Friday, May 5, 11:00—13:00 (Lisbon time)

Centre of Philosophy of the University of Lisbon

The University of Lisbon

Location: Matos Romão Room

Camillo Fiore

(The University of Buenos Aires)

Title:

Recapture Results Revindicated

Abstract:

A well-known objection to non-classical logics is that they are too weak; in particular, they cannot prove a number of important mathematical results. A promising strategy to answer the objection consists in proving so-called recapture results, which show that classical logic can be used in mathematics and other unproblematic contexts. However, the strategy has recently come under fire. First, typical recapture results are formulated in a purely logical language and do not generalize nicely to languages containing the kind of vocabulary that usually motivates non-classical theories. Second, proofs of recapture results typically employ classical principles that are not valid in the targeted non-classical system; hence, non-classical theorists do not seem entitled to those results. In this talk, I analyze these problems and provide solutions on behalf of the non-classical camp. As for the first problem, I provide a novel recapture result, which generalizes nicely to non-logical languages. As for the second problem, I argue that it relies on an ambiguity and that, once the ambiguity is removed, the objection is dissolved.

(This is joint work with Lucas Rosenblatt.)