
John Buridan’s Sophismata and Interval Temporal SemanticsHistory of Philosophy and Logical Analysis 13 (1): 131147. 2010.

Castagnoli, Luca. 2010. Ancient SelfRefutation: The Logic and History of the SelfRefutation Argument from Democritus to Augustine. Cambridge: Cambridge University Press (394 pages, ISBN 9780521896313 (hardback)) (review)History of Philosophy and Logical Analysis 16 (1): 398402. 2013.

1A Simple Semantics for Aristotelian Apodeictic SyllogisticsIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 454469. 2010.

1Three 13thcentury views of quantified modal logicIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 389406. 2008.

10Contradictions, Impossibility, and Triviality: A Response to Jc BeallJournal of Analytic Theology 7 (1): 544559. 2019.ㅤ

4Reasoning About Obligations in Obligationes: A Formal ApproachIn Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10, Csli Publications. pp. 533568. 2014.

9Aristotle's syllogistics: Marko Malink: Aristotle’s modal syllogistics Boston: Harvard University Press, 2013, 384pp, $49.95 HBMetascience 23 (3): 573579. 2014.In this masterful book, Marko Malink sets out to do what no one has succeeded in doing before: To provide a consistent and coherent model adequate for the entirety of Aristotle’s claims about valid and invalid syllogisms, both apodeictic and modal (p. 2). The fact that Malink attains his goal is impressive enough to almost—but not quite—overshadow the drawbacks of the model (which, to be fair, he points out himself in various places).After an introduction, where notation for categorical claims i…Read more

3Three 13thcentury views of quantified modal logicIn Carlos Areces & Robert Goldblatt (eds.), Advances in Modal Logic, Volume 7, Csli Publications. pp. 389406. 2008.

5The Logic of Where and While in the 13th and 14th CenturiesIn Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11, Csli Publications. pp. 535550. 2016.Medieval analyses of molecular propositions include many nontruthfunctional connectives in addition to the standard modern binary connectives (conjunction, disjunction, and conditional). Two types of nontruthfunctional molecular propositions considered by a number of 13th and 14thcentury authors are temporal and local propositions, which combine atomic propositions with `while' and `where'. Despite modern interest in the historical roots of temporal and tense logic, medieval analyses of `wh…Read more

10John Buridan's Sophismata and interval temporal semanticsLogical Analysis and History of Philosophy 13 133147. 2010.In this paper we look at the suitability of modern intervalbased temporal logic for modeling John Buridan’s treatment of tensed sentences in his Sophismata. Building on the paper [Øhrstrøm 1984], we develop Buridan’s analysis of temporal logic, paying particular attention to his notions of negation and the absolute/relative nature of the future and the past. We introduce a number of standard modern propositional interval temporal logics to illustrate where Buridan’s intervalbased temporal anal…Read more

14A simple semantics for Aristotelian apodeictic syllogisticsAdvances in Modal Logic 8 454469. 2010.We give a simple definition of validity for syllogisms involving necessary and assertoric premises which validates all and only the Aristotelian apodeictic syllogisms.

8Interactive Logic in the Middle AgesLogic and Logical Philosophy 21 (4): 439471. 2012.Recently logic has shifted emphasis from static systems developed for purely theoretical reasons to dynamic systems designed for application to real world situations. The emphasis on the applied aspects of logic and reasoning means that logic has become a pragmatic tool, to be judged against the backdrop of a particular application. This shift in emphasis is, however, not new. A similar shift towards “interactive logic” occurred in the high Middle Ages. We provide a number of different examples …Read more

54A Curious Dialogical Logic and its Composition ProblemJournal of Philosophical Logic 43 (6): 10651100. 2014.Dialogue semantics for logic are twoplayer logic games between a Proponent who puts forward a logical formula φ as valid or true and an Opponent who disputes this. An advantage of the dialogical approach is that it is a uniform framework from which different logics can be obtained through only small variations of the basic rules. We introduce the composition problem for dialogue games as the problem of resolving, for a set S of rules for dialogue games, whether the set of Sdialogically valid f…Read more

104Prior on an Insolubilium of Jean BuridanSynthese 188 (3): 487498. 2012.We present Prior's discussion of a puzzle about valditity found in the writings of the fourteenthcentury French logician Jean Buridan and show how Prior's study of this puzzle may have provided the conceptual inspiration for his development of hybrid logic

76Against TruthConditional Theories of Meaning: Three Lessons from the Language of FictionRes Philosophica 93 (2): 441459. 2016.Fictional discourse and fictional languages provide useful test cases for theories of meaning. In this paper, we argue against truthconditional accounts of meaning on the basis of problems posed by language(s) of fiction. It is wellknown how fictional discourse  discourse about nonexistent objects  poses a problem for truthconditional theories of meaning. Less wellconsidered, however, are the problems posed by fictional languages, which can be created to either be meaningful or not to b…Read more

6The ontological argumentIn Michael Bruce & Steven Barbone (eds.), Just the Arguments: 100 of the Most Important Arguments in Western Philosophy, Wileyblackwell. 2011.

82Logic and the Condemnations of 1277Journal of Philosophical Logic 39 (2): 201227. 2010.The struggle to delineate the relationship between theology and logic flourished in the thirteenth century and culminated in two condemnations in early 1277, one in Paris and the other in Oxford. To see how much and what kind of effect ecclesiastical actions such as condemnations and prohibitions to teach had on the development of logic in the Middle Ages, we investigate the events leading up to the 1277 actions, the condemned propositions, and the parts of these condemnations connected to modal…Read more

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6Book Review: Jean Buridan, Treatise on Consequences (review)Studia Logica 104 (6): 13191323. 2016.

21The ontological argument and Russell's antinomyLogic and Logical Philosophy 18 (34): 309312. 2009.In this short note we respond to the claim made by Christopher Viger in [4] that Anselm’s socalled ontological argument falls prey to Russell’s paradox. We show that Viger’s argument is based on a flawed premise and hence does not in fact demonstrate what he claims it demonstrates

58Modal and temporal logics for abstract space–time structuresStudies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (3): 673681. 2007.In the 4th century BC, the Greek philosopher Diodoros Chronos gave a temporal definition of necessity. Because it connects modality and temporality, this definition is of interest to philosophers working within branching time or branching spacetime models. This definition of necessity can be formalized and treated within a logical framework. We give a survey of the several known modal and temporal logics of abstract spacetime structures based on the real numbers and the integers, considering t…Read more

75Arthur Prior and Medieval LogicSynthese 188 (3): 349366. 2012.Though Arthur Prior is now best known for his founding of modern temporal logic and hybrid logic, much of his early philosophical career was devoted to history of logic and historical logic. This interest laid the foundations for both of his groundbreaking innovations in the 1950s and 1960s. Because of the important rôle played by Prior's research in ancient and medieval logic in his development of temporal and hybrid logic, any student of Prior, temporal logic, or hybrid logic should be famili…Read more

24Sit Verum Obligationes and Counterfactual ReasoningVivarium 53 (1): 90113. 2015.In the early 1980s, Paul V. Spade advanced the thesis that obligational reasoning was counterfactual reasoning, based upon his interpretation of the obligationes of Walter Burley, Richard Kilvington, and Roger Swyneshed. Eleonore Stump in a series of contemporary papers argued against Spade’s thesis with respect to Burley and Swyneshed, provisionally admitting it for Kilvington with the caveat that Kilvington’s theory is by no means clear or nonidiosyncratic. In this paper, we revisit the conne…Read more

29Deceit and indefeasible knowledge: the case of dubitatioJournal of Applied NonClassical Logics 21 (34): 503519. 2011.The current trend in knowledge revision in the Dynamic Epistemic Logic tradition focuses on the addition of new knowledge, rather than the possibility of losing knowledge. Yet there are natural situations, such as an agent who does not want another agent to know that she knows a certain piece of information, where there is a need to be able to model the retraction of a proposition from a knowledge base. One situation where this is systematically required is the variant of the medieval theory of …Read more

79Medieval Disputationes de obligationibus as Formal Dialogue SystemsArgumentation 27 (2): 143166. 2013.Formal dialogue systems model rulebased interaction between agents and as such have multiple applications in multiagent systems and AI more generally. Their conceptual roots are in formal theories of natural argumentation, of which Hamblin’s formal systems of argumentation in Hamblin (Fallacies. Methuen, London, 1970, Theoria 37:130–135, 1971) are some of the earliest examples. Hamblin cites the medieval theory of obligationes as inspiration for his development of formal argumentation. In an o…Read more
Areas of Specialization
Logic and Philosophy of Logic 
Medieval and Renaissance Philosophy 