This paper investigates how naive theories of truth fare with respect to a set of extremely plausible principles of restricted quantification. It is first shown that both nonsubstructural theories as well as certain substructural theories cannot validate all those principles. Then, pursuing further an approach to the semantic paradoxes that the author has defended elsewhere, the theory of restricted quantification available in a specific naive theory that rejects the structural property of contraction is explored. It is shown that the theory validates all the principles in question, and it is argued that other prima facie plausible principles that the theory fails to validate are objectionable on independent grounds.

## References

[3] Beall, J. C.,

*Spandrels of Truth*, Oxford University Press, Oxford, 2009. MR2906982 10.1093/acprof:oso/9780199285495.003.0009[3] Beall, J. C.,*Spandrels of Truth*, Oxford University Press, Oxford, 2009. MR2906982 10.1093/acprof:oso/9780199285495.003.0009[4] Beall, J. C., “Free of detachment: Logic, rationality, and gluts,”

*Noûs*, vol. 49 (2015), pp. 410–23. MR3349170 10.1111/nous.12029[4] Beall, J. C., “Free of detachment: Logic, rationality, and gluts,”*Noûs*, vol. 49 (2015), pp. 410–23. MR3349170 10.1111/nous.12029[5] Beall, J. C., R. Brady, A. Hazen, G. Priest, and G. Restall, “Relevant restricted quantification,”

*Journal of Philosophical Logic*, vol. 35 (2006), pp. 587–98. MR2252731 10.1007/s10992-005-9008-5[5] Beall, J. C., R. Brady, A. Hazen, G. Priest, and G. Restall, “Relevant restricted quantification,”*Journal of Philosophical Logic*, vol. 35 (2006), pp. 587–98. MR2252731 10.1007/s10992-005-9008-5[7] Curry, H. B., “The inconsistency of certain formal logics,”

*Journal of Symbolic Logic*, vol. 7 (1942), pp. 115–17. MR7366 10.2307/2269292[7] Curry, H. B., “The inconsistency of certain formal logics,”*Journal of Symbolic Logic*, vol. 7 (1942), pp. 115–17. MR7366 10.2307/2269292[9] Field, H., “Naive truth and restricted quantification: Saving truth a whole lot better,”

*Review of Symbolic Logic*, vol. 7 (2014), pp. 147–91. MR3244967 10.1017/S1755020313000312[9] Field, H., “Naive truth and restricted quantification: Saving truth a whole lot better,”*Review of Symbolic Logic*, vol. 7 (2014), pp. 147–91. MR3244967 10.1017/S1755020313000312[10] Heim, I., “Artikel und Definitheit,” pp. 487–535 in

*Semantik/Semantics: Ein internationales Handbuch der zeitgenössischen Forschung. An International Handbook of Contemporary Research*, edited by A. von Stechow and D. Wunderlich, vol. 6 of*Handbücher zur Sprach- und Kommunikationswissenschaft*, de Gruyter, Berlin, 1991.[10] Heim, I., “Artikel und Definitheit,” pp. 487–535 in*Semantik/Semantics: Ein internationales Handbuch der zeitgenössischen Forschung. An International Handbook of Contemporary Research*, edited by A. von Stechow and D. Wunderlich, vol. 6 of*Handbücher zur Sprach- und Kommunikationswissenschaft*, de Gruyter, Berlin, 1991.[13] Lokhorst, G.-J. C., “Deontic linear logic with Petri net semantics,” Technical report, Center for the Philosophy of Information and Communication Technology, Department of Philosophy, Erasmus University of Rotterdam, 1997.[13] Lokhorst, G.-J. C., “Deontic linear logic with Petri net semantics,” Technical report, Center for the Philosophy of Information and Communication Technology, Department of Philosophy, Erasmus University of Rotterdam, 1997.

[14] McCawley, J. D., “A program for logic,” pp. 498–544 in

*Semantics of Natural Language*, edited by D. Davidson and G. Harman, vol. 40 of*Synthese Library*, Reidel, Dordrecht, 1972.[14] McCawley, J. D., “A program for logic,” pp. 498–544 in*Semantics of Natural Language*, edited by D. Davidson and G. Harman, vol. 40 of*Synthese Library*, Reidel, Dordrecht, 1972.[18] Restall, G., “Multiple conclusions,” pp. 189–205 in

*Logic, Methodology and Philosophy of Science: Proceedings of the Twelfth International Congress*, edited by P. Hájek, L. Valdés Villanueva, and D. Westerståhl, College Publications, London, 2005.[18] Restall, G., “Multiple conclusions,” pp. 189–205 in*Logic, Methodology and Philosophy of Science: Proceedings of the Twelfth International Congress*, edited by P. Hájek, L. Valdés Villanueva, and D. Westerståhl, College Publications, London, 2005.[19] Ripley, D., “Conservatively extending classical logic with transparent truth,”

*Review of Symbolic Logic*, vol. 5 (2012), pp. 354–78. MR2924365 10.1017/S1755020312000056[19] Ripley, D., “Conservatively extending classical logic with transparent truth,”*Review of Symbolic Logic*, vol. 5 (2012), pp. 354–78. MR2924365 10.1017/S1755020312000056[24] Weir, A., “Naive truth and sophisticated logic,” pp. 218–49 in

*Deflationism and Paradox*, edited by B. Armour-Garb and J. C. Beall, Oxford University Press, Oxford, 2005.[24] Weir, A., “Naive truth and sophisticated logic,” pp. 218–49 in*Deflationism and Paradox*, edited by B. Armour-Garb and J. C. Beall, Oxford University Press, Oxford, 2005.[25] Zardini, E., “A model of tolerance,”

*Studia Logica*, vol. 90 (2008), pp. 337–68. MR2470080 10.1007/s11225-008-9156-z[25] Zardini, E., “A model of tolerance,”*Studia Logica*, vol. 90 (2008), pp. 337–68. MR2470080 10.1007/s11225-008-9156-z[26] Zardini, E., “Towards first-order tolerant logics,” pp. 35–38 in

*Philosophy, Mathematics, Linguistics: Aspects of Interaction*, edited by O. Prozorov, Russian Academy of Sciences, St. Petersburg, 2009.[26] Zardini, E., “Towards first-order tolerant logics,” pp. 35–38 in*Philosophy, Mathematics, Linguistics: Aspects of Interaction*, edited by O. Prozorov, Russian Academy of Sciences, St. Petersburg, 2009.[27] Zardini, E., “Truth without contra(di)ction,”

*Review of Symbolic Logic*, vol. 4 (2011), pp. 498–535. MR2867903 10.1017/S1755020311000177[27] Zardini, E., “Truth without contra(di)ction,”*Review of Symbolic Logic*, vol. 4 (2011), pp. 498–535. MR2867903 10.1017/S1755020311000177[28] Zardini, E., “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*, vol. 1 (2013), pp. 309–19.[28] Zardini, E., “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*, vol. 1 (2013), pp. 309–19.[29] Zardini, E., “Naive modus ponens,”

*Journal of Philosophical Logic*, vol. 42 (2013), pp. 575–93. MR3081009 10.1007/s10992-012-9239-1[29] Zardini, E., “Naive modus ponens,”*Journal of Philosophical Logic*, vol. 42 (2013), pp. 575–93. MR3081009 10.1007/s10992-012-9239-1[30] Zardini, E., “Context and consequence: An intercontextual substructural logic,”

*Synthese*, vol. 191 (2014), pp. 3473–500. MR3254634 10.1007/s11229-014-0490-6[30] Zardini, E., “Context and consequence: An intercontextual substructural logic,”*Synthese*, vol. 191 (2014), pp. 3473–500. MR3254634 10.1007/s11229-014-0490-6[31] Zardini, E., “Evans tolerated,” pp. 327–52 in

*Vague Objects and Vague Identity*, edited by K. Akiba and A. Abasnezhad, vol. 33 of*Logic, Epistemology, and the Unity of Science*, Springer, Dordrecht, 2014.[31] Zardini, E., “Evans tolerated,” pp. 327–52 in*Vague Objects and Vague Identity*, edited by K. Akiba and A. Abasnezhad, vol. 33 of*Logic, Epistemology, and the Unity of Science*, Springer, Dordrecht, 2014.[32] Zardini, E., “Naive truth and naive logical properties,”

*Review of Symbolic Logic*, vol. 7 (2014), pp. 351–84. MR3214403 10.1017/S1755020314000045[32] Zardini, E., “Naive truth and naive logical properties,”*Review of Symbolic Logic*, vol. 7 (2014), pp. 351–84. MR3214403 10.1017/S1755020314000045[34] Zardini, E., “Breaking the chains: Following-from and transitivity,” edited by C. Caret and O. Hjortland, to appear in

*Foundations of Logical Consequence*(2014).[34] Zardini, E., “Breaking the chains: Following-from and transitivity,” edited by C. Caret and O. Hjortland, to appear in*Foundations of Logical Consequence*(2014).[35] Zardini, E., “És la veritat una mentida? Perspectives sobre les paradoxes semàntiques,” to appear in

*Anuari de la Societat Catalana de Filosofia*(2014).[35] Zardini, E., “És la veritat una mentida? Perspectives sobre les paradoxes semàntiques,” to appear in*Anuari de la Societat Catalana de Filosofia*(2014).[37] Zardini, E., “Getting one for two, or the contractors’ bad deal: Towards a unified solution to the semantic paradoxes,” pp. 461–93 in

*Unifying the Philosophy of Truth*, edited by T. Achourioti, H. Galinon, José Martínez Fernández, and K. Fujimoto, vol. 36 of*Logic, Epistemology and the Unity of Science*, Springer, Dordrecht, 2015.[37] Zardini, E., “Getting one for two, or the contractors’ bad deal: Towards a unified solution to the semantic paradoxes,” pp. 461–93 in*Unifying the Philosophy of Truth*, edited by T. Achourioti, H. Galinon, José Martínez Fernández, and K. Fujimoto, vol. 36 of*Logic, Epistemology and the Unity of Science*, Springer, Dordrecht, 2015.[38] Zardini, E., “The opacity of truth,” to appear in

*Topoi*(2014). MR3214403 10.1017/S1755020314000045[38] Zardini, E., “The opacity of truth,” to appear in*Topoi*(2014). MR3214403 10.1017/S1755020314000045[39] Zardini, E., “$\forall$ and $\omega$,” pp. 489–526 in

*Quantifiers, Quantifiers, and Quantifiers: Themes in Logic, Metaphysics, and Language*, edited by A. Torza, Springer, Basel, 2015. MR3381846[39] Zardini, E., “$\forall$ and $\omega$,” pp. 489–526 in*Quantifiers, Quantifiers, and Quantifiers: Themes in Logic, Metaphysics, and Language*, edited by A. Torza, Springer, Basel, 2015. MR3381846