Dialogical logic is a game-theoretical approach to logic. Logic is studied with the help of certain games, which can be thought of as idealized argumentations. Two players, the Proponent, who puts forward the initial thesis and tries to defend it, and the Opponent, who tries to attack the Proponent’s thesis, alternately utter argumentative moves according to certain rules. For a long time the dialogical approach had been worked out only for classical and intuitionistic logic. The seven papers of this dissertation (...) show that this narrowness was uncalled for. The initial paper presents an overview and serves as an introduction to the other papers. Those papers are related by one central theme. As each of them presents dialogical formulations of a different non-classical logic, they show that dialogical logic constitutes a powerful and flexible general framework for the development and study of various logical formalisms and combinations thereof. As such it is especially attractive to logical pluralists that reject the idea of “the single correct logic”. The collection contains treatments of free logic, modal logic, relevance logic, connexive logic, linear logic, and multi-valued logic. (shrink)

There is an argument (first presented by Fitch), which tries to show by formal means that the anti-realistic thesis that every truth might possibly be known, is equivalent to the unacceptable thesis that every truth is actually known (at some time in the past, present or future). First, the argument is presented and some proposals for the solution of Fitch's Paradox are briefly discussed. Then, by using Wehmeier's modal logic with subjunctive marks (S5*), it is shown how the derivation can (...) be blocked if one respects adequately the distinction between the indicative and the subjunctive mood. Essentially, this proposal amounts to the one by Edgington which was formulated with the help of the actuality-operator. Finally it is shown how the criticisms by Williamson against Edgington can be answered by the formulation of a new conception of possible knowledge that \alpha (thereby \alpha being in the indicative mood and thus referring to the actual world). This conception is based on the concept of same de re knowledge in different possible worlds. (shrink)

We investigate and compare two major approaches to enhancing the expressive capacities of modal languages, namely the addition of subjunctive markers on the one hand, and the addition of scope-bearing actuality operators, on the other. It turns out that the subjunctive marker approach is not only every bit as versatile as the actuality operator approach, but that it in fact outperforms its rival in the context of cross-world predication.

Le but de cet article est de montrer comment les logiques dites multivalentes peuvent être formulées dans le cadre de la logique dialogique. Pour formuler les règles de particule pour ces logiques on introduit l’idée de différents modes d’assertion. En donnant ensuite les règles de particule et les règles structurelles appropriées, on peut reconstruire dialogiquement les systèmes standards de logiques multivalentes. Cela est fait explicitement pour la logique `a trois valeurs de Łukasiewicz (L3c). En remplaçant la règle structurelle classique par (...) sa contrepartie intuitionniste on obtient des versions intuitionnistes de systèmes multivalents (par exemple L3i). Les systèmes dialogiques multivalents L3c et L3i sont illustrés par quelques exemples et pour conclure on formule les tableaux stratégiques correspondants. (shrink)

Le but de cet article est de montrer comment les logiques dites multivalentes peuvent être formulées dans le cadre de la logique dialogique. Pour formuler les règles de particule pour ces logiques on introduit l’idée de différents modes d’assertion. En donnant ensuite les règles de particule et les règles structurelles appropriées, on peut reconstruire dialogiquement les systèmes standards de logiques multivalentes. Cela est fait explicitement pour la logique `a trois valeurs de Łukasiewicz (L3c). En remplaçant la règle structurelle classique par (...) sa contrepartie intuitionniste on obtient des versions intuitionnistes de systèmes multivalents (par exemple L3i). Les systèmes dialogiques multivalents L3c et L3i sont illustrés par quelques exemples et pour conclure on formule les tableaux stratégiques correspondants. (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)

Non-classical views about important issues in logic and its philosophy are a distinctive trait of Shahid Rahman's work. This volume has been designed, on the occasion of his 50th birthday, as a gathering place for unconventional approaches, original ideas and attempts to question well-established standards. Some of the world top philosophers and logicians contributed to a brilliant collection of papers, some of which doubtlessly leave their mark on the work to come in logic and in philosophy of formal sciences. Contributors (...) are: Philippe Balbiani, Diderik Batens, Johan van Benthem, Giacomo Bonanno, Walter A. Carnielli, Newton C. A. Da Costa, Michel Crubellier, Francisco A. Doria, Dov M. Gabbay, Olivier Gasquet, Gerhard Heinzmann, Andreas Herzig, Jaakko Hintikka, Justine Jacot, Reinhard Kahle, Erik C. W. Krabbe, Decio Krause, Franck Lihoreau, Kuno Lorenz, Ilkka Niiniluoto, Graham Priest, Stephen Read, Manuel Rebuschi, Greg Restall, Gabriel Sandu, Gerhard Schurz, Francois Schwarzentruber, Yaroslav Shramko, Goran Sundholm, John Symons, Christian Thiel, Nicolas Troquard, Tero Tulenheimo, Jean Paul Van Bendegem, Daniel Vanderveken, Yde Venema, Heinrich Wansing, Jan Wolenski and John Woods. (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)

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)

In this paper we provide an interpretation of Aristotle's rule for the universal quantifier in Topics Θ 157a34–37 and 160b1–6 in terms of Paul Lorenzen's dialogical logic. This is meant as a contribution to the rehabilitation of the role of dialectic within the Organon. After a review of earlier views of Aristotle on quantification, we argue that this rule is related to the dictum de omni in Prior Analytics A 24b28–29. This would be an indication of the dictum’s origin in (...) the context of dialectical games. One consequence of our approach is a novel explanation of the doctrine of the existential import of the quantifiers in dialectical terms. After a brief survey of Lorenzen's dialogical logic, we offer a set of rules for dialectical games based on previous work by Castelnérac and Marion, to which we add here the rule for the universal quantifier, as interpreted in terms of its counterpart in dialogical logic. We then give textual evidence of the use of that rule in Plato's dialogues, thus showing that Aris... (shrink)

This text provides a comprehensive analysis of historical archives, letters, and primary sources to offer unique insight into how Fröbel's pedagogy of kindergarten and play has been understood, interpreted, and modified throughout history and in particular, as a consequence of it's adoption in the US. Tracing the development, modification, and global spread of the kindergarten movement, this volume demonstrates the far-reaching impacts of Fröbel's work, and asks how far contemporary understandings of the kindergarten pedagogy reflect the educationalist's original intentions. Recognizing (...) that Fröbel's pedagogy has at times been simplified or misunderstood, the book tackles issues caused by translation, or transfer to non-German speaking countries such as the US, and so demonstrates how and why contemporary research and Froebelian practice is in the danger of diverging from the original ideas expressed in Fröbel's work. By returning to original documents produced by Fröbel, Wasmuth traces various interpretations, and explains how and why some of these understandings established themselves in the context of US Early Childhood Education, whilst others did not. This insightful text will be of great interest to graduate and postgraduate students, researchers, academics, professionals and policy makers in the fields of early childhood education, history of education, Philosophy of Education and Teacher Education. (shrink)

Kant is generally conceived to have offered little attention to the fact that we experience the world in and through our bodies. This book argues that this standard image of the great German philosopher is radically wrong. Not only does Kant - throughout his career and in works published before and after the Critique of pure reason - reflect constantly upon the fact that human life is embodied, but the Critique of pure reason itself may be read as a critical (...) reflection aimed at exploring some significant philosophical implications of this fact. Bringing this aspect of Kant's philosophy into focus is important, not only because it sheds new light on our understanding of Kant's work, but also because it is relevant to contemporary discussions in philosophy about embodiment, learning and practice. By taking his philosophy of embodiment into account, the author makes Kant stand out as a true contemporary in new and unexpected ways. (shrink)

Telegraphy, the distant ancestor of Internet and GSM (Global System for Mobile Communications), was invented by Samuel Morse in 1838. One year later, William Grove invented the fuel cell. Although numerous highly successful innovations stemming from telegraphy may be observed, the development of fuel cells has been insignificant, slow, and erratic and has not yet resulted in notable positive socioeconomic effects. By comparing the modern development of fuel cells and hydrogen technology, that is, a potential radical innovation in energy generation, (...) with some aspects related to the evolution of two highly successful radical innovations, Internet and GSM, the author focuses on the role of innovation regimes and policy in a sectorial system of innovations perspective. In the slow pace in fuel cells and hydrogen technology development, two factors seem to interact negatively: weak and fragmented innovation regimes in the energy sector and the current hegemony of market-oriented R&D policies. (shrink)

Poster presented at the conference "Toward a Science of Consciousness" , Tucson, Arizona, April 10-15, 2000.

This paper first advances and discusses the hypothesis that so-called “iconic” or (for the auditory sphere) “echoic” memory is actually a form of perception of the past. Such perception is made possible by parallel inputs with differential delays which feed independently into the sensorium. This hypothesis goes well together with a set of related psychological and phenomenological facts, as for example: Sperling’s results about the visual sensory buffer, the facts that we seem to see movement and hear temporal Gestalts, and (...) the fact that we sometimes seem to hear sounds only after they have stopped. In it most simple form, and formulated in the somewhat misleading information processing idiom, my hypothesis says that each one of a number of parallel input lines with different delays feeds into a spatially separate sensory unit. The set of such units then holds information about the immediate past in what one might call a “chronotopic” sensory map. This contrasts with the idea (common in sensory buffer theory) that the received sensory information is kept (while possibly decaying) in the same unit for some time after it occurred. The hypothesis also contradicts the theory that all sensory information passes through the same unit but is then successively passed through a unidirectional chain of separate units, where the past experiences then become represented (the shift register hypothesis). The main advantage of my theory, beside the natural explanations it offers for the above-mentioned kind of phenomena, is that it postulates a parallel – and therefore robust – rather than a serial mechanism for the registering of temporal information. It can of course easily be modified to fit more complex models of the sensory cerebral code(s) as well as of the chronotopic representation as such. -/- In the second part of my poster, I advance a corresponding hypothesis for those motor commands which control brief movements. At closer inspection, most socalled “ballistic” movements do not seem to be truly ballistic (in the sense in which the movement of a cannonball is so) since the brain must exert some kind of feedforward control over the later part of their trajectory. I suggest that this control is at least sometimes realized by means of differentially delayed output from a chronotopic representation of successive segments of the movement. Not only could this be a biologically natural way of ensuring efficient adaptability of the movement; the hypothesis also explains the not uncommon experience of “seeing the whole movement laid out in advance” when it is initiated. (shrink)

This volume offers a critical analysis and illustration of the challenges and promises of ‘stateless’ law thought, pedagogy and approaches to governance - that is, understanding and conceptualizing law in a post-national condition. Confronting the ‘transnational challenge’ posed to the traditional theoretical and institutional structures that underlie the teaching and study of law in the university, the book brings new insight to the ongoing and crucial conversation about the future shape of legal scholarship, education and practice that is emblematic of (...) the early twenty-first century. (shrink)