3:00 hs to 4:15 hs – Andreas Fjellstad, “Metainferential troubles for the validity predicate”
Abstract: With the help of a metasequent calculus, this talk explores the possibility and relevance of distinguishing between understanding the validity schema as metainference and as metametainference for obtaining a faithful validity-predicate for classical logic. We will (1) reconstruct Hlobil’s admissibility Curry and Hlobil’s positive proposal involving a distinction between derivable and admissible rules in the metasequent calculus, (2) make some observations with regard to Hlobil’s proposal and the validity schema, and (3) use the observations to develop a new proposal for when a validity predicate is faithful with regard to the logic’s metainferences which in the case of classical logic requires that the validity schema is understood as a metametainference.
4:15 to 4:30 hs – Coffee break
4:30 hs to 5:45 hs – Bruno Da Re, Federico Pailos, Damián Szmuc and Paula Teijeiro, “Some considerations about duality and metainferences”
Abstract: It is well known that at the level of inferences, LP and K3 are dual, and ST and TS are self-dual. But what about metainferences? Is there any sense in which ST and TS are dual at this level? In this talk, we try to answer these questions, in order to take a step forward in a broader explanation of the notion of duality between logics at the level of metainferences.
5:45 to 6:00 hs – Coffee break
6:00 to 7:15 – Ulf Hlobil, “Towards a Self-Sufficient Logic for Inferentialists”
Abstract: For semantic inferentialists, the basic semantic concept is consequence or validity (understood as wider than merely logical validity). An inferentialist theory of meaning should be able to given an account of that concept, as it is used in formulating the inferentialist theory. I sketch an inferentialist theory of meaning that does that. The logic of that theory is non-monotonic, non-transitive and doesn’t obey substitution. I offer some philosophical elucidations of the notion of validity in terms of reasoning under suppositions. I close by considering two objections: The first objection is that my theory only weakly represents validity, while it should strongly represent validity. The second objection is that so-called Validity Detachment fails in my theory and that this is a problem.