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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 nonclassical logic should be expressed in a nonclassical metalanguage. The paper starts by reviewing a budget of paradoxes involving the logical properties of validity, inconsistency, and compatibility. The author’s favored substructural approach to naive truth is then presented and it is explained how that approach can be extended in a very natural way so as to solve a certain paradox of validity. However, three individually decisive reasons are later provided for thinking that no approach adopting a classical metalanguage can adequately account for all the features involved in the paradoxes of logical properties. Consequently, the paper undertakes the task to do better, and, building on the system already developed, introduces a theory in a nonclassical metalanguage that expresses an adequate logic of naive truth and of some naive logical properties.

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Ashworth, E. (1974). Language and Logic in the Post-Medieval Period. Dordrecht, Netherlands: Reidel.
Avron, A. (1988). The semantics and proof theory of linear logic. Theoretical Computer Science, 57, 161184.
Avron, A. (1991). Simple consequence relations. Information and Computation, 92, 105140.
Beall, J. C. (2009). Spandrels of Truth. Oxford, UK: Oxford University Press.
Beall, J. C., & Murzi, J. (2013). Two flavors of Curry’s paradox. The Journal of Philosophy, 110, 143165.
Brady, R. (2006). Universal Logic. Stanford, CA: CSLI Publications.
Burge, T. (1978). Buridan and epistemic paradox. Philosophical Studies, 34, 2135.
Field, H. (2006). Truth and the unprovability of consistency. Mind, 115, 567605.
Field, H. (2008). Saving Truth from Paradox. Oxford, UK: Oxford University Press.
Greenough, P. (2001). Free assumptions and the liar paradox. American Philosophical Quarterly, 38, 115135.
Grelling, K., & Nelson, L. (1908). Bemerkungen zu den Paradoxien von Russell und Burali-Forti. Abhandlungen der Fries’schen Schule, 2, 301334.
Gupta, A., & Belnap, N. (1993). The Revision Theory of Truth. Cambridge, MA: MIT Press.
Kaplan, D., & Montague, R. (1960). A paradox regained. Notre Dame Journal of Formal Logic, 1, 7990.
Kripke, S. (1975). Outline of a theory of truth. The Journal of Philosophy, 72, 690716.
Mates, B. (1965). Pseudo-Scotus on the soundness of consequentiae. In Tymieniecka, A.-T., editor. Contributions to Logic and Methodology in Honor of J.M. Bocheński. Amsterdam, Netherlands: North-Holland, pp. 132141.
McGee, V. (1991). Truth, Vagueness, and Paradox. Indianapolis, IN: Hackett.
Meyer, R., Routley, R., & Dunn, M. (1979). Curry’s paradox. Analysis, 39, 124128.
Montague, R. (1963). Syntactic treatments of modality, with corollaries on reflection principles and finite axiomatizability. Acta Philosophica Fennica, 16, 153167.
Moruzzi, S., & Zardini, E. (2007). Conseguenza logica. In Coliva, A., editor. Filosofia analitica, Roma, Italy: Carocci, pp. 157194.
Prawitz, D. (1965). Natural Deduction. Stockholm, Sweden: Almqvist och Wiksell.
Priest, G. (2003). Beyond the Limits of Thought (second edition). Oxford, UK: Oxford University Press.
Priest, G. (2006). In Contradiction (second edition). Oxford, UK: Oxford University Press.
Priest, G. (2010). Hopes fade for saving truth. Philosophy, 85, 109140.
Priest, G. (2013). Fusion and confusion. Topoi. Forthcoming.
Read, S. (1979). Self-reference and validity. Synthese, 42, 265274.
Read, S. (2001). Self-reference and validity revisited. In Yrjönsuuri, M., editor. Medieval Formal Logic, Dordrecht, Netherlands: Kluwer, pp. 183196.
Ripley, D. (2012). Conservatively extending classical logic with transparent truth. The Review of Symbolic Logic, 5, 354378.
Russell, B. (1903). The Principles of Mathematics. Cambridge, UK: Cambridge University Press.
Russell, B. (1908). Mathematical logic as based on the theory of types. American Journal of Mathematics, 30, 222262.
Scott, D. (1974). Completeness and axiomatizability in many-valued logic. In Henkin, L., editor. Proceedings of the Tarski Symposium, Providence, RI: American Mathematical Society, pp. 411435.
Shapiro, L. (2011). Deflating logical consequence. The Philosophical Quarterly, 61, 320342.
Tarski, A. (1930). Fundamentale Begriffe der Methodologie der deduktiven Wissenschaften. I. Monatshefte für Mathematik und Physik, 37, 361404.
Tarski, A. (1933). Pojȩcie prawdy w jȩzykach nauk dedukcyjnych. Warsaw, Poland: Nakładem Towarzystwa Naukowego Warszawskiego.
Weir, A. (2005). Naive truth and sophisticated logic. In Armour-Garb, B., and Beall, J. C., editors. Deflationism and Paradox. Oxford, UK: Oxford University Press, pp. 218249.
Zardini, E. (2008a). Truth and what is said. Philosophical Perspectives, 22, 545574.
Zardini, E. (2008b). A model of tolerance. Studia Logica, 90, 337368.
Zardini, E. (2011). Truth without contra(di)ction. The Review of Symbolic Logic, 4, 498535.
Zardini, E. (2012). Truth preservation in context and in its place. In Dutilh-Novaes, C., and Hjortland, O., editors. Insolubles and Consequences. London, UK: College Publications, pp. 249271.
Zardini, E. (2013a). It is not the case that [P and ‘It is not the case that P’ is true] nor is it the case that [P and ‘P’ is not true]. Thought, 1, 309319.
Zardini, E. (2013b). Naive modus ponens. Journal of Philosophical Logic, 42, 575593.
Zardini, E. (2013c). Context and consequence. An intercontextual substructural logic. Synthese. Forthcoming.
Zardini, E. (2013d). Getting one for two, or the contractors’ bad deal. Towards a unified solution to the semantic paradoxes. In Achourioti, T., Fujimoto, K., Galinon, H., and Martínez, J., editors. Unifying the Philosophy of Truth. Dordrecht, Netherlands: Springer. Forthcoming.
Zardini, E. (2013e). Naive logical properties and structural properties. The Journal of Philosophy. Forthcoming.
Zardini, E. (2013f). Restriction by non-contraction. Notre Dame Journal of Formal Logic. Forthcoming.
Zardini, E. (2013g). ∀ and ω. Manuscript.
Zardini, E. (2013h). The bearers of logical consequence. Manuscript.
Zardini, E. (2013i). The opacity of truth. Manuscript.
Zardini, E. (2013j). The underdetermination of the meaning of logical words by rules of inference. Manuscript.
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The Review of Symbolic Logic
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