The Dialogical Roots of Equality: Dialogues for Immanent Reasoning

  • Shahid Rahman
  • Zoe McConaughey
  • Ansten Klev
  • Nicolas Clerbout
Part of the Logic, Argumentation & Reasoning book series (LARI, volume 18)


In this chapter we will spell out all the relevant rules of dialogues for immanent reasoning, that is, the dialogical framework incorporating features of Constructive Type Theory—a dialogical framework making the players’ reasons for asserting a proposition explicit. The rules can be divided, just as in the standard framework, into rules determining local meaning and rules determining global meaning. These include:
  1. 1.
    Concerning local meaning (Sect. 7.1):
    1. (a)

      formation rules (p. 105);

    2. (b)

      rules for the synthesis of local reasons (p. 108); and

    3. (c)

      rules for the analysis of local reasons (p. 109).

  2. 2.
    Concerning global meaning, we have the following (structural) rules (Sect. 7.2):
    1. (a)

      rules for the resolution of instructions (p. 112);

    2. (b)

      rules for the substitution of instructions (p. 113);

    3. (c)

      equality rules determined by the application of the Socratic rules (p. 113); and

    4. (d)

      rules for the transmission of equality (p. 115).



  1. Cardascia, P. (2016). Dialogique des matrices. Revista de Humanidades de Valparaíso, 6.Google Scholar
  2. Clerbout, N. (2014a). First-order dialogical games and tableaux. Journal of Philosophical Logic, 43(4), 785–801.CrossRefGoogle Scholar
  3. Clerbout, N. (2014b). Étude sur quelques sémantiques dialogiques: Concepts fondamentaux et éléments de métathéorie. London: College Publications.Google Scholar
  4. Clerbout, N. (2014c). Finiteness of plays and the dialogical problem of decidability. IfCoLog Journal of Logics and their Applications, 1(1), 115–140.Google Scholar
  5. Clerbout, N., & Rahman, S. (2015). Linking game-theoretical approaches with constructive Type theory: Dialogical strategies as CTT-demonstrations. Dordrecht, The Netherlands: Springer.CrossRefGoogle Scholar
  6. Felscher, W. (1985). Dialogues as a foundation for intuitionistic logic. In D. Gabbay & F. Guenthner (Eds.), Handbook of philosophical logic, 3 (pp. 341–372). Dordrecht, The Netherlands: Kluwer.Google Scholar
  7. Keiff, L. (2007). Le Pluralisme dialogique: Approches dynamiques de l’argumentation formelle. PhD thesis, Lille.Google Scholar
  8. Martin-Löf, P. (1984). Intuitionistic type theory. Notes by Giovanni Sambin of a Series of Lectures given in Padua, June 1980. Naples, Italy: Bibliopolis.Google Scholar
  9. Rahman, S., & Tulenheimo, T. (2009). From games to dialogues and back: Towards a general frame for validity. In O. Majer, A. Pietarinen, & T. Tulenheimo (Eds.), Games: Unifying logic, language and philosophy (pp. 153–208). Dordrecht, The Netherlands: Springer.CrossRefGoogle Scholar
  10. Rahman, S., Clerbout, N., & Keiff, L. (2009). On dialogues and natural deduction. In G. Primiero & S. Rahman (Eds.), Acts of knowledge: History, philosophy and logic: Essays dedicated to Göran Sundholm (pp. 301–336). London: College Publications.Google Scholar
  11. Ranta, A. (1994). Type-theoretical grammar. Oxford, UK: Clarendon Press.Google Scholar
  12. Sundholm, G. (1986). Proof Theory and Meaning. In In D. Gabbay & F. Guenthner (Eds.), Handbook of philosophical logic, 3 (pp. 471–506). Dordrecht, The Netherlands: Kluwer.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Shahid Rahman
    • 1
  • Zoe McConaughey
    • 2
    • 3
  • Ansten Klev
    • 4
  • Nicolas Clerbout
    • 5
  1. 1.Département de philosophie CNRS, UMR 8163 - STL - Savoirs Textes LangageUniv. LilleLilleFrance
  2. 2.Univ. Lille, CNRS, UMR 8163 - STL - Savoirs Textes LangageLilleFrance
  3. 3.Département de philosophie & Centre Interuniversitaire de Recherche en Science et TechnologieUniversité du Québec à MontréalMontréalCanada
  4. 4.Institute of PhilosophyCzech Academy of SciencesPragueCzechia
  5. 5.Universidad de ValparaísoValparaísoChile

Personalised recommendations