Applied Proof Theory Workshop
To mark the end of the ARC Project Meaning in Action, there will be a workshop on the project themes on 5-6 November 2020 (AEST). Due to the situation with COVID-19, all the talks will be held online. If you would like to participate, please contact Shawn Standefer for details.
Greg Restall (Melbourne)
Shawn Standefer (Melbourne)
Dave Ripley (Monash)
Rajeev Goré (ANU)
Teresa Kouri Kissel (Old Dominion)
Natalia Buacar (UBA, CONICET)
Rosalie Iemhoff (Utrecht)
Andrew Arana (Université Paris 1 Panthéon-Sorbonne)
Titles and abstracts will be added closer to the date of the workshop. All times are listed in Melbourne local time (AEST). Find your local time.
10:00—11:30: Teresa Kouri Kissel, “Proof-Theoretic Pluralism, Harmony and Identity”
12:30—14:00: Shawn Standefer
15:30—17:00: Rajeev Goré
18:00—19:30: Rosalie Iemhoff
10:00—11:30: Natalia Buacar
12:30—14:00: Greg Restall
15:30—17:00: Dave Ripley
18:00—19:30: Andrew Arana
Videos of talks will be available after the workshop on the Melbourne Logic Group Vimeo page.
Teresa Kouri Kissel “Proof-Theoretic Pluralism, Harmony and Identity”
Abstract: Ferrari and Orlandelli (2019) propose that an admissibility condition on a proof-theoretic logical pluralism be that the logics in question must be harmonious, in the sense of Dummett. This allows them to develop an innovative pluralism, which shows variance on two levels. On one level, we have a pluralism which makes sense of that proposed in Restall (2014): the connectives remain fixed across all admissible logics, since they share the same operational rules. But, thanks to their system, we can also admit some logics which do not share connective meanings, and hence have different operational rules. This allows for us to have a pluralism at two levels: the level of validity and the level of connective meanings.
This system is proposed as a refinement to that of Restall (2014) in response to objections proposed by Kouri (2016). In the spirit of the Kouri (2016) objections, I argue here that there are some logics we want to admit to our system which are not harmonious. I show how this leads to a possible three-level logical pluralism, where we have pluralism at the level of validity, connective meanings, and in what makes a logic admissible.