•  104
    Prior on an Insolubilium of Jean Buridan
    Synthese 188 (3): 487-498. 2012.
    We present Prior's discussion of a puzzle about valditity found in the writings of the fourteenth-century 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
  •  82
    Logic and the Condemnations of 1277
    Journal of Philosophical Logic 39 (2): 201-227. 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
  •  79
    Formal dialogue systems model rule-based interaction between agents and as such have multiple applications in multi-agent 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
  •  76
    Fictional discourse and fictional languages provide useful test cases for theories of meaning. In this paper, we argue against truth-conditional accounts of meaning on the basis of problems posed by language(s) of fiction. It is well-known how fictional discourse -- discourse about non-existent objects -- poses a problem for truth-conditional theories of meaning. Less well-considered, however, are the problems posed by fictional languages, which can be created to either be meaningful or not to b…Read more
  •  75
    Arthur Prior and Medieval Logic
    Synthese 188 (3): 349-366. 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 ground-breaking 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
  •  58
    Modal and temporal logics for abstract space–time structures
    with Joel Uckelman
    Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (3): 673-681. 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 space-time 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 space-time structures based on the real numbers and the integers, considering t…Read more
  •  56
    The logic of categorematic and syncategorematic infinity
    Synthese 192 (8): 2361-2377. 2015.
    The medieval distinction between categorematic and syncategorematic words is usually given as the distinction between words which have signification or meaning in isolation from other words and those which have signification only when combined with other words . Some words, however, are classified as both categorematic and syncategorematic. One such word is Latin infinita ‘infinite’. Because infinita can be either categorematic or syncategorematic, it is possible to form sophisms using infinita …Read more
  •  54
    A Curious Dialogical Logic and its Composition Problem
    with Jesse Alama and Aleks Knoks
    Journal of Philosophical Logic 43 (6): 1065-1100. 2014.
    Dialogue semantics for logic are two-player 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 S-dialogically valid f…Read more
  •  47
    A Quantified Temporal Logic for Ampliation and Restriction
    Vivarium 51 (1-4): 485-510. 2013.
    Temporal logic as a modern discipline is separate from classical logic; it is seen as an addition or expansion of the more basic propositional and predicate logics. This approach is in contrast with logic in the Middle Ages, which was primarily intended as a tool for the analysis of natural language. Because all natural language sentences have tensed verbs, medieval logic is inherently a temporal logic. This fact is most clearly exemplified in medieval theories of supposition. As a case study, w…Read more
  •  29
    Deceit and indefeasible knowledge: the case of dubitatio
    Journal of Applied Non-Classical Logics 21 (3-4): 503-519. 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
  •  24
    Sit Verum Obligationes and Counterfactual Reasoning
    Vivarium 53 (1): 90-113. 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 non-idiosyncratic. In this paper, we revisit the conne…Read more
  •  21
    The ontological argument and Russell's antinomy
    Logic and Logical Philosophy 18 (3-4): 309-312. 2009.
    In this short note we respond to the claim made by Christopher Viger in [4] that Anselm’s so-called 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
  •  19
    Articulating Medieval Logic
    Philosophical Quarterly 66 (263): 432-435. 2016.
  •  14
    A simple semantics for Aristotelian apodeictic syllogistics
    Advances in Modal Logic 8 454-469. 2010.
    We give a simple definition of validity for syllogisms involving necessary and assertoric premises which validates all and only the Aristotelian apodeictic syllogisms.
  •  14
    Quaestiones circa logicam (review)
    Speculum 86 (3): 719-720. 2011.
  •  10
    John Buridan's Sophismata and interval temporal semantics
    Logical Analysis and History of Philosophy 13 133-147. 2010.
    In this paper we look at the suitability of modern interval-based 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 interval-based temporal anal…Read more
  •  10
    Contradictions, Impossibility, and Triviality: A Response to Jc Beall
    Journal of Analytic Theology 7 (1): 544-559. 2019.
  •  9
    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
  •  8
    Interactive Logic in the Middle Ages
    Logic and Logical Philosophy 21 (4): 439-471. 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
  •  6
  •  5
    The Logic of Where and While in the 13th and 14th Centuries
    In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11, Csli Publications. pp. 535-550. 2016.
    Medieval analyses of molecular propositions include many non-truthfunctional connectives in addition to the standard modern binary connectives (conjunction, disjunction, and conditional). Two types of non-truthfunctional molecular propositions considered by a number of 13th- and 14th-century 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
  •  4
    Reasoning About Obligations in Obligationes: A Formal Approach
    In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10, Csli Publications. pp. 533-568. 2014.
  •  3
    Three 13th-century views of quantified modal logic
    In Carlos Areces & Robert Goldblatt (eds.), Advances in Modal Logic, Volume 7, Csli Publications. pp. 389-406. 2008.
  •  1
    Three 13th-century views of quantified modal logic
    In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 389-406. 2008.
  •  1
    A Simple Semantics for Aristotelian Apodeictic Syllogistics
    In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 454-469. 2010.