Why Play Logical Games?

Game semantics has almost achieved the status of a paradigm in computer science but philosophers are slow to take notice. One reason for this might be the lack of a convincing philosophical account of logical games, what it means to play them, for the proponent to win, etc., pointedly raised by Wilfrid Hodges as the ‘Dawkins question’. In this paper, I critically examine two available answers: after a brief discussion of an argument by Tennant against Hintikka games, I focus on Lorenzen's attempt at providing a direct foundation for his game rules in the life-world, showing some of the difficulties inherent to that project. I then propose an alternative based on the theory of assertions developed by Dummett and Brandom.

[1]  Giorgi Japaridze,et al.  Introduction to computability logic , 2003, Ann. Pure Appl. Log..

[2]  Arnim von Stechow,et al.  Semantics From Different Points of View , 1979 .

[3]  Nicholas Rescher,et al.  The heritage of logical positivism , 1985 .

[4]  J. Brown,et al.  Constructivism and science : essays in recent German philosophy , 1989 .

[5]  Giorgi Japaridze.  A Constructive Game Semantics for the Language of Linear Logic , 1997, Ann. Pure Appl. Log..

[6]  Herman Parret,et al.  Meaning and understanding , 1981 .

[7]  R. Brandom,et al.  Between Saying and Doing: Towards an Analytic Pragmatism , 2008 .

[8]  Ahti-Veikko Pietarinen,et al.  Signs of Logic: Peircean Themes on the Philosophy of Language, Games, and Communication , 2006 .

[9]  S. Shelah,et al.  Annals of Pure and Applied Logic , 1991 .

[10]  Samson Abramsky,et al.  Socially Responsive‚ Environmentally Friendly Logic , 2006 .

[11]  G. Mints,et al.  Games, logic, and constructive sets , 2003 .

[12]  Jaakko Hintikka,et al.  Game-Theoretical Semantics , 1997, Handbook of Logic and Language.

[13]  C. Gethmann.  Lebenswelt und Wissenschaft : Studien zum Verhältnis von Phänomenologie und Wissenschaftstheorie , 1991 .

[14]  J.F.A.K. van Benthem,et al.  The Epistemic Logic of IF Games , 2003 .

[15]  Kuno Lorenz,et al.  basic objectives of dialogue logic in historical perspective , 2001, Synthese.

[16]  Robert Brandom,et al.  Between Saying and Doing: Towards an Analytic Pragmatism , 2008 .

[17]  Karl Bühler,et al.  Theory of Language: The Representational Function of Language , 2011 .

[18]  P. Lorenzen.  Die Dialogische Begründung Von Logikkalkülen , 1982 .

[19]  P. Lorenzen,et al.  Aufbau der exakten Fundamentalwissenschaft , 1964 .

[20]  Friedrich Kambartel.  Constructive Pragmatics and Semantics , 1979 .

[21]  Wilfrid Hodges,et al.  Compositional Semantics for a Language of Imperfect Information , 1997, Log. J. IGPL.

[22]  Alasdair Urquhart.  Truth and games: Essays in honour of Gabriel Sandu. edited by Tuomo Aho and Ahti-Veikko Pietarinen, Acta Philosophica Fennica, vol. 78. Societas Philosophica Fennica, Helsinki, 2006, vi + 322 pp. , 2008, Bulletin of Symbolic Logic.

[23]  Paul Lorenzen,et al.  Normative logic and ethics , 1984 .

[24]  J. Hintikka,et al.  Game-Theoretical Semantics , 1997 .

[25]  Radha Jagadeesan,et al.  Games and Full Completeness for Multiplicative Linear Logic , 1994, J. Symb. Log..

[26]  Suomen Filosofinen Yhdistys,et al.  Obligationes 14th Century Logic of Disputational Duties , 1994 .

[27]  Helge Rückert,et al.  Why dialogical logic , 2001 .

[28]  Walter Felscher,et al.  Dialogues, strategies, and intuitionistic provability , 1985 .

[29]  J. Dewey.  Studies In Logical Theory , 1904 .

[30]  J. Hintikka.  The Principles of Mathematics Revisited: Introduction , 1996 .

[31]  W. Alston.  Philosophy of Language , 1964 .

[32]  Andrew M. Pitts,et al.  Semantics and Logics of Computation: List of Contributors , 1997 .

[33]  Ulrich Berger,et al.  Computational Logic , 2001, NATO ASI Series.

[34]  Protophysics of Time , 1989 .

[35]  Catarina Dutilh Novaes.  Formalizing Medieval Logical Theories, Suppositio, Consequentiae and Obligationes , 2007, Logic, Epistemology, and the Unity of Science.

[36]  John Stuart Mill,et al.  On Liberty and Other Essays , 1859 .

[37]  The Pragmatic Understanding of Language and the Argumentative Function of Logic , 1989 .

[38]  C.-H. Luke Ong,et al.  On Full Abstraction for PCF: I, II, and III , 2000, Inf. Comput..

[39]  H. Wansing.  Essays on Non-Classical Logic , 2001 .

[40]  H. Edmund.  The crisis of the European sciences and the transcendental phenomenology , 1988 .

[41]  J. Hintikka.  Logic, language-games and information : Kantian themes in the philosophy of logic , 1973 .

[42]  Jaakko Hintikka,et al.  Logic, Language-Games And Information , 1972 .

[43]  Á. Szábó.  The Beginnings of Greek Mathematics , 1978 .

[44]  Martin Hyland.  Semantics and Logics of Computation: Game Semantics , 1997 .

[45]  Jean-Yves Girard,et al.  Locus Solum: From the rules of logic to the logic of rules , 2001, Mathematical Structures in Computer Science.

[46]  Jaakko Hintikka,et al.  Paradigms For Language Theory And Other Essays , 1997 .

[47]  D. Prawitz.  Meaning and proofs: on the conflict between classical and intuitionistic logic , 2008 .

[48]  Dov M. Gabbay,et al.  Handbook of Philosophical Logic , 2002 .

[49]  Peter Schroeder-Heister,et al.  Lorenzen’s operative justification of intuitionistic logic , 2008 .

[50]  I. Levi,et al.  Making It Explicit , 1994 .

[51]  A. Pietarinen,et al.  On Peirce's late proof of pragmaticism , 2006 .

[52]  Daniel Vanderveken.  Logic, Thought and Action , 2005, Logic, Epistemology, and the Unity of Science.

[53]  M. Nivat.  Fiftieth volume of theoretical computer science , 1988 .

[54]  Towards an Analytic Pragmatism , 2008 .

[55]  J. van Leeuwen,et al.  Theoretical Computer Science , 2003, Lecture Notes in Computer Science.

[56]  F. Kambartel,et al.  Constructing a pragmatic foundation for semantics , 1981 .

[57]  S. Abramsky.  Semantics of Interaction: an introduction to Game Semantics , 1997 .

[58]  Wilfrid Hodges.  I—Wilfrid Hodges: A Sceptical Look , 2001 .

[59]  Andreas Blass,et al.  A Game Semantics for Linear Logic , 1992, Ann. Pure Appl. Log..

[60]  Walter Felscher.  Dialogues as a Foundation for Intuitionistic Logic , 2002 .

[61]  Erik C. W. Krabbe,et al.  From axiom to dialogue , 1982 .

[62]  P. Lorenzen.  Einführung in die operative Logik und Mathematik , 1955 .

[63]  James Robert Brown,et al.  Constructivism and Science , 1989 .

[64]  S. Abramsky.  Game Semantics , 1999 .

[65]  Paul Lorenzen,et al.  Logical Propaedeutic: Pre-School of Reasonable Discourse , 1984 .

[66]  Shahid Rahman,et al.  On How to Be a Dialogician , 2005, Logic, Thought and Action.

[67]  R. Hilpinen.  On C. S. Peirce's Theory of the Proposition: Peirce as a Precursor of Game-Theoretical Semantics , 1982 .

[68]  J. Beall,et al.  Logical pluralism , 2000 .

[69]  Jean-Yves Girard,et al.  Linear Logic , 1987, Theor. Comput. Sci..

[70]  Mark van Atten,et al.  One Hundred Years of Intuitionism (1907-2007) , 2008 .

[71]  Johan van Benthem,et al.  Handbook of Logic and Language , 1996 .

[72]  R. Brandom,et al.  Articulating Reasons: An Introduction to Inferentialism , 2002 .

[73]  Jean-Yves Girard,et al.  On the meaning of logical rules I: syntax vs. semantics , 1998 .

[74]  Michael Dummett,et al.  The logical basis of metaphysics , 1991 .

[75]  Randall E. Auxier,et al.  The philosophy of Jaakko Hintikka , 2006 .

[76]  Wilfrid Hodges,et al.  Logic and Games , 2001 .

[77]  M. Dummett.  Frege: Philosophy of Language , 1973 .

[78]  P. Lorenzen.  Differential and integral;: A constructive introduction to classical analysis , 1971 .

[79]  Hans Albert,et al.  Treatise on Critical Reason , 1985 .

[80]  Jean-Yves Girard.  On the meaning of logical rules I : Syntax versus semantics , 1999 .

[81]  D. Prawitz.  Natural Deduction: A Proof-Theoretical Study , 1965 .

[82]  E. Krabbe.  Argumentation: Approaches to Theory Formation , 1982 .