AS&P - “Abstraction, Structures and Proofs” - C. Franks, 30 June

[antpic...@gmail.com]

Dear all,

we remind you the fourth talk in our online seminar series titled “Abstraction, Structures and Proofs” (https://sites.google.com/view/wientuebingen/home-page). 

Curtis Franks (University of Notre Dame), Universal Constructions and Higher-order Collapse

The program of proof-theoretic semantics (PTS) seeks to characterize the meanings of logical operators in terms of characteristic rules of inference. We argue that the concept of a universal construction is the best way to formalize this method of specifying meaning. From this point of view, operators have a natural polarity: some familiar operators that Gentzen studied (⊃, ∧, ¬, and ∀) appear as right-universal constructions, while the others (∨, ∃) appear as left-universal constructions. The same idea can be used to specify the meanings of operators that Gentzen did not treat. The “multiplicative or” (unlike its “additive” counterpart) and the first-order identity predicate = both have right-universal constructions, while the unary predicate for being a natural number N has a left-universal construction. The roles of natural deduction’s introduction and elimination rules are sensitive to the operator’s polarity.

Most advocates of PTS have preferred a uniform, asymmetric theory of meaning, according to which it is either always an operator’s introduction rule or always an operator’s elimination rule that defines that operator. We will see that developing such an asymmetric account leads to cumbersome higher-order rules that seem to be more general than the lower-level rules arrived at on our symmetric account. But we will show that higher-order rules arrived at in this way uniformly collapse: They are interderivable with their lower-level counterparts. This observation underscores the idea that what really matter for PTS are the universal constructions of logical operators, not the particular forms of their presentation.

The talk is scheduled for 30 June at 18:00 Italy time (CEST) at the following link:  https://univienna.zoom.us/j/65905790676?pwd=LVTYTpl8SW37Thdyl2QR9MUBlfNAZJ.1 

ID riunione: 659 0579 0676

Codice d’accesso: 918117

This seminar is part of a series of events jointly organised by the University of Wien (Ludovica Conti, Georg Schiemer) and the University of Tübingen (Antonio Piccolomini d'Aragona). Further details can be found on the project website, accessible via this link: https://sites.google.com/view/wientuebingen/home-page ) 

Hope to see you online soon! 

Best regards,

Antonio and Ludovica