Immanent Reasoning or Equality in Action [electronic resource] : A Plaidoyer for the Play Level /
Rahman, Shahid.author.
McConaughey, Zoe.author.
Klev, Ansten.author.
Clerbout, Nicolas.author.
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.
1. Introduction: Some Brief Historical and Philosophical Remarks -- 2. A Brief Introduction to Constructive Type Theory -- 3. Basic Notions for Dialogical Logic -- 4. Advanced Dialogues: Play Level -- 5. Advanced Dialogues: Strategy Level -- 6. Local Reasons and Dialogues for Immanent Reasoning -- 7. The Dialogical Roots of Equality: Dialogues for Immanent Reasoning -- 8. The Remarkable Case of the Axiom of Choice -- 9. From Dialogical Strategies To CTT-Demonstrations And Back -- 10. Material Dialogues -- 11. Concluding Remarks: A Plaidoyer for the Play Level.
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.
Logic.
Logic, Symbolic and mathematical.
Computer science.
Logic.
Mathematical Logic and Foundations.
Mathematical Logic and Formal Languages.