AS&P - “Abstraction, Structures and Proofs” - W. Stafford, 28 April

[antpic...@gmail.com]

Dear all,

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

Will Stafford (Kansas State University), Reducing an Assumption; Proof-Theoretic Semantics and the Justification of Logic    

According to Dummett, proof-theoretic semantics is intended to demonstrate that logic is self-justifying. The naive approach to proof-theoretic semantics takes any collection of rules of inference to determine the meaning of a word.  While this offers a prima facie attractive justification of logic, it leads to inconsistency.  Dummett and Prawitz's alternative is proof-theoretic validity which requires rules of inference to be reducible to the rules that introduce terms. This paper considers three explanations offered by Dummett and Prawitz of why reduction to introduction rules justifies rules of inference.  In each case the role of reduction in the justification of rules of inference is inadequate.  Taking the insights of the earlier three approaches and insights from inferentialist semantics for type theory, we propose a modified proof-theoretic validity in which reductions form part of the meanings of the logical connectives. 

The talk is scheduled for 28 April at 18:00 Italy time at the following link: https://univienna.zoom.us/j/69599614901?pwd=NNmp1p3JqdIdUmdyoNy4ZfFd7AayoG.1 (Meeting ID: 695 9961 4901. Code:  985525).

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