BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Cian Dorr (New York University) DTSTART:20230427T180000Z DTEND:20230427T190000Z DTSTAMP:20260423T021445Z UID:OLS/119 DESCRIPTION:Title: No n-Extensional Higher Order Logic with Substitution\nby Cian Dorr (New York University) as part of Online logic seminar\n\n\nAbstract\nThe most w idely studied systems of classical higher-order logic are ‘extensional ’ in the sense that they validate the schema ∀x₁…xₙ(Fx₁…xₙ ↔Gx₁…xₙ) → (F=G): intuitively\, this means that they coextensive properties or relations are identical. Although this seems philosophical ly suspect for obvious reasons\, the space of logics that keep the classic al laws for propositional connectives and quantifiers while dropping exten sionality has been surprisingly little explored. This talk will explore a natural way of weakening extensionality by replacing it with the rule ⊦ Fx₁…xₙ↔Gx₁…xₙ / ⊦F=G\, or equivalently\, a rule that allow s provably materially equivalent formulae to be intersubstituted anywhere. I will give several very different axiomatizations of this system\, ther eby cementing the case for its naturalness. After that I will discuss a r ange of possible extensions of the system\, some of which restore certain arguably attractive consequences of extensionality\, and others of which t ake the view in a more “fine-grained” direction by systematically addi ng claims of non-identity which the basic system leaves unsettled. Finall y\, I will describe a technique for constructing set-theoretic models of t he system\, which can be used to prove the consistency of many of the afor ementioned extensions. \n\nThe talk will be based on a forthcoming paper coauthored with Andrew Bacon\, available here: https://philarchive.org/rec /BACC-8.\n LOCATION:https://researchseminars.org/talk/OLS/119/ END:VEVENT END:VCALENDAR