Philosophy of Math and Logic

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Journal Articles

  1. “Axiomatizations of arithmetic and the first-order/second-order divide". Synthese 196, 2583–2597, 2019.

  2. (With R. French) "Paradoxes and structural rules from a dialogical perspective". Philosophical Issues 28, 129-158, 2018.

  3. (With H. Veluwenkamp) "Reasoning biases, non-monotonic logics, and belief revision". Theoria 83(1), 29-52, 2017.

  4. "Reductio ad absurdum from a dialogical perspective". Philosophical Studies 173(10), 2605-2628, 2016.

  5. "A dialogical, multi-agent account of the normativity of logic". Dialectica 69, 587-609, 2015. 

  6. "The undergeneration of permutation invariance as a criterion for logicality". Erkenntnis 79, 81-97, 2014.

  7. "Mathematical reasoning and external symbolic systems". Logique & Analyse 221, 45-65, 2013.

  8. “Reassessing logical hylomorphism and the demarcation of logical constants”. Synthese 185, 387-410, 2012.

  9. "Towards a practice-based philosophy of logic: formal languages as a case study". Philosophia Scientiae 16(1), 71-102, 2012.

  10. (With E. Andrade-Lotero) “A contentious trinity: levels of entailment in Brandom's pragmatist inferentialism”. Philosophia 40(1), 41-53, 2012.

  11. “The different ways in which logic is (said to be) formal”. History and Philosophy of Logic 32, pp. 303-332, 2011.

  12. “Lessons on truth from medieval solutions to the Liar paradox”. Philosophical Quarterly 61, pp. 58-78, 2011.

  13. “A comparative taxonomy of medieval and modern approaches to Liar sentences”. History and Philosophy of Logic 29(3), pp. 227 – 261, 2008.

  14. “Buridan’s consequentia: consequence and inference within a token-based semantics”. History and Philosophy of Logic 26(4), 2005, pp. 277-297, 2005.

  15. “The Buridanian account of inferential relations between doubly-quantified propositions: a proof of soundness”. History and Philosophy of Logic 25(3), 2004, pp. 215-234, 2004.

Chapters in Volumes

  1. "The beauty (?) of mathematical proofs”. In A. Aberdein, M. Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. London, Bloomsbury, 2019, 63-94.

  2. "A dialogical conception of explanation in mathematical proofs". In Ernest, P. (ed.), Philosophy of Mathematics Education Today. Berlin, Springer, 2018.

  3. "5 questions in the philosophy of logic". In Tracy Lupher and Thomas Adajian (eds.), Philosophy of Logic: 5 Questions. Copenhagen, Automatic Press, 2016.

  4. “Surprises in Logic”. In M. Palis (ed.), LOGICA Yearbook 2009. London, College Publications, 2010.

  5. “Judgments, contents and their representations”. In G. Primiero & S. Rahman (eds.), Acts of Knowledge: History, Philosophy and Logic. London, College Publications, pp. 183-206, 2009.

  6. “Tarski’s hidden theory of meaning”. In S. Rahman, T. Tulenheimo & E. Genot (eds.), Unity, Truth and the Liar – The modern relevance of medieval solutions to Semantic paradoxes. Berlin, Springer, pp. 41-63, 2008.

  7. “Contradiction: the real challenge for paraconsistent logic”. In J.Y. Beziau, W.A. Carnielli and D. Gabbay (eds.), Handbook of Paraconsistency. In the series Logic and Cognitive Systems, London, College Publications, pp. 465-480, 2007.

  8. “In search of the intuitive notion of logical consequence”. LOGICA Yearbook 2004, Prague, Filosofia, 2005, pp. 109-123, 2005.

  9. “A medieval reformulation of the de dicto / de re distinction”. LOGICA Yearbook 2003, Prague, Filosofia, 2004, pp. 111- 124, 2004.