Validity and Truth-Preservation

Chapter
Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 36)

Abstract

The revisionary approach to semantic paradox is commonly thought to have a somewhat uncomfortable corollary, viz. that, on pain of triviality, we cannot affirm that all valid arguments preserve truth (Beall 2007, 2009; Field 2008, (2009b). We show that the standard arguments for this conclusion all break down once (i) the structural rule of contraction is restricted and (ii) how the premises can be aggregated—so that they can be said to jointly entail a given conclusion—is appropriately understood. In addition, we briefly rehearse some reasons for restricting structural contraction.

Keywords

Truth-preservation Validity Naïve view of truth Curry’s Paradox Contraction Modus Ponens Substructural logics Incompleteness Theorems 

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.University of SalzburgSalzburgAustria
  2. 2.University of ConnecticutStorrsUSA

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