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Published online by Cambridge University Press:  08 October 2021

Zach Weber
Zach Weber
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University of Otago, New Zealand
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Paradoxes and Inconsistent Mathematics , pp. 303 - 318
Publisher: Cambridge University Press
Print publication year: 2021

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References

Abad, J. (2008). The inclosure schema and the solution to the paradoxes of self-reference. Synthese, 160(2):183–202.Google Scholar
Aczel, P. (1988). Non-Well-Founded Sets. Number 14 in CSLI Lecture Notes. CSLI Publications.Google Scholar
Allwein, G. and Dunn, J. M. (1993). Kripke semantics for linear logic. Journal of Symbolic Logic, 58(2):514–545.Google Scholar
Anderson, A. R. and Belnap, N. D. (1975). Entailment: The Logic of Relevance and Necessity, volume 1. Princeton University Press.Google Scholar
Anderson, A. R., Belnap, N. D., and Dunn, J. (1992). Entailment: The Logic of Relevance and Necessity, volume 2. Princeton University Press.Google Scholar
Armstrong, M. (1979). Basic Topology. Springer.Google Scholar
Arntzenius, F. (2012). Space, Time, and Stuff. Oxford University Press.CrossRefGoogle Scholar
Arruda, A. I. and Batens, D. (1982). Russell’s set versus the universal set in paraconsistent set theory. Logique et Analyse, 25(8):121–133.Google Scholar
Asenjo, F. (1966). A calculus of antinomies. Notre Dame Journal of Formal Logic, 7:103–105.Google Scholar
Asenjo, F. (1975). Logic of antinomies. Notre Dame Journal of Formal Logic, 16:17–44.CrossRefGoogle Scholar
Asenjo, F. G. (1989). Toward an antinomic mathematics. In [Priest et al., 1989], pages 394–414.Google Scholar
Austin, D. F., editor (1988). Philosophical Analysis. Kluwer.Google Scholar
Azzouni, J. (2006). Tracking Reason: Proof, Consequence, and Truth. Oxford University Press.CrossRefGoogle Scholar
Bacon, A. (2013). Non-classical metatheory for non-classical logics. Journal of Philosophical Logic, (42):335–355.CrossRefGoogle Scholar
Badia, G. (2017). The Languages of Relevant Logic. PhD thesis, University of Otago.Google Scholar
Badia, G. and Weber, Z. (2019). A substructural logic for inconsistent mathematics. In Reiger, A. and Young, G., editors, Dialetheism and Its Applications, pp. 155–176. Springer.Google Scholar
Badici, E. (2008). The liar paradox and the inclosure schema. Australasian Journal of Philosophy, 86(4):583–596.Google Scholar
Barendregt, H. (1984). The Lambda Calculus: Its Syntax and Semantics. North Holland.Google Scholar
Barnes, E. (2010). Ontic vagueness: a guide for the perplexed. Nous, 44(4):601–627.Google Scholar
Barwise, J. and Moss, L. (1996). Vicious Circles. CSLI Publications.Google Scholar
Batens, D. (2019). Looting liars masking models. In Baskent, C. and Ferguson, T., editors, Graham Priest on Dialetheism and Paraconsistency, pages 139–164. Springer.Google Scholar
Batens, D. (2020). Adaptive fregean set theory. Studia Logica, 108:903–939.Google Scholar
Batens, D., Mortensen, C., Priest, G., and van Bendegem, J.-P., editors (2000). Frontiers of Paraconsistent Logic. Research Studies Press.Google Scholar
Beall, J. (1999). From full blooded platonism to really full blooded platonism. Philosophia Mathematica, 7(3):322–325.Google Scholar
Beall, J., editor (2003). Liars and Heaps. Oxford University Press.Google Scholar
Beall, J., editor (2007). Revenge of the Liar. Oxford University Press.Google Scholar
Beall, J. (2009). Spandrels of Truth. Oxford University Press.CrossRefGoogle Scholar
Beall, J. (2011). Multiple-conclusion LP and default classicality. Review of Symbolic Logic, 4(2):326–336.Google Scholar
Beall, J. (2013a). Free of detachment: logic, rationality, and gluts. Noûs, 49(2):410–423.CrossRefGoogle Scholar
Beall, J. (2013b). Shrieking against gluts: the solution to the “just true” problem. Analysis, 73(3):438–445.Google Scholar
Beall, J. (2014a). End of inclosure. Mind, 123(491):829–849.CrossRefGoogle Scholar
Beall, J. (2014b). Finding tolerance without gluts. Mind, 123(491):791–811.CrossRefGoogle Scholar
Beall, J., Brady, R. T., Hazen, A., Priest, G., and Restall, G. (2006). Relevant restricted quantification. Journal of Philosophical Logic, 35:587–598.Google Scholar
Beall, J. and Colyvan, M. (2001a). Heaps of gluts and hyde-ing the sorites. Mind, 110:401–408.Google Scholar
Beall, J. and Colyvan, M. (2001b). Looking for contradictions. Australasian Journal of Philosophy, 79:564–9.Google Scholar
Beall, J., Glanzberg, M., and Ripley, D. (2018). Formal Theories of Truth. Oxford University Press.Google Scholar
Beall, J. and Murzi, J. (2013). Two flavors of curry paradox. Journal of Philosophy, 110(3):143–165.CrossRefGoogle Scholar
Beall, J., Priest, G., and Weber, Z. (2011). Can u do that? Analysis, 71(2):280–285.Google Scholar
Beall, J. and Restall, G. (2006). Logical Pluralism. Oxford University Press.Google Scholar
Beardon, A. F. (2012). Algebra and Geometry. Cambridge University Press.Google Scholar
Běhounek, L. and Cintula, P. (2005). Fuzzy class theory. Fuzzy Sets and Systems, 154(1):34–55.Google Scholar
Běhounek, L. and Haniková, Z. (2015). Set theory and arithmetic in fuzzy logic. In Montagna, F., editor, Petr Hajek on Mathematical Fuzzy Logic, pages 63–89. Springer. Outstanding Contributions to Logic Series, volume 6.Google Scholar
Bell, J. L. (2008). A Primer of Infinitesimal Analysis. Cambridge University Press. Second Edition.CrossRefGoogle Scholar
Bell, J. L. (2014). Intuitionistic Set Theory. College Publications. Studies in Logic 50.Google Scholar
Belnap, N. D. and Dunn, J. M. (1981). Entailment and the disjunctive syllogism. Contemporary Philosophy: A New Survey, 1:337–366.Google Scholar
Berberain, S. K. (1977). A First Course in Real Analysis. Springer.Google Scholar
Berto, F. (2008). Adunaton and material exclusion. Australasian Journal of Philosophy, 86(2):165–190.Google Scholar
Birkhoff, G. and Maclane, S. (1999). Algebra, Third Edition. American Mathematical Society. First Edition 1967.Google Scholar
Bishop, E. (1967). Foundations of Constructive Analysis. McGraw-Hill.Google Scholar
Bishop, E. and Bridges, D. S. (1985). Constructive Analysis. Springer.Google Scholar
Black, M. (1951). Achilles and the tortoise. Analysis, 11:91–101.Google Scholar
Blizard, W. (1989). Multiset theory. Notre Dame Journal of Formal Logic, 30(1):36–66.Google Scholar
Bolzano, B. (1950 [1851]). Paradoxes of the Infinite. Routledge and Keegan Paul. Translated by F. Prihonsky.Google Scholar
Bolzano, B. (1973). Theory of Science. D. Reidel Publishing. Edited, with an introduction, by J. Berg. Translated by B. Terrell.Google Scholar
Boolos, G. (1971). The iterative conception of set. Journal of Philosophy, 68(8):215–231. Reprinted in in [Boolos, 1998].Google Scholar
Boolos, G. (1998). Logic, Logic and Logic. Harvard University Press.Google Scholar
Boos, W. (1983). A self-referential “cogito.” Philosophical Studies, 44(2):269–290.Google Scholar
Boyer, C. (1959). The History of the Calculus and Its Conceptual Development. Dover Publications.Google Scholar
Braddon-Mitchell, D. and Miller, K. (2006). The physics of extended simples. Analysis, 66(3):222–226.Google Scholar
Brady, R. (1971). The consistency of the axioms of the axioms of abstraction and extensionality in a three-valued logic. Notre Dame Journal of Formal Logic, 12: 447–453.Google Scholar
Brady, R., editor (2003). Relevant Logics and Their Rivals, Volume II: A Continuation of the Work of Richard Sylvan, Robert Meyer, Val Plumwood and Ross Brady. Ashgate.Google Scholar
Brady, R. (2006). Universal Logic. CSLI Publications.Google Scholar
Brady, R. and Mortensen, C. (2014). Logic. In Oppy, G. and Trakakis, N., editors, History of Philosophy in Australia and New Zealand, pp. 679–705. Springer, Dordrecht.Google Scholar
Brady, R. T. (1989). The non-triviality of dialectical set theory. In [Priest et al., 1989], pages 437–470.CrossRefGoogle Scholar
Brady, R. T. and Routley, R. (1989). The non-triviality of extensional dialectical set theory. In [Priest et al., 1989], pages 415–436.Google Scholar
Brentano, F. (1988). Philosophical Investigations on Space, Time and the Continuum. Croom Helm. B. Smith (trans).Google Scholar
Bridges, D. and Vita, L. S. (2011). Apartness and Uniformity: A Constructive Development. Springer.Google Scholar
Brown, B. and Priest, G. (2004). Chunk and permeate i: the infinitesimal calculus. Journal of Philosophical Logic, 33:379–388.Google Scholar
Brown, J. (2008). Philosophy of Mathematics. Routledge. Second Edition.Google Scholar
Bueno, O. and Colyvan, M. (2012). Just what is vagueness? Ratio, 25:19–33.Google Scholar
Burgess, J. P. (2005). No requirement of relevance. In Shapiro, S., editor, The Oxford Handbook of Philosophy of Mathematics and Logic, pages 727–750. Oxford University Press.Google Scholar
Burgess, J. P. and Woods, J. (2015). Review of the Boundary Stones of Thought by Ian Rumfitt. Notre Dame Philosophical Reviews, October 24, 2015.Google Scholar
Buskes, G. and van Rooij, A. (1997). Topological Spaces: From Distance to Neighborhood. Springer.Google Scholar
Cantini, A. (2003). The undecidability of Grĭsin’s set theory. Studia Logica, 74(3):345–368.Google Scholar
Cantor, G. (1895). Beiträge zur begründung der transfiniten mengenlehre (zweiter artikel). Mathematische Annalen, 49:207–246.Google Scholar
Cantor, G. (1915). Contributions to the Founding of the Theory of Transfinite Numbers. Dover. Edited, translated, and introduced by P. E. B. Jourdain, from [Cantor, 1895].Google Scholar
Cantor, G. (1967). Letter to Dedekind. In [van Heijenoort, 1967], pages 113–117. 1899.Google Scholar
Caret, C. R. and Hjortland, O. T., editors (2015). Foundations of Logical Consequence. Oxford University Press.Google Scholar
Caret, C. R. and Weber, Z. (2015). A note on contraction-free logic for validity. Topoi, 31(1):63–74.Google Scholar
Carnielli, W. and Coniglio, M. E. (2016). Paraconsistent Logic: Consistency, Contradiction and Negation. Springer.Google Scholar
Carnielli, W., Coniglio, M., and Marcos, J. (2007). Logics of formal inconsistency. In Gabbay, D. and Guenthner, F., editors, Handbook of Philosphical Logic, volume 14, pages 1–93. Springer-Verlag.Google Scholar
Carr, M. H. (2007). The Surface of Mars. Cambridge University Press.Google Scholar
Casati, F. and Fujikawa, N. (2019). Nothingness, meinongianism, and inconsistent mereology. Synthese, 196:3739–3772.CrossRefGoogle Scholar
Casati, R. (2003). The Shadow Club. Knopf.Google Scholar
Casati, R. and Varzi, A. C. (1999). Parts and Places: The Structures of Spatial Representation. MIT Press.Google Scholar
Chang, C. (1963). The axiom of comprehension in infinite valued logic. Mathematica Scandinavia, 13:9–30.Google Scholar
Chisholm, R. M. (1984). Boundaries as dependent particulars. Grazer philosophische Studien, 10:87–95.Google Scholar
Chvalovský, K. and Cintula, P. (2012). Note on deduction theorems in contraction-free logics. Mathematical Logic Quarterly, 58(3):236–243.Google Scholar
Cintula, P. and Paoli, F. (2016). Is mutliset consequence trivial? Synthese, https://doi.org/10.1007/s11229-016-1209-7.Google Scholar
Clarke, B. L. (1985). Individuals and points. Notre Dame Journal of Formal Logic, 26:61–75.Google Scholar
Cogburn, J. (2017). Garcian Meditations. Edinburgh University Press.Google Scholar
Cohen, P. J. (1966). Set Theory and the Continuum Hypothesis. W. A. Benjamin.Google Scholar
Cohen, S. M., Curd, P., and Reeve, C., editors (2000). Readings in Ancient Greek Philosophy: From Thales to Aristotle. Hackett.Google Scholar
Cohn, P. (2003). Basic Algebra: Groups, Rings, and Fields. Springer.CrossRefGoogle Scholar
Colyvan, M. (2008a). The ontological commitments of inconsistent theories. Philosophical Studies, 141(1):115–123.Google Scholar
Colyvan, M. (2008b). Vagueness and truth. In Dyke, H., editor, From Truth to Reality: New Essays in Logic and Metaphysics, pp. 29–40. Routledge.Google Scholar
Colyvan, M. (2009). Applying inconsistent mathematics. In New Waves in Philosophy of Mathematics, pp. 160–172. Palgrave Macmillan.Google Scholar
Colyvan, M. (2012). An Introduction to the Philosophy of Mathematics. Cambridge University Press.Google Scholar
Conway, J. (1976). On Numbers and Games. Academic Press.Google Scholar
Cook, R. T. (2014). There is no paradox of logical validity. Logical Universalis, 8(3–4):447–467.Google Scholar
Cotnoir, A. and Baxter, D., editors (2014). Composition as Identity. Oxford University Press.Google Scholar
Curry, H. B. (1942). The inconsistency of certain formal logics. Journal of Symbolic Logic, 7:115–117.CrossRefGoogle Scholar
da Costa, N. (2000). Paraconsistent mathematics. In [Batens et al., 2000], pages 165–180.Google Scholar
da Costa, N. C., Krause, D., and Bueno, O. (2007). Paraconsistent logics and paraconsistency. In [Jacquette, 2007], pages 791–912.Google Scholar
da Costa, N. C. A. (1974). On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15:497–510.CrossRefGoogle Scholar
Dainton, B. (2010). Time and Space. McGill-Queen’s University Press. Second Edition.Google Scholar
Dauben, J. W. (1979). Georg Cantor: His Mathematics and Philosophy of the Infinite. Princeton. University Press.Google Scholar
Dedekind, R. (1901). Essays on the Theory of Numbers. Dover. Ed. and trans. by W. W. Beman, 1901. Includes Stetigkeit und irrationale Zahlen [1872] and Was sind und was sollen die Zahlen? [1888]. Dover Edition 1963.Google Scholar
Della Rocca, M. (2008). Spinoza. Routledge.Google Scholar
Deloup, F. (2005). The fundamental group of the circle is trivial. American Mathematical Monthly, 112(5):417–425.Google Scholar
Devlin, K. J. (1979). Fundamentals of Contemporary Set Theory. Springer. Second Edition 1993, retitled “The Joy of Sets.”Google Scholar
Dicher, B. and Paoli, F. (2019). ST, LP, and tolerant metainferences. In Baskent, C. and Ferguson, T., editors, Graham Priest on Dialetheism and Paraconsistency, pages 383–408. Springer.Google Scholar
Dietrich, E. (2015). Excellent Beauty. Columbia University Press, New York.Google Scholar
Dillon, M. (1997). Merleau-Ponty’s Ontology. Northwestern University Press.Google Scholar
Drake, F. (1974). Set Theory: An Introduction to Large Cardinals. North Holland.Google Scholar
Dummett, M. (1978). Truth and Other Enigmas. Oxford University Press.Google Scholar
Dummett, M. (1991). Frege: Philosophy of Mathematics. Duckworth.Google Scholar
Dümont, J. and Mau, F. (1998). Are there true contradictions? A critical discussion of Graham Priest’s Beyond the Limits of Thought. Journal for General Philosophy of Science, 29(2):289–299.Google Scholar
Dunn, J. (1987). Relevant predication 1: The formal theory. Journal of Philosophical Logic, 16:347–381.Google Scholar
Dunn, J. and Restall, G. (2002). Relevance logic. In Gabbay, D. M. and Günthner, F., editors, Handbook of Philosophical Logic, volume 6, pages 1–128. Kluwer. Second Edition.Google Scholar
Dunn, J. M. (1979). A theorem in 3-valued model theory with connections to number theory, type theory, and relevant logic. Studia Logica, 38:149–169.Google Scholar
Dunn, J. M. (1980). Relevant Robinson’s arithmetic. Studia Logica, 38:407–418.Google Scholar
Dunn, J. M. (1988). The impossibility of certain higher-order non-classical logics with extensionality. In [Austin, 1988], pages 261–280.Google Scholar
Dzhafarov, E. N. and Dzhafarov, D. (2010). Sorites without vagueness I: classificatory sorites. Theoria, 76(1):4–24.Google Scholar
Estrada-González, L. (2016). Prospects for triviality. In Anreas, H. and Verdée, P., editors, Logical Studies of Paraconsistent Reasoning in Science and Mathematics. Springer.Google Scholar
Etchemendy, J. (1990). The Concept of Logical Consequence. Harvard University Press.Google Scholar
Euclid, (1956). The Thirteen Books of the Elements. Dover. Edited, translated, and annotated by T. L. Heath.Google Scholar
Feferman, S. (1984). Toward useful type-free theories, I. Journal of Symbolic Logic, 49(1):75–111.Google Scholar
Field, H. (2008). Saving Truth from Paradox. Oxford University Press.Google Scholar
Field, H. (2020). Properties, propositions, and conditionals. Australasian Philosophical Review, forthcoming.Google Scholar
Field, H., Lederman, H., and Øgaard, T. F. (2017). Prospects for a naive theory of classes. Notre Dame Journal of Formal Logic, 58(4):461–506.Google Scholar
Fitch, F. (1964). Universal metalanguages for philosophy. The Review of Metaphysics, 17(3):396–402.Google Scholar
Forster, T. (1982). Axiomatising set theory with a universal set. Typeset 1997.Google Scholar
Forster, T. (1995). Set Theory with a Universal Set. Clarendon Press.Google Scholar
Fraenkel, A. (1953). Abstract Set Theory. Amsterdam.Google Scholar
Fraenkel, A. Bar-Hillel, Y., and Levy, A. (1958). Foundations of Set Theory. North Holland.Google Scholar
Frankel, C. (2005). Worlds on Fire: Volcanoes on the Earth, Moon, Mars, Venus, and Io. Cambridge University Press.Google Scholar
Franks, C. (2009). The Autonomy of Mathematical Knowledge. Cambridge University Press.Google Scholar
Frege, G. (1885). Ü ber formale Theorien der Arithmetik. Sitzungsberichte der Jenaischen Gesellschaft für Medizin und Naturwissenschaft, 2:94–104. Reprinted in Collected Papers on Mathematics, Logic, and Philosophy. Basil Blackwell, 1984.Google Scholar
Frege, G. (1893/1903a). The Basic Laws of Arithmetic. Oxford. Translated and edited by P. A. Ebert and M. Rossberg, with C. Wright; appendix by R. T. Cook.Google Scholar
Frege, G. (1893/1903b). Grundgesetze der Arithmetik, Begriffsschriftlich abgeleitet. Verlag Hermann Pohle.Google Scholar
French, R. (2016). Structural reflexivity and the paradoxes of self-reference. Ergo, 3(5):113–131.Google Scholar
French, R. and Ripley, D. (2015). Contractions of noncontractive consequence relations. Review of Symbolic Logic, 8(3):506–528.Google Scholar
Friedman, H. and Meyer, R. (1992). Whither relevant arithmetic? Journal of Symbolic Logic, 57:824–31.Google Scholar
Galatos, N., Jipsen, P., Kowalski, T., and Ono, H. (2007). Residuated Lattices. Elsevier.Google Scholar
Geach, P. (1955). On insolubilia. Analysis, 15:71–72.CrossRefGoogle Scholar
Gilles, D., editor (1992). Revolutions in Mathematics. Oxford Unviersity Press.CrossRefGoogle Scholar
Gilmore, P. C. (1974). The consistency of partial set theory without extensionality. In [Jech, 1974], pages 147–153.Google Scholar
Girard, J.-Y. (1998). Light linear logic. Information and Computation, 143:175–204.Google Scholar
Girard, P. and Weber, Z. (2019). Modal logic without contraction in a metatheory without contraction. Review of Symbolic Logic, 4(12):685–701.Google Scholar
Goddard, L. and Routley, R. (1973). The Logic of Significance and Context. Scottish Academic Press.Google Scholar
Gödel, K. (1964). What is Cantor’s continuum problem? In Benacerraf, P. and Putnam, H., editors, Philosophy of Mathematics, pages 258–273. Cambridge University Press. Paper originally written in 1947.Google Scholar
Goldblatt, R. (1998). Lectures on the Hyperreals. Springer.Google Scholar
Goodship, L. (1996). On dialethism. Australasian Journal of Philosophy, 74(1):153–161.Google Scholar
Grey, J. (2008). Plato’s Ghost: The Modernist Transformation of Mathematics. Princeton University Press.Google Scholar
Grimeisen, G. (1972). Continuous relations. Mathematische Zeitschrift, 127:35–44.Google Scholar
Gris̆in, V. (1982). Predicate and set theoretic calculi based on logic without contraction rules. Mathematics of USSR–Izvestija, 18(1):41–59.Google Scholar
Gupta, A. and Belnap, N. (1993). The Revision Theory of Truth. MIT Press.Google Scholar
Hájek, A. (2016). Philosophical heuristics and philosophical methodology. In Cappelen, H., Gendler, T., and Hawthorne, J., editors, Oxford Handbook of Philosophical Methodology. Oxford University Press.Google Scholar
Halbach, V. (2014). Axiomatic Theories of Truth. Cambridge University Press. Second Revised Edition.Google Scholar
Hallett, M. (1984). Cantorian Set Theory and Limitation of Size. Clarendon Press.Google Scholar
Halmos, P. (1974). Naive Set Theory. Springer.Google Scholar
Hamkins, J. D. and Kikuchi, M. (2016). Set-theoretic mereology. Logic and Logical Philosophy, 25(3):285–308.Google Scholar
Hatcher, A. (2001). Algebraic Topology. Cambridge University Press.Google Scholar
Hausdorff, F. (1957). Set Theory. Chelsea Publishing Co.. Third Edition. First Edition 1914.Google Scholar
Hausdorff, F. (2005). Hausdorff on Ordered Sets. American Mathematical Society. Edited, with notes, by J. M. Plotkin.Google Scholar
Hellman, G. and Shapiro, S. (2018). Varieties of Continua. Oxford University Press.Google Scholar
Heyting, A. (1956). Intuitionism: An Introduction. North Holland.Google Scholar
Hilbert, D. (1902a). Foundations of Geometry. Open Court Classics.Google Scholar
Hilbert, D. (1902b). Mathematical problems. Bulletin of the American Mathematical Society, 8:437–479. Translated from the 1900 address by Mary Winston Newton.Google Scholar
Hilbert, D. (1925). On the infinite. In van Heijenoort 1967, pp. 367–392.Google Scholar
Hindley, J. R. and Seldin, J. P. (2008). Lambda-Calculus and Combinators. Cambridge University Press.Google Scholar
Hinkis, A. (2013). Proofs of the Cantor–Bernstein Theorem: A Mathematical Excursion. Birkhäuser.Google Scholar
Hinnion, R. and Libert, T. (2003). Positive abstraction and extensionality. Journal of Symbolic Logic, 68(3):828–836.Google Scholar
Hocking, J. G. and Young, G. S. (1961). Topology. Dover.Google Scholar
Hoffman, B. (1966). About Vectors. Dover.Google Scholar
Holmes, M. R., Forster, T., and Libert, T. (2012). Alternative set theories. In Gabbay, D., Kanamori, A., and Woods, J., editors, Handbook of the History of Logic, Vol. 6, Sets and Extensions in the Twentieth Century, pages 559–632. Elsevier/North-Holland.Google Scholar
Horgan, T. (1994). Robust vagueness and the forced-march sorites paradox. Philosophical Perspectives, 8:159–188.Google Scholar
Hudson, H. (2005). The Metaphysics of Hyperspace. Oxford University Press.Google Scholar
Humberstone, L. (2006). Variations on a theme of Curry. Notre Dame Journal of Formal Logic, 47(1):101–131.Google Scholar
Humberstone, L. (2011). The Connectives. MIT.Google Scholar
Hyde, D. (1994). Why higher-order vagueness is a pseudo-problem. Mind, 103:35–41.Google Scholar
Hyde, D. (1997). From heaps and gaps to heaps of gluts. Mind, 106:440–460.Google Scholar
Hyde, D. (2008). Vagueness, Logic, and Ontology. Ashgate.Google Scholar
Hyde, D. and Raffman, D. (2018). Sorites paradox. In Zalta, E., editor, Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/sorites-paradox/.Google Scholar
Hyde, D. and Sylvan, R. (1993). Ubiquitous vagueness without embarrassment. Acta Analytica, 10(1):7–29. Reprinted In Hyde, D. and Priest, G., editors, Sociative Logics and Their Applications, pages 189–1199. Ashgate.Google Scholar
Istre, E. (2017). Normalized Naive Set Theory. PhD Thesis, University of Canterbury.Google Scholar
Jacquette, D., editor (2007). Philosophy of Logic. Elsevier.Google Scholar
Jané, I. (1995). The role of the absolute infinite in Cantor’s conception of set. Erkenntnis, 42:375–402.Google Scholar
Jänich, K. (1984). Topology. Springer-Verlag.Google Scholar
Jänich, K. (2010). Vector Analysis. Springer.Google Scholar
Jaśkowski, S. (1969). Propositional calculus for contradictory deductive systems. Studia Logica, 24:143–57. Originally published in Polish in 1948.Google Scholar
Jech, T., editor (1974). Axiomatic Set Theory. American Mathematical Society.Google Scholar
Jech, T. (1978). Set Theory. Academic Press.Google Scholar
Jones, V. (1998). A credo of sorts. In Dales, H. and Oliveri, G., editors, Truth in Mathematics, pages 203–214. Clarendon Press.Google Scholar
Kahan, W. (1987). Branch cuts for complex elementary functions, or much ado about nothing’s sign bit. In Iserles, A. and Powell, M. J. D., editors, The State of the Art in Numerical Analysis. Clarendon Press, Oxford.Google Scholar
Kanamori, A. (1994). The Higher Infinite: Large Cardinals in Set Theory from Their Beginnings. Springer-Verlag.Google Scholar
Keefe, R. (2000). Theories of Vagueness. Cambridge University Press.Google Scholar
Kelley, J. L. (1955). General Topology. Springer-Verlag.Google Scholar
Kitcher, P. (1989). Explanatory unification and the causal structure of the world. In Kitcher, P. and Salmon, W., editors, Scientific Explanation, pages 410–505. University of Minnesota Press.Google Scholar
Kleene, S. C. (1952). Introduction to Metamathematics. North-Holland.Google Scholar
Komori, Y. (1989). Illiative combinatory logic based on BCK-logic. Mathematica Japonica, 34:585–596.Google Scholar
Koslicki, K. (2008). The Structure of Objects. Oxford University Press.Google Scholar
Kripke, S. (1975). Outline of a theory of truth. Journal of Philosophy, 72:690–716.Google Scholar
Kroon, F. (2004). Realism and dialetheism. In [Priest et al., 2004].Google Scholar
Kunen, K. (1980). Set Theory: An Introduction to Independence Proofs. North Holland.Google Scholar
Kuratowski, K. (1962). Introduction to Set Theory and Topology. Pergamon. Trans. by L. Boron.Google Scholar
Lakatos, I. (1976). Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge University Press.Google Scholar
Lamb, E. (2014). The saddest thing I know about the integers. Scientific American. Roots of Unity blog, http://blogs.scientificamerican.com/roots-of-unity/the-saddest-thing-i-know-about-the-integers/.Google Scholar
Landini, G. (2009). Russell’s schema, not Priest’s inclosure. History and Philosophy of Logic, 30(2):105–139.Google Scholar
Lavine, S. (1994). Understanding the Infinite. Harvard University Press.Google Scholar
Lawvere, W. (1969). Diagonal arguments and Cartesian closed categories. Lecture Notes in Mathematics, 92:134–145.Google Scholar
Lawvere, W. and Schanuel, S. (2009). Conceptual Mathematics: A First Introduction to Categories. Cambridge University Press. First appeared from Buffalo Workshop Press 1991.Google Scholar
Lee, J. M. (1997). Riemannian Manifolds: An Introduction to Curvature. Springer.Google Scholar
Leibniz, G. (1714). The Monadology. Early Modern Texts. Trans. J. Bennett, 2017.Google Scholar
Leibniz, G. (1951). Selections. Scribners. Edited by P. Wiener.Google Scholar
Leibniz, G. (2002). The Labyrinth of the Continuum: Writings on the Continuum Problem, 1672–1686. Yale University Press. Translated and edited by R. T. W. Arthur.Google Scholar
Levy, A. (1979). Basic Set Theory. Springer Verlag. Reprinted by Dover in 2002.Google Scholar
Lewis, D. (1991). Parts of Classes. Basil Blackwell.Google Scholar
Lewis, D. (1999). Many, but almost one. In Papers in Metaphysics and Epistemology, pages 164–182. Cambridge University Press.Google Scholar
Lewis, D. K. (1986). On the Plurality of Worlds. Blackwell.Google Scholar
Libert, T. (2005). Models for paraconsistent set theory. Journal of Applied Logic, 3:15–41.Google Scholar
Lycan, W. (2010). What is a paradox? Analysis, 70(4):615–622.Google Scholar
MacCaull, W. (1996). Kripke semantics for logics with BCK implication. Bulletin of the Section of Logic, 25:41–51.Google Scholar
Maddy, P. (1983). Proper classes. Journal of Symbolic Logic, 48:113–139.Google Scholar
Mancosu, P., editor (2008). The Philosophy of Mathematical Practice. Oxford University Press.Google Scholar
Mancosu, P. (2011). Explanation in mathematics. In Zalta, E., editor, Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/.Google Scholar
Mares, E. (2004a). Relevant Logic. Cambridge University Press.Google Scholar
Mares, E. (2004b). Semantic dialetheism. In [Priest et al., 2004], pages 264–275.Google Scholar
Mares, E. (2019). The universality of relevance. In Weber, Z., editor, Ultralogic as Universal? by Richard Routley. Synthese Library, Springer.Google Scholar
Mares, E. and Paoli, F. (2014). Logical consequence and the paradoxes. Journal of Philosophical Logic, 43:439–469.Google Scholar
Martin, B. (2014). Dialetheism and the impossibility of the world. Australasian Journal of Philosophy, 93(1):61–75.Google Scholar
Martin, N. and Pollard, S. (1996). Closure Spaces and Logic. Kluwer.Google Scholar
Mates, B. (1981). Skeptical Essays. University of Chicago Press.Google Scholar
McCarty, C. (2008). Completeness and incompleteness for intuitionistic logic. Journal of Symbolic Logic, 73(4):1315–1327.Google Scholar
McDaniel, K. (2007). Extended simples. Philosophical Studies, 133(1):131–141.Google Scholar
McGee, V. (1990). Truth, Vagueness, and Paradox. Hackett.Google Scholar
McKubre-Jordens, M. and Weber, Z. (2012). Real analysis in paraconsistent logic. Journal of Philosophical Logic, 41(5):901–922.Google Scholar
McKubre-Jordens, M. and Weber, Z. (2016). Paraconsistent measurement of the circle. Australasian Journal of Logic, 14(1):268–280.Google Scholar
Meadows, T. (2015). Unpicking Priest’s bootstraps. Thought: A Journal of Philosophy, 4(3):181–188.Google Scholar
Meadows, T. and Weber, Z. (2016). Computation in non-classical foundations? Philosophers’ Imprint, 16:1–17.Google Scholar
Mendelson, B. (1975). Introduction to Topology. Allyn and Bacon, Inc.Google Scholar
Meyer, R. K. (1975). Arithmetic formulated relevantly. Typescript, Australasian Journal of Logic, 18(5):154–288.Google Scholar
Meyer, R. K. (1976). The consistency of arithmetic. typescript, Australasian Journal of Logic, 18(5):289–379.Google Scholar
Meyer, R. K. (1985a). A farewell to entailment. In Dorn, G., et al., editors, Foundations of Logic and Linguistics, pages 577–636. Springer Science and Business Media.Google Scholar
Meyer, R. K. (1985b). Proving semantical completeness “relevantly” for R. Logic Research Paper (23). RSSS Australian National University.Google Scholar
Meyer, R. K. (1996). Kurt Gödel and the consistency of R##. In Hajek, P., editor, Gödel ’96: Logical Foundations of Mathematics, Computer Science and Physics – Kurt Gödel’s Legacy, Brno, Czech Republic, August 1996, Proceedings, pages 247–256. Springer-Verlag.Google Scholar
Meyer, R. K. (1998). ⊃-E is admissible in “true” relevant arithmetic. Journal of Philosophical Logic, 27:327–351.Google Scholar
Meyer, R. K. and Mortensen, C. (1984). Inconsistent models for relevant arithmetics. Journal of Symbolic Logic, 49:917–929.Google Scholar
Meyer, R. K. and Mortensen, C. (1987). Alien intruders in relevant arithmetic. Technical Report, TR-ARP(9/87).Google Scholar
Meyer, R. K. and Ono, H. (1994). The finite model property for BCK and BCIW. Studia Logica, 53:107–118.Google Scholar
Meyer, R. K. and Restall, G. (1999). “Strenge” arithmetics. Logique et Analyse, 42:205–220.Google Scholar
Meyer, R. K. and Routley, R. (1977). Extensional reduction (I). The Monist, 60:355–369.Google Scholar
Meyer, R. K., Routley, R., and Dunn, J. M. (1978). Curry’s paradox. Analysis, 39:124–128.Google Scholar
Meyer, R. K. and Urbas, I. (1986). Conservative extension in relevant arithmetic. Mathematical Logic Quarterly, 32(1-5):45–50.Google Scholar
Miller, K. (2009). Stuff. American Philosophical Quarterly, 46(1):1–18.Google Scholar
Moore, G. (1993). G. E. Moore: Selected Writings. Routledge Baldwin, T., editor.Google Scholar
Moore, G. H. (1982). Zermelo’s Axiom of Choice. Springer Verlag.Google Scholar
Mortensen, C. (1988). Inconsistent number systems. Notre Dame Journal of Formal Logic, 29:45–60.Google Scholar
Mortensen, C. (1989). Anything is possible. Erkenntnis, 30:319–337.Google Scholar
Mortensen, C. (1995). Inconsistent Mathematics. Kluwer Academic Publishers.Google Scholar
Mortensen, C. (2010). Inconsistent Geometry. College Publications.Google Scholar
Moschovakis, Y. (2010). Kleene’s amazing second recursion theorem. Bulletin of Symbolic Logic, 16(2):189–239.Google Scholar
Munkres, J. R. (2000). Topology. Prentice Hall.Google Scholar
Murzi, J. and Rossi, L. (2020). Generalized revenge. Australasian Journal of Philosophy, 98:153–177.Google Scholar
Myhill, J. (1960). Some remarks on the notion of proof. Journal of Philosophy, 57:461–471.Google Scholar
Myhill, J. (1975). Levels of implication. In Anderson, A. R., Marcus, R. C., and Martin, R. M., editors, The Logical Enterprise, pages 179–85. Yale University Press.Google Scholar
Myhill, J. (1984). Paradoxes. Synthese, 60:129–143.Google Scholar
Nietzsche, F. (1976). The Portable Nietzsche. Penguin. Translated, edited, and with an introduction by W. Kaufmann.Google Scholar
Odifreddi, P. (1989). Classical Recursion Theory. North Holland.Google Scholar
Øgaard, T. F. (2016). Paths to triviality. Journal of Philosophical Logic, 45(3):237–276.Google Scholar
Øgaard, T. F. (2017). Skolem functions in non-classical logics. Australasian Journal of Logic, 14(1):181–225.Google Scholar
Omori, H. (2015). Remarks on naive set theory based on LP. Review of Symbolic Logic, 8(2):279–295.Google Scholar
Omori, H. and Weber, Z. (2019). Just true? On the metatheory for paraconsistent truth. Logique et Analyse, 248:415–433.Google Scholar
Ono, H. (2010). Logics without the contraction rule and residuated lattices. Australasian Journal of Logic, 8:50–81.Google Scholar
Ono, H. and Komori, Y. (1985). Logic without the contraction rule. Journal of Symbolic Logic, 50:169–201.Google Scholar
Paul, L. (2006). Coincidence as overlap. Noûs, 40(4):623–659.Google Scholar
Pavlović, D. (1992). On the structure of paradoxes. Archive for Mathematical Logic, 31(6):397–406.Google Scholar
Petersen, U. (2000). Logic without contraction as based on inclusion and unrestriced abstraction. Studia Logica, 64:365–403.Google Scholar
Pitts, A. M. and Taylor, P. (1989). A note on Russell’s paradox in locally Cartesian closed categories. Studia Logica, 48(3):377–387.Google Scholar
Potter, M. (2004). Set Theory and Its Philosophy. Clarendon Press.Google Scholar
Pratt-Harmon, I. (2007). First order mereotopology. In Aiello, M., Pratt-Harmon, I. E., and van Benthem, J., editors, Handbook of Spatial Logics, pages 13–98. Springer.Google Scholar
Priest, G. (1979). The logic of paradox. Journal of Philosophical Logic, 8:219–241.Google Scholar
Priest, G. (1980). Sense, entailment and modus ponens. Journal of Philosophical Logic, 9:415–435.Google Scholar
Priest, G. (1989). Reductio ad absurdum et modus tollendo ponens. In [Priest et al., 1989], pages 613–626.Google Scholar
Priest, G. (1990). Boolean negation and all that. Journal of Philosophical Logic, 19:201–215.Google Scholar
Priest, G. (1991a). The limits of thought – and beyond. Mind, 100(3):361–370.Google Scholar
Priest, G. (1991b). Minimally inconsistent LP. Studia Logica, 50:321–331.Google Scholar
Priest, G. (1994a). Is arithmetic consistent? Mind, 103(411):337–349.Google Scholar
Priest, G. (1994b). What could the least inconsistent number be? Logique et Analyse, 145:3–12.Google Scholar
Priest, G. (1997a). Inconsistent models of arithmetic part I: finite models. Journal of Philosophical Logic, 26:223–35.Google Scholar
Priest, G. (1997b). On a paradox of Hilbert and Bernays. Journal of Philosophical Logic, 26:45–56.Google Scholar
Priest, G. (2000). Inconsistent models of arithmetic, II: the general case. Journal of Symbolic Logic, 65:1519–1529.Google Scholar
Priest, G. (2002a). Beyond the Limits of Thought. Oxford University Press. Second Edition. First Edition 1995, Cambridge University Press.Google Scholar
Priest, G. (2002b). Paraconsistent logic. In Gabbay, D. M. and Günthner, F., editors, Handbook of Philosophical Logic, volume 6, pages 287–394. Kluwer. Second Edition.Google Scholar
Priest, G. (2003). A site for sorites. In [Beall, 2003], pages 9–24.Google Scholar
Priest, G. (2005). Towards Non-Being. Oxford University Press.Google Scholar
Priest, G. (2006a). Doubt Truth Be a Liar. Oxford University Press.Google Scholar
Priest, G. (2006b). In Contradiction: A Study of the Transconsistent. Oxford University Press. Second Edition.Google Scholar
Priest, G. (2006c). Spiking the field artillery. In Beall, J. and Armour-Garb, B., editors, Deflationism and Paradox, pp. 41–52. Oxford University Press.Google Scholar
Priest, G. (2007). Revenge, field, and ZF. In [Beall, 2007], pp. 225–233.Google Scholar
Priest, G. (2008). An Introduction to Non-Classical Logic. Cambridge University Press. Second Edition.Google Scholar
Priest, G. (2010). Inclosures, vagueness, and self-reference. Notre Dame Journal of Formal Logic, 51(1):69–84.Google Scholar
Priest, G. (2013a). Indefinite extensibility – dialetheic style. Studia Logica, 101:1263–1275.Google Scholar
Priest, G. (2013b). Mathematical pluralism. Journal of the IGPL, 21:4–13.Google Scholar
Priest, G. (2014). One. Oxford University Press.Google Scholar
Priest, G. (2015). Fusion and confusion. Topoi, 34(1):55–61.Google Scholar
Priest, G. (2016). Thinking the impossible. Philosophical Studies, 173:2649–2662.Google Scholar
Priest, G. (2017a). A note on the axiom of countability. IfCoLog Journal of Logics and Their Applications, 4:1351–1356. First published in Al-Mukhatabat, 2012, 1(23–32).Google Scholar
Priest, G. (2017b). What if? The exploration of an idea. Australasian Journal of Logic, 14(1). Special issue: Non-Classicality, edited by Z. Weber, P. Girard, and M. McKubre-Jordens, M.Google Scholar
Priest, G. (2019a). Dialetheism and the sorites paradox. In Ohms, S. and Zardini, E., editors, The Sorites Paradox, pages 135–150. Cambridge University Press.Google Scholar
Priest, G. (2019b). Some comments and replies. In Baskent, C. and Ferguson, T., editors, Graham Priest on Dialetheism and Paraconsistency, pages 575–675. Springer.Google Scholar
Priest, G. (2020), Metatheory and dialetheism. Logical Investigations 26 (2020):48–59.Google Scholar
Priest, G., Beall, J., and Armour-Garb, B., editors (2004). The Law of Non-Contradiction. Clarendon Press.Google Scholar
Priest, G. and Routley, R. (1983). On Paraconsistency. Research School of Social Sciences, Australian National University. Reprinted as introductory chapters in [Priest et al., 1989].Google Scholar
Priest, G. and Routley, R. (1989a). Applications of paraconsistent logic. In [Priest et al., 1989], pages 367–393.Google Scholar
Priest, G. and Routley, R. (1989b). The philosophical significance and inevitability of paraconsistency. In [Priest et al., 1989], pages 483–537.Google Scholar
Priest, G., Routley, R., and Norman, J., editors (1989). Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag.Google Scholar
Putnam, H. (1990). Realism with a Human Face. Harvard University Press.Google Scholar
Putnam, H. (1994). Peirce’s continuum. In Ketner, K., editor, Peirce and Contemporary Thought: Philosophical Inquiries. Fordham University Press.Google Scholar
Quine, W. (1969). Set Theory and Its logic. Harvard University Press.Google Scholar
Rayo, A. and Uzquiano, G., editors (2006). Absolute Generality. Oxford University Press.Google Scholar
Reinhard, W. N. (1974). Remarks on reflection principles, large cardinals, and elementary embeddings. In [Jech, 1974].Google Scholar
Restall, G. (1992). A note on naïve set theory in LP. Notre Dame Journal of Formal Logic, 33:422–432.Google Scholar
Restall, G. (1994). On Logics without Contraction. PhD Thesis, University of Queensland.Google Scholar
Restall, G. (2010a). Models for substructural arithmetics. Australasian Journal of Logic, 8:82–99.Google Scholar
Restall, G. (2010b). On t and u and what they can do. Analysis, 70(4):673–676.Google Scholar
Restall, G. (2013). Assertion, denial and non-classical theories. In Tanaka, K., Berto, F., Mares, E., and Paoli, F., editors, Paraconsistency: Logic and Applications, pages 81–99. Springer.Google Scholar
Ripley, D. (2013). Paradoxes and failures of cut. Australasian Journal of Philosophy, 91(1):139–164.Google Scholar
Ripley, D. (2015a). Comparing substructural theories of truth. Ergo, 2(13):299–328.Google Scholar
Ripley, D. (2015b). Contraction and closure. Thought, 4:131–138.Google Scholar
Ripley, D. (2015c). Embedding denial. In [Caret and Hjortland, 2015], pages 289–309.Google Scholar
Ripley, D. (2015d). Naive set theory and nontransitive logic. Review of Symbolic Logic, 8(3):553–571.Google Scholar
Rizza, D. (2013). Deconstructing a topological sorites. Philosophia Mathematica, 21(3):361–364.Google Scholar
Robinson, A. (1966). Non-Standard Analysis. North Holland.Google Scholar
Rogers, J. (1995). The Giant Planet Jupiter. Cambridge University Press.Google Scholar
Rosenblatt, L. (2021). On structural contraction and why it fails. Synthese 198, pages 2695–2720.Google Scholar
Rossberg, M. (2013). Too good to be “just true”. Thought, 2(1):1–8.Google Scholar
Routley, R. (1975). Universal semantics. Journal of Philosophical Logic, 4:327–356.Google Scholar
Routley, R. (1977). Ultralogic as Universal? First appeared in two parts in The Relevance Logic Newsletter 2(1):51–90, January 1977 and 2(2):138-175, May 1977; reprinted as appendix to [Routley, 1980b], pp. 892–962; new edition as The Sylvan Jungle, volume 4, edited by Z. Weber, Synthese Library, 2019.Google Scholar
Routley, R. (1979). Dialectical logic, semantics and metamathematics. Erkenntnis, 14:301–331.Google Scholar
Routley, R. (1980a). The choice of logical foundations: non-classical choices and the ultralogical choice. Studia Logica, 39(1):77–98.Google Scholar
Routley, R. (1980b). Exploring Meinong’s Jungle and Beyond. Philosophy Department, RSSS, Australian National University, Canberra. Departmental Monograph number 3.Google Scholar
Routley, R. (1983). Nihilism and nihilist logics. Discussion Papers in Environmental Philosophy, no. 4, Department of Philosophy at the Australian National University.Google Scholar
Routley, R. and Meyer, R. K. (1976). Dialectical logic, classical logic and the consistency of the world. Studies in Soviet Thought, 16:1–25.Google Scholar
Routley, R., Plumwood, V., Meyer, R. K., and Brady, R. T. (1982). Relevant Logics and Their Rivals. Ridgeview.Google Scholar
Routley, R. and Routley, V. (1985). Negation and contradiction. Revista Colombiana de Matemáticas, 19:201–231.Google Scholar
Rubin, H. and Rubin, J. E. (1985 [1963]). Equivalents of the Axiom of Choice. North Holland.Google Scholar
Rudin, W. (1953). Principles of Mathematical Analysis. McGraw-Hill. Third Edition 1976.Google Scholar
Russell, B. (1905a). On denoting. Mind, 14(56):479–493.Google Scholar
Russell, B. (1905b). On some difficulties in the theory of transfinite numbers and order types. Proceedings of the London Mathematical Society, 4:29–53.Google Scholar
Russell, B. (1959). My Philosophical Development. Allen and Unwin.Google Scholar
Russell, G. (2018). Logical nihilism: could there be no logic? Philosophical Issues, 28(1):308–324.Google Scholar
Sainsbury, R. M. (1995). Paradoxes. Cambridge University Press. Second Edition.Google Scholar
Sartre, J.-P. (1958). Being and Nothingness. Methuen. Trans. H. Barnes.Google Scholar
Scharp, K. (2013). Replacing Truth. Oxford University Press.Google Scholar
Schröder, B. S. (2003). Ordered Sets: An Introduction. Birkhaüser.Google Scholar
Shapiro, L. (2011). Deflating logical consequence. Philosophical Quarterly, 61(243):320–342.Google Scholar
Shapiro, S. (1997). Philosophy of Mathematics: Structure and Ontology. Oxford University Press.Google Scholar
Shapiro, S. (2002). Incompleteness and inconsistency. Mind, 111:817–832.Google Scholar
Shapiro, S., editor (2005). The Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press.Google Scholar
Shapiro, S. (2006). Vagueness in Context. Oxford University Press.Google Scholar
Shapiro, S. (2014). Varieties of Logic. Oxford University Press.Google Scholar
Shapiro, S. and Wright, C. (2006). All things indefinitely extensible. In [Rayo and Uzquiano, 2006], pages 255–304.Google Scholar
Shirahata, M. (1994). Linear Set Theory. PhD Thesis, Stanford University.Google Scholar
Shirahata, M. (1999). Fixpoint theorem in linear set theory. Typescript.Google Scholar
Sider, T. (2000). Simply possible. Philosophy and Phenomenological Research, 60(3):585–590.Google Scholar
Sider, T. (2001). Four-Dimensionalism. Oxford University Press.Google Scholar
Simons, P. (2004). Extended simples: a third way between atoms and gunk. The Monist, 87:371–85.Google Scholar
Skolem, T. (1963). Studies on the axiom of comprehension. Notre Dame Journal of Formal Logic, 4:162–170.Google Scholar
Slaney, J. (1982). The square root of two is irrational (and no funny business). Typescript.Google Scholar
Slaney, J. K. (1989). RWX is not Curry-paraconsistent. In [Priest et al., 1989], pages 472–480.Google Scholar
Slaney, J. K., Meyer, R. K., and Restall, G. (1996). Linear arithmetic desecsed. Technical Report TR-ARP-2-96, Automated Reasoning Project, Australian National University.Google Scholar
Slote, M. (2011). The Impossibility of Perfection. Oxford University Press.Google Scholar
Smith, B. (1997). Boundaries: an essay in mereotopology. In Hahn, L., editor, The Philosophy of Roderick Chisholm, Library of Living Philosophers, pages 534–561. Open Court.Google Scholar
Smith, N. (2012). Logic: The Laws of Truth. Princeton University Press.Google Scholar
Smith, N. J. (2000). The principle of uniform solution (of the paradoxes of self-reference). Mind, 109:117–22.Google Scholar
Smith, N. J. (2008). Vagueness and Degrees of Truth. Oxford University Press.Google Scholar
Smith, P. (2007). An Introduction to Gödel’s Theorems. Cambridge University Press.Google Scholar
Smullyan, R. and Fitting, M. (1996). Set Theory and the Continuum Problem. Clarendon Press.Google Scholar
Smullyan, R. M. (1991). Some unifying fixed point principles. Studia Logica, 50(1):129–141.Google Scholar
Sorensen, R. (1985). An argument for the vagueness of “vague.” Analysis, 27:34–37.Google Scholar
Sorensen, R. (1994). A thousand clones. Mind, 103:47–54.Google Scholar
Sorensen, R. (2001). Vagueness and Contradiction. Oxford University Press.Google Scholar
Sorensen, R. (2008). Seeing Dark Things: The Philosophy of Shadows. Oxford University Press.Google Scholar
Spivak, M. (2006). Calculus. Cambridge University Press. Third Edition.Google Scholar
Steen, L. A. and Jr, J. A. S. (1978). Counterexamples in Topology. Springer-Verlag.Google Scholar
Stillwell, J. (1998). Numbers and Geometry. Springer.Google Scholar
Sylvan, R. (1992). On interpreting truth tables and relevant truth table logic. Notre Dame Journal of Formal Logic, 33(2):207–215.Google Scholar
Sylvan, R. and Copeland, J. (2000). Computability is logic relative. In Hyde, D. and Priest, G., editors, Sociative Logics and Their Applications, pages 189–199. Ashgate.Google Scholar
Takeuti, G. and Zaring, W. M. (1971). Introduction to Axiomatic Set Theory. Springer-Verlag.Google Scholar
Tappenden, J. (2002). The liar and sorites paradoxes: toward a unified treatment. In Williamson, T. and Graff, D., editors, Vagueness. Ashgate. Reprinted from Journal of Philosophy, 90(11):551–577.Google Scholar
Tarski, A. (1944). The semantic conception of truth and the foundations of semantics. Philosophy and Phenomenological Research, 4:341–376.Google Scholar
Tarski, A. (1956a). The concept of truth in formalized languages. In [Tarski, 1956b], pages 152–278. Polish original 1933.Google Scholar
Tarski, A. (1956b). Logic, Semantics, Metamathematics: Papers from 1923 to 1938. Clarendon Press. Translated by J. H. Woodger.Google Scholar
Tedder, A. (2015). Axioms for finite collapse models of arithmetic. Review of Symbolic Logic, 3:529–539.Google Scholar
Terui, K. (2004). Light affine set theory: a naive set theory of polynomial time. Studia Logica, 77:9–40.Google Scholar
Terui, K. (2014). Open problems: Brouwer’s fixed point theorem and Cantor’s naive set theory in substructural and fuzzy logics. Typescript.Google Scholar
Thomasson, A. L. (2007). Ordinary Objects. Oxford University Press.Google Scholar
Thomas, M. (2014). A conjecture about the interpretation of classical mathematics in naive set theory, presented at the LMU Paraconsistent Reasoning in Science and Mathematics Conference in June 2014, at http://sites.google.com/a/uconn.edu/morgan-thomas/ (accessed May 11, 2020).Google Scholar
Tieszen, R. (2005). Phenomenology, Logic, and the Philosophy of Mathematics. Cambridge University Press.Google Scholar
Tits, J. (1957). Sur les analogues algébriques des groupes semi-simples complexes. In Colloque d’algebre superieure, pages 261–289. Librairie Gauthier-Villars.Google Scholar
Unger, P. (1979). There are no ordinary things. Synthese, 41:117–154.Google Scholar
Unger, P. (1980). The problem of the many. Midwest Studies in Philosophy, 5:411–67.Google Scholar
van Aken, J. (1986). Axioms for the set theoretic hierarchy. Journal of Symbolic Logic, 51(4):992–1004.Google Scholar
van Atten, M. (2007). Brouwer Meets Husserl: On the Phenomenology of Choice Sequences. Synthese Library, Springer.Google Scholar
van Bendegem, J. P. (2003). Classical arithmetic is quite unnatural. Logic and Logical Philosophy, 11:231–249.Google Scholar
van Dalen, D. (1997). How connected is the intuitionistic continuum? Journal of Symbolic Logic, 62(4):1147–1150.Google Scholar
van Heijenoort, J., editor (1967). From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931. Harvard University Press.Google Scholar
van Inwagen, P. (1990). Material Beings. Cornell University Press.Google Scholar
Varzi, A. (1997). Boundaries, continuity and contact. Noûs, 31:26–58.Google Scholar
Varzi, A. (2014). Counting and countenancing. In Cotnoir, A. and Baxter, D., editors, Composition as Identity, pages 47–69. Oxford University Press.Google Scholar
Varzi, A. (2004). Boundary. In Zalta, E. N., editor, The Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/.Google Scholar
Wansing, H. and Priest, G. (2015). External curries. Journal of Philosophical Logic, 44(4):453–471.Google Scholar
Weber, Z. (2009). Paradox and Foundation. PhD Thesis, University of Melbourne.Google Scholar
Weber, Z. (2010a). Explanation and solution in the inclosure argument. Australasian Journal of Philosophy, 88(2):353–357.Google Scholar
Weber, Z. (2010b). Extensionality and restriction in naive set theory. Studia Logica, 94(1):87 – 104.Google Scholar
Weber, Z. (2010c). A paraconsistent model of vagueness. Mind, 119(476):1025–1045.Google Scholar
Weber, Z. (2010d). Transfinite numbers in paraconsistent set theory. Review of Symbolic Logic, 3(1):71–92.Google Scholar
Weber, Z. (2012). Transfinite cardinals in paraconsistent set theory. Review of Symbolic Logic, 5(2):269–293.Google Scholar
Weber, Z. (2014). Naive validity. Philosophical Quarterly, 64(254):99–114.Google Scholar
Weber, Z. (2016a). On paraconsistent downward Löwenheim–Skolem theorems. In Arazim, P. and Dancak, M., editors, Logica Yearbook 2015. College Publications.Google Scholar
Weber, Z. (2016b). On closure and truth in substructural theories of truth. Synthese, https://doi.org/10.1007/s11229-016-1226-6.Google Scholar
Weber, Z. (2019). At the limits of thought. In Baskent, C. and Ferguson, T., editors, Graham Priest on Dialetheism and Paraconsistency, pages 555–574. Springer (Outstanding Contributions to Logic).Google Scholar
Weber, Z. (2020). Property identity and relevant conditionals. Australasian Philosophical Review, (forthcoming).Google Scholar
Weber, Z., Badia, G., and Girard, P. (2016). What is an inconsistent truth table? Australasian Journal of Philosophy, 94(3):533–548.Google Scholar
Weber, Z. and Colyvan, M. (2010). A topological sorites. Journal of Philosophy, 107(6):311–325.Google Scholar
Weber, Z. and Cotnoir, A. (2015). Inconsistent boundaries. Synthese, 192(5):1267–1294.Google Scholar
Weber, Z. and Omori, H. (2019). Observations on the trivial world. Erkenntnis, 5(84):975–994.Google Scholar
Weber, Z., Ripley, D., Priest, G., Hyde, D., and Colyvan, M. (2014). Tolerating gluts. Mind, 123(491):791–811.Google Scholar
Weir, A. (1998). Naive set theory is innocent! Mind, 107:763–798.Google Scholar
Weir, A. (2004). There are no true contradictions. In Priest, G., Beall, J. C., and Armour-Garb, B., editors, The Law of Non-Contradiction, pages 385–417. Clarendon Press.Google Scholar
Weyl, H. (1919). The Continuum. Dover.Google Scholar
White, R. (1979). The consistency of the axiom of comprehension in the infinite valued predicate logic of łukasiewicz. Journal of Philosophical Logic, 8:503–534.Google Scholar
White, R. B. (1993). A consistent theory of attributes in a logic without contraction. Studia Logica, 52:113–142.Google Scholar
Whitehead, A. N. and Russell, B. (1910). Principia Mathematica. Cambridge University Press. In three volumes, 1910–1913.Google Scholar
Whittle, B. (2004). Dialetheism, logical consequence and hierarchy. Analysis, 64(4):318–326.Google Scholar
Willard, S. (1970). General Topology. Addison-Wesley.Google Scholar
Williamson, T. (1994). Vagueness. Routledge.Google Scholar
Williamson, T. (2014). Logic, metalogic and neutrality. Erkenntnis, 79(2):211–231.Google Scholar
Wilson, W. (1931). On semi-metric spaces. American Journal of Mathematics, 53:361–373.Google Scholar
Wittgenstein, L. (1922). Tractatus Logico-Philosophicus. Routledge. Translated by D. E. Pears and B. F. McGuinness.Google Scholar
Wittgenstein, L. (1953). Philosophical Investigations. Blackwell. Trans. G. E. M. Anscome.Google Scholar
Wittgenstein, L. (1956). Remarks on the Foundations of Mathematics. MIT Press. Edited by G. H. von Wright, R. Rees, and G. E. M. Anscome.Google Scholar
Woods, J. (2003). Paradox and Paraconsistency. Cambridge University Press.Google Scholar
Woods, J. (2019). Logical partisanhood. Philosophical Studies, 176:1203–1224.Google Scholar
Wright, C. (1976). Language mastery and the sorites paradox. In Evans, G. and McDowell, J., editors, Truth and Meaning. Oxford University Press.Google Scholar
Yanofsky, N. S. (2003). A universal approach to self-referential paradoxes, incompleteness and fixed points. Bulletin of Symbolic Logic, 9(3):362–386.Google Scholar
Young, G. (2005). Revenge: Dialetheism and Its Expressive Limitations. PhD Thesis, University of Glasgow.Google Scholar
Zalta, E. (2007). Frege’s theorem. Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/.Google Scholar
Zardini, E. (2011). Truth without contra(di)ction. Review of Symbolic Logic, 4:498–535.Google Scholar
Zermelo, E. (1967). Investigations in the foundations of set theory. In [van Heijenoort, 1967], pages 200–215.Google Scholar
Zhong, H. (2012). Definability and the structure of logical paradoxes. Australasian Journal of Philosophy, 90(4):779–788.Google Scholar
Zimmerman, D. (1996). Could extended objects be made out of simple parts? An argument for atomless gunk. Philosophy and Phenomenological Research, 56:1–29.Google Scholar

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  • Bibliography
  • Zach Weber, University of Otago, New Zealand
  • Book: Paradoxes and Inconsistent Mathematics
  • Online publication: 08 October 2021
  • Chapter DOI: https://doi.org/10.1017/9781108993135.017
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  • Bibliography
  • Zach Weber, University of Otago, New Zealand
  • Book: Paradoxes and Inconsistent Mathematics
  • Online publication: 08 October 2021
  • Chapter DOI: https://doi.org/10.1017/9781108993135.017
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Bibliography
  • Zach Weber, University of Otago, New Zealand
  • Book: Paradoxes and Inconsistent Mathematics
  • Online publication: 08 October 2021
  • Chapter DOI: https://doi.org/10.1017/9781108993135.017
Available formats
×