In the 1970s, Paul Lorenzen and Kuno Lorenz developed "dialogical logic" based on philosophical, historical, and game-theoretical considerations. It is a dynamic and pragmatist framework that takes the form of dialogues while being set in dialogical foundations. Since then, logicians have developed this framework in various directions, resulting in distinct traditions of dialogical logic. McConaughey's course will deal with the dialogical framework in the Lorenzen and Lorenz tradition.
In a first part, this course will give an overview of the grounding principles of the dialogical framework, introduce key notions, such as the distinction between a logical framework (standard, natural deduction, dialogical, etc.) and a logic (classical, intuitionistic, modal, etc.), and give a didactic tutorial of its formal aspects. Special attention will be given to the integration of various logics within this framework, resulting in the dialogical pluralism developed by Shahid Rahman and his collaborators in Lille (France). A second part of the course will look at the historical roots of the dialogical approach to logic by focusing on the logical texts of the Greek father of logic, Aristotle, and by sketching out a dialogical interpretation of his logic broadly construed, encompassing syllogistic (his logic proper), dialectic, and the theory of scientific inquiry. Finally, a third part of the course will go back to the modern dialogical framework in order to show how it can be used to reconstruct Aristotle’s assertoric syllogistic on dialogical grounds. This will require more expressive power from the dialogical framework, which is found by introducing language from Per Martin-Löf’s "constructive type theory" and thus using the dialogical variant "immanent reasoning" (Rahman, McConaughey, Klev, Clerbout).
Through its three parts, this course will deal with formal logic and philosophy of logic with a didactic presentation of the dialogical framework, how it deals with meaning and rules, how it distinguishes the definition of propositions and of proofs, and how it allows for pluralism by integrating various logics (intuitionistic, classical, propositional or first-order, modal, syllogistic). What is more, by giving an overview of Aristotle’s logic and how we arrived with the form of the Organon we now have, historical grounds will be provided for the dialogical approach to modern logic.
Topics related to this course can be found here and here. Here are the slides.