Arguably Argumentative: A Formal Approach to the Argumentative Theory of Reason

Abstract

We propose a formal approach to the argumentative theory of reason, combining argumentation theory and modal logic in a novel way. We show that the resulting framework can be used to model important mechanisms identified by the theory, including how confirmation bias and other problematic modes of reasoning may in fact serve an important argumentative purpose that can give rise to classically sound conclusions through the process of social deliberation. We go on to suggest that the argumentative theory is based on an understanding of intelligent reasoning and rationality that sees these notions as irreducibly social, and that the argumentative theory itself provides a possible starting point in the search for new theoretical foundations based on this understanding. Moreover, we suggest that formal logic can aid in the investigation of foundational issues, and we sketch the development of an axiomatic approach to the study of rational deliberation.

Dynamic epistemic logics for abstract argumentation

“…Another option is not to assume (c), the existence of an objective attack relation R between members of A. Proposals like Dyrkolbotn and Pedersen (2016), Baumeister et al (2018b) avoid (c). This goes in hand with the very minimal assumption that agents only share a "pool" of arguments A, but no constraint on how these arguments interact with each other.…”

“…We do not integrate constraint (h) as it discards the natural intuition that different agents are aware of different sets of arguments. 42 Under this assumption the agents' view can only differ with respect to the attack relations, as in Dyrkolbotn andPedersen (2016), Cayrol et al (2007). Again, this condition isolates a specific subclass of our MAFs, those for which, A i = A, which can be captured axiomatically by imposing all awareness atoms as axioms.…”

“…Yet I may not be able to see the attack from the second argument to the first.45 Given two potentially conflicting arguments a and b, it may be the case that two individuals disagree on their relative weights and therefore on whether a attacks b or vice versa. SeeDyrkolbotn and Pedersen (2016) for examples and discussion. A milder assumption is that awareness of attacks is shared, i.e.…”