Abstract
The semantical paradoxes are not a scientific subject like Inductive Definitions, Algebraic Geometry or Plasma Physics. At least not yet. On the other hand the paradoxes exert a strong fascination and many a philosopher or logician has spent some thought on them, mostly in relative isolation. The literature on the paradoxes is vast but scattered, repetitive and disconnected. This made it impossible to give a presentation in which all ideas in the literature receive their due.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Peter Aczel and Sol Feferman. Consistency of the unrestricted abstraction principle using an intensional equivalence operator. In J.P. Seldin and J.R. Hindley, editors, To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pages 67–98. Academic Press, New York, 1980.
Aczel et al.,1991] P. Aczel, P. Carlisle, and N. Mendier. Two frameworks of theories and their implementation in isabelle. In G. M. Plotkin et al., editors, Logical Frameworks,pages 5–39. Cambridge University Press, Cambridge, 1991.
P. Aczel. The strength of Martin-Löf’s intuitionistic type theory with one universe. In S. Mietissen and J. Vaänänen, editors, Proceedings of the Symposiums in Mathematical Logic in Oulu 1974 and Helsinki 1975, pages 1–32. Report no. 2, Dept.of Philosophy, University of Helsinki, 1977.
Peter Aczel. An introduction to inductive definitions. In Jon Barwise, editor, Handbook of Mathematical Logic, pages 739–782. North Holland, Amsterdam, 1977.
Aczel, 1980] Peter Aczel. Frege structures and the notions of proposition, truth and set. In Jon Barwise et al., editors, The Kleene Symposium,pages 31–59. North Holland, Amsterdam, 1980.
S. Akama. Curry’s Paradox in contractionless constructive logic. Journal of Philosophical Logic, 25: 135–150, 1996.
Aldo Antonelli. A Revision-Theoretic Analysis of the Arithmetical Hierarchy. Notre Dame Journal of Formal Logic, 35: 204–218, 1994.
Aldo Antonelli. The complexity of revision. Notre Dame Journal of Formal Logic, 35:67–72, 1994. A correction appears in Antonelli’s ms. The Complexity of Revision, revised
Aldo Antonelli. Non-well-founded sets via revision rules. Journal of Philosophical Logic, 23: 633–679, 1994.
Peter Apostoli. The analytic conception of truth and the foundations of arithmetic. Journal of Symbolic Logic, 65: 33–102, 2000.
L. Aqvist. Modal logic and quantified sentences. Theoretical Linguistics, 9: 111–129, 1982.
Mohammad Ardeshir and Wim Ruitenburg. Basic Propositional calculus i. Mathematical Logic Quarterly, 44: 317–343, 1998.
Nicholas Asher and Hans Kamp. The knower’s paradox and representational theories of attitudes. In J. Halpern, editor, TARK’86, pages 131–148. Morgan-Kaufman, Los Angeles, 1986.
Nicholas Asher and Hans Kamp. Self-reference, attitudes, and paradox. In Gennaro Chierchia, Barbara H. Partee, and Raymond Turner, editors, Properties, Types and Meaning, volume 1, pages 85–118. Kluwer, Dordrecht, 1989.
J. Azzoudi. A simple axiomatizable theory of truth. Notre Dame Journal of Formal Logic,32:458–493, 1991.
Jon Barwise and J. Etchemendy. The liar: an essay on truth and circularity. Oxford University Press, Oxford, 1987.
Jon Barwise and L. Moss. Vicious Circles. On the Mathematics of NonWellfounded Phenomena. CSLI Publications, Stanford, 1996.
Jon Barwise et al. The Kleene Symposium. North Holland, Amsterdam, 1980.
Jon Barwise. Handbook of Mathematical Logic. North Holland, Amsterdam, 1977.
G. Bealer and U. Mönnich. Property theories. In Dov Gabbay and Franz Günthner, editors, Handbook of Philosophical Logic, volume IV, pages 133–251. Reidel, Dordrecht, 1989.
George Bealer. Quality and Concept. Clarendon Press, Oxford, 1982.
G. Bealer. Property theory: the type-free approach vs. the church approach. Journal of Philosophical Logic, 23: 139–171, 1994.
H. Behman. Zu den Widersprüchen der Logik und der Mengenlehre. Jahresbericht der Deutschen Mathematiker-Vereiningung, 40: 37–48, 1931.
Nuel Belnap and Anil Gupta. The Revision Theory of Truth. MIT Press, Cambridge, 1993.
Nuel Belnap and Anil Gupta. The Revision Theory of Truth. MIT Press, Cambridge, 1993.
Nuel Belnap. Gupta’s rule of revision theory of truth. Journal of Philosophical Logic, 11: 103–116, 1982.
Nuel Belnap. On rigorous definitions. Philosophical Studies, 72: 115–146, 1993.
P. Benacerraf and H. Putnam, editors. Philosophy of Mathematics. Prentice Hall, 1964.
J. van Benthem. Four paradoxes. Journal of Philosophical Logic, 7: 49–72, 1978.
C. Bernardi and G. D’Agostino. Translating the hypergame paradox: remarks on the set of founded elements of a relation. Journal of Philosophical Logic, 25: 545–557, 1997.
Stephen Blarney. Partial Logic. In Dov Gabbay and Franz Günthner, editors, Handbook of Philosophical Logic, volume III, pages 1–70. Reidel, Dordrecht, 1986.
Ulrich Blau. Vom Henker, vom Lügner and von ihrem Ende. Erkenntnis, 19: 27–44, 1983.
Ulrich Blau. Die Logik der Unbestimmheiten and Paradoxien. Erkenntnis, 22: 369–459, 1985.
I.M. Bocheàski. A History of Formal Logic. Chelsea, New York, 1961.
D.A. Bochvar. On a three-valued logical calculus and its application to the analysis of the classical extended functional calculus. History and Philosophy of Logic,2:87–112, 1981. English translation of the original article.
D. Bonevac. Paradoxes of fulfillment. Journal of Philosophical Logic, 19: 229–252, 1990.
G. Boolos. The consistency of Frege’s Foundations of Arithmetic. In J. J. Thompson, editor, On Being and Saying: Essays in honour of Richard Cartwright, pages 3–20. MIT Press, Cambridge, Mass, 1990. Reprinted in [Demopoulos, 1995, pp. 211–233] and in [Boolos, 1998, 183–2011.
G. Boolos. The Logic of Provability. Cambridge University Press, Cambridge, 1993.
G. Boolos. Logic, Logic and Logic. Harvard University Press, Cambridge, Mass, 1998.
Boyd et al.,1969] R. Boyd, G. Hensel, and H. Putnam. A recursion-theoretic characterization of the ramified analytical hierarchy. Transactions of the American Mathematical Society,141/142:37–62, 1969.
A. T. Brady. The consistency of the axioms of abstraction and extensionality in a three-valued logic. Notre Dame Journal of Formal Logic, 12: 447–452, 1971.
M. W. Bunder. The naturalness of illative combinatory logic as a basis for mathematics. In J. P. Seldin and J. R. Hindley, editors, To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pages 55–64. Academic Press, New York, 1980.
M. Bunder. The simple consistency of a set theory based on the logic CSQ. Notre Dame Journal of Formal Logic, 24: 431–449, 1983.
Tyler Burge. Semantical paradox. Journal of Philosophy,76:83–118, 1979. Reprinted in [Martin, 1984, pp. 83–118].
Tyler Burge. The liar paradox: tangles and chains. Philosophical Studies, 41: 352–366, 1982.
Tyler Burge. Epistemic paradox. Journal of Philosophy, 81: 5–29, 1984.
John Burgess. The Truth Is Never Simple. Journal of Symbolic Logic, 51: 663–681, 1986.
John Burgess. Addendum to The truth is never simple’. Journal of Symbolic Logic, 53: 390–392, 1988.
James Cain and Zlatan Damnjanovic. On the weak Kleene scheme in Kripke’s theory of truth. Journal of Symbolic Logic, 56: 1452–1468, 1991.
Andrea Cantini. A note on three-valued logic and tarski theorem on truth definitions. Studia Logica, 39: 405–415, 1980.
Andrea Cantini. Tarski extensions of theories. In S. Bernini, editor, Atti del Congresso Nazionale di Logica, Montecatini Tenne, 1–5 Ottobre 1979, pages 219–237. Bibliopolis, Napoli, 1981.
Andrea Cantini. Notes on Formal Theories of Truth. Zeitschrift fir mathematische Logik and Grundlagen der Mathematik, 35: 97–130, 1989.
Andrea Cantini. A Theory of Truth Formally Equivalent to ID’. Journal of Symbolic Logic, 55: 244–259, 1990.
Andrea Cantini. Extending the first-order theory of combinators with self-referential truth. Journal of Symbolic Logic, 58: 477–513, 1993.
Andrea Cantini. Logical Frameworks for Truth and Abstraction. An Axiomatic Study, volume 135 of Studies in Logic and the Foundations of Mathematics. Elsevier, Amsterdam, 1996.
J. Cargile. Paradoxes: a study in form and predication. Cambridge University Press, Cambridge, 1979.
G. Chaitin. Berry’s paradox. Communications of ACM, 31: 20–29, 1979.
C. C. Chang. The axiom of comprehension in infinite-valued logic. Mathematica Scandinava, 13: 19–39, 1963.
C. C. Chang. Infinite-valued logic as a basis for set theory. In Y. Bar Hillel, editor, Logic, Methodology und Philosophy of Science: Proceedings of the 1964 International Congress, pages 93–100. North Holland, Amsterdam, 1965.
André Chapuis and Anil Gupta. Circularity, Definition, and Truth. Indian Council of Philosophical Research, 1999.
André Chapuis. Alternative revision theories of truth. Journal of Philosophical Logic, 25: 399–423, 1996.
André Chapuis. Recent theories of truth. Journal of Indian Council of Philosophical Research, 15: 89–123, 1998.
André Chapuis. Rationality and circularity. In André Chapuis and Anil Gupta, editors, Circularity, Definition, and Truth. Indian Council of Philosophical Research, New Delhi, 1999.
A. Chauvin. Theory of objects and set theory: introduction and semantics. Notre Dame Journal of Formal Logic, 20: 37–54, 1979.
G. Chierchia and R. Turner. Semantics and property theory. Linguistics und Philosophy, 11: 261–302, 1988.
Chierchia et al.,1989] G. Chierchia, B. H. Partee, and R. Turner. Properties, types and meaning, vol. 1,volume 38 of Studies in Linguistics and Philosophy. Kluwer, 1989.
C.H. Chihara. Ontology and the Vicious Circle Principle. Cornell University Press, 1973.
C.H. Chihara. The semantic paradoxes; a diagnostic investigation. Philosophical Review, 88: 590–618, 1979.
C.H. Chihara. Language and Negation. Joseph Publishing Company, 1980.
C.H. Chihara. Priest, the Liar and Gödel. Journal of Philosophical Logic, 13: 117124, 1984.
I. Chung. A study in paradoxes. PhD thesis, University of Minnesota, 1989.
Alonzo Church. Comparison of Russell’s resolution of the semantical antinomies with that of Tarski. Journal of Symbolic Logic, 41: 747–760, 1976.
N. Cocchiarella. Whither Russell’s paradox of predication? In M. Munitz, editor, Logic and Ontology, pages 133–158. New York University Press, New York, 1973.
N. Cocchiarella. Logical Investigations of Predication Theory and the Problem of Universals. Bibliopolis, Naples, 1986.
N. Cocchiarella. Cantor’s power-set theorem versus Frege’s double-correlation thesis. History and Philosophy of Logic, 13: 179–201, 1992.
Curry et al.,1958] H. B. Curry, R. Feys, and W. Craig. Combinatory Logic,volume I. North Holland, 1958.
Marian David. Correspondence and Disquotation: An Essay on the Nature of Truth. Oxford University Press, 1994.
Donald Davidson. On saying that. In D. Davidson and J. Hintikka, editors, Words and Objections, Essays on the Work of W. V. Quitte, pages 158–174. Reidel, Dordrecht, 1999.
N. Davies. A first-order theory of truth, knowledge and belief. In J. van Eijck, editor, Logic in AI, pages 170–179. Springer, Berlin, 1991.
W. Demopoulos. Frege’s Philosophy of Mathematics. Harvard University Press, Harvard, 1995.
David DeVidi and Graham Solomon. Tarski on “essentially richer” metalanguages. Journal of Philosophical Logic, 28: 1–28, 1999.
B. H. Dowden. The Liar Paradox and Tarski’s Undefnability Theorem. PhD thesis, Stanford University, 1979.
B. H. Dowden. Accepting inconsistencies from the paradoxes. Journal of Philosophical Logic, 13: 125–130, 1984.
R. Epstein. A theory of truth based on a medieval solution of the liar paradox. History and Philosophy of Logic, 13: 144–177, 1992.
Solomon Feferman. Set-theoretical foundations on category theory. In S. MacLane, editor, Reports of the Midwest Category Seminar, III,volume 106 of Lecture Notes in Mathematics,pages 201–247. Springer, Berlin, 1969. with an appendix by G. Kreisel.
Solomon Feferman. Non-extensional type-free theories of partial operations and classifications i. In J. Diller and G. H. Müller, editors, Proof Theory Symposium, Kiel 1974, volume 500 of Springer Lecture Notes, pages 73–118. Springer, Berlin, 1974.
Solomon Feferman. A language and axioms for explicit mathematics. In J.N. Crossley, editor, Algebra and Logic, volume 450 of Lecture Notes in Mathematics, pages 87–139. Springer, Berlin, 1975.
Solomon Feferman. Categorical foundations and foundations for category theory. In R. Butts and J. Hintikka, editors, Logic, Foundations of Mathematics and Computability, pages 149–169. Reidel, Dordrecht, 1977.
Solomon Feferman. Constructive theories of functions and classes. In M. Boffa, D. van Dalen, and K. McAloon, editors, Logic Colloquium 1978, Lecture Notes in Mathematics, pages 159–224. North Holland, Amsterdam, 1979.
Solomon Feferman. Towards useful type-free theories. Journal of Symbolic Logic,49:75–111, 1984. Reprinted in [Martin, 1984, pp. 237–288].
Solomon Feferman. Reflecting on Incompleteness. Journal of Symbolic Logic, 56: 1–49, 1991.
Hartry Field. The deflationary conception of truth. In G. MacDonald and C. Wright, editors, Fact, Science and Morality, pages 55–117. Blackwell, Oxford, 1986.
Kit Fine and Timothy McCarthy. Truth without satisfaction. Journal of Philosophical Logic, 13: 397–421, 1984.
P. Finsler. Aufsätze zur Mengenlehre. Wissenschaftliche Buchgesellschaft, 1975.
F. B. Fitch. An extension of basic logic. Journal of Symbolic Logic, 13: 95–106, 1948.
R B. Fitch. The system cÖ of combinatory logic. Journal of Symbolic Logic, 28: 87–97, 1963.
R B. Fitch. Universal metalanguages in philosophy. Review of Metaphysics, 17: 396402, 1964.
F. B. Fitch. A consistent modal set theory, abstract. Journal of Symbolic Logic, 31: 701, 1966.
F. B. Fitch. A complete and consistent modal set theory. Journal of Symbolic Logic, 32: 93–103, 1967.
R. B. Fitch. A theory of logical essences. The Monist, 51: 104–109, 1967.
Fitch, 1974] R B. Fitch. Elements of Combinatory Logic. Yale University Press, 1974.
R B. Fitch. A consistent combinatory logic with an inverse to equality. Journal of Symbolic Logic, 45: 529–543, 1980.
Melvin Fitting. Notes on the mathematical aspects of Kripke’s theory of truth. Notre Dame Journal of Formal Logic, 27: 75–88, 1986.
Melvin Fitting. Bilattices and the theory of truth. Journal of Philosophical Logic, 18: 225–256, 1989.
Melvin Fitting. A theory of truth that prefers falsehood. Journal of Philosophical Logic, 26: 477–500, 1997.
R. Flagg and J. Myhill. An extension of Frege structures. In Lecture Notes in Pure and Applied Mathematics 106, pages 197–217. M.Dekker, New York, 1987.
R. Flagg and J. Myhill. Implications and analysis in classical Frege structures. Annals of Pure and Applied Logic, 34: 33–85, 1987.
R. Flagg and J. Myhill. A type-free system extending (zfc). Annals of Pure and Applied Logic, 43: 79–97, 1989.
R. Flagg. tc-continuous lattices and comprehension principles for Frege structures. Annals of Pure and Applied Logic, 36: 1–16, 1987.
B. C. van Fraassen. Singular terms, truth-value gaps, and free logic. Journal of Philosophy, pages 481–494, 1966.
B. C. van Fraassen. Presupposition, implication and self-reference. Journal of Philosophy, 65: 135–152, 1968.
B. C. Van Fraassen. Presupposition, implication and self-reference. Journal of Philosophy, 65: 135–152, 1968.
B. C. van Fraassen. Inference and self-reference. Synthèse, 21: 425–438, 1970.
B. C. Van Fraassen. Inference and selfreference. In D. Davidson and G. Harman, editors, Semantics of Natural Language, pages 695–708. D. Reidel, Dordrecht, 1972.
G. Frege. Über Sinn und Bedeutung. In Frege [1975b1, pages 40–65. also reprinted in e.g. [Hamish, 1994, pp. 142–160].
Gottlob Frege, editor. Funktion, Begriff Bedeutung. Vandenhoeck and Ruprecht, 1975.
Harvey Friedman and Michael Sheard. An Axiomatic Approach to Self-Referential Truth. Annals of Pure and Applied Logic, 33: 1–21, 1987.
H. Friedman and M. Sheard. The disjunction and existence properties for axiomatic systems of truth. Annals of Pure and Applied Logic, 33, 1988.
H. Gaifman. Paradoxes of infinity and self-application i. Erkenntnis, 20: 131–155, 1983.
H. Gaifman. Pointers semantics: solution to self-referential puzzles i. In M. Vardi, editor, TARK’88, pages 43–59, 1988.
Haim Gaifman. Pointers to Truth. Journal of Philosophy, 89: 223–261, 1992.
Giorgo Germano. Metamathematische Begriffe in Standardtheorien. Archiv fir mathematische Logik, 13: 22–38, 1970.
P. C. Gilmore. The consistency of partial set theory without extensionality. In T. Jech, editor, Axiomatic Set Theory, part I, volume 13 of Proceedings of Symposia in Pure Mathematics, pages 147–153. AMS, Providence, RI, 1974.
P. C. Gilmore. Combining unrestricted abstraction with universal quantification. In J. Seldin and R. Hindley, editors, To FL B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pages 99–123. Academic Press, New York, 1980.
P. C. Gilmore. Natural deduction based set theories: a new resolution of the old paradoxes. Journal of Symbolic Logic, 51: 393–411, 1986.
L. Goddard and M. Johnston. The nature of reflexive paradoxes: part i. Notre Dame Journal of Formal Logic, 24: 491–508, 1983.
Kurt Gödel. Russell’s mathematical logic. In P. A. Schlipp, editor, The Philosophy of Bertrand Russell,pages 123–153. Tudor, New York, 1944. Reprinted in (Benacerraf and Putnam, 1964, pp. 211–232].
Patrick Grim and Paul St. Denis. The Philosophical Computer: Exploratory Essays in Philosophical Computer Modeling. MIT Press, Cambridge (Mass. ), 1998.
Patrick Grim. The Incomplete Universe: Totality, Knowledge, and Truth. MIT Press, Cambridge (Mass. ), 1991.
V. N. Grishin. A non-standard logic and its application to set theory. In Studies in Formalized Languages and Nonclassical Logics, pages 135–171. Izdat, Nauka, Moskow, 1974. in Russian.
V. N. Grishin. Predicate and set theoretic calculi based on logic without contraction rules. Izvestiya Akndemii Nauk SSSR Seriya Matematicheskaya, 45:47–68, 1981. in Russian. English translation in: Math. USSR Izv., 18:41–59, 1982.
Willem Groeneveld. Dynamic semantics and circular propositions. Journal of Philosophical Logic, 23: 267–306, 1994.
Dorothy Grover. Propositional Quantifiers. Journal of Philosophical Logic, 1: 111, 1972.
Dorothy Grover. Inheritors and paradox. Journal of Philosophy, 74: 590–604, 1977.
Dorothy Grover. A Prosentential Theory of Truth. Princeton University Press, Princeton, 1992.
Anil Gupta and Robert L. Martin. A fixed point theorem for the weak kleene valuation scheme. Journal of Philosophical Logic, 13: 131–135, 1984.
Anil Gupta. Modal Logic and Truth. Journal of Philosophical Logic, 7: 441–472, 1978.
Anil Gupta. Truth and Paradox. Journal of Philosophical Logic, 11:1–60, 1982. Reprinted in [Martin, 1984, pp. 175–236].
Anil Gupta. The meaning of truth. In E. LePore, editor, New Directions in Semantics, pages 453–480. Academic Press, London, 1987.
A. Gupta. Remarks on definitions and the concept of truth. In Proceedings of the Aristotelian Society, pages 227–246, 1989.
A. Gupta. Review of: J.Barwise and J. Etchemendy. The Liar: an Essay in Truth and Circularity. Philosophy of Science, 56: 697–709, 1989.
Anil Gupta. A Critique of Deflationism. Philosophical Topics, 21: 57–81, 1993.
Anil Gupta. Minimalism. In J. Tomberlin, editor, Philosophical Perspectives 7: Philosophy of Language. Ridgeview Publishing Company, Atascadero, 1993.
Susan Haack. Philosophy of Logics. Cambridge University Press, Cambridge, 1978.
Petr Hâjek, Jeff Paris, and J. C. Sheperdson. The Liar Paradox and Fuzzy Logic. Journal of Symbolic Logic, 65: 339–346, 2000.
Volker Halbach and Leon Horsten. Recent Developments in the Theory of Truth. In Volker Halbach and Leon Horsten, editors, Principles of Truth, pages 11–35. Dr. Hänsel-Hohenhausen, Frankfurt a.M., 2002.
Halbach et al.,2003] V. Halbach, H. Leitgeb, and P. Welch. Possible worlds semantics for modal notions conceived as predicates. Journal of Philosophical Logic32:179–223, 2003.
Volker Halbach. A system of complete and consistent truth. Notre Dame Journal of Formal Logic, 35: 311–327, 1994.
Volker Halbach. Tarski-Hierarchien. PhD thesis, Ludwigs-Maximilians-Universität, Centrum für Informations and Sprachverarbeitung, München, 1994.
Volker Halbach. Tarski-hierarchies. Erkenntnis, 43: 339–367, 1995.
Volker Halbach. Axiomatische Wahrheitstheorien. Akademie Verlag, Berlin, 1996.
Volker Halbach. Classical symmetric truth. In G. Meggle and P. Steinacker, editors, Proceedings of the 2nd Conference ssPerspectives in Analytical Philosophy“, volume 1, pages 87–92. de Gruyter, 1997.
Volker Halbach. Tarskian and Kripkean truth. Journal of Philosophical Logic, 26: 69–80, 1997.
Volker Halbach. Conservative Theories of Classical Truth. Studia Logica, 62: 353370, 1999.
Volker Halbach. Disquotationalism and infinite conjunctions. Mind, 108: 1–22, 1999.
Volker Halbach. Disquotationalism fortified. In André Chapuis and Anil Gupta, editors, Circularity, Definitions, and Truth, pages 155–176. Indian Council of Philosophical Research, New Delhi, 2000.
Volker Halbach. How Innocent is Detlationism? Synthese, 126: 167–194, 2000.
Volker Halbach. Truth and Reduction. Erkenntnis, 53: 97–126, 2000.
Volker Halbach. Disquotational Truth and Analyticity. Journal of Symbolic Logic, 66: 1959–1973, 2001.
Volker Halbach. Semantics and Deflationism. PhD thesis, Universität Konstanz, 2001.
Volker Halbach. Modalized Disquotationalism. pages 75–101. Dr HänselHohenhausen, Frankfurt a.M, 2002.
Volker Halbach. Der Preis der Wahrheit. In Wolfgang Spotlit, Peter Schröder-Heister, and Erik Olsson, editors, Logik in der Philosophie. Synchron-Wissenschafsverlag der Autoren, Heidelberg, 2004. To appear.
Joel Hamkins and Andy Lewis. Infinite time Turing machines. Journal of Symbolic Logic, 65: 567–604, 2000.
B. Hansson. Paradoxes in a semantic perspective. In J. Hintikka, I. Niiniluoto, and Saarinen E., editors, Essays on Mathematical and Philosophical Logic, volume 122 of Synthese Library, pages 371–358. Reidel, Dordrecht, 1979.
J. Hardy. Three problems for the singular theory of truth. Journal of Philosophical Logic, 26: 501–520, 1997.
and Kozen, 1984] D. Harel and D. Kozen. A programming language for inductive sets and applications. Inform. Control, 63: 118–139, 1984.
R.M. Harnish. Basic Topics in the Philosophy of Language. Harvester Wheatsheaf, New York, 1994.
Geoffrey Hellman. Review of Martin and Woodruff 1975, Kripke 1975, Gupta 1982 and Herzberger 1982. Journal of Symbolic Logic, 50: 1068–1071, 1985.
Hans G. Herzberger and Radhika Herzberger. Bhartrhari’s paradox. Journal of Indian Philosophy, 9: 1–17, 1981.
Hans G. Herzberger. Paradoxes of grounding in semantics. Journal of Philosophy, 67: 145–167, 1970.
Hans G. Herzberger. Notes on periodicity. Unpublished manuscript, 1980.
H. G. Herzberger. Naive semantics and the Liar paradox. Journal of Philosophy, 79: 479–497, 1982.
Hans Herzberger. Notes on Naive Semantics. Journal of Philosophical Logic, 11: 61–102, 1982.
J. Hintikka. Truth definitions, Skolem functions and axiomatic set theory. BSL, pages 303–337, 1998.
Paul Horwich. Truth. Basil Blackwell, Oxford, 1990.
Paul Horwich. Truth. Oxford University Press, Oxford, second edition, 1998.
Jan E. M. Houben. Bhartrhari’s solution to the Liar and some other paradoxes. Journal of Indian Philosophy, 23: 381–401, 1985.
G. E. Hughes. John Buridan on Self-Reference. Cambridge University Press, Cambridge, 1982.
B. Jacobs. The inconsistency of Higher order extensions of Martin-Löf’s type theory. Journal of Philosophical Logic, 18: 399–422, 1989.
Reinhard Kahle. Applikative Theorien und Frege-Strukturen. PhD thesis, Universität Bern, Institut für Informatik und angewandte Mathematik, 1997.
F. Kammeradine. Set theory and nominalisation I. Journal of Logic and Computation, 2: 579–604, 1992.
E Kammeradine. Set theory and nominalisation II. Journal of Logic and Computation, 2: 687–707, 1992.
D. Kaplan and R. Montague. A paradox regained. Notre Dame Journal of Formal Logic, 1: 79–90, 1960.
David Kaplan. On the logic of demonstratives. Journal of Philosophical Logic, 8: 8198, 1978.
Richard Kaye. Models of Peano Arithmetic. Oxford Logic Guides. Oxford University Press, 1991.
W. Kindt. Über sprachen mit wahrheitsprädikat. In C. Habel and S. Kanngiesser, editors, Sprachdynamik und Sprachstruktur. Niemeyer, Tübingen, 1976.
W. Kindt. The introduction of truth predicates into first-order languages. hi F. Guenthner and S. J. Schmidt, editors, Formal Semantics and Pragmatics for Natural Languages, pages 359–371. Reidel, Dordrecht, 1978.
J. P. King. Reconciling Austinian and Russellian accounts of the Liar Paradox. Journal of Philosophical Logic, 23: 451–494, 1994.
Richard Kirkham. Theories of Truth: a Critical Introduction. MIT Press, Cambridge, Massachusetts, 1992.
R. Koons. Doxastic Paradoxes without self-reference. In M. Vardi, editor, TARK’88. Morgan Kaufmann, Los Altos, CA, 1988.
Robert C Koons. Paradoxes of Belief and Strategic Rationality. Cambridge University Press, Cambridge, UK, 1992.
Robert C. Koons. Review of Revision Theory of Truth. Notre Dame Journal of Formal Logic, 35: 600–631, 1994.
Henryk Kotlarski. Full satisfaction classes: a survey. Notre Dame Journal of Formal Logic, 32: 573–579, 1991.
Adam Kovach. Deflationism and the Derivation Game. Mind, 106: 575–579, 1997.
Alexandre Koyré. Épiménide le Menteur. Hermann et Cie, Paris, 1947.
J. Krajcek. A possible modal formulation of comprehension scheme. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 33: 461–480, 1987.
J. Krajeek. Some results and problems in the modal set theory mst. Zeitschrift Pr mathematische Logik und Grundlagen der Mathematik, 34: 123–134, 1988.
S. Krajewski. Nonstandard satisfaction classes. In Set Theory and Hierarchy Theory, Lecture notes in mathematics, pages 121–145. Springer, 1976.
Philip Kremer. Kripke and the logic of truth. Journal of Philosophical Logic, 17: 225278, 1986.
Philip Kremer. The Gupta-Belnap systems Sb and S* are not axiomatizable. Notre Dame Journal of Formal Logic, 34: 583–596, 1993.
Saul Kripke. Outline of a Theory of Truth. Journal of Philosophy, 72: 690–712, 1975.
E Kroon. Stenius on the paradoxes. Theoria, 4: 178–211, 1984.
Lee, Byeong-Deok. The paradox of belief instability and a revision theory of belief. PhD thesis, Department of Philosophy, Indiana University, Bloomington, 1998.
Hannes Leitgeb. Truth and the liar in De Morgan-valued models. Notre Dame Journal of Formal Logic, 40: 496–514, 1999.
Hannes Leitgeb. Theories of Truth which have no Standard Models. Studia Logica, 68: 68–87, 2001. 2001.
Hannes Leitgeb. Truth as translation: Part A. Journal of Philosophical Logic, 30: 281–307, 2001.
Hannes Leitgeb. Truth as translation: Part B. Journal of Philosophical Logic, 30: 309–328, 2001.
E. G. K. Lopez-Escobar. A formal logic for the study of paradoxes. Technical Report TR 79–11, University of Maryland, Department of Mathematics, College Park, Maryland, 1979.
Benedikt Löwe and Philip D. Welch. Set-Theoretic Absoluteness and the Revision Theory of Truth. Studia Logica, 68: 21–41, 2001.
Benedikt Löwe. Revision sequences and computers with an infinite amount of time. Journal of Logic and Computation, 11:25–40, 2001.
Penelope Maddy. Proper classes. Journal of Symbolic Logic, 48: 113–139, 1983.
Z. Manna and A. Shamir. The theoretical aspects of the optimal fixed-point. Siam Journal of Computing, 5: 414–426, 1976.
Z. Manna and A. Shamir. The convergence of functions to fixed-points of recursive definitions. Theoretical Computer Science, 6: 109–141, 1978.
Gary Mar and Paul St. Denis. What the Liar taught Achilles. Journal of Philosophical Logic, 28: 29–46, 1999.
Robert L. Martin and Peter W. Woodruff. On representing `true-in-L’ in L. Philosophia,5:213–217, 1975. Reprinted in [Martin, 1984, pp. 47–52].
Robert L. Martin, editor. The Paradox of the Liar. Yale University Press, New Haven, 1970. Second edition: Ridgeview Pub., Atascadero, CA, 1978.
R. L. Martin. On puzzling logical validity. Philosophical Review, 86: 454–473, 1977.
Donald A Martin. Revision and its rivals. In Villanueva [ 1979 ], pages 407–418.
R. M. Martin. The truth about kripke’s `truth’. In Pragmatics, Truth and Language, pages 173–180. D. Reidel, Dordrecht, 1979.
Robert L. Martin, editor. Recent Essays on Truth and the Liar Paradox. Oxford University Press, Oxford, 1984.
D. A. Martin. Review of: J. barwise and j. etchemendy, The Liar: an Essay in Truth and Circularity. Journal of Symbolic Logic, 57: 252–254, 1992.
T. McCarthy. Ungroundedness in classical languages. Journal of Philosophical Logic, 17: 61–74, 1988.
Brian E. McDonald. On meaningfulness and truth. Journal of Philosophical Logic, 29: 433–482, 2000.
Vann McGee. Revision. In Villanueva [ 1979 ], pages 387–406.
Vann McGee. How Truthlike Can a Predicate Be? Journal of Philosophical Logic, 14: 399–410, 1985.
V. McGee. Applying Kripke’s theory. Journal of Philosophy, 87: 530–539, 1989.
Vann McGee. Truth, Vagueness and Paradox. Hackett Publishing, Indianapolis, 1991.
Vann McGee. Maximal consistent sets of instances of Tarski’s schema (T). Journal of Philosophical Logic, 21: 235–241, 1992.
Vann McGee. The Analysis of `x-is true’ as `For any-p, if x = `p’, then-p’. In André Chapuis and Anil Gupta, editors, Circularity, Definitions, and Truth, pages 255–272. Journal of Indian Council of Philosophical Research, New Delhi, 2000.
Matthew McGrath. Weak Defiationism. Mind, 106: 69–98, 1997.
J. L. McKie. Truth, Probability and Paradox: studies in Philosophical Logic. Oxford, 1973.
D. McLarty. Anti-foundation and self-reference. Journal of Philosophical Logic, 22: 19–28, 1993.
C. Menzel. A complete, type-free “second-order” logic and its philosophical foundations. Technical report, CSLI, 1986.
Richard Montague. On the paradox of grounded classes. Journal of Symbolic Logic, 20: 140, 1950.
Richard Montague. Syntactic treatments of modality, with corollaries on reflexion principles and finite axiomatizability. Acta Philosophica Fennica, 16: 153–167, 1963.
Moschovakis, 1974]’ M. Moschovakis, Yiannis. Elementary Induction on Abstract Structures. North Holland, Amsterdam, 1974.
M. Moschovakis, Yiannis. On the basic notions in the theory of induction. In R. E. Butts and J. Hintikka, editors, Logic, Foundations of Mathematics and Computability Theory, pages 207–236. D. Reidel, Dordrecht, 1977.
Y. N. Moschovakis. Sense and reference as algorithm and value. In Logic Colloquium ‘80, Springer Lecture Notes in Logic, pages 210–249. Springer-Verlag, 1990.
L. Moss. Review of: J. Barwise and J. Etchemendy. The Liar: an Essay in Truth and Circularity. Bulletin of the American Mathematical Society, 20: 216–225, 1989.
John Myhill. A system which can define its own truth. Fundamenta Mathematicae, 37: 190–192, 1950.
J. Myhill, Levels of implications. In R. B. Marcus, A. R. Anderson, and R. M. Martin, editors, The Logical Enterprise, pages 179–185. Yale University Press, New Haven, 1975.
John Myhill. Paradoxes. Synthese, 60: 129–143, 1984.
M. Negri. An autoapplicable truth predicate. Bollettino dell’Unione Matematica Italiana, 3-B: 29–39, 1989.
N. N. Nepeïvoda. A new notion of predicative truth and definability. Mathematiceskie Zumetki, 13:735–745,1973. English translation in: Mathematical Notes of the Academy of Sciences of the USSR, 13, 439–445.
Karl-Georg Niebergall. Simultane objektsprachliche Axiomatisierung von Notwendigkeits-and Beweisbarkeitsprädikaten. Master’s thesis, Ludwigs-Maximilians-Universität München, 1991.
G. Niemi. Modality and Self Reference. University Microfilms, Ann Arbor, 1970.
U. Nortmann. Vier Philosophen über semantische Paradoxien. History and Philosophy of Logic, 16: 217–244, 1995.
F. Orilia. Type-free Property Theory, Exemplification and Russell’s paradox. Notre Dame Journal of Formal Logic, 32: 432–447, 1991.
Francesco Orilia. Predication, Analysis and Reference. CLUEB, collana Heuresis, Linguaggio, Logica, Scienza, diretta da Alberto Pasquinelli and Giorgio Sandri, Bologna, 1999.
Francesco Orilia. Belief Revision and the Alethic Paradoxes. In A. Chapuis and A. Gupta, editors, Circularity, Definition and Truth, pages 273–296. Indian Council of Philosophical Research, New Delhi, India, 2000. Distribuito fuori dall’India da Ridgeview Publishing Company, Atascadero, CA, USA.
Francesco Orilia. Meaning and Circular Definitions. Journal of Philosophical Logic, 29: 155–169, 2000.
Francesco Orilia. Property Theory and the Revision Theory of Definitions. Journal of Symbolic Logic, 65: 212–246, 2000.
Wray Otway. Logic in quotes. Journal of Philosophical Logic, 1987.
Charles Parsons. The liar paradox. Journal of Philosophical Logic,3:381–412, 1974. reprinted in [Martin, 1984, pp. 9–461.
C. Parsons. Postscript to `the liar paradox’, 1982.
Terrence Parsons. Assertion, denial and the Liar paradox. Journal of Philosophical Logic, 13: 137–152, 1984.
D. Pavlovic. On the structure of paradoxes. Archive for Mathematical Logic, 31: 397406, 1992.
U. Pedersen. Logic without contraction as based on inclusion and unrestricted abstraction. Studie Logica, 64: 3065–403, 2000.
D. Perlis and V. S. Subrahmanian. Meta-languages, reflection principles and self-reference. In D. M. Gabbay, C. J. Hogger, and J. A. Robinson, editors, Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 2. Clarendon Press, Oxford, 1994.
D. Perlis. Languages with self-reference I: foundations. Artificial Intelligence, 25: 30 1322, 1985.
D. Perlis. Languages with selfreference II: Knowledge, belief and modality. Artificial Intelligence, 34: 179–212, 1988.
D. Perlis. Truth and meaning. Artificial Intelligence, 39: 245–250, 1989.
G. Plotkin. An illative theory of relations. In R. Cooper, K. Mukai, and J. Perry, editors, Situation Theory and Its Applications, pages 134–146. CSLI, Stanford, 1990.
J. L. Pollock. The liar strikes back. Journal of Philosophy, 74: 604–606, 1977.
Sir Karl R. Popper. Self reference and meaning in ordinary language. Mind,63:162–169, 1954. Reprinted in [Popper, 1972, pp. 304–311].
Sir Karl R. Popper. Conjectures and Refutations. Routledge and Kegan Paul, London, 1972.
D. Prawitz. Natural Deduction: A Prooftheoretical Study. Alqvist and Wiksell, Stockholm, 1965.
Graham Priest. The logic of paradox. Journal of Philosophical Logic, 8: 219–241, 1969.
Graham Priest. The logic of paradox revisited. Journal of Philosophical Logic, 13: 153179, 1984.
Graham Priest: In Contradiction: A Study of the Transconsistent. M. Nijhoff, Dordrecht, 1987.
G. Priest. Reasoning about truth. Artificial Intelligence, 39: 231–244, 1989.
Arthur N. Prior. Correspondence theory of truth. In Paul Edwards, editor, The Encyclopedia of Philosophy, vol. 2, pages 223–232. New York: Macmillan, 1967.
Lorenz Puntel. Wahrheitstheorien in der neueren Philosophie. Wissenschaftliche Buchgesellschaft, Darmstadt, third edition, 1993.
W. V. O. Quine. Paradox. Scientific American of April, pages 84–96, 1962.
E P. Ramsey. The foundations of mathematics. In Proceedings of the London Mathematical Society, volume 25, pages 338–384, 1925. Also in F. R. Ramsey, Foundations, pp. 152–212, Routledge and Kegan Paul, London, 1978.
W. J. Reinhardt. Remarks on significance and meaningful applicability. In L. P. de Alcantara, editor, Mathematical Logic and Formal Systems, volume 94 of Lecture Notes in Pure and Applied Mathematics, pages 227–242, New York, 1985. Marcel Dekker.
William Reinhardt. Some Remarks on Extending and Interpreting Theories with a Partial Predicate for Truth. Journal of Philosophical Logic, 15: 219–251, 1986.
N. Rescher and R. Brandom. The logic of inconsistency. Rowman and Littlefield, Totowa, 1979.
Jim des Rivières and Hector J. Levesque. The Consistency of Syntactical Treatments of Knowledge. In Joseph Y. Halpern, editor, Theoretical Aspects of Reasoning About Knowledge: Proceedings of the 1986 Conference, pages 115–130, Los Altos, 1986. Morgan Kaufmann.
D. K. Roy. On berry’s paradox and non diagonal constructions. Complexity, 4: 35–38, 1999.
W. Ruitenburg. Constructive Logic and the paradoxes. Modern Logic,1(4):271301, 1991.
W. Ruitenburg. Basic Logic and Fregean Set Theory. In M. Bezem and J. W. Klop, editors, Dirk van Dalen Festschrift, number 5 in Quaestiones Infinitae, pages 121–142. Department of Philosophy, Utrecht University, Utrecht, 1993.
Paul Schweizer. A Syntactical Approach to Modality. Journal of Philosophical Logic, 21: 1–31, 1992.
D. S. Scott. Combinators and classes. In C. Böhm, editor, A-Calculus and Computer Science Theory, volume 37 of Lecture Notes in Computer Science, pages 1–26, Berlin, 1975. Springer Verlag.
J. P. Seldin and J. R. Hindley, editors. To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism. Academic Press, New York, 1980.
Michael Sheard. A Guide to Truth Predicates in the Modem Era. Journal of Symbolic Logic, 59: 1032–1054, 1994.
Shen-Yuting Paradox of the class of all grounded classes. Journal of Symbolic Logic, 18: p114, 1953.
K. Simmons. On a medieval solution to the liar paradox. History and Philosophy of Logic, 8, 1987.
K. Simmons. The diagonal argument and the liar. Journal of Philosophical Logic, 19: 277–303, 1990.
Keith Simmons. Universality and the Liar: An Essay on Truth and the Diagonal Argument. Cambridge University Press, Cambridge, UK, 1993.
K. Simmons. Deflationary Truth and the Liar. Journal of Philosophical Logic, 28: 455–488, 1999.
T. A. Skolem. A set theory based on a certain three valued logic. Mathematica Scandinava, 8: 127–136, 1960.
T. A. Skolem. Studies on the axiom of comprehension. Notre Dame Journal of Formal Logic, 4: 162–170, 1963.
B. Skyrms. Return of the Liar, three valued logic and the concept of truth. American Philosophical quarterly, 7: 153–161, 1970.
B. Skyrms. Intensional aspects of semantical self-reference. In R. M. Martin, editor, Pragmatics, Truth and Language, pages 119–132. D. Reidel, Dordrecht, 1984.
J. Smith. An interpretation of Martin-Löf’s type theory in a type-free theory of propositions. Journal of Symbolic Logic, 49: 730–753, 1984.
Stuart Smith. Non-standard Syntax and Semantics and Full Satisfaction Classes. PhD thesis, Yale University, New Haven, Connecticut, 1984.
Stuart Smith. Nonstandard characterizations of recursive saturation and resplendency. Journal of Symbolic Logic, 52: 842–863, 1987.
Stuart Smith. Nonstandard definability. Annals of Pure and Applied Logic, 42: 21–43, 1989.
C. Smorynski. The incompleteness theorems. In J. Barwise, editor, Handbook of Mathematical Logic, pages 821–865. North Holland, Amsterdam, 1977.
R. M. Smullyan. Languages in which self-reference is possible. Journal of Symbolic Logic, 22:55–67, 1957. Reprinted in The Philosophy of Mathematics, J. Hintikka, ed. pp. 64–77. Oxford University Press, Oxford, 1969.
R. M. Smullyan. What Is the Name of This Book? Penguin Books, Harmondsworth, 1981.
R. M. Smullyan. Chameleonic Languages. Synthese, 60: 201–224, 1984.
Scott Soames. What is a theory of truth? Journal of Philosophy, 81: 411–429, 1984.
Scott Soames. Understanding Truth. Oxford University Press, New York, 1999.
Ernest Sosa. The Truth of Modest Realism. Philosophical Issues, 3 Science and Knowledge:77–95, 1993.
Paul V. Spade. Lies, Language, and Logic in the Late Middle Ages. Variorum Reprints, London, 1988.
E. Stenius. Das Problem der logischen Antinomien. Societas Scientiarum Fennica, Commentationes Phys. Math., 1967.
A. Tarski. Der wahrheitsbegriff in den formalisierten Sprachen. Studia Philosophica, 1:261–405, 1935. Reprinted as [Tarski, 19561. The paper is a translation of the Polish Pojgie prawdy w jgzykach nauk dedukcyjnych, Prace Towarzystwa Naukowego Warszawskiego, Wydzial III matematyczno-fizycznych, no. 34, Warsaw 1933.
A. Tarski. The semantic conception of truth. Philosophy and Phenomenological Research,4:341–375, 1944. Reprinted in e.g. [Harnish, 1994, pp. 536–570].
A. Tarski. The concept of truth in formalised languages. In A. Tarski, editor, Logic, Semantics, Metamathematics, pages 152–278. Oxford University Press, Oxford, 1956. This paper is a translation of [Tarski, 1935 ].
A. Tarski. Truth and proof. Scientific American of June 1969, 220: 63–70, 75–77, 1969.
Neil Tennant. Conservativeness, Incompleteness and Deflationism. Draft, 1999.
R. H. Thomason. A semantical study of constructive falsity. Zeitschrift für mathematische Logik und Grundlagen der Matematik, 15: 247–257, 1969.
R. H. Thomason. Necessity, quotation and truth: an indexical theory. Philosophie, 5: 219–241, 1975.
R. Thomason. A note on syntactical treatments of modality. Synthèse, 44: 391–395, 1980.
R. Thomason. Paradoxes and semantic representation. In J. Y. Halpern, editor, TARK’86. Morgan Kaufmann, Los Altos, CA, 1986.
Raymond Turner. Montague semantics, nominalization and Scott’s domains. Linguistics and Philosophy, 6: 259–288, 1983.
Raymond Turner. Nominalization and Scott domains II. Notre Dame Journal of Formal Logic, 26: 463–478, 1985.
Raymond Turner. Three theories of nominalized predicates. Studia Logica, 44: 165186, 1985.
Raymond Turner. A theory of properties. Journal of Symbolic Logic, 52: 445–472, 1987.
Raymond Turner. Logics of truth. Notre Dame Journal of Formal Logic, 31: 308–329, 1990.
Raymond Turner. Truth and Modality for Knowledge Representation. Pitman, London, 1990.
A. Tzouvaras. Logic of knowledge and utterance and the Liar. Journal of Philosophical Logic, 27: 85–108, 1998.
Enrique Villanueva, editor. Truth, number 8 in Philosophical Issues, Atascadero, CA, 1979. Ridgeview Publishing Company.
A. Visser. A propositional logic with explicit fixed points. Studia Logica, 40: 155–175, 1981.
Albert Visser. Four-valued semantics and the liar. Journal of Philosophical Logic, 13: 181–212, 1984.
Albert Visser. Semantics and the liar paradox. In D. M. Gabbay and Franz Günthner, editors, Handbook of Philosophical Logic, volume IV, pages 617–706. Reidel, Dordrecht, 1989.
Philip D. Welch. On Gupta—Belnap Revision Theories of truth, Kripkean Fixed points, and the Next Stable Set. Bulletin for Symbolic Logic, 7: 345–360, 2001.
Philip D. Welch. On Revision Operators. Journal of Symbolic Logic, 68: 689–711, 2003.
R. B. White. The consistency of the axiom of comprehension in the infinite value predicate logic of lukasiewicz. Journal of Philosophical Logic, pages 509–534, 1979.
R. B. White. A demostrably consistent type-free extension of the logic BCK. Mathematica Japonica, 32: 149–169, 1987.
R. B. White. A consistent theory of attributes in a logic without contraction. Studia Logica, 52: 113–142, 1993.
Peter Woodruff. Paradox, truth and logic I: Paradox and truth. Journal of Philosophical Logic, 13: 867–896, 1984.
Stephen Yablo. Grounding, dependence, and paradox. Journal of Philosophical Logic, 11: 117–137, 1982.
Stephen Yablo. Truth and reflection. Journal of Philosophical Logic, 14: 297–349, 1985.
Aladdin M. Yaqúb. The Liar Speaks the Truth: A Defense of the Revision Theory of Truth. Oxford University Press, New York, 1993.
W. S Zwicker. Playing games with games: the hypergame paradox. American Mathematical Monthly, 94: 507–514, 1987.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Visser, A. (2002). Semantics and the Liar Paradox. In: Gabbay, D.M., Guenthner, F. (eds) Handbook of Philosophical Logic. Handbook of Philosophical Logic, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0466-3_3
Download citation
DOI: https://doi.org/10.1007/978-94-017-0466-3_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6554-4
Online ISBN: 978-94-017-0466-3
eBook Packages: Springer Book Archive