• Anderson, Alan and Nuel Belnap, 1975, Entailment: The logic of relevance and necessity I, Princeton: Princeton University Press. (Scholar)
• Anderson, Alan, Nuel Belnap, and J. Michael Dunn, 1992, Entailment: The logic of relevance and necessity II, Princeton: Princeton University Press. (Scholar)
• Barcan Marcus, Ruth. 1990, “A Backwards Look at Quine’s Animadversions on Modalities,” in R. Bartrett and R. Gibson (eds.), Perspectives on Quine, Cambridge: Blackwell. (Scholar)
• Barrio, Eduardo Alejandro., Federico Pailos, and Damian Szmuc, 2020, “A Hierarchy of Classical and Paraconsistent Logics”, J Philos Logic, 49: 93–120. doi:10.1007/s10992-019-09513-z (Scholar)
• Barwise, Jon, 1985, “Model-theoretic logics: background and aims”, in Model-theoretic logics, edtied by Jon Barwise and Soloman Feferman (eds.), New York, Springer-Verlag, pp. 3–23. (Scholar)
• Beall, Jc and Greg Restall, 2006, Logical Pluralism, Oxford: Oxford University Press. (Scholar)
• Brouwer, L.E.J., 1949, “Consciousness, Philosophy and Mathematics”, Journal of Symbolic Logic, 14(2): 132–133. (Scholar)
• –––, 1964b, “Intuitionism and Formalism”, in Philosophy of mathematics: selected readings edited by P. Benacerraf and H. Putnam, Englewood Cliffs, NJ, Cambridge University Press, (eds.), 77–89. (Scholar)
• Cobreros, Pablo, Paul Egré, David Ripley, and Robert van Rooij, 2012, “Tolerance and Mixed Consequence in the S’valuationist Setting”, Studia logica, 100(4), 855–877. (Scholar)
• –––, 2012, “Tolerant, classical, strict”, Journal of Philosophical Logic, 41(2), 347–385. (Scholar)
• Cook, Roy, 2002, “Vagueness and mathematical precision”, Mind, 111: 227–247. (Scholar)
• Corcoran, John, 1973, “Gaps between logical theory and mathematical practice”, The methodological unity of science, ed. by M. Bunge, Dordrecht: D. Reidel, 23–50. (Scholar)
• Davidson, Donald, 1984, Inquiries into truth and interpretation, Oxford: Clarendon Press. (Scholar)
• Dummett, Michael, 2000, Elements of intuitionism, second edition, Oxford: Oxford University Press. (Scholar)
• –––, 1978, “The philosophical basis of intuitionistic logic”, in Truth and other enigmas, Cambridge, MA, Harvard University Press, 215–247. (Scholar)
• Gödel, Kurt, 1930, “Die Vollständigkeit der Axiome des logischen Funktionenkalkuls”, Montatshefte für Mathematik und Physik 37, 349–360; translated as “The completeness of the axioms of the functional calculus of logic”, in van Heijenoort 1967, 582–591. (Scholar)
• Harman, Gilbert, 1984, “Logic and reasoning”, Synthese, 60, 107–127. (Scholar)
• Heyting, A., 1956, Intuitionism, Amsterdam: North-Holland Publishing. (Scholar)
• Kerr, Alison Duncan, 2019, “A plea for KR”, Synthese, 198(4): 3047–3071.
• Lycan, William, 1984, Logical form in natural language, Cambridge, MA: The MIT Press. (Scholar)
• Montague, Richard, 1974, Formal philosophy, ed. by R. Thomason, New Haven: Yale University Press. (Scholar)
• Kennedy, Juliette, and Jouko Väänänen, 2021, Logicality and modelclasses. Bulletin of Symbolic Logic, 27(4): 385–414.
• Priest, Graham, 2006a, In contradiction, a study of the transconsistent, second, revised edition, Oxford: Clarendon Press. (Scholar)
• –––, 2006b, Doubt truth to be a liar, Oxford: Clarendon Press. (Scholar)
• Quine, W. V. O., 1960, Word and object, Cambridge, MA: The MIT Press. (Scholar)
• –––, 1953, “Three grades of modal involvement”, Proceedings of the XI^th International Congress of Philosophy, 14, Amsterdam, North Holland Publishing Company, 65–81. (Scholar)
• –––, 1986, Philosophy of logic, second edition, Cambridge, Massachusetts: Harvard University Press. (Scholar)
• –––, 1986, Philosophy of logic, second edition, Englewood Cliffs: Prentice-Hall. (Scholar)
• Read, Stephen, 1988, Relevant logic, Oxford: Oxford University Press. (Scholar)
• Resnik, Michael, 1996, “Ought there to be but one true logic”, in Logic and Reality: Essays on the Legacy of Arthur Prior, J. Copeland (ed.), Oxford: Oxford University Press, 489–517. (Scholar)
• Ripley, David, 2013, “Paradoxes and Failures of Cut”, Australasian Journal of Philosophy, 91(1): 139–164. (Scholar)
• Rumfitt, Ian, 2015, The Boundary Stones of Thought: An Essay in the Philosophy of Logic, Oxford: Oxford University Press. (Scholar)
• Shapiro, Stewart, 1991, Foundations without Foundationalism, Oxford: Clarendon Press. (Scholar)
• –––, 1996, The limits of logic: Second-order logic and the Skolem paradox, The international research library of philosophy, Dartmouth Publishing Company, 1996. (An anthology containing many of the significant later papers on the Skolem paradox.) (Scholar)
• –––, 1998, “Logical consequence: models and modality”, in The philosophy of mathematics today, edited by M. Schirn, Oxford: Oxford University Press, 131–156. (Scholar)
• –––, 2014, Varieties of Logic, Oxford: Oxford University Press. (Scholar)
• Shapiro, Stewart and Teresa Kouri Kissel, Classical, first order logic, Cambridge Elements, Cambridge, Cambridge University Press.
• Tennant, Neil, 1997, The taming of the true, Oxford: Clarendon Press. (Scholar)
• Van Heijenoort, Jean, 1967, From Frege to Gödel, Cambridge, Massachusetts: Harvard University Press. An anthology containing many of the major historical papers on mathematical logic in the early decades of the twentieth century. (Scholar)
• Wang, Hao, 1974, From Mathematics to Philosophy, London, Routledge and Kegan Paul. (Scholar)
• Williamson, Timothy, 2017, “Semantic paradoxes and abductive methodology”, in Reflections on the liar edited by Bradley Armour-Garb, Oxford, Oxford University Press, 325–346. (Scholar)

Further Reading

There are many fine textbooks on mathematical logic. A sample follows.

• Boolos, George S., John P. Burgess, and Richard C. Jeffrey, 2007, Computability and logic, fifth edition, Cambridge, England: Cambridge University Press. Elementary and intermediate level. (Scholar)
• Bergmann, Merrie, James Moor, and Jack Nelson, 2013, The logic book, sixth edition, New York: McGraw-Hill. Elementary and intermediate level. (Scholar)
• Church, Alonzo, 1956, Introduction to mathematical logic, Princeton: Princeton University Press. Classic textbook. (Scholar)
• Enderton, Herbert, 1972, A mathematical introduction to logic, New York: Academic Press. Textbook in mathematical logic, aimed at a mathematical audience.
• Forbes, Graeme, 1994, Modern Logic, Oxford: Oxford University Press. Elementary textbook. (Scholar)
• Mendelson, Elliott, 1987, Introduction to mathematical logic, third edition, Princeton: van Nostrand. Intermediate. (Scholar)