Local Reasons and Dialogues for Immanent Reasoning

Abstract

In this chapter we will provide the logical framework of dialogues for immanent reasoning, the dialogical framework incorporating features of Constructive Type Theory and making explicit the players’ reasons for asserting a proposition. We will therefore be using the material provided in Chaps. 2, 3, 4, and 5 on CTT and on the standard dialogical framework and assume the reader is familiar enough with it. The framework of dialogues for immanent reasoning takes a further step in the task of making explicit the dynamic foundations of reasoning, based on equality in action: reasons adducing statements are introduced in the object-language, and the Proponent’s task in formal dialogues is to force the Opponent to provide herself the reasons the Proponent needs in order to justify his thesis; once the Opponent has produced her reasons, the Proponent uses equality rules (the Socratic rule for instance) to copy these reasons and use them to his own ends. In this respect, CTT proof-objects are adapted to the dialogical framework, yielding two new elements in our framework: local reasons, the backbone of dialogues for immanent reasoning at the play level which will be introduced in this chapter and the next (Chaps. 6 and 7 ); and strategic reasons, justifications at the strategy level corresponding to proof-objects which will be the object of Chap. 9. Having local reasons in the dialogical framework provides a structure in which the reasons given and asked for actually appear in the object-language, and the Proponent can then (locally) justify his statements by explicitly copying the Opponent’s reasons for his own statements.