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23Between Square and Hexagon in Oresme’s Livre du Ciel et du MondeHistory and Philosophy of Logic 41 (1): 36-47. 2019.In logic, Aristotelian diagrams are almost always assumed to be closed under negation, and are thus highly symmetric in nature. In linguistics, by contrast, these diagrams are used to study lexicalization, which is notoriously not closed under negation, thus yielding more asymmetric diagrams. This paper studies the interplay between logical symmetry and linguistic asymmetry in Aristotelian diagrams. I discuss two major symmetric Aristotelian diagrams, viz. the square and the hexagon of oppositio…Read more
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34Boolean considerations on John Buridan's octagons of oppositionHistory and Philosophy of Logic 40 (2): 116-134. 2018.This paper studies John Buridan's octagons of opposition for the de re modal propositions and the propositions of unusual construction. Both Buridan himself and the secondary literature have emphasized the strong similarities between these two octagons (as well as a third one, for propositions with oblique terms). In this paper, I argue that the interconnection between both octagons is more subtle than has previously been thought: if we move beyond the Aristotelian relations, and also take Boole…Read more
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30Aristotelian diagrams for semantic and syntactic consequenceSynthese 198 (1): 187-207. 2018.Several authors have recently studied Aristotelian diagrams for various metatheoretical notions from logic, such as tautology, satisfiability, and the Aristotelian relations themselves. However, all these metalogical Aristotelian diagrams focus on the semantic (model-theoretical) perspective on logical consequence, thus ignoring the complementary, and equally important, syntactic (proof-theoretical) perspective. In this paper, I propose an explanation for this discrepancy, by arguing that the me…Read more
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24Believing in Logic and Philosophy, KU Leuven, Belgium, 2014. Supervised by Stefaan CuypersBulletin of Symbolic Logic 24 (2): 201-202. 2018.status: published.
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55A Hexagon of Opposition for the Theism/Atheism DebatePhilosophia 47 (2): 387-394. 2019.Burgess-Jackson has recently suggested that the debate between theism and atheism can be represented by means of a classical square of opposition. However, in light of the important role that the position of agnosticism plays in Burgess-Jackson’s analysis, it is quite surprising that this position is not represented in the proposed square of opposition. I therefore argue that the square of opposition should be extended to a slightly larger, more complex Aristotelian diagram, viz., a hexagon of o…Read more
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Future Directions for Logic; Proceedings of PhDs in Logic III - Vol. 2 of IfColog Proceedings (edited book)College Publications. 2012.
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16De dynamische wending in de epistemische logica [The Dynamic Turn in Epistemic Logic]Tijdschrift Voor Filosofie 78 (2): 365-391. 2016.This article describes the historical development of epistemic logic, focusing on the dynamic turn that has taken place in the last few decades. Although this dynamic turn was mainly motivated by technical considerations in computer science and game theory, it is argued that it can also be relevant from a more philosophical perspective: the application of dynamic epistemic logics to analyze prima facie static notions, theorems, etc. fits perfectly in a Wittgensteinian approach to philosophy as c…Read more
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41Using Syllogistics to Teach MetalogicMetaphilosophy 48 (4): 575-590. 2017.This article describes a specific pedagogical context for an advanced logic course and presents a strategy that might facilitate students’ transition from the object-theoretical to the metatheoretical perspective on logic. The pedagogical context consists of philosophy students who in general have had little training in logic, except for a thorough introduction to syllogistics. The teaching strategy tries to exploit this knowledge of syllogistics, by emphasizing the analogies between ideas from …Read more
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84In the recent debate on future contingents and the nature of the future, authors such as G. A. Boyd, W. L. Craig, and E. Hess have made use of various logical notions, such as the Aristotelian relations of contradiction and contrariety, and the ‘open future square of opposition.’ My aim in this paper is not to enter into this philosophical debate itself, but rather to highlight, at a more abstract methodological level, the important role that Aristotelian diagrams can play in organizing and clar…Read more
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29De logische geometrie van Johannes Buridanus' modale achthoekTijdschrift Voor Filosofie 79 (2): 217-238. 2017.In order to elucidate his logical analysis of modal quantified propositions (e.g. ‘all men are necessarily mortal’), the 14th century philosopher John Buridan constructed a modal octagon of oppositions. In the present paper we study this modal octagon from the perspective of contemporary logical geometry. We argue that the modal octagon contains precisely six squares of opposition as subdiagrams, and classify these squares based on their logical properties. On a more abstract level, we show that…Read more
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33Thomas van Aquino, niet-normale modale logica's en het probleem van toekomstige contingentiesTijdschrift Voor Filosofie 79 (2): 259-276. 2017.Thomas Aquinas maintained that God foreknows future contingent events and that his foreknowledge does not entail that they are necessarily the case. More specifically, he stated that if God knows a future contingent event, this future contingent event will be necessarily the case de sensu composito, but not de sensu diviso. After emphasizing the unified nature of Aquinas’ notion of necessity, we propose an interpretation of his theses by restating them within the framework of non-normal modal lo…Read more
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14Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford, Oxford University Press, 2008Tijdschrift Voor Filosofie 71 (3): 635-637. 2009.
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26Carrie Jenkins, Grounding Concepts. An Empirical Basis for Arithmetical Knowledge. Oxford, Oxford University Press, 2008Tijdschrift Voor Filosofie 71 (4): 796-798. 2009.
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24Kathrin Koslicki, The Structure of Objects. Oxford, Oxford University Press, 2008Tijdschrift Voor Filosofie 71 (2): 411-413. 2009.
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17Leila Haaparanta (ed.), The Development of Modern Logic. Oxford, Oxford University Press, 2009Tijdschrift Voor Filosofie 72 (3): 606-607. 2010.
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55Herman Cappelen and John Hawthorne, Relativism and Monadic Truth. Oxford, Oxford University Press, 2009Tijdschrift Voor Filosofie 72 (1): 173-174. 2010.
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31Martin Peterson, An Introduction to Decision Theory. Cambridge, Cambridge University Press, 2009Tijdschrift Voor Filosofie 73 (3): 591-594. 2011.
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18Frank Jackson, Language, Names, and Information. Cambridge (MA), Wiley-Blackwell, 2010Tijdschrift Voor Filosofie 73 (3): 594-596. 2011.
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19Boudewijn de Bruin, Explaining Games. The Epistemic Programme in Game Theory. Dordrecht, Springer, 2010Tijdschrift Voor Filosofie 73 (4): 789-791. 2011.
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21Jerome Kagan, The Three Cultures. Natural Sciences, Social Sciences, and the Humanities in the 21st Century. New York, Cambridge University Press, 2009Tijdschrift Voor Filosofie 73 (1): 188-190. 2011.
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24Vincent F. Hendricks and Olivier Roy (eds.), Epistemic Logic: 5 Questions. Sl, Automatic Press/VIP, 2010. Vincent F. Hendricks and Duncan Pritchard (eds.), Epistemology: 5 Questions. Sl, Automatic Press/VIP, 2008 (joint review) (review)Tijdschrift Voor Filosofie 73 (3): 596-598. 2011.
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89Some remarks on the model theory of epistemic plausibility modelsJournal of Applied Non-Classical Logics 21 (3-4): 375-395. 2011.The aim of this paper is to initiate a systematic exploration of the model theory of epistemic plausibility models (EPMs). There are two subtly different definitions in the literature: one by van Benthem and one by Baltag and Smets. Because van Benthem's notion is the most general, most of the paper is dedicated to this notion. We focus on the notion of bisimulation, and show that the most natural generalization of bisimulation to van Benthem-type EPMs fails. We then introduce parametrized bisim…Read more
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12Structures of oppositions in public announcement logicIn Jean-Yves Béziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition, Springer Verlag. pp. 313--339. 2012.
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37Sanford Goldberg, Relying on Others. An Essay in Epistemology. Oxford, Oxford University Press, 2010Tijdschrift Voor Filosofie 74 (1): 160-163. 2012.
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5Fenrong Liu, Reasoning about Preference Dynamics. Springer, Dordrecht, 2011 (forthcoming)Tijdschrift Voor Filosofie 74 (4): 818-820. 2012.
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36Johan van Benthem, Amitabha Gupta and Rohit Parikh (eds.), Proof, Computation and Agency. Logic at the Crossroads. Dordrecht, Springer, 2011. Johan van Benthem, Amitabha Gupta and Eric Pacuit (eds.), Games, Norms and Reasons. Logic at the Crossroads. Dordrecht, Springer, 2011 (joint review) (review)Tijdschrift Voor Filosofie 74 (2): 379-381. 2012.
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18Robert Kowalski, Computational Logic and Human Thinking. Cambridge, Cambridge University Press, 2011Tijdschrift Voor Filosofie 75 (2): 395-397. 2013.
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26Adriane A. Rini and Max J. Cresswell, The World-Time Parallel. Tense and Modality in Logic and Metaphysics. Cambridge, Cambridge University Press, 2012 (review)Tijdschrift Voor Filosofie 75 (1): 168-171. 2013.
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68Contemporary Epistemic Logic and the Lockean ThesisFoundations of Science 18 (4): 599-610. 2013.This paper studies the Lockean thesis from the perspective of contemporary epistemic logic. The Lockean thesis states that belief can be defined as ‘sufficiently high degree of belief’. Its main problem is that it gives rise to a notion of belief which is not closed under conjunction. This problem is typical for classical epistemic logic: it is single-agent and static. I argue that from the perspective of contemporary epistemic logic, the Lockean thesis fares much better. I briefly mention that …Read more
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92Logical Geometries and Information in the Square of OppositionsJournal of Logic, Language and Information 23 (4): 527-565. 2014.The Aristotelian square of oppositions is a well-known diagram in logic and linguistics. In recent years, several extensions of the square have been discovered. However, these extensions have failed to become as widely known as the square. In this paper we argue that there is indeed a fundamental difference between the square and its extensions, viz., a difference in informativity. To do this, we distinguish between concrete Aristotelian diagrams and, on a more abstract level, the Aristotelian g…Read more
Leuven, Vlaams-Brabant, Belgium
Areas of Specialization
Science, Logic, and Mathematics |
Logic and Philosophy of Logic |
Philosophy of Mathematics |