Dialogical Logic Dialogical logic is an approach to logic in which the meaning of the logical constants and the notion of validity are explained in game-theoretic terms. The meaning of logical constants like “and”, “or”, “implies”, “not”, “every”, and so forth, is given in terms of how assertions containing these logical constants can … Continue reading Dialogical Logic →.

Even when inconsistencies are present in our premise set, we can sensibly distinguish between good and bad arguments relying on these premises. In making this distinction, the inconsistency-adaptive approach of Batens strikes a particularly nice balance between inconsistency-tolerance and inferential strength. In this paper, we use the machinery of Batens’ approach to extend the paraconsistent approach to dialogical logic as developed by Rahman and Carnielli. In bringing these frameworks closer together, we obtain a dynamic mechanism for the systematic (...) study of dialogues in which two parties exchange arguments over a central claim, in the possible presence of inconsistencies. (shrink)

The title reflects my conviction that, viewed semantically,modal logic is fundamentally dialogical; this conviction is based on the key role played by the notion of bisimulation in modal model theory. But this dialogical conception of modal logic does not seem to apply to modal proof theory, which is notoriously messy. Nonetheless, by making use of ideas which trace back to Arthur Prior (notably the use of nominals, special proposition symbols which ‘name’ worlds) I will show how (...) to lift the dialogical conception to modal proof theory. I argue that this shift to hybrid logic has consequences for both modal and dialogical logic, and I discuss these in detail. (shrink)

Dialogue semantics for logic are two-player logic games between a Proponent who puts forward a logical formula φ as valid or true and an Opponent who disputes this. An advantage of the dialogical approach is that it is a uniform framework from which different logics can be obtained through only small variations of the basic rules. We introduce the composition problem for dialogue games as the problem of resolving, for a set S of rules for dialogue games, (...) whether the set of S-dialogically valid formulas is closed under modus ponens. Solving the composition problem is fundamental for the dialogical approach to logic; despite its simplicity, it often requires an indirect solution with the help of significant logical machinery such as cut-elimination. Direct solutions to the composition problem can, however, sometimes be had. As an example, we give a set N of dialogue rules which is well-justified from the dialogical point of view, but whose set N of dialogically valid formulas is both non-trivial and non-standard. We prove that the composition problem for N can be solved directly, and introduce a tableaux system for N. (shrink)

This article aims to present a Free Dialogic Logic [FDL] as a general framework for hypothesis generation in the practice of modelling in science. Our proposal is based on the idea that the inferential function that models fulfil during the modelling process (surrogate reasoning) should be carried out without ontological commitments. The starting point to achieve our objective is that the scientific consideration of models without a target is a symptom that, on the one hand, the Applicability of (...) class='Hi'>Logic should be considered among the conditions of adequacy that should take into account all modeling process and, on the other, that the inferential apparatus at the base of the surrogate reasoning process must be rid of realistic assumptions that lead to erroneous conclusions. In this sense, we propose as an alternative an ontologically neutral inferential system in the perspective of dialogical pragmatism. (shrink)

The present paper, that provides an introduction to standard dialogical logic, has mainly didactic purposes. Thus, the study of the metalogical properties has been left totally by side. However, two sections have been added for those readers willing to go through a technically more demanding material. The first one contains a technically rigorous presentation of standard dialogical logic the second one presents, some very recent work towards a logic with content, applied to modal logic, (...) where modal logic is developed in a purely dialogical way: instead of worlds, we have contexts, constituted by hypothetical assertions and where transitions between worlds are understood as extending contexts by the means of questions. (shrink)

A dialogical version of (modal) epistemic logic is outlined, with an intuitionistic variant. Another version of dialogical epistemic logic is then provided by means of the S4 mapping of intuitionistic logic. Both systems cast new light on the relationship between intuitionism, modal logic and dialogical games.

The failure of logical omniscience is perfectly compatible with deductive closure if we link the latter with the strategy level and the failure of logical omniscience with the play level.

There seems to be something mysterious about applications of for- mal systems, including those of logic, to empirical reality 1 . If logic is to be applied to empirical situations, like those described in an ordinary lan- guage, then { it seems to some people { its statements cannot be necessary, or analytic, propositions. However, they are both applicable and necessary. This supposed puzzle constitutes a signicant part of the problem of philo- sophical foundations of logic 2 (...) . To this mind of the present writer, there is no mystery of applications, since any empirical, or even ostensive, predicate can be involved in cer- tain meaning postulates, e.g. \No red is green", which are both empirical and necessary propositions; empirical as they involve ostensibly dened predicated; necessary, as it is enough to know their meaning to state, their validity. The case of logical theorems can be considered at the same footing, logical constants being treated as dened ostensively. Nevertheless, not an individual state of mind but the actual state of scholarly discussions makes something a problem; in the present state of foundational discussions on logic, the \mystery of applications" preserves its vitality, hence any new way of dealing with it proves welcome. (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)

Many of the discussions about conditionals can best be put as follows:can those conditionals that involve an entailment relation be formulatedwithin a formal system? The reasons for the failure of the classical approachto entailment have usually been that they ignore the meaning connectionbetween antecedent and consequent in a valid entailment. One of the firsttheories in the history of logic about meaning connection resulted from thestoic discussions on tightening the relation between the If- and the Then-parts of conditionals, which in (...) this context was called. This theory gave a justification for the validity of what we todayexpress through the formulae ¬ and ¬. Hugh MacColl and, more recently, Storrs McCall searched for a formal system in which the validity ofthese formulae could be expressed. Unfortunately neither of the resulting systems is very satisfactory. In this paper we introduce dialogical games with the help of a new connexive If-Then (), the structural rules of which allow the Proponent to develop winning strategies not only for the above-mentioned connexive theses but also for ¬ and ¬. Further on, we developthe corresponding tableau systems and conclude with some remarks on possibleperspectives and consequences of the dialogical approach to connexivity including the loss of uniform substitution leading to a new concept of logical form. (shrink)

Many of the discussions about conditionals can best be put as follows:can those conditionals that involve an entailment relation be formulatedwithin a formal system? The reasons for the failure of the classical approachto entailment have usually been that they ignore the meaning connectionbetween antecedent and consequent in a valid entailment. One of the firsttheories in the history of logic about meaning connection resulted from thestoic discussions on tightening the relation between the If- and the Then-parts of conditionals, which in (...) this context was called συναρτησις(connection). This theory gave a justification for the validity of what we todayexpress through the formulae ¬(a → ¬ a) and ¬(¬ a → a). Hugh MacColl and, more recently, Storrs McCall (from 1877 to 1906 and from1963 to 1975 respectively) searched for a formal system in which the validity ofthese formulae could be expressed. Unfortunately neither of the resulting systems is very satisfactory. In this paper we introduce dialogical games with the help of a new connexive If-Then (“→”), the structural rules of which allow the Proponent to develop (formal) winning strategies not only for the above-mentioned connexive theses but also for (a → b) → ¬(a → ¬ b) and (a → b) → ¬(¬ a → b). Further on, we developthe corresponding tableau systems and conclude with some remarks on possibleperspectives and consequences of the dialogical approach to connexivity including the loss of uniform substitution leading to a new concept of logical form. (shrink)

This paper argues that adopting a particular dialogical account of logical consequence quite directly gives rise to an interesting form of logical pluralism, the form of pluralism in question arising out of the requirement that deductive proofs be explanatory.

The logics of formal inconsistency are logics tolerant to some amount of contradiction, but in which some versions of explosion still hold. The main result of this paper is a reconstruction of two such logics in the dialogical framework. By doing so, we achieve two things. On the one hand, we provide a formal approach to argumentative situations where some contradictions may occur while keeping the idea that there may still be situations in which some propositions are ‘safe’ in (...) the sense of immunity to the contradictions. On the other hand, we open a new line of study on these logics, in the context of the game-theoretical approach to semantics born in the 1960s, with various interesting perspectives, some of which are discussed at the end of this article. (shrink)

Being a pragmatic and not a referential approach to semantics, dialogi-cal logic does not understand semantics as mapping names, propositions and relationships into the real world to obtain an abstract counterpart of it, but as dealing (handeln) with them in a particular way. This allows a very simple formulation of free logic the core of which can be expressed in a nutshell, namely: in an argumentation, it sometimes makes sense to restrict the introduction of singular terms in the (...) context of quantification to a formal use o f them. That is, the proponent is allowed to use a constant if f this constant has been explicitly conceded by the opponent. More technically, we show a new, dialogical way to build free logic systems fo r first-order logic with classical and intuitionistic features and present their corresponding tableaux. I. In tro d u ctio n I I. F r e e logics ON DIALOGUES A ND ONTOLOGY THE DIAL OGICAL APPROACH TO FREE LOGIC The proposition "God does not exist" contains a paradox sometimes referred to as Plato's beard: if God does not exist and the proposition should be true, standard referential semantics fo r quantified logic fails to give meaning to the name "God". But, given compositionality, since the meaning of a sentence is combined from the meanings o f its parts,-G o d d o e s not exist" does not evaluate. It is easy to see that related difficulties appear in every formula that contains singular terms. In standard logic, it is impossible to state that God is either good or evil without presupposing his existence, or that the round * My work on this article has been supported by the Fritz-Thyssen-Stiftung which I wish to thank expressly. (shrink)

Currently, our official rationality is still of a Cartesian kind; we are still embedded in a mechanistic order that takes it that separate, countable entities (spatial forms), related logically to each other, are the only ‘things’ that matter to us—an order clearly suited to advances in robotics. Unfortunately, it is an order that renders invisible ‘relational things’, non-objective things that exist in time, in the transitions from one state of affairs to another, things that ‘point’ toward possibilities in the future, (...) which mean something to us. I have called such things, hermeneutical–dialogical ‘things’ as they gradually emerge in our back-and-forth, step-by-step relations to the others and otherneses in our surroundings; they consist in the ‘promissory’ things sustaining our trust in each other and in our authorities, in our social organizations and social institutions, and in our culture. Clearly, we need to understand better, not only what robots can, and cannot do, but also the long-term ethical and political implications of inserting robotic activities into our everyday ways of relating ourselves to our surroundings if we are to avoid the dystopian futures envisaged by some. Descartes’ aim of “making ourselves, as it were, masters and possessors of nature,” forgets our larger task of our making ourselves into human beings—of doing together in dialog what we cannot do apart. (shrink)

In classical India, Jain philosophers developed a theory of viewpoints ( naya-vāda ) according to which any statement is always performed within and dependent upon a given epistemic perspective or viewpoint. The Jainas furnished this epistemology with an (epistemic) theory of disputation that takes into account the viewpoint in which the main thesis has been stated. The main aim of our paper is to delve into the Jain notion of viewpoint-contextualisation and to develop the elements of a suitable logical system (...) that should offer a reconstruction of the Jainas’ epistemic theory of disputation. A crucial step of our project is to approach the Jain theory of disputation with the help of a theory of meaning for logical constants based on argumentative practices called dialogical logic . Since in the dialogical framework the meaning of the logical constants is given by the norms or rules for their use in a debate, it provides a meaning theory closer to the Jain context-sensitive disputation theory than the main-stream formal model-theoretic semantics. (shrink)

The core ideas of the dialogicalapproach to modal propositional logic are explainedby means of an elementary example. Subsequently,ways of extending this approach to the system G ofso-called provability logic are checked, therebyraising the question whether the dialogician is inneed of shaping his Nichtverzögerungsregel(non-delay-rule), in order to get it sufficiently precise,in different ways for different modal systems.

The core ideas of the dialogicalapproach to modal propositional logic are explainedby means of an elementary example. Subsequently,ways of extending this approach to the system G ofso-called provability logic are checked, therebyraising the question whether the dialogician is inneed of shaping his Nichtverzögerungsregel(non-delay-rule), in order to get it sufficiently precise,in different ways for different modal systems.

The dialogical approach to paraconsistency as developed by Rahman and Camielli ([1]), Rahman and Roetti ([2]) and Rahman ([3], [4] and [5]) suggests a way ofstudying the dynamic process ofarguing with inconsistencies. In his paper on Paraconsistency and Dialogue Logic ([6]) Van Bendegem suggests that an adaptive version of paraconsistency is the natuml way of capturing the inherent dynamics of dialogues. The aim of this paper is to develop a fomulation of dialogical paraconsistent logic in the (...) spirit of an adaptive approach and 'Which explores the possibility of eliminating inconsistencies by tœans oflogicalpreference stmtegies. (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)

According to Douglas Walton, the concept of presumption relates to both logical and dialogical components. Logically, a presumption is the conclusion of a presumptive defeasible inference. Dialogically, the function of a presumptions to shift the burden of proof to the respondent in order to move the dialogue forward when the proponent, due to an objective lack of evidence, cannot present a sufficiently persuasive proposition. Presumptive status, assigned only at the argumentation stage of dialogue, is provisional: a particular presumption stands (...) until further counter-indications are found. This paper points out some possible difficulties pertaining to Walton’s dialogical model of presumption. Firstly, once a presumption's typical practical function is made precise, Walton’s idea of presumption starts to lose its conceptual cohesion, thereby becoming applicable in the opening stage of dialogue, as well. Secondly, cohesion is lost also in practical contexts, since Walton's "seat belts" example might indicate that presumptions are not evidentially defeasible if the practical stakes are raised high enough. Most importantly, contextual evaluation may reveal that presumptions do not shift the burden of proof in any specific or genuine way. (shrink)

Recent literature on dialogical logic discusses the case of tonk and the notion harmony in the context of a rule-based theory of meaning. Now, since the publications of those papers, a dialogical version of constructive type theory has been developed. The aim of the present paper is to show that, from the dialogical point of view, the harmony of the CTT-rules is the consequence of a more fundamental level of meaning characterized by the independence of players. (...) We hope that the following paper will contribute to a better understanding of the dialogical notion of meaning. (shrink)

Dialogic: Education for the Digital Age argues that despite rapid advances in communications technology, most educational research still relies on traditional approaches to education, built upon the logic of print, and dependent on the notion that there is a single true representation of reality. In practice, the use of the Internet disrupts this traditional logic of education by offering an experience of knowledge as participatory and multiple. The challenge identified in Wegerif's text is the growing need to develop (...) a new understanding of education that will encourage us to provide new policies, and hold the potential to transform educational pedagogy and meet the realities of the digital age. This new logic of education is dialogic and characterises education as learning to learn, think and thrive in the context of working with multiple perspectives and ultimate uncertainty. The book builds upon the simple contrast between observing dialogue from an outside point of view, and participating in a dialogue from the inside, before pinpointing an essential feature of dialogic: the gap or difference between voices in dialogue which is understood as an irreducible source of meaning. Each chapter of the book applies this dialogic thinking to a specific challenge facing education, re-thinking the challenge and revealing a new theory of education. Areas covered in the book include: - dialogical learning and cognition - dialogical learning and emotional intelligence - educational technology, dialogic 'spaces' and consciousness - global dialogue and global citizenship - dialogic theories of science and maths education. (shrink)

Being a pragmatic and not a referential approach tosemantics, the dialogical formulation ofparaconsistency allows the following semantic idea tobe expressed within a semi-formal system: In anargumentation it sometimes makes sense to distinguishbetween the contradiction of one of the argumentationpartners with himself (internal contradiction) and thecontradiction between the partners (externalcontradiction). The idea is that externalcontradiction may involve different semantic contextsin which, say A and ¬A have been asserted.The dialogical approach suggests a way of studying thedynamic process of contradictions through (...) which thetwo contexts evolve for the sake of argumentation intoone system containing both contexts.More technically, we show a new, dialogical, way tobuild paraconsistent systems for propositional andfirst-order logic with classical and intuitionisticfeatures (i.e. paraconsistency both with and withouttertium non-datur) and present theircorresponding tableaux. (shrink)

We present a new proof of soundness/completeness of tableaux with respect to dialogical games in Classical First-Order Logic. As far as we know it is the first thorough result for dialogical games where finiteness of plays is guaranteed by means of what we call repetition ranks.

This article begins with an introduction to defeasible (nonmonotonic) reasoning and a brief description of a computer program, EVID, which can perform such reasoning. I then explain, and illustrate with examples, how this program can be applied in computational representations of ordinary dialogic argumentation. The program represents the beliefs and doubts of the dialoguers, and uses these propositional attitudes, which can include commonsense defeasible inference rules, to infer various changing conclusions as a dialogue progresses. It is proposed that computational representations (...) of this kind are a useful tool in the analysis of dialogic argumentation, and, in particular, demonstrate the important role of defeasible reasoning in everyday arguments using commonsense reasoning. (shrink)

In this paper, an interpretation of "necessity", inspired by a Leibnizian idea and based on the method of dialogical logic, is introduced. The semantic rules corresponding to such an account of necessity are developed, and then some peculiarities, and some potential advantages, of the introduced dialogical explanation, in comparison with the customary explanation offered by the possible worlds semantics, are briefly discussed.

The notions of burden of proof and presumption are central to law, but as noted in McCormick on Evidence, they are also the slipperiest of any of the family of legal terms employed in legal reasoning. However, recent studies of burden of proof and presumption (Prakken et al. 2005; Prakken and Sartor 2006). Gordon et al. (2007) offer formal models that can render them into precise tools useful for legal reasoning. In this paper, the various theories and formal models are (...) comparatively evaluated with the aim of working out a more comprehensive theory that can integrate the components of the argumentation structure on which they are based. It is shown that the notion of presumption has both a logical component and a dialectical component, and the new theory of presumption developed in the paper, called the dialogical theory, combines these two components. (shrink)

Since Plaza [1989], which is most of the time considered as the inaugural paper on announcement logics in public communication contexts, a lot of papers on dynamic epistemic logics have been published. The most famous dynamic epistemic logic is known by the name of PAL (Public Announcement Logic). The logic PAC is an extension of PAL with the common knowledge operator (CG). Soundness and completeness proofs of those logics are presented in van Ditmarsch et al. [2008], in (...) Balbiani et al. [2010] and in de Boer [2007]. Each of them used either a model-theoretic approach or a tableaux calculus. In the present paper, we propose an alternative approach to PAC based on the dialogical framework. (shrink)

The objective in this paper is to demonstrate the indispensability of Peirce’s double consciousness to foster abductive reasoning, so that internal/external dialogue inform the worthiness of hunches. These forms of dialogue establish a mental give-and-take forum in which novel meanings/effects are particularly highlighted and noticed. Such attentional shifts are compelled by surprising states of affairs within the beholder’s internal, interpretive competencies, or from external factors (pictures, gestural or linguistic performatives). The dialogic nature of these signs pre-forms operations not possible non-dialogically; (...) they command, interrogate, or suggest alterations to established conduct/beliefs in contexts in which propositional/argumentative conflicts are obviated. This inquiry proposes experimental methodologies to measure when double consciousness (via private/inner speech) mediates hypothesis-making. Vygotsky’s conflict of motive at four distinct developmental stages constitutes the foundation for the proposed experiments. Designs draw upon Vygotsky’s ‘double stimulation’ paradigms that force decision-making processes when conflicts of motive surface. Paradigms include forced imitation of one model while ignoring another (imitating bear, not dragon), and altering a visual array to depict logical sequencing accurately (the “Cycles Test”; “The Odd One Out”). These conflicts require children to change their conduct/beliefs to accommodate to atypical states of affairs. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 36.1 (2003) 48-76 [Access article in PDF] Dialogic Characteristics of Philosophical Discourse:The Case of Plato's Dialogues 1 Frédéric Cossutta The dialogic is increasingly acknowledged as a fundamental factor in the study of human language, a factor that transcends its explicit presence in dialogue. Habermas and Apel are examples of philosophers who do not think of the dialogic as subordinate to the monologic, an approach to reflexive (...) consciousness inherited from Cartesianism; they also invest it with a constitutive dimension when they demonstrate its foundational role in knowledge and ethics. In their eyes, dialogue does not so much constitute ordinary human activity as create the conditions of its possibility. Thus with Apel this pragmatic dimension becomes transcendental, a dimension logically independent of the social or historical circumstances within which it is brought to bear, and one that is capable of playing the role of ideal regulator in the establishment of any community that is authentically human.My aim in this paper is to investigate the role that this dialogic dimension plays in philosophical discourse. If it is constitutive, and not derived, as Habermas and Apel claim, then it should be found at work in the history of philosophy. Indeed a number of philosophers and historians of philosophy have recently claimed an implicit dialogicity at the core of Descartes's Meditations, although these are actually presented in the form of a soliloquy (cf. Jacques 1979; Beyssade and Marion 1994; Bouvier 1996). But while it is true that every philosophy exhibits interdiscursive and intertextual dimensions even at the moment that it attempts to efface all traces of this interplay to present itself as a closed system, may we not question this dialogical property as constitutive of philosophical discourse as such? Philosophers who present their doctrines in the form of dialogues often use this form merely for the purposes of polemic, refutation, or instruction. There is, however, one famous exception: Plato, whose philosophy [End Page 48] is developed for the most part through a series of fictional dialogues, to which his talent gives an intrinsic "literary" quality. We thus have a case in which we can justifiably examine the philosophical value of the dialogue form. Historians of philosophy usually claim that the elements of his dialogues are no more than expressions of an underlying and constitutive dialectical dimension, though there is some dissent. 2 But I shall show that all of the elements of the dialogues, even the prologues and the settings, play a role that is intrinsically philosophical. Studying these elements will enable us to reveal the philosophical status of the dialogical dimension.I shall consider three hypotheses: (1) Though Plato's dialogues are literary rather than actual, their form cannot be reduced to the empty shell for an otherwise purely monological thought; there is an effective dialogism at work in both the early and the later Dialogues. This statement can be more easily accepted if it is recalled that philosophical activity for Plato consists of dialegsthai (Dixsaut 1985). 3 (2) In Plato, in effect, dialogue constitutes philosophical speech itself. The link between dialogue as a way of embodying doctrine and dialectics as an expression of the process of thought is intrinsic and necessary. Insofar as this link is necessary, dialogic activity cannot be characterized as an empirical practice of conversation, nor can it be reconstructed as a literary genre; rather, it is informed throughout by a philosophical theory whose explanation it makes generally available. (3) As a consequence, dialogic interplay at work in the Dialogues follows pragmatic rules that are not empirical in nature but possess a transcendental dimension and require ethical presuppositions. A parallel may thus be drawn between the Platonist conception of dialogue and the theory developed by Karl Otto Apel as "transcendental pragmatics" (1987 and 1994). This last point I shall dwell upon at length. Plato's Dialogues: Dialogism or hidden monologism? Paradoxically, the very thinkers who regard language as constitutively dialogic refuse to see this dialogism in Plato. It is true that at first sight the Platonic dialogues seem to turn the... (shrink)

This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Paraconsistent logic comprises a major logical (...) theory and offers the broadest possible perspective on the debate of negation in logic and philosophy. It is a powerful tool for reasoning under contradictoriness as it investigates logic systems in which contradictory information does not lead to arbitrary conclusions. Reasoning under contradictions constitutes one of most important and creative achievements in contemporary logic, with deep roots in philosophical questions involving negation and consistency This book offers an invaluable introduction to a topic of central importance in logic and philosophy. It discusses the history of paraconsistent logic; language, negation, contradiction, consistency and inconsistency; logics of formal inconsistency and the main paraconsistent propositional systems; many-valued companions, possible-translations semantics and non-deterministic semantics; paraconsistent modal logics; first-order paraconsistent logics; applications to information processing, databases and quantum computation; and applications to deontic paradoxes, connections to Eastern thought and to dialogical reasoning. (shrink)

After acknowledging that the crisis of the present-day-world is in its very essence the crisis of reason, I consider both the logical notion of reason and an odyssey which reason accomplished within the spread of the modern and postmodern Western history. Doing that, I regard reason not as a subjective human power, being a conventional and formal notion which means nothing if it would not be taken in action of great groups of people and in connection with material contents from (...) which the most important are values or sets of values. I indicate two main kinds of hitherto existing rationality as paradigms of acting reason: (1) metaphysical rationality and (2) instrumental rationality. I put on a thesis that, at all contemporary conditionings: social, cultural, political, also philosophical and others, the two paradigms of rationality have exhausted nowadays their creative possibilities. It has come a time which inclines for looking for another kind of rationality better corresponding to the existing, at present, challenges that would fit better to the state of the contemporary philosophical awareness. The instrumental rationality seems to be ambiguous in consequences and, additionally, has an inclination to turn into irrationality. On the other hand, the traditional metaphysical rationality lost its power of being effective because of historical evolution of the philosophy itself. The 20th century has been by many currents of contemporary philosophy, and by many philosophers, announced as post-metaphysical or even antimetaphysical. I am of an opinion that, taking into account many essential threats of further existence of humankind as well as of physical world, the problem of the socalled metaphysics of foundations has lost its importance. All efforts of philosophers, and all reasoning and acting people, should be directed towards shaping a new kind of rationality as a new paradigm which could function within all contemporary existing civilizations. My proposal is to label this new kind of rationality with the term dialogical rationality. And I think that this rationality could be something that would unite peoples, nations, regions, civilizations, cultures, religions, philosophical directions etc., beyond all hitherto existing differences and controversies, and in the name of the most important present values as well as for diminishing, if not annihilating, great threats. The concept of dialogical rationality is discussed on the basis of views belonging to the greatest achievements of contemporary philosophy like philosophy of dialogue, views of Jaspers, Popper, Habermas, representatives of postmodernism, and others. (shrink)

The implicit dimension of enthymemes is investigated from a pragmatic perspective to show why a premise can be left unexpressed, and how it can be used strategically. The relationship between the implicit act of taking for granted and the pattern of presumptive reasoning is shown to be the cornerstone of kairos and the fallacy of straw man. By taking a proposition for granted, the speaker shifts the burden of proving its un-acceptability onto the hearer. The resemblance of the tacit premise (...) with what is commonly acceptable or has been actually stated can be used as a rhetorical strategy. (shrink)

PREFACEProf. Göran Sundholm of Leiden University inspired the group of Logic at Lille and Valparaíso to start a fundamental review of the dialogical conception of logic by linking it to constructive type logic. One of Sundholm's insights was that inference can be seen as involving an implicit interlocutor. This led to several investigations aimed at exploring the consequences of joining winning strategies to the proof-theoretical conception of meaning. The leading idea is, roughly, that while introduction rules (...) lay down the conditions under which a winning strategy for the Proponent may be built, the elimination rules lay down those elements of the Opponent's assertions that the Proponent has the right to use for building winning strategy. It is the pragmatic and ethical features of obligations and rights that naturally lead to the dialogical interpretation of natural deduction.During the Visiting Professorship of Prof. Sundholm at Lille in (2012) the group of Lille started delving into the ways of implementing Per Martin-Löf's Constructive Type Theory with the dialogical perspective. In particular, Aarne Ranta's (1988) paper, the first publication on the subject, was read and discussed during Sundholm’s seminar. The discussions strongly suggested that the game-theoretical conception of quantifiers as deploying interdependent moves provide a natural link between CTT and dialogical logic. This idea triggered several publications by the group of Lille in collaboration with Nicolas Clerbout and Juan Redmond at the University of Valparaíso, including the publication of the book (2015) by Clerbout / Rahman that provides a systematic development of this way of linking CTT and the dialogical conception of logic. However the Clerbout / Rahman book was written from the CTT perspective on dialogical logic, rather than the other way round. The present book should provide the perspective from the other side of the dialogue between the Dialogical Framework and Constructive Type Theory. The main idea of our present study is that Sundholm's (1997) notion of epistemic assumption is closely linked to the Copy-Cat Rule or Socratic Rule that distinguishes the dialogical framework from other game-theoretical approaches. One way to read the present book is as a further development of Sundholm’s extension of Austin's (1946, p. 171) remark on acts of assertion to inference. Indeed, Sundholm (2013, p. 17) gave the following forceful formulation: When I say therefore, I give others my authority for asserting the conclusion, given theirs for asserting the premisses.Per Martin-Löf, in recent lectures, have utilized the dialogical perspective on epistemic assumptions to get out of a certain circle that threatens the explanation of the notions of inference and demonstration. A demonstration may be explained as a chain of (immediate) inferences starting from no premisses. That an inference J1... Jn—————Jis valid means that the conclusion J can be made evident on the assumption that J1, …, Jn are known. The notion of epistemic assumption thus enters in the explanation of valid inference. We cannot, however, in this explanation understand 'known' in the sense of demonstrated, for then we are explaining the notion of inference in terms of demonstration, whereas demonstration has been explained in terms of inference. Martin-Löf suggests that we here understand 'known' in the sense of asserted, so that epistemic assumptions are judgements others have made, judgements for which others have taken the responsibility; that the inference is valid then means that, given that others have taken responsbility for the premisses, I can take responsibility for the conclusion:The circularity problem is this: if you define a demonstration to be a chain of immediate inferences, then you are defining demonstration in terms of inference. Now we are considering an immediate inference and we are trying to give a proper explanation of that; but, if that begins by saying: Assume that J1, …, Jn have been demonstrated – then you are clearly in trouble, because you are about to explain demonstration in terms of the notion of immediate inference, hence when you are giving an account of the notion of immediate inference, the notion of demonstration is not yet at your disposal. So, to say: Assume that J1, …, Jn have already been demonstrated, makes you accusable of trying to explain things in a circle. The solution to this circularity problem, it seems to me now, comes naturally out of this dialogical analysis. […]The solution is that the premisses here should not be assumed to be known in the qualified sense, that is, to be demonstrated, but we should simply assume that they have been asserted, which is to say that others have taken responsibility for them, and then the question for me is whether I can take responsibility for the conclusion. So, the assumption is merely that they have been asserted, not that they have been demonstrated. That seems to me to be the appropriate definition of epistemic assumption in Sundholm's sense. One of the main tenets of the present study is that the further move of relating the Socratic Rule rule with judgemental equality provides both a simpler and more direct way to implement the constructive type theoretical approach within the dialogical framework. Such a reconsideration of the Socratic Rule, roughly speaking, amounts to the following. 1.A move from P that brings-forward a play-object in order to defend an elementary proposition A can be challenged by O. 2.The answer to such a challenge, involves P bringing forward a definitional equality that expresses the fact that the play-object chosen by P copies the one O has chosen while positing A. For short, the equality expresses at the object-languaje level that the defence of P relies on the authority given to O to be able to produce the play-objects she brings forward. More generally, according to this view, a definitional equality established by P and brought forward while defending the proposition A, expresses the equality between a play-object (introduced by O) and the instruction for building a play-object deployed by O while affirming A. So it can be read as a computation rule that indicates how to compute O's instructions. Let us recall that from the strategic point of view, O's moves correspond to elimination rules of demonstrations. Thus, the dialogical rules that prescribe how to introduce a definitional equality – correspond – at the strategic level – to the definitional equality rules for CTT as applied to the selector-functions involved in the elimination rules. So, what we are doing here is extending the dialogical interpretation of Sundholm's epistemic assumption to the rules that set up the definitional equality of a type.The present work is structured in the following way:•In the Introduction we state the main tenets that guide our book•Chapter II contains a brief overview of Constructive Type Theory penned by Ansten Klev with exercises and their solutions. •Chapter III offers a novel presentation of the dialogical conception of logic. In fact, the first two sections of the chapter provide an overview of standard dialogical logic – including solved exercises, slightly adapted to the content of the present volume. The rest of the sections develop a new dialogical approach to Constructive Type Theory. •Chapters IV and V contain the main body of our study, namely the relation between the Socratic Rule, epistemic assumptions, and equality. The chapter provides the reader with thoroughly worked out examples with comments. •After the Final Remarks the book containsa.An appendix containing a an overview of all the rules for the new formulation of dialogical approach to constructive type theory developed in the book; b.a brief outline of Per Martin-Löf's informal presentation of the demonstration of the axiom of choice.c.two examples of a tree-shaped graph of an extensive strategy. Acknowledgments: Many thanks to Mark van Atten (Paris1), Giuliano Bacigalupo (Zürich), Charles Zacharie Bowao (Univ. Ma Ngouabi de Brazzaville, Congo), Christian Berner (Lille3), Michel Crubellier (Lille3), Pierre Cardascia (Lille3), Oumar Dia (Dakar), Marcel Nguimbi ((Univ. Marien Ngouabi de Brazzaville, Congo), Adjoua Bernadette Dango (Lille3 / Alassane Ouattara de Bouaké, Côte d'Ivoire), Steephen Rossy Eckoubili (Lille3), Johan Georg Granström (Zürich), Gerhard Heinzmann (Nancy2), Muhammad Iqbal (Lille3), Matthieu Fontaine (Lille3), Radmila Jovanovic (Belgrad), Hanna Karpenko (Lille3), Laurent Keiff (Lille3), Sébastien Magnier (Saint Dennis, Réunion), Clément Lion (Lille3), Gildas Nzokou (Libreville), Fachrur Rozie (Lille3), Helge Rückert (Mannheim), Mohammad Shafiei (Paris1), and Hassan Tahiri (Lisbon), for rich interchanges, suggestions on the main claims of the present study and proof-reading of specific sections of the text. Special thanks to Gildas Nzokou (Libreville), Steephen Rossy Eckoubili (Lille3) and Clément Lion (Lille3), with whom a Pre-Graduate Textbook in French on dialogical logic and CTT is in the process of being worked out – during the visiting-professorship in 2016 of the former. Eckoubili is the author of the sections on exercises for dialogical logic, Nzokou cared of those involving the development of CTT-demonstrations out of winning-strategies. Special thanks also to Ansten Klev (Prague) for helping with technical details and conceptual issues on CTT, particularly so as author of the chapter introducing CTT. (shrink)

This paper focuses on an explanation in a newspaper article: why new European Union citizens will come to the UK from Eastern Europe (e.g., because of available jobs). Using a corpus-based method of analysis, I show how regular target readers have been positioned to generate premises in dialogue with the explanation propositions, and thus into an understanding of the explanation as an argument, one which contains a biased conclusion not apparent in the text. Employing this method, and in particular ‘corpus (...) comparative statistical keywords’, I show how two issues can be freshly looked at: implicit premise recovery; the argument/explanation distinction. (shrink)

Classical phenomenology -- The transcendental tradition -- The logical investigations of the I -- From the I to the ego -- The grammar of the transcendental ego -- Strawson on the primacy of personhood -- Wittgenstein on the lure of words -- The grammar of the transcendental ego -- Zahavi on transcendental subjectivity as intersubjectivity -- Contemporary arguments for the transcendental ego : Marbach, Soffer -- Schutz, Theunissen on social phenomenology -- Husserl's later thought -- The multidiscipline of dialogical (...) phenomenology -- Sociolinguistics -- Personal pronouns : reconsidering the traditional view -- Egocentrism and polycentrism -- Person deixis and polycentrism -- Anscombe -- Wittgenstein -- Personal pronouns : reconsidering the traditional view -- I and we : a relational community -- Benveniste and I : you connectedness -- Objectification in the third person -- Castaneda's phenomeno-logic of the I -- Developmental perspectives -- Piaget's legacy -- Recent research on the sociality of children -- Proto-conversations in infancy -- The dialogic model of Jaffe and Feldstein -- From proto-conversation to conversation -- Perspectives from blindness and autism -- Polycentrism and personal pronoun acquisition: loveland and others -- An egocentric model of personal pronoun acquisition : Charney and others -- Philosophical implications and directions for future research -- Philosophy of dialogue -- Rosenstock-Huessy's grammatical method of social research -- Rosenzweig's speech-thinking -- Buber's I and you -- The primordial duality in Buber, Humboldt, Plato -- Buber and his critics -- Rosenstock-Huessy -- Levinas -- Dialogical phenomenology -- The dialogic dimension of meaning and experience -- The practice of phenomenology -- Implications for politics and feminism. (shrink)

In this book Catarina Dutilh Novaes—the accomplished philosopher of logic and historian of logic—takes a wide-angle view of the field and argues that the great.