Naive Truth and Naive Logical Properties

A unified answer is offered to two distinct fundamental questions: whether a nonclassical solution to the semantic paradoxes should be extended to other apparently similar paradoxes (in particular, to the paradoxes of logical properties) and whether a non-classical logic should be expressed in a non-classical metalanguage. The ∗Earlier versions of the material in this paper have been presented in 2011 at the 7 Barcelona Workshop on Issues in the Theory of Reference on Paradoxes of Truth and Denotation (University of Barcelona); in 2012, at the 4 PETAF Workshop on Modality (University of Stockholm) and at the Jowett Society (University of Oxford); in 2013, at the LOGOS Semantic Paradoxes and Vagueness Seminar (University of Barcelona), at a NIP research seminar (University of Aberdeen) and at a research seminar at the University of the Azores. I would like to thank all these audiences for very stimulating comments and discussions. Special thanks go to Andrew Bacon, Franz Berto, Cian Dorr, Hartry Field, Joost Joosten, Dan López de Sa, José Mart́ınez, Julien Murzi, Peter Pagin, Josh Parsons, Matteo Plebani, Graham Priest, Steve Read, Dave Ripley, Sven Rosenkranz, Rui Sampaio da Silva, Tim Williamson, Crispin Wright and two anonymous referees. At different stages during the writing of the paper, I have benefitted from a UNAM Postdoctoral Research Fellowship, from an AHRC Postdoctoral Research Fellowship and from the FP7 Marie Curie Intra-European Research Fellowship 301493 on A Non-Contractive Theory of Naive Semantic Properties: Logical Developments and Metaphysical Foundations (NTNSP), as well as from partial funds from the project CONSOLIDER-INGENIO 2010 CSD2009-00056 of the Spanish Ministry of Science and Innovation on Philosophy of Perspectival Thoughts and Facts (PERSP), from the FP7 Marie Curie Initial Training Network 238128 on Perspectival Thoughts and Facts (PETAF), from the project FFI2011-25626 of the Spanish Ministry of Science and Innovation on Reference, SelfReference and Empirical Data and from the project FFI2012-35026 of the Spanish Ministry of Economy and Competition on The Makings of Truth: Nature, Extent, and Applications of Truthmaking.