Linked bibliography for the SEP article "Inconsistent Mathematics" by Chris Mortensen
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If everything goes well, this page should display the bibliography of the aforementioned article as it appears in the Stanford Encyclopedia of Philosophy, but with links added to PhilPapers records and Google Scholar for your convenience. Some bibliographies are not going to be represented correctly or fully up to date. In general, bibliographies of recent works are going to be much better linked than bibliographies of primary literature and older works. Entries with PhilPapers records have links on their titles. A green link indicates that the item is available online at least partially.
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- Beall, J.C. and G. Restall, 2006, Logical Pluralism, Oxford: The Clarendon Press. (Scholar)
- Benham, R., C. Mortensen and G. Priest, 2014, “Chunk and Permeate III: The Dirac Delta Function”, Synthese, 191(13): 3057-3062. doi:10.1007/s11229-014-0473-7 (Scholar)
- Berto, F., 2007, How to Sell a Contradiction, London: College Publications. (Scholar)
- Brady, R., 1971, “The Consistency of the Axioms of Abstraction and Extensionality in a Three-Valued Logic”, Notre Dame Journal of Formal Logic, 12: 447–453. (Scholar)
- –––, 1989, “The Nontriviality of Dialectical Set Theory”, in G. Priest, R. Routley and J. Norman (eds.), Paraconsistent Logic, Munich: Philosophia Verlag. (Scholar)
- –––, 2006, Universal Logic, Stanford: CSLI Publications. (Scholar)
- Brown, B., and G. Priest, 2004, “Chunk and Permeate: A Paraconsistent Inference Strategy. Part I: The Infinitesimal Calculus”, The Journal of Philosophical Logic, 33: 379–388. (Scholar)
- Burgess, J., 1981, “Relevance, a Fallacy?”, Notre Dame Journal of Formal Logic, 22: 97–104. (Scholar)
- Colyvan, M., 2000, “Applying Inconsistent Mathematics”, New Waves in the Philosophy of Mathematics, O.Bueno and O. Limmbo (eds.), London: Palgrave McMillan, 160-172. (Scholar)
- Da Costa, Newton C.A., 1974, “On the Theory of Inconsistent Formal Systems”, Notre Dame Journal of Formal Logic, 15: 497–510. (Scholar)
- –––, 2000, “Paraconsistent
Mathematics”, in D. Batens et al. (eds.), Frontiers
of Paraconsistent Logic, Hertfordshire: Research Studies Press,
165–180. (Scholar)
- Davies, E.B., 2005 “A Defence of Mathematical Pluralism
”, Philosophia Mathematica, 13: 252–276. (Scholar)
- Estrada-González, L., 2010, “Complement-Topoi and Dual Intuitionistic Logic”, Australasian Journal of Logic, 9: 26–44. (Scholar)
- –––, 2015a, “The Evil Twin: The Basics of
Complement-toposes”, in Beziau, Chakraborty and Dutta (eds.),
New Directions in Paraconsistent Logic, Dordrecht: Springer:
375-425. (Scholar)
- –––, 2015b, “From (paraconsistent) topos
logic to Universal (topos) logic”, in Koslow and Buchsbaum
(eds.), The Road to Universal Logic: Festschrift for Jean-Yves
Beziau on his Fiftieth Birthday, Dordrecht: Springer,
263-295. (Scholar)
- –––, 2016, “Prospects for
Triviality”, in H. Andreas and P. Verdee (eds.), Logical
Studies of Paraconsistent Reasoning in Science and Mathematics,
Dordrecht: Springer, 81-89. (Scholar)
- Goodman, N., 1981, “The Logic of Contradictions”, Zeitschrift fur Mathematische Logic und Grundlagen der Arithmetik, 27: 119–126. (Scholar)
- Hatcher, W. S., 1982, The Logical Foundations of Mathematics, Oxford: Pergamon. (Scholar)
- Hellman, G. and J. Bell, 2006, “Pluralism and the Foundations of Mathematics”, in C.K. Waters et al. (eds.), Scientific Pluralism (Minnesota Studies in the Philosophy of Science, Volume XIX), Minneapolis: University of Minnesota Press. (Scholar)
- Kripke, S., 1975, “Outline of a Theory of Truth”, The Journal of Philosophy, 72: 690–716. (Scholar)
- McKubre-Jordens, M., and Zach Weber, 2012, “Real Analysis and Paraconsistent Logic”, Journal of Philosophical Logic, 41(5): 901–922. (Scholar)
- Meyer, R. K., 1976, “Relevant Arithmetic”, Bulletin of the Section of Logic of the Polish Academy of Sciences, 5: 133–137. (Scholar)
- Meyer, R. K. and C. Mortensen, 1984, “Inconsistent Models for Relevant Arithmetics”, The Journal of Symbolic Logic, 49: 917–929. (Scholar)
- Mortensen, C., 1983, “Reply to Burgess and to Read”, Notre Dame Journal of Formal Logic, 24: 35–40. (Scholar)
- –––, 1990, “Models for Inconsistent and Incomplete Differential Calculus”, Notre Dame Journal of Formal Logic, 31: 274–285. (Scholar)
- –––, 1995, Inconsistent Mathematics, Kluwer Mathematics and Its Applications Series, Dordrecht: Kluwer. [Errata available online.] (Scholar)
- –––, 1997, “Peeking at the Impossible”, Notre Dame Journal of Formal Logic, 38: 527–534. (Scholar)
- –––, 2000, “Prospects for Inconsistency”, in D. Batens et al. (eds.), Frontiers of Paraconsistent Logic, London: Research Studies Press, 203–208. (Scholar)
- –––, 2002a, “Towards a Mathematics of Impossible Pictures”, in W. Carnielli, M. Coniglio and I. D’Ottaviano (eds.), Paraconsistency: The Logical Way to the Infinite, (Lecture Notes in Pure and Applied Mathematics, Volume 228), New York: Marcel Dekker, 445–454. (Scholar)
- –––, 2002b, “Paradoxes Inside and Outside Language”, Language and Communication, 22: 301–311. (Scholar)
- –––, 2003, “Closed Set Logic”, in R. Brady (ed.), Relevant Logics and Their Rivals (Volume II), Aldershot: Ashgate, pp. 252-262 (especially 255-6). (Scholar)
- –––, 2006, “An Analysis of Inconsistent and Incomplete Necker Cubes”, Australasian Journal of Logic, 4: 216–225. (Scholar)
- –––, 2010, Inconsistent Geometry (Studies in Logic, Volume 27), London: College Publications (King’s College). (Scholar)
- –––, 2011, “Merge”, Australasian Journal of Logic, 9: 135–141. (Scholar)
- –––, 2013, “Arithmetic Starred”, in K. Tanaka, F. Berto, E. Mares and F. Paoli (eds.), Paraconsistency: Logic and Applications, Dordrecht: Springer, 309–314. (Scholar)
- –––, 2019, “Euclid's Geometry: the Case of
Contradiction”, Journal of Modern Greek Studies
(Australia and New Zealand), Special Issue, 2019, 71–83. (Scholar)
- –––, 2019a, “Dialethism and Impossible
Figures”, in A. Rieger and G. Young (eds.), Dialetheism and
Its Applications, Cham: Springer International Publishing,
185–194. (Scholar)
- –––, 2022, The Impossible Arises,
Bloomington, Indiana University Press. (Scholar)
- Paris, J., and Pathmanathan, N., 2006, “A Note on
Priest’s Finite Arithmetics”, The Journal of
Philosophical Logic, 35: 529–537. (Scholar)
- Paris, J., and Sirokofskich, A., 2008, “On LP-models of Arithmetic”, The Journal of Symbolic Logic, 73(1): 212–226. (Scholar)
- Priest, G., 1987, In Contradiction, Dordrecht: Nijhoff; second expanded edition, Oxford: The Clarendon Press, 2006. (Scholar)
- –––, 1997, “Inconsistent Models for Arithmetic: I, Finite Models”, The Journal of Philosophical Logic, 26: 223–235. (Scholar)
- –––, 2000, “Inconsistent Models for
Arithmetic: II, The General Case”, The Journal of Symbolic
Logic, 65: 1519–29. (Scholar)
- –––, 2013, “Mathematical Pluralism”, Logic Journal of IGPL, 21(1): 4–13: doi:10.1093/jzs018 (Scholar)
- Priest, G., R. Routley and J. Norman (eds.), 1989, Paraconsistent Logic, Munich: Philosophia Verlag. (Scholar)
- Restall, G., 2007, “Review of Brady Universal
Logic”, Bulletin of Symbolic Logic, 13(4):
544–547. (Scholar)
- Robinson, A., 1974, Non-standard Analysis, Amsterdam:
North-Holland, revised edition. (Scholar)
- Routley, R. and V. Routley, 1972, “The Semantics of First Degree Entailment”, Noûs, 6: 335–359. (Scholar)
- Shapiro, S., 2002, “Inconsistency and Incompleteness”,
Mind, 111: 817–832. (Scholar)
- –––, “Structures and Logics: a Case for (a) Relativism”, Erkenntnis, 79: 309–329. (Scholar)
- Tedder, A., 2015,“Axioms for Finite Collapse Models of Arithmetic”, The Review of Symbolic Logic, 8(3): 529-539. (Scholar)
- Van Bendegem, J-P., 2014, “Inconsistency in Mathematics and
the Mathematics of Inconsistency”, Synthese, 191(13),
3063-3078. (Scholar)
- Weber, Z., 2010, “Transfinite Numbers in Paraconsistent Set Theory”, The Review of Symbolic Logic, 3(1): 71-92. (Scholar)
- –––, 2012, “Transfinite Cardinals in Paraconsistent Set Theory”, The Review of Symbolic Logic, 5(2): 269–293. (Scholar)
- –––, 2013, “Notes on Inconsistent Set Theory”, in K. Tanaka, F. Berto, E. Mares and F. Paoli (eds.), Paraconsistency: Logic and Applications, Dordrecht: Springer, 315–328. (Scholar)
- ––– and Cotnoir, A.J., 2015, “Inconsistent
Boundaries”, Synthese, 192: 1267–1294.
doi:10.1007/511229-014-0614-2 (Scholar)
- Weber, Z., and M. McKubre-Jordens, 2017, “Paraconsistent Measurement of the Circle”, Australasian Journal of Logic, 14(1): doi:10.26686/ajl.v14i1.4034 (Scholar)