Next on PTS Seminar: Masanobu Toyooka, Dec 9, 11am (UTC+0) & Recording of last session online

[PTS Network]

Dear all,

Thank you for the great turnout at our last session of the PTS Seminar series, we really appreciate it! For those who couldn't attend: the recording of Ekaterina Piotrovskaya's presentation is now available online on our youtube channel: https://www.youtube.com/watch?v=HPaZFtBEYaM.

And the next session is also coming up soon!

On Tuesday, December 9, 11am (UTC+0), Masanobu Toyooka (Tohoku University) will present his work with the title "Categoricity and Expressibility of Classical Connectives".

Here is the abstract:

This talk explores the categoricity and the expressibility of classical connectives, inspired by the studies of Carnap, Gabbay, and Garson. In 1943, Carnap observed that the classical single-succedent consequence relation did not ``carve out'' the two-valued truth table of disjunction, implication, or negation. This phenomenon, which is currently called ``the categoricity problem'', may be regarded as problematic for a moderate inferentialist who advocates classical logic but refuses semantic holism. Gabbay (1978) generalized Carnap's study and dealt with an arbitrary n-place connective having the two-valued truth table. In the paper, the existence of a single-succedent consequence relation that carves out the truth table of a connective is investigated.

After the studies of Carnap and Gabbay, Garson (2001, 2010) investigated which semantic clause was carved out by the set of rules for a connective in the natural deduction system rather than by the classical single-succedent consequence relation. In order to interpret a rule, two different measures were considered: ``global measure'' and ``local measure''. Garson revealed that these two measures carved out different semantic clauses for a connective.

This talk deals with an arbitrary n-place connective having the two-valued truth table and observes the possibility of carving out the truth table, as Gabbay did. However, our approach diverges from Gabbay's one in the following two points: (i) we work not only on a consequence relation but also on a rule, as Garson did, both global and local measures being employed to interpret it; (ii) we do not limit our attention to single-succedent syntactic objects but introduce four different forms of syntactic objects. These treatments generate various benchmarks of the possibility of carving out the two-valued truth table for a connective. In the conclusion, it is revealed which connective has the two-valued truth table that can be carved out according to each benchmark.

We will send the Zoom link over this list on the day before the session.
Please make sure to convert the time correctly to your specific time zone!

All the best,

Sara Ayhan, Hermógenes Oliveira, Antonio Piccolomini d'Aragona & Will Stafford