This monograph proposes a new way of implementing interaction in logic. It also provides an elementary introduction to Constructive Type Theory. The authors equally emphasize basic ideas and finer technical details. In addition, many worked out exercises and examples will help readers to better understand the concepts under discussion. One of the chief ideas animating this study is that the dialogical understanding of definitional equality and its execution provide both a simple and a direct way of implementing the CTT approach (...) within a game-theoretical conception of meaning. In addition, the importance of the play level over the strategy level is stressed, binding together the matter of execution with that of equality and the finitary perspective on games constituting meaning. According to this perspective the emergence of concepts are not only games of giving and asking for reasons, they are also games that include moves establishing how it is that the reasons brought forward accomplish their explicative task. Thus, immanent reasoning games are dialogical games of Why and How. (shrink)

We now move to the demonstration of the left-to-right direction of the equivalence result. Let us assume that there is a winning $$\mathbf {P}$$ P -strategy in the dialogical game for $$\varphi $$ φ.

This volume includes a target paper, taking up the challenge to revive, within a modern (formal) framework, a medieval solution to the Liar Paradox which did ...

In this paper, we provide a detailed critical review of current approaches to ecthesis in Aristotle’s Prior Analytics, with a view to motivate a new approach, which builds upon previous work by Marion & Rückert (2016) on the dictum de omni. This approach sets Aristotle’s work within the context of dialectic and uses Lorenzen’s dialogical logic, hereby reframed with use of Martin-Löf's constructive type theory as ‘immanent reasoning’. We then provide rules of syllogistic for the latter, and provide proofs of (...) e-conversion, Darapti and Bocardo and e-subalternation, while showing how close to Aristotle’s text these proofs remain. (shrink)

RésuméCette première étude permet notamment de dégager ce résultat épistémologique: les différentes formes d’“inférence co-relationnelle” connues dans la jurisprudence islamique sous le nom de qiyās représentent une forme innovante et sophistiquée de raisonnement qui permet non seulement d'avoir une conception épistémologique plus claire du raisonnement légal en général, mais aussi de produire une mécanique bien huilée pour le “raisonnement parallèle”; cette mécanique du “raisonnement parallèle” peut être déployée selon un large spectre dans différents cadres de résolution de problèmes et ne (...) semble pas se réduire aux formes standard de l'argumentation analogique étudiées en philosophie des sciences contemporaine. Nous n'aborderons cependant dans la présente étude que le cas de la dénommée “inférence co-relationnelle du facteur occasionnel”, et ce seulement dans le contexte de la jurisprudence islamique. (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)

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)

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)

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 (CTT) 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.La bibliografía reciente sobre lógica dialógica, estudia el caso de tonk y la noción de armonia en el contexto de una teoría del significado basado en reglas. Ahora bien, desde la publicación de tales textos, la teoría dialógica ha sido vinculada con la Teoría Constructiva de Tipos (CTT). El objetivo principal del presente artículo es mostrar que, desde un punto de vista dialógico, la armonía de las reglas de la CTT es consecuencia de un nivel más fundamental de significado caracterizado por la independencia de los jugadores. Esperamos que el presente trabajo contribuya a una mejor comprensión de la nocion dialógica de significado. (shrink)

The passionate and staunch defence of logic of the controversial thinker Ibn Ḥazm, Abū Muḥammad ʿAlī b. Aḥmad b. Saʿīd of Córdoba (384-456/994-1064), had lasting consequences in the Islamic world. Indeed, his book Facilitating the Understanding of the Rules of Logic and Introduction Thereto, with Common Expressions and Juristic Examples (Kitāb al-Taqrīb li-ḥadd al-manṭiq wa-l-mudkhal ilayhi bi-l-alfāẓ al-ʿāmmiyya wa-l-amthila al-fiqhiyya), composed in 1025-1029, was well known and discussed during and after his time; and it paved the way for the studies (...) of his compatriots Ibn Bājjah (d. 1138), Ibn Ṭufayl (1185), and Ibn Rushd (1198), who each gave demonstrative reasoning a privileged place within the methods of attaining knowledge. Unfortunately, as too often in the history of science, Ibn Ḥazm’s innovative perspectives and contributions in logic have been overlooked or considered with an attitude of contempt. On the one hand, his work has been seen, at best, as promulgating the benefits of studying Aristotle’s logic, so that his contribution is assessed as more didactical than conceptual. And on the other hand, those who do examine his innovations often consider them to be mistaken. As indicated by Chejne (1984, p. 2) contempt towards the logical work of Ibn Ḥazm was also present in its reception by the Eastern philosophers who accused him of deviating from Aristotelian logic and of dabbling in things beyond his capability. However, a reassessment of his work on logic has since begun, by delving into the ways the thinker of Córdoba studied the links between deontic and modal qualification of propositions. In this context Lameer’s (2013) paper on the logical sources of Ibn Ḥazm is worth mentioning; the author (p. 417, footnote 1) observes that, although, strictly speaking, it was al-Fārābī who first drew the parallelism between deontic and modal concepts, it was Ibn Ḥazm who developed it and worked it out in a more precise manner. A primary aim of this paper is to help fill some of these gaps by stressing the role of the work of Ibn Ḥazm in developing a notion of deontic necessity deeply rooted in legal normativity, and in explicitly discussing the transference between deontic and modal concepts. According to our view; the basic units of Islamic deontic logic are what we might call, indulging in terminological anachronism, heteronomous imperatives. As it turns out, the heteronomy of imperatives within Islamic legal systems contrasts with those of the purely moral realm, which seem to be closer to an autonomous conception of moral law. There it concurs again with Leibniz’s proposal to define obligatory as “what is necessary for a good person to do”. In the present paper, we will focus on the heteronomous imperatives of legal systems rather than on the imperatives of the purely moral realm. In this context, the work of Ibn Ḥazm extends the parallelism between the necessity of events and that of human actions stressed by his predecessors. According to our understanding, Ibn Ḥazm’s parallelism can be rendered explicit formally by means of a conditional (or hypothetical) structure shared by both deontic and modal propositions. Moreover, this structure makes apparent that this parallelism displays an underlying system of “degrees”. Indeed, while in the domain of events, given some conditions, it makes sense to distinguish between an event that is more likely to happen than another. Ibn Ḥazm speaks of near and distant possibility (such as the higher degree of likelihood of rain, given the condensation of clouds in December, and its lower degree, when the condensation occurs in summer); and, in the domain of actions, the Islamic notion of weighting actions determines degrees of virtue (or of legal and moral value). So whereas the degree of virtue of performing a forbidden act as determined by the distribution of sanction and reward is 0, we obtain the same value by pondering the likelihood of an impossible event to take place. Furthermore, as discussed in section II.3.2, the system of values at work in the parallelism can be seen as opening the way to a more direct correspondence. Thus, while in the realm of nature, likelihood of occurrence of an event is dependent upon the conditions specific to the occurrence of that event; while, in the realm of jurisprudence, likelihood of performing an action is dependent upon the distribution of reward and sanction specific to that action (being that, given the choice to perform or not perform a given action, those that will be rewarded are more likely to be performed than those that are not). According to this perspective, the point of the parallelism is that both deontic and modal qualifications measure the degree of an action or event to become actual; that is – indulging once more in anachronism (but this time from the Leibnizian background) – the degree measures how feasible (facile) an action or event may be. This suggests that Ibn Ḥazm’s perspectives already herald the links to probability and possibility explored by Leibniz six centuries later – see for example Leibniz’s (1671, A VI, I, p. 424-26) use of probability in the context of conditional right. Nevertheless, it also shows a crucial difference to the approach developed in the Elementa Jura Naturalis: whereas Leibniz’s studies seek to define what is to be just or virtuous, the logical system of deontic imperatives within Islamic jurisprudence presupposes that what is to be virtuous has already been settled. Determining what is to be virtuous is not achieved by logical reasoning within the system of legal jurisprudence, but by delving into the higher objectives of the Sharīʿa. While developing our point, we will delve into the logical structure of the heteronomous imperatives. This distinguishes our contribution from the existing literature, such as the papers of Chejne (1984), Lameer (2014), and Guerrero (1997, 2010, 2014), which do not provide a logical analysis of the deontic concepts put into work by Ibn Ḥazm. The true antecedent to the present paper is the work of Farid Zidani (2007, 2015), who, so far as we know, was the first to undertake such a task. Some of our own developments and general epistemological thoughts go beyond Ibn Ḥazm’s framework and motivations; mainly those contained in sections II.3.2 and IV. However, according to our view, these reflections suggest that Ibn Ḥazm’s approach has the substance for a broader and deeper exploration of the logic of norms. The paper is structured as follows:I.Ibn Ḥazm’s Logic of Heteronomous Imperatives. After presenting some extracts of the relevant text, we proceed by providing a formal reconstruction of the five forms of deontic modalities. II. A Landmark in the History of the Logical Analysis of Norms. Duties and Modalities. In this section, we study the transferences from deontic to modal necessity and possibility. We briefly compare the deontic system of Islamic Jurisprudence with that of Leibniz.III. Leibniz and Hypothetical Imperatives in Law.IV. Beyond Ibn Ḥazm: Conclusions and the Work Ahead. We will conclude the paper by discussing briefly some conceptual points that distinguish the logic of heteronomous imperatives from contemporary deontic logic. Our final words will discuss deontic-modal parallelism in the context of Ibn Ḥazm’s rejection of reasoning by conjecture and what we call “the internalization of nature.”. (shrink)

In her book Fiction and Metaphysics (1999) Amie Thomasson, influenced by the work of Roman Ingarden, develops a phenomenological approach to fictional entities in order to explain how non-fictional entities can be referred to intrafictionally and transfictionally, for example in the context of literary interpretation. As our starting point we take Thomasson’s realist theory of literary fictional objects, according to which such objects actually exist, albeit as abstract and artifactual entities. Thomasson’s approach relies heavily on the notion of ontological dependence, (...) but its precise semantics has not yet been developed. Moreover, the modal approach to the notion of ontological dependence underlying the Artifactual Theory has recently been contested by several scholars. The main aims of this paper are (i) to develop a semantic approach to the notion of ontological dependence in the context of the Artifactual Theory of fiction, and in so doing bridge a number of philosophical and logical gaps; (ii) to generalize Thomasson’s categorial theory of ontological dependence by reconstructing ontological categories of entities purely in terms of different structures of ontological dependence, rather than in terms of the basic kinds of entities the categorical entities depend on. (shrink)

the demise of the logical positivism programme. The answers given to these qu- tions have deepened the already existing gap between philosophy and the history and practice of science. While the positivists argued for a spontaneous, steady and continuous growth of scientific knowledge the post-positivists make a strong case for a fundamental discontinuity in the development of science which can only be explained by extrascientific factors. The political, social and cultural environment, the argument goes on, determine both the questions and (...) the terms in which they should be answered. Accordingly, the sociological and historical interpretation - volves in fact two kinds of discontinuity which are closely related: the discontinuity of science as such and the discontinuity of the more inclusive political and social context of its development. More precisely it explains the discontinuity of the former by the discontinuity of the latter subordinating in effect the history of science to the wider political and social history. The underlying idea is that each historical and - cial context generates scientific and philosophical questions of its own. From this point of view the question surrounding the nature of knowledge and its development are entirely new topics typical of the twentieth-century social context reflecting both the level and the scale of the development of science. (shrink)

This monograph proposes a new way of studying the different forms of correlational inference, known in the Islamic jurisprudence as qiyās. According to the authors’ view, qiyās represents an innovative and sophisticated form of dialectical reasoning that not only provides new epistemological insights into legal argumentation in general but also furnishes a fine-grained pattern for parallel reasoning which can be deployed in a wide range of problem-solving contexts and does not seem to reduce to the standard forms of analogical reasoning (...) studied in contemporary philosophy of science and argumentation theory. After an overview of the emergence of qiyās and of the work of al-Shīrāzī penned by Soufi Youcef, the authors discuss al-Shīrāzī’s classification of correlational inferences of the occasioning factor. The second part of the volume deliberates on the system of correlational inferences by indication and resemblance. The third part develops the main theoretical background of the authors’ work, namely, the dialogical approach to Martin-Löf's Constructive Type Theory. The authors present this in a general form and independently of adaptations deployed in parts I and II. Part III also includes an appendix on the relevant notions of Constructive Type Theory, which has been extracted from an overview written by Ansten Klev. The book concludes with some brief remarks on contemporary approaches to analogy in Common and Civil Law and also to parallel reasoning in general. (shrink)

The present study on al-Dīn Suhrawardī's Ḥikmat al-Ishrāq, develops some preliminary explorations on his logic under the background of his remarkable epistemology of pis some witness of d resence. The paper paves the way for responding to the challenges of Tony Street on the compatibility of Suhrawardī's critique of Ibn Sīnā with the development of a temporal and modal syllogism that at first sight seems quite close to that of Ibn Sīnā. In fact, Suhrawardī's modalities are to be understood as (...) the different ways a predicate relates to its subject rather than as propositional operators. Accordingly, necessarily necessary modality relates actual instances (presences) of the Subject-Term with actual (presences) of the Predicate-Term; in contrast, necessarily contingent modality relates these terms conditionally, notably involving states of the Subject-Term within time intervals. Suhrawardī's main innovation, so we claim, is the explicit dialectical role presences or actual instances have in his modal-temporal logic, and particularly so in shaping his notion of contingency that admits both a generic and an individual or de re form of plenitude. (shrink)

Despite the fact that it has been more than 40 years since Henry Corbin and Hossein Ziai pointed out that the work of Shihāb al-Dīn Suhrawardī (549/1155, 587/1191) has not yet been systematically studied, a thorough investigation of his work is still in its infancy. The present brief study, which aims to contribute to filling such a gap by further developing some of the points contained in Rahman & Seck's (2022) paper, articulates some remarks on the relevance of Suhrawardī's epistemology (...) of presence for contemporary studies on temporal logic. More specifically, we will focus our brief presentation on the fruitfulness of his postulate of the priority of experience of immediate knowledge discussed in the Ḥikmat al-Ishrāq and how this postulate is related to the concept of self-consciousness (وعي الذاتي).Thus the particularity of this study is that Suhrawardī's epistemology of presence, unlike contemporary temporal logic developed for example by Prior, emphasizes the temporalization of the instantiation of an event or the performance of an act rather than of the propositions that express that event or act. Moreover, in Suhrawardī's modal syllogistic, there is an analysis of contingency that differs from most contemporary authors and that also involves several dimensions of time. More generally, Suhrawardī's notion of direct knowledge offers new insights into the logical and ontological status of the now. (shrink)

La réflexion philosophique sur la non-existence est une thématique qui a été abordée au commencement même de la philosophie et qui suscite, depuis la publication en 1905 de « On Denoting » par Russell, les plus vifs débats en philosophie analytique. Cependant, le débat féroce sur la sémantique des noms propres et des descriptions définies qui surgirent suite à la publication du « On Referring » par Strawson en 1950 n’engagea pas d’étude systématique de la sémantique des fictions. En fait, (...) le développement systématique d’un lien qui articule approches logiques, philosophiques et littéraires de la fiction devait attendre les travaux de John Woods publiés en 1974 dans son livre The Logic of Fiction : A Philosophical Sounding of Deviant Logic. Un des enjeux les plus excitants du livre de Woods se situe au niveau de l’interaction entre les points de vue internalistes ou interne-à-l’histoire (principalement pragmatiques) et les points de vue externalistes ou externe-à-la-fiction (principalement sémantiques). Sur ce point, Woods fut le premier à formuler une sémantique pour l’opérateur de fiction à lire comme « selon l’histoire… » en relation à la notion logique de portée, ce qui permettait l’étude de l’internalisme et de l’externalisme. Suite au livre de Woods, loin de s’essouffler, les débats trouvaient une nouvelle impulsion. Le fait pertinent pour notre article est que la tradition phénoménologique également, l’étude de la fiction a joué un rôle central. En effet, l’une des problématiques les plus sujettes à controverses dans l’intentionnalité est celle de l’indépendance à l’existence, c’est-à-dire le fait que les actes intentionnels n’ont pas besoin d’être forcément dirigés vers un objet existant. Influencée par les travaux de Roman Ingarden (1893-1970), l’un des plus importants disciples de Husserl, Amie L. Thomasson développe le concept phénoménologique de dépendance ontologique en vue d’expliquer les processus de références inter- et transfictionnels – dans le contexte de l’interprétation littéraire par exemple. L’enjeu essentiel de cet article est de proposer une reconstruction multimodale bi-dimensionnelle de la théorie des personnages fictionnels de Ingarden-Thomasson. Cette théorie qui entend prendre au sérieux le fait que les fictions sont des créations montre la voie pour une articulation entre les approches internalistes et externalistes. Nous motivons certains changements quant à l’approche artéfactuelle - incluant une sémantique appropriée pour l’opérateur de fictionalité qui, nous l’espérons, éveillera l’intérêt des théoriciens de la littérature. L’article est à d’autres égards un panorama de la façon dont différents concepts d’intentionnalité pourraient fonder différentes sémantiques formelles pour la fictionalité. Nous proposerons enfin un cadre dialogique qui est une extension modale d’un certain système de preuve développé par Matthieu Fontaine et Juan Redmond. Le cadre dialogique développe la contrepartie inférentielle de la sémantique bi-dimensionnelle introduite par Shahid Rahman et Tero Tulenheimo dans un article récent. (shrink)

RésuméAristote n'a pas développé une théorie de la quantification du prédicat, mais une étude récente de Hasnawi a montré qu'Ibn Sīnā a consacré à celle-ci une étude rigoureuse. Assumant la structure aristotélicienne sujet-prédicat, Ibn Sīnā qualifie les propositions qui comportent un prédicat quantifié, de propositions déviantes. Une conséquence de cette approche avicennienne est que la seconde quantification est absorbée par le prédicat. La distinction claire ainsi opérée entre un sujet quantifié, qui pose le domaine de la quantification, et une partie (...) prédicative, qui construit une proposition sur ce domaine, correspond structurellement à la distinction, faite dans la théorie constructive des types, entre le type des ensembles et le type des propositions.Aristote n'a pas non plus combiné son analyse logique de la quantification avec sa théorie ontologique des relations ou de l’égalité. Ibn Sīnā, en revanche, a utilisé les syllogismes qui nécessitent une logique de l’égalité et il a examiné des cas où la quantification se combine, via l’égalité, avec des termes singuliers. En outre, ces réflexions sont essentielles pour sa théorie des nombres qui est fondée sur l'interaction entre l’un et le multiple. Lorsqu'on combine la théorie métaphysique de l’égalité telle qu'on la trouve chez Ibn Sīnā avec son travail sur la quantification du prédicat, il en résulte tout naturellement une logique de l’égalité. En effet, l'interaction entre la quantification du prédicat et l’égalité peut être appliquée aux exemples de syllogismes mentionnés par Ibn Sīnā dans lesquels ces notions interviennent. En utilisant les instruments formels fournis par la théorie constructive des types de Martin-Löf, cet article établit des liens entre la métaphysique d'Ibn Sīnā et son travail logique, liens qui ont été discutés en relation avec d'autres sujets par Thom et Street. Ibn Sīnā n'a pas développé une logique de l'identité, mais il a développé les moyens conceptuels de le faire. (shrink)

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)

The relation between logic and knowledge has been at the heart of a lively debate since the 1960s. On the one hand, the epistemic approaches based their formal arguments in the mathematics of Brouwer and intuitionistic logic. Following Michael Dummett, they started to call themselves `antirealists'. Others persisted with the formal background of the Frege-Tarski tradition, where Cantorian set theory is linked via model theory to classical logic. Jaakko Hintikka tried to unify both traditions by means of what is now (...) known as `explicit epistemic logic'. Under this view, epistemic contents are introduced into the object language as operators yielding propositions from propositions, rather than as metalogical constraints on the notion of inference. The Realism-Antirealism debate has thus had three players: classical logicians, intuitionists and explicit epistemic logicians. The editors of the present volume believe that in the age of Alternative Logics, where manifold developments in logic happen at a breathtaking pace, this debate should be revisited. Contributors to this volume happily took on this challenge and responded with new approaches to the debate from both the explicit and the implicit epistemic point of view. (shrink)

The main aim of our paper is to implement Leibniz's analysis of the conditional right in the framework of a dialogical approach to Public Announcement Logic. According to our view, on one hand: PAL furnishes a dynamic epistemic operator which models communication exchange between different agents that seems to be very close to Leibniz understanding of the dynamics between the truth of a proposition and the knowledge of the truth of that proposition (Leibniz calls the latter certification of its truth); (...) on the other hand, the dialogical approach provides a semantics for the dynamic epistemic operator in the context of conditional right by means of which: (i) the exchange between agents leading to a public announcement amounts to the (contractual) interaction of commitments of both the benefactor and the beneficiary of a conditional right (ii) the notion of certification is understood as an action, namely as a move where the beneficiary asks the benefactor to stand to his commitments, (iii) some restrictions specific to the logical nature of the head and the tail of the conditional right can be implemented by combining PAL with some features of linear logic within the same theory of meaning. (shrink)

One of the epistemological results emerging from this initial study is that the different forms of co-relational inference, known in the Islamic jurisprudence as qiyās, represent an innovative and sophisticated form of reasoning that not only provides new epistemological insights into legal reasoning in general but also furnishes a fine-grained pattern for parallel reasoning which can be deployed in a wide range of problem-solving contexts and does not seem to reduce to the standard forms of analogical argumentation studied in contemporary (...) philosophy of science. However, in the present paper we will only discuss the case of so-called co-relational inferences of the occasioning factor and only in the context of Islamic jurisprudence. (shrink)

The work of Hugh MacColl (1837–1909) suffered the same fate after his death as before it:despite being vaguely alluded to and in part even commended, on the whole it has remained an unknown quantity. Even worse, those of his ideas which have played a decisive role in the history of logic have been credited to his successors; this is especially the case with the definition of strict implication and the first formal development of formal modal logic. This paper takes an (...) initial step towards a rectification of this unfortunate misrepresentation, presenting a bibliography of MacColl’s most significant publications with particular regard to their reception. (shrink)

The main aim of the paper is to offer a solution compatible with Graham Priest’s Noneism and Amie Thomasson’s Artifactual theory which stresses the epistemic features of the notion of individuality in fiction in a framework where individuals are conceived of as functions (the framework is known as the world-lines-semantics of Hintikka). According to our view, it is the endorsement of a reader’s perspective that extends the range of the values of the functions (individuals) and that offers an alternative solution (...) to cases of identity inside and outside the scope of a fictionality (or representation) operator. More technically, this proposal can be seen as both extending the notion of individuality of the Artifactual theory and furnishing an epistemic twist to Priest’s principle of freedom. (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)

Science is a dynamic process in which the assimilation of new phenomena, perspectives, and hypotheses into the scientific corpus takes place slowly. The apparent disunity of the sciences is the unavoidable consequence of this gradual integration process. Some thinkers label this dynamical circumstance a ‘crisis’. However, a retrospective view of the practical results of the scientific enterprise and of science itself, grants us a clear view of the unity of the human knowledge seeking enterprise. This book provides many arguments, case (...) studies and examples in favor of the unity of science. These contributions touch upon various scientific perspectives and disciplines such as: Physics, Computer Science, Biology, Neuroscience, Cognitive Psychology, and Economics. (shrink)

While discussing his notion of objective knowledge Popper introduces the idea of dispensability of knowing subjects, the autonomy of knowledge and the argumentative function of language. The main claim of our paper is that, on our view, objective knowledge produced by argumentative interaction is not achieved by dispensing knowing subjects but by differentiating between the play and the strategic levels of argumentation, where a distinction should be drawn between a particular concrete knowing subject engaged in that interaction, say Karl, and (...) an arbitrary one. Moreover, the theory of meaning deployed at the level of plays, the so-called local meaning, provides already some kind of objective knowledge, since it is player-independent and it does not reduce to the purely logical one of the strategy level. In fact, despite our criticism we think that Popper's discussion of the notion objective knowledge still deserves to be reflected on, particularly so in view of new results concerning the formalization of Brouwer’s Creating Subject and the dialogical interpretation of the notion of epistemic assumption. (shrink)

Nowadays, there is a quite considerable amount of literature on the use of analogy or more generally of inferences by parallel reasoning in contemporary legal reasoning, and particularly so within Common Law. These studies are often motivated by researches in artificial intelligence seeking to develop suitable software-support for legal reasoning. Recently; Rahman/Iqbal/Soufi (2020) developed a dialogical approach in the framework of Constructive Type Theory to what in Islamic Jurisprudence was called qiyās or correlational inferences. In their last chapter the authors (...) suggested that such an approach contributes to the study of patterns of reasoning by precedent cases within contemporary common Law. In the present paper we will further motivate the deployment within Civil and Common Law of the dialogical framework developed in Rahman/Iqbal/Soufi (2020). After a presentation of Scott Brewer's take on analogy within Common Law, that has striking structural similarities to reasoning by precedent case rooted in ratio legis (known in Islamic Jurisprudence as qiyās al-'illa or correlational inference by the occasioning factor), we will illustrate the implementation of the framework with a brief discussion of some cases of legal reasoning based in Spanish Civil Law but where the accent is put in the emerging ruling rather than in the existing of a case as in Common Law. Moreover; quite surprisingly, the case under study suggests that even cases of Law-interpretation fit the argumentation pattern of qiyās al-'illa. A caveat: in the present paper we will focus mainly in discussing the dynamics of the meaning constitution involved rather than in setting the rules of the underlying dialogical framework, the latter is the subject of a follow-up paper. (shrink)

The main aim of this paper is to study the notion of conditional right by means of constructive type theory (CTT) which provides the means to develop a system of contentual inferences rather than of syntactic derivations. Moreover, in line with Armgardt, we will first study the general notion of dependence as triggered by hypotheticals and then the logical structure of dependence specific to conditional right. I will develop this idea in a dialogical framework where the distinction between play-object and (...) strategy-object leads to the further distinction between two basic kinds of pieces of evidence and where meanings is constituted by the interaction of obligations and entitlements. The present paper is based on Rahman (2015). However, though the underlying CTT-analysis is the same, the dialogical reconstruction makes use of a new way of linking dialogical logic and CTT. Introduction. (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)

This volume reflects on the effects of recent discoveries in genetics on a broad range of scientific fields. In addition to neuroscience, evolutionary biology, anthropology and medicine, contributors analyze the effects of genetics on theories of health, law, epistemology and philosophy of biology. Social and moral concerns about the relationship between genetics, society and the individual also figure prominently. Genetic discoveries fuel central contemporary public policy debates concerning, for example, human cloning, equitable access to healthcare or the role of genetics (...) in medicine. Perhaps more fundamentally, advances in genetics are altering our perception of human life and death. An interview with François Jacob by Anne Fagot-Largeault opens the volume. In this interview, Jacob, who shared a Nobel Prize with André Lwoff and Jacques Monod for their discoveries concerning genetic control of enzyme and virus synthesis, addresses many of the central methodological epistemological and ethical questions covered in the volume. The dynamic interdisciplinary character of this volume makes it relevant to scholars from many disciplines, from biology, philosophy and the social sciences. (shrink)

Nowadays, there is a quite considerable amount of literature on the use of analogy or more generally of inferences by parallel reasoning in contemporary legal reasoning and particularly so within Common Law. These studies are often motivated by research in artificial intelligence seeking to develop suitable software-support for legal reasoning. Recently, Rahman et al. developed a dialogical approach in the framework of Constructive Type Theory to what in Islamic Jurisprudence was called qiyās or correlational inferences. In their last chapter the (...) authors suggested that such an approach contributes to the study of patterns of reasoning by precedent cases within contemporary Common Law. In the present paper we will further motivate the deployment of the dialogical framework developed in Rahman et al. within Civil and Common Law. After a presentation of Scott Brewer’s take on analogy within Common Law, that has striking structural similarities to reasoning by precedent case rooted in ratio legis, we will illustrate the implementation of the framework with a brief discussion of some cases of legal reasoning based on Spanish Civil Law but where the accent is put in the emerging ruling rather than in the existing of a case in Common Law. Moreover, quite surprisingly, the case under study suggests that even cases of Law interpretation fit the argumentation pattern of qiyās al-‘illa. A caveat: in the present paper we will focus mainly in discussing the dynamics of the meaning constitution involved rather than in setting the rules of the underlying dialogical framework, the latter is the subject of a follow-up paper. (shrink)