Universidad de Sevilla (both authors)
Freedom, Commitment, and Abductive Hypotheses in Dialogical Logic
Following the well-known scheme of Peirce (CP 5.189), abduction may be conceived as an inference by means of which hypotheses are introduced. How can we constrain the use of hypotheses in argumentative interaction? As stressed by Krabbe (2001), the introduction and possible retraction of hypotheses in the context of argumentative interactions seemingly display some kind of freedom regarding the commitments endorses by the agents. Here, we propose to study possible responses to this problem in the context of dialogical logic, by taking into account already existent devices that have been designed to handle the use of hypotheses. We begin with a succinct presentation of (the fundamental notions of) dialogical logic. Then, we extend the framework to abductive reasoning, and the related difficulties. Finally, we discuss some possible ways to constrain the use of hypotheses in a dialogical framework
In dialogical logic, the notion of proof is approached through a game of argumentation between the Proponent of a thesis and the Opponent who criticizes that thesis. Semantics is defined at the level of interaction. Validity is determined by the existence of winning strategies: The thesis is valid if there is a winning strategy for the Proponent; that is, he can defend the thesis no matter how the Opponent plays. Our proposal deals with the exciting challenge of thinking about a dialogical framework for abduction. When is a player allowed to introduce a hypothesis? Which kind of hypothesis can be introduced? What is the commitment borne by the hypothetical moves performed by a player?
One of the most important rules is the formal rule which introduces asymmetry by preventing the Proponent from introducing atomic formulas. This means that in order to defend his thesis, the Proponent needs to rely on the concessions made by the Opponent when he challenges the Proponent’s thesis. In other words, the Opponent endorses a commitment for the concessions which can be used without further justification by the Proponent. Now, abductive dialogues are ampliative; i.e. the Proponent must be allowed to introduce new hypothetical information in the course of the dialogue, even in the absence of related Opponent’s concessions. This led Barés and Fontaine (2017) to characterize abductive problems in terms of “concession-problem”, and more generally abductive dialogues in terms of “unconceded-preserving” dialogues. This terminology obviously echoes the model proposed by Gabbay and Woods (2005), according to which abduction is an ignorance-preserving inference triggered in response to an ignorance-problem. In view of distinguishing assertions of standard deductive dialogues from hypotheses of abductive dialogues, new rules can be introduced, by means of which another notion commitment is characterized. The result is another conception of the notion of commitment in dialogues which serves as a basis to characterize the use of conjectures in argumentation.
References
Barés Gómez, C. & Fontaine, M. (2017). Argumentation and Abduction in Dialogical Logic. In L. Magnani & T. Bertolotti (eds) Springer Handbook of Model-Based Science (295-314). Cham: Springer.
Gabbay, D. & Woods, J. (2005). The Reach of Abduction. Insight and Trials. Amsterdam: Elsevier.
Krabbe, E. (2001). The Problem of Retraction in Critical Discussion. Synthese 127: 141-59.
Peirce, C. S. (1931-1958). Collected Papers of Charles Sanders Peirce. Cambridge: Harvard University Press.