Immanent Reasoning or Equality in Action: A Plaidoyer for the Play Level

Description

This monograph proposes a new way of implementing interaction in logic. It also provides an elementary introduction to Constructive Type Theory (CTT). The authors equally emphasize basic ideas and finer technical details. In addition, many worked out exercises and examples will help readers to better understand the concepts under discussion. One of the chief ideas animating this study is that the dialogical understanding of definitional equality and its execution provide both a simple and a direct way of implementing the CTT approach within a game-theoretical conception of meaning. In addition, the importance of the play level over the strategy level is stressed, binding together the matter of execution with that of equality and the finitary perspective on games constituting meaning. According to this perspective the emergence of concepts are not only games of giving and asking for reasons (games involving Why-questions), they are also games that include moves establishing how it is that the reasons brought forward accomplish their explicative task. Thus, immanent reasoning games are dialogical games of Why and How. Front Matter ....Pages i-xx Introduction: Some Brief Historical and Philosophical Remarks (Shahid Rahman, Zoe McConaughey, Ansten Klev, Nicolas Clerbout)....Pages 1-15 A Brief Introduction to Constructive Type Theory (Shahid Rahman, Zoe McConaughey, Ansten Klev, Nicolas Clerbout)....Pages 17-55 Basic Notions for Dialogical Logic (Shahid Rahman, Zoe McConaughey, Ansten Klev, Nicolas Clerbout)....Pages 57-74 Advanced Dialogues: Play Level (Shahid Rahman, Zoe McConaughey, Ansten Klev, Nicolas Clerbout)....Pages 75-87 Advanced Dialogues: Strategy Level (Shahid Rahman, Zoe McConaughey, Ansten Klev, Nicolas Clerbout)....Pages 89-109 Local Reasons and Dialogues for Immanent Reasoning (Shahid Rahman, Zoe McConaughey, Ansten Klev, Nicolas Clerbout)....Pages 111-129 The Dialogical Roots of Equality: Dialogues for Immanent Reasoning (Shahid Rahman, Zoe McConaughey, Ansten Klev, Nicolas Clerbout)....Pages 131-184 The Remarkable Case of the Axiom of Choice (Shahid Rahman, Zoe McConaughey, Ansten Klev, Nicolas Clerbout)....Pages 185-196 From Dialogical Strategies to CTT-Demonstrations and Back (Shahid Rahman, Zoe McConaughey, Ansten Klev, Nicolas Clerbout)....Pages 197-229 Material Dialogues (Shahid Rahman, Zoe McConaughey, Ansten Klev, Nicolas Clerbout)....Pages 231-275 Concluding Remarks: A Plaidoyer for the Play Level (Shahid Rahman, Zoe McConaughey, Ansten Klev, Nicolas Clerbout)....Pages 277-307 Back Matter ....Pages 309-332