Logic, language games and ludics

Wittgenstein’s language games can be put into a wider service by virtue of elements they share with some contemporary opinions concerning logic and the semantics of computation. I will give two examples: manifestations of language games and their possible variations in logical studies, and their role in some of the recent developments in computer science. It turns out that the current paradigm of computation that Girard termed Ludics bears a striking resemblance to members of language games. Moreover, the kind of interrelations that are emerging could be scrutinised from the viewpoint of logic that virtually necessitates game-theoretic conceptualisations, demonstrating the fact that the meaning of utterances may, in many situations, be understood as Wittgenstein’s language games of ‘showing or telling what one sees’. This provides motivation for the use of games in relation to logic and formal semantics that some commentators have called for. Many of the ideas can be traced to C.S. Peirce, for whom signs were vehicles of strategic communication. The conclusion about Wittgenstein is that the notions of saying and showing converge in his late philosophy.

[1]  John Dewey,et al.  Chance, love, and logic , 1923 .

[2]  D. Hilbert Über das Unendliche , 1926 .

[3]  C. Hartshorne,et al.  Collected Papers of Charles Sanders Peirce , 1935, Nature.

[4]  R. Goodstein,et al.  Remarks on the Foundations of Mathematics , 1957, The Mathematical Gazette.

[5]  G. Vlastos,et al.  Ludwig Wittgenstein: A Memoir , 1958 .

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

[7]  Andreas Blass,et al.  Degrees of indeterminacy of games , 1972 .

[8]  J. M. Smith,et al.  The Logic of Animal Conflict , 1973, Nature.

[9]  Ian Hacking,et al.  What is logic , 1979 .

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

[11]  Charles S. Peirce,et al.  The essential Peirce , 1992 .

[12]  D. Roberts The existential graphs , 1992 .

[13]  Andreas Blass Is Game Semantics Necessary? , 1993, CSL.

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

[15]  Karl Menger,et al.  Reminiscences of the Vienna Circle and the Mathematical Colloquium , 1994 .

[16]  Robert J. Leonard,et al.  From Parlor Games to Social Science: Von Neumann, Morgenstern, and the Creation of Game Theory, 1928-1994 , 1995 .

[17]  Jaakko Hintikka,et al.  Ludwig Wittgenstein: Half-Truths and One-and-a-Half-Truths , 1996 .

[18]  Andreas Blass,et al.  Some Semantical Aspects of Linear Logic , 1997, Log. J. IGPL.

[19]  J. Hintikka Game-Theoretical Semantics as a Synthesis of Verificationist and Truth-Conditional Meaning Theories , 1998 .

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

[21]  L. Wittgenstein Wittgenstein's Nachlass the Bergen Electronic Edition , 2000 .

[22]  Ahti-Veikko Pietarinen,et al.  Partiality and Games: Propositional Logic , 2001, Log. J. IGPL.

[23]  Jean-Yves Girard Locus Solum: From the Rules of Logic to the Logic of Rules , 2001, CSL.

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

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

[26]  Five Topics in Conversations with Wittgenstein (Numbers; Concept-Formation; Time-Reactions; Induction; Causality) , 2002 .

[27]  A. Pietarinen Peirce's game-theoretic ideas in logic , 2003 .

[28]  A. Pietarinen Games as formal tools versus games as explanations in logic and science , 2003 .

[29]  Ahti-Veikko Pietarinen,et al.  Semantic Games In Logic and Epistemology , 2004, Logic, Epistemology, and the Unity of Science.