, Volume 34, Issue 1, pp 89–98 | Cite as

Paradoxes of Logical Equivalence and Identity



In this paper a principle of substitutivity of logical equivalents salve veritate and a version of Leibniz’s law are formulated and each is shown to cause problems when combined with naive truth theories.


Curry’s paradox Validity Semantic paradox Leibniz’s law Property theory 


  1. Bacon A (2013a) A new conditional for naive truth theory. Notre Dame J Formal Log 54(1):87–104CrossRefGoogle Scholar
  2. Bacon A (2013b) Non-classical meta-theory for non-classical logic. J Philos Log 42(2):335–355CrossRefGoogle Scholar
  3. Beall JC (2009) Spandrels of truth. Oxford University Press, USACrossRefGoogle Scholar
  4. Beall JC, Murzi J (2013) Two flavors of curry paradox. J Philos CX(5):143–165Google Scholar
  5. Brady R (2006) Universal logic. CSLI Publications, StanfordGoogle Scholar
  6. Cresswell MJ (1967) Propositional identity. Logique et Analyse 40:283–291Google Scholar
  7. Field H (2008) Saving truth from paradox. Oxford University Press, USACrossRefGoogle Scholar
  8. Field H What is logical validity? In Colin C, Ole H (eds) Foundations of logical consequence. Oxford University Press, Oxford (forthcoming)Google Scholar
  9. Friedman H, Sheard M (1987) An axiomatic approach to self-referential truth. Ann Pure Appl Log 33:1–21CrossRefGoogle Scholar
  10. Grišin VN (1981) Predicate and set-theoretical calculi based on logic without the contraction rule, mathematical ussr izvestiya 18 (1982), 41–59. English translaion, Izvéstia Akademii Nauk SSSR, 45:47–68Google Scholar
  11. Halbach V (1994) A system of complete and consistent truth. Notre Dame J Formal Log 35(3):311–327CrossRefGoogle Scholar
  12. Murzi J, Shapiro L (2013) Validity and truth-preservation. In: Unifying the philosophy of truth. Springer (forthcoming)Google Scholar
  13. Priest G (2001) An introduction to non-classical logic. Cambridge University Press, CambridgeGoogle Scholar
  14. Priest G (2006) In contradiction: a study of the transconsistent. Oxford University Press, OxfordCrossRefGoogle Scholar
  15. Priest G Fusion and confusion. Topoi (forthcoming)Google Scholar
  16. Ripley D (2013) Paradoxes and failures of cut. Aust J Philos 91(1):139–164CrossRefGoogle Scholar
  17. Schiffer S (2003) The things we mean. Clarendon Oxford, OxfordCrossRefGoogle Scholar
  18. Welch P (2008) Ultimate truth vis-a-vis stable truth. Rev Symb Log 1(01):126–142CrossRefGoogle Scholar
  19. Whittle B (2004) Dialetheism, logical consequence and hierarchy. Analysis 64(284):318–326CrossRefGoogle Scholar
  20. Zardini E (2013) Naive modus ponens. J Philos Log 42(4):1–19CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.University of Southern CaliforniaLos AngelesUSA

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