Skip to main content

From Games to Dialogues and Back

Towards a General Frame for Validity

  • Chapter

Part of the book series: Logic, Epistemology, and the Unity of Science ((LEUS,volume 15))

Abstract

In this article two game-theoretically flavored approaches to logic are systematically compared: dialogical logic founded by Paul Lorenzen and Kuno Lorenz, and the game-theoretical semantics of Jaakko Hintikka. For classical proposi-tional logic and for classical first-order logic, an exact connection between ‘in-tuitionistic dialogues with hypotheses’ and semantic games is established. Various questions of a philosophical nature are also shown to arise as a result of the comparison, among them the relation between the model-theoretic and proof-theoretic approaches to the philosophy of logic and mathematics.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Blackburn, P., de Rijke, M., and Venema, Y. (2002). Modal Logic. Cambridge University Press, Cambridge.

    Google Scholar 

  • Blass, A. (1992). A game semantics for linear logic. Annals of Pure and Applied Logic, 56: 183–220.

    Article  Google Scholar 

  • Carlson, L. (1983). Dialogue Games. An Approach to Discourse Analysis. Reidel, Dordrecht.

    Google Scholar 

  • Dascal, M., Hintikka, J., and Lorenz, K. (1995). Jeux dans le langage/Games in Language/Spiel in der Sprache. In Dascal, M., Gerhardus, D., Lorenz, K., and Meggle, G., editors, Sprach-philosophie/Philosophy of Language/La Philosophie du langage, pages 1371–1390. De Gruyter, Berlin.

    Google Scholar 

  • Felscher, W. (1985). Dialogues, strategies and intuitionistic provability. Annals of Pure and Applied Logic, 28:217–254.

    Article  Google Scholar 

  • Haas, G. (1980). Hypothesendialoge, konstruktiver Sequenzenkalköl und die Rechtfertigung von Dialograhmenregeln. In Gethmann, C. F., editor, Theorie des wissenschaftlichen Argu-mentierens, pages 136–161. Suhrkamp, Frankfurt.

    Google Scholar 

  • Henkin, L. (1950). Completeness in the theory of types. Journal of Symbolic Logic, 15(2): 81–91.

    Article  Google Scholar 

  • Henkin, L. (1961). Some remarks on infinitely long formulas. In Infinitistic Methods, pages 167–183. Pergamon, Oxford.

    Google Scholar 

  • Hintikka, J. (1968). Language-games for quantifiers. Americal Philosophical Quarterly Monograph Series 2: Studies in Logical Theory. Basil Blackwell, Oxford.

    Google Scholar 

  • Hintikka, J. (1973). Logic, Language-Games and Information: Kantian Themes in the Philosophy of Logic. Clarendon, Oxford.

    Google Scholar 

  • Hintikka, J. (1987). Game-theoretical semantics as a synthesis of verificationist and truth-conditional meaning theories. In LePore, E., editor, New Directions in Semantics. Academic, London.

    Google Scholar 

  • Hintikka, J. (1993). The original Sinn of Wittgenstein's philosophy of mathematics. In Puhl, K., editor, Wittgenstein's Philosophy of Mathematics, pages 24–51. Hölder—Pichler—Tempsky, Vienna.

    Google Scholar 

  • Hintikka, J. (1996). The Principles of Mathematics Revisited. Cambridge University Press, Cambridge.

    Google Scholar 

  • Hintikka, J. (2002). Hyperclassical logic (a.k.a. IF logic) and its implications for logical theory. Bulletin of Symbolic Logic, 8(3):404–423.

    Article  Google Scholar 

  • Hintikka, J. and Rantala, V. (1976). A new approach to infinitary languages. Annals of Mathematical Logic, 10:95–115.

    Article  Google Scholar 

  • Hintikka, J. and Sandu, G. (1997). Game-theoretical semantics. In van Benthem, J. and ter Meulen, A., editors, Handbook of Logic and Language, pages 361–410. Elsevier, Amsterdam.

    Chapter  Google Scholar 

  • Hintikka, M. B. and Hintikka, J. (1986). Investigating Wittgenstein. Basil Blackwell, Oxford.

    Google Scholar 

  • Hodges, W. (1997). Model theory. In Rota, G.-C., editor, Encyclopedia of Mathematics and Its Applications, volume 42. Cambridge University Press, Cambridge. First published 1993.

    Google Scholar 

  • Hodges, W. (2006). Logic and games. In Zalta, E. N., editor, The Stanford Encyclopedia of Philosophy (Summer 2006 Edition). http://plato.stanford.edu/archives/sum2006/ entries/logic-games/.

    Google Scholar 

  • Hyttinen, T. (1990). Model theory for infinite quantifier logics. Fundamenta Mathematicæ, 134:125–142.

    Google Scholar 

  • Kamlah, W. and Lorenzen, P. (1973). Logische Propädeutik. Bibilographisches Institut, Mannheim.

    Google Scholar 

  • Karttunen, M. (1984). Model theory for infinitely deep languages. Annales Academiæ Scien-tiarum Fennicæ, 50.

    Google Scholar 

  • Kontchakov, R., Kurucz, A., and Zakharyaschev, M. (2005). Undecidability of first-order intu-itionistic and modal logics with two variables. Bulletin of Symbolic Logic, 11(3):428–438.

    Article  Google Scholar 

  • Krynicki, M. and Mostowski, M. (1995). Henkin quantifiers. In Krynicki, M., Mostowski, M., and Sczerba, L. W., editors, Quantifiers: Logics, Models and Computation, volume 1, pages 193–262. Kluwer, Dordrecht.

    Google Scholar 

  • Lorenz, K. (1961). Arithmetik und Logik als Spiele. Ph.D. thesis, Christian-Albrechts-Universität Zu Kiel.

    Google Scholar 

  • Lorenz, K. (1970). Elemente der Sprachkritik. Suhrkamp, Frankfurt.

    Google Scholar 

  • Lorenz, K. (2001). Basic objectives of dialogue logic in historical perspective. Synthese, 127:255–263.

    Article  Google Scholar 

  • Lorenzen, P. and Lorenz, K. (1978). Dialogische Logik. Wissenschaftliche Buchgesellschaft, Darmstadt.

    Google Scholar 

  • Lorenzen, P. and Schwemmer, O. (1975). Konstruktive Logik, Ethik und Wissenschaftstheorie. Bibilographisches Institut, Mannheim.

    Google Scholar 

  • Makkai, M. (1977). Admissible sets and infinitary logic. In Barwise, J., editor, Handbook of Mathematical Logic, pages 233–281. North-Holland, Amsterdam.

    Chapter  Google Scholar 

  • Osborne, M. J. and Rubinstein, A. (1994). A Course in Game Theory. MIT, Cambridge, MA.

    Google Scholar 

  • Rahman, S. (1994). Über Dialoge, Protologische Kategorien und andere Seltenheiten. Peter Lang, Frankfurt.

    Google Scholar 

  • Rahman, S. and Keiff, L. (2005). On how to be a dialogician. In Vanderveken, D., editor, Logic, Thought and Action, volume 2: Logic, Epistemology and Unity of Science, pages 359–408. Springer, Dordrecht.

    Chapter  Google Scholar 

  • Ranta, A. (1988). Propositions as games as types. Synthese, 76:377–395.

    Article  Google Scholar 

  • Saarinen, E. (1978). Dialogue semantics versus game-theoretical semantics. In Proceedings of the Biennial Meeting of the Philosophy of Science Association (PSA), volume 2: Symposia and Invited Papers, pages 41–59. The University of Chicago Press, Chicago, IL.

    Google Scholar 

  • Sandu, G. and Pietarinen, A.-V. (2001). Partiality and games: Propositional logic. Logic Journal of the IGPL, 9(1):107–127.

    Article  Google Scholar 

  • Sandu, G. and Pietarinen, A.-V. (2003). Informationally independent connectives. In Mints, G. and Muskens, R., editors, Games, Logic, and Constructive Sets, pages 23–41. CSLI, Stanford.

    Google Scholar 

  • Schwalbe, U. and Walker, P. (2001). Zermelo and the early history of game theory. Games and Economic Behaviour, 34:123–137.

    Article  Google Scholar 

  • Skolem, Th. (1920). Logisch-kombinatorische Untersuchungen über die Erfüllbarkeit oder Be-weisbarkeit mathematischer Sätze nebst einem Theoreme über dichte Mengen. Skrifter utgit av Videnskabsselskapet i Kristiania, I. Matematisk-naturvidenskabelig klasse no. 4.

    Google Scholar 

  • Stegmüller, W. (1964). Remarks on the completeness of logical systems relative to the validity-concepts of P. Lorenzen and K. Lorenz. Notre Dame Journal of Formal Logic, 5:81–112.

    Article  Google Scholar 

  • Sundholm, G. (2002). Proof theory and meaning. In Gabbay, D. M. and Guenthner, F., editors, Handbook of Philosophical Logic, volume 9, pages 165–198. Kluwer, Dordrecht, second edition.

    Google Scholar 

  • Tarski, A. (1983). The concept of truth in the languages of the deductive sciences. In Corcoran, J., editor, A. Tarski: Logic, Semantics, Metamathematics. Papers from 1923 to 1938, pages 152–278. Hackett, Indianapolis, IN. Polish; original in Prace Towarzystwa Naukowego Warszawskiego, Wydzial III Nauk Matematyczno—Fizycznych 34, Warsawm, 1933.

    Google Scholar 

  • Tarski, A. and Vaught, R. L. (1956). Arithmetical extensions of relational systems. Compositio Mathematica, 13:81–102.

    Google Scholar 

  • van Benthem, J. (2001a). Games in dynamic epistemic logic. Bulletin of Economic Research, 53(4):219–248. Proceedings LOFT-4, Torino, Bonanno, G. and van der Hoek, W., editors.

    Article  Google Scholar 

  • van Benthem, J. (2001b). Logic and Games. Lecture Notes (Draft Version), ILLC, Amsterdam.

    Google Scholar 

  • van Benthem, J. (2002). Extensive games as process models. Journal of Logic, Language and Information, 11:289–313.

    Article  Google Scholar 

  • Vaught, R. L. (1973). Descriptive set theory in lε1ε. In Mathias, A. and Rogers, H., editors, Cambridge Summer School in Mathematical Logic, volume 337 of Lecture Notes in Mathematics, pages 574–598. Springer, Berlin.

    Chapter  Google Scholar 

  • von Neumann, J. and Morgenstern, O. (2004). Theory of Games and Economic Behavior. Princeton University Press, Princeton, NJ, sixtieth-anniversary edition. (First appeared in 1944.)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer Science + Business Media B.V.

About this chapter

Cite this chapter

Rahman, S., Tulenheimo, T. (2009). From Games to Dialogues and Back. In: Majer, O., Pietarinen, AV., Tulenheimo, T. (eds) Games: Unifying Logic, Language, and Philosophy. Logic, Epistemology, and the Unity of Science, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9374-6_8

Download citation

Publish with us

Policies and ethics