3rd PTS Seminar: Mariela Rubin (University of Buenos Aires), February 25, 5pm (UTC+0)

[PTS Network]

Dear all,

The third session of the Proof-Theoretic Semantics Seminar Series is coming up!

This is a series of periodic online talks delivered by early career researchers working in proof-theoretic semantics or akin fields, organised by the PTS-Network.

On February 25, 5pm (UTC+0): Mariela Rubin (University of Buenos Aires) will present her work with the title "A substructural route to Gibbard's collapse result".

Here is the abstract:
"In 1980, Gibbard proved that when one extends classical logic logic with a symbol meant to model the indicative conditional that validates the equivalence known as Import-Export, that is supraclassical, —that is, if φ classically implies ψ, then 'if φ then ψ' is a theorem of the extended logic— and if one assumes that the indicative conditional is at least as strong as the material conditional, then both collapse into the material. Later on, Fitelson showed that it is not necessary to assume classical logic, rather intuitionistic logic suffices for the collapse to happen. These results are usually stated in terms of a dilemma: either one accepts that the indicative conditional is something in between the intuitionistic and the material conditional or one endorses a semantics for indicative conditionals that invalidates Import-Export or Supraclassicality.

In this work, I will show that the collapse can happen in even weaker logics, in particular in many non-contractive and non-monotonic logics. I will also show that it is not necessary to assume anything about the rest of the language (in particular about conjunctions), yet there are some structural assumptions needed to derive the collapse. As a consequence of this result, several non-monotonic conditionals will also collapse to the indicative. I will show it three times. First without assuming anything about the non-conditional fragment of the language. Then I will prove it twice with two different sets of more conservative assumptions.

Following Belnap's famous arguments about tonk (1962), I will reflect on how the consequence relation influences the meaning of the connectives one is defining and I will argue that if one thinks the meaning of a conditional in terms of the rules it validates, then some of these conditionals are good candidates to model indicatives."

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

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