified once one adopts a dialogical perspective. (shrink)

Fourteenth-century treatises on paradoxes of the liar family, especially Bradwardine's and Buridan's, raise issues concerning the meaning of sentences, in particular about closure of sentential meaning under implication, semantic pluralism and the ontological status of 'meanings', which are still topical for current theories of meaning. I outline ways in which they tend to be overlooked, raising issues that must be addressed by any respectable theory of meaning as well as pointing in the direction of possible answers. I analyse a Bradwardinian (...) theory of sentential meaning as it emerges from his treatment of liar sentences, exploring where it requires more thorough elaboration if it is to be a fully developed theory of sentential meaning. (shrink)

Some fourteenth-century treatises on paradoxes of the liar family offer a promising starting-point for the formulation of full-fledged theories of truth with systematic relevance in their own right. In particular, Bradwardine's thesis that sentences typically say more than one thing gives rise to a quantificational approach to truth, and Buridan's theory of truth based on the notion of suppositio allows for remarkable metaphysical parsimony. Bradwardine's and Buridan's theories both have theoretical advantages, but fail to provide a satisfactory account of truth (...) because both are committed to the thesis, fatal for both, that every sentence signifies/implies its own truth. I close with remarks on Greg Restall's recent model-theoretic formalization of Bradwardine's theory of truth. (shrink)

The very first dedicated, comprehensive companion to medieval logic, covering both the Latin and Arabic sister traditions.