CANCELED Julien Murzi: Naive Logical Properties and Higher-Order Reasoning

Lecture by Julien Murzi (University of Kent; Munich Center for Mathematical Philosophy), organized by Grolog

Abstract

Elia Zardini (2013) and Hartry Field (2014) have recently argued that a key semantic ingredient of the v-Curry Paradox, a validity-involving version of Curry's Paradox, is in tension with Goedel's Second Incompleteness Theorem. Moreover, Zardini points to some paradoxes of consistency and incompatibility which, in his view, 'cannot be adequately solved by simply changing the logic' of one's theory, but rather call for a radical weakening of the logic of one's metatheory---in particular, of the metatheoretical counterpart of the rule of structural contraction (Zardini, 2014).

I show that Goedelian reservations, if sound, equally apply to the paradoxes of naive logical properties. But I also argue that they are not sound, and that, insofar as restrictions of structural contraction are to be motivated by the existence of unstable sentences, sentences whose truth is incompatible with that of some of their consequences (Zardini, 2011; Zardini2014), the paradoxes of naive logical properties may not be solved by weakening such a rule.

When & where?

Thu November 20, 2014
Faculty of Philosophy, room TBA