publications
Books
(2021) Paradoxes and Inconsistent Mathematics. Cambridge University Press.
(2022) Paraconsistency in Mathematics. Cambridge Elements, Cambridge University Press.
Edited volumes
(2019) Editor, Ultralogic as Universal? by Richard Routley. Volume IV of The Sylvan Jungle, with contributions. Synthese Library, Springer [link].
(2019) Editor (with Petr Cintula), "Non-classical modal and predicate logic" special issue of Logic Journal of the IGPL, 27(4) [LINK].
(2017) Editor (with P Girard and M McKubre-Jordens), "Non-Classicality: Logic, Mathematics, Philosophy" special issue of Australasian Journal of Logic 14(1) [Link].
(2011) Editor [with Eric Dietrich], special issue of Essays in Philosophy: "Philosophy's Future: Science or something else?" 12(2). [Link]
Articles / Chapters / Essays / Reviews / etc
(forthcoming) True, untrue, valid, invalid, provable, unprovable. Logic and Logical Philosophy.
(forthcoming) The (In)consistency of Consistency (with Graham Priest and Hitoshi Omori). In Walter Carnielli on Reasoning, Pararconsistency, and Probability, ed. H Antunes, A Freire, and A Rodrigues. Springer (Trends in Logic).
(2022) Paraconsistent metatheory: new proofs with old tools (with G Badia and P Girard). Journal of Philosophical Logic, 51:825-856.
(2022) Review of Non-Being: new essays on the metaphysics of non-existence. Sarah Bernstein and Tyron Goldschmidt (eds). Notre Dame Philosophical Reviews. [link]
(2022) This paradoxical life. Aeon, January 11. [link]
(2021) A theorem and a paradox. Inference 6(3). [link]
(2021) Mathematical Pluralism and Relevant Arithmetic. Australasian Journal of Logic 18(5):569-596.
(2021) On closure and truth in substructural theories of truth. Synthese 199: 725-739. (online 2016) [Link]
(2020) Property identity and relevant conditionals. Australasian Philosophical Review 4(2):147-155. (Published September 2021) [Link]
(2019) Just true? On the metatheory for paraconsistent truth (with Hitoshi Omori). Logique et Analyse, 248:415-433.
(2019) Richard Routley/Sylvan (with Dominic Hyde and Filippo Casati). Stanford Encyclopedia of Philosophy.
(2019) Modal logic without contraction in a metatheory without contraction (with Patrick Girard). Review of Symbolic Logic, 12(4):685-701 [link].
(2019) A substructural logic for inconsistent mathematics (with Guillermo Badia). In Dialetheism and its applications, ed. A Reiger and G Young, Springer (Trends in logic), 2019.
(2019) At the limits of thought. In Graham Priest on Dialetheism and Paraconsistency, ed. C Baskent and T Ferguson, Outstanding Contributions to Logic Series, Springer, 2019.
(2019) Observations on the trivial world (with Hitoshi Omori). Erkenntnis, 84(5):975-994. [Link]
(2019) Atheism and dialetheism; or, 'Why I am not a (paraconsistent) Christian'. Australasian Journal of Philosophy, 97(2): 401-407.
(2019) Editor's introduction, Ultralogic as universal? by Richard Routley, Synthese Library, Springer.[Link]
(2018) Dialetheism (with G Priest and Franz Berto). Stanford Encyclopedia of Philosophy, [LINK].
(2017) Paraconsistent measurement of the circle (with M. McKubre-Jordens). Australasian Journal of Logic 14(1): 268-280 [Link].
(2017) A guide to logical pluralism for non-logicians. Think - philosophy for everyone 16(47):93-114. (Link)
(2017) Intrinsic Value and the Last Last Man. Ratio, 30(2):165-180. [Link]
(2016) Computation in non-classical foundations? (with Toby Meadows) Philosopher's Imprint, 16(13):1-17 [link]
(2016) What is an inconsistent truth table? (with G Badia and P Girard). Australasian Journal of Philosophy, 94(3):533-548 [preprint]
(2016) Dialetheism. In Oxford Bibliographies in Philosophy, ed. Duncan Pritchard, Oxford Unviersity Press. [link]
(2016) Paraconsistent Computation and Dialetheic Machines. In Logical Studies of Paraconsistent Reasoning in Science and Mathematics, ed H Andreas and P Verdee, Springer (Trends in Logic).
(2016) On Paraconsistent Downward Lowenheim-Skolem Theorems. In LOGICA Yearbook 2015, ed. P Arazim and M Dancak. College Publications, London.
(2015) Bad Worlds (with Patrick Girard). Thought, 4:93-101 [Link].
(2015) Inconsistent Boundaries (with A.J. Cotnoir). Synthese 192(5):1267-1294 [Link]
(2015) A note on contraction-free logic for validity [with Colin Caret]. Topoi 31(1): 63-74 [Link]
(2014) Tolerating Gluts (with D. Ripley, G. Priest, D. Hyde and M. Colyvan). Mind 123(491):791-811. [Link]
(2014) Naive Validity. Philosophical Quarterly, 64(254): 99-114 [preprint].
(201x) Sorites in Paraconsistent Mathematics. In On the Sorites Paradox, ed. Ali Abasnezhad and Otavio Bueno, Springer, waiting to appear.
(2013) Paraconsistent Logic (with G Priest and K Tanaka) Stanford Encyclopedia of Philosophy [Link]
(2013) Figures, Formulae, and Functors. In Visual Reasoning With Diagrams, edited by Sun-Joo Shin and Amirouche Moktefi, 153-170, Springer. [Link]
(2013) Notes on Inconsistent Set Theory. In Paraconsistency: Logic and Applications, ed. F Berto, E Mares, F Paoli, and K Tanaka, 315 - 328, Springer [Link].
(2013) Existence and [\E]xistence (with Heather Dyke). Journal of Experimental and Theoretical AI special issue, "Paradox and Mind" ed. E Dietrich, 25(3): 367-376. [Link].
2013) Review of Mark Colyvan, Introduction to the Philosophy of Mathematics, Australasian Journal of Philosophy 91(4): 828.
(2013) Review of Lloyd Humbersone, The Connectives, Philosophy in Review 33(4): 305 -7. [Link]
(2012) Transfinite Cardinals in Paraconsistent Set Theory. Review of Symbolic Logic 5(2):269-293 [Link].
(2012) Real Analysis in Paraconsistent Logic (with M McKubre-Jordens). Journal of Philosophical Logic, 41(5): 901 - 922. [Link]
(2012) Review of Chris Mortensen, Inconsistent Geometry. Australasian Journal of Philosophy 90(3): 611 - 614.
(2012) Review of Piotr Lukowski, Paradoxes. Philosophy in Review 32(12): 307 - 309. [Link]
(2011) Can u do that? (with Jc Beall and Graham Priest). Analysis 71(2): 280-285. [Link]
(2011) Reply to Bjørdal. Review of Symbolic Logic 4(1): 109-113. [Link]
(2011) Editor's Introduction to special issue of Essays in Philosophy, ed. E. Dietrich and Z. Weber, 12(2): 195-199. [Link]
(2011) Review of Michael Potter, Wittgenstein's Notes on Logic. Metaphilosophy 42(1-2): 166-170. [Link]
(2010) A Paraconsistent Model of Vagueness. Mind 119(476): 1025-1045. [Link]
(2010) A Topological Sorites (with Mark Colyvan). Journal of Philosophy, 107(6): 311-325. [Link]
(2010) Paraconsistent Logic. In J. Fieser and B. Dowden (eds.), Internet Encyclopedia of Philosophy. [Link]
(2010) Transfinite Numbers in Paraconsistent Set Theory. Review of Symbolic Logic 3(1): 71-92. [Link]
(2010) Extensionality and Restriction in Naive Set Theory. Studia Logica 94(1): 87-104. [Link]
(2010) Explanation and Solution in the Inclosure Argument. Australasian Journal of Philosophy 88(2): 353-357. [Link]
(2010) Set Theory, Foundations of Mathematics, Russell and Whitehead's Principia, Halmos' Naive Set Theory, Bolzano. In Key Terms in Logic, ed. F Russo and J Williamson. Continuum. [Link]
(2010) Review of Jc Beall, Spandrels of Truth, Bulletin of Symbolic Logic, 16(2): 284-286.
(2009) Review of On Preserving: Essays on Preservationism and Paraconsistent Logic. Peter Schotch, Bryson Brown, Raymond Jennings (eds). Notre Dame Philosophical Reviews. [Link]
(2009) Inconsistent Mathematics. In J. Fieser and B. Dowden (eds.), Internet Encyclopedia of Philosophy. [Link]
(2007) On Paraconsistent Ethics. South African Journal of Philosophy 26: 239–244.
The Reasoner
(2013) Guest Editor, The Reasoner 7(11). Editorial and interview with Walter Carnielli.
(2011) Guest Editor, The Reasoner 5(1). Editorial and interview with Alan Musgrave. [Link]
(2011) A rose by any other name? The Reasoner 5(2).
(2010) Guest Editor of The Reasoner 4(6), June 2010: Editorial and interview with Greg Restall. [Link]
(2010) On Reconstructing Proofs in Paraconsistent Mathematics. The Reasoner 4(4). [Link]