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559Fictional Modality and the Intensionality of Fictional ContextsAustralasian Journal of Logic 19 (4): 124-132. 2022.In, Kosterec attempts to provide ``model-theoretic proofs'' of certain theses involving the normal modal operators $\Diamond$ and $\square$ and the truth-in-fiction operator $F$ which he then goes on to show have counterexamples in Kripke models. He concludes from this that the embedding of modal logic under the truth-in-fiction operator is unsound. We show instead that it is the ``model-theoretic proofs'' that are themselves unsound, involving illicit substitution, a subtle error that neverthel…Read more
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553Lorhard, Ramus, and Timpler and “The birth of ontology”.Journal of Knowledge Structures and Systems 3 (2): 48-56. 2022.This review article offers a discussion of some aspects of the historical and conceptual context when the term “ontology” (Lat. ontologia) was first introduced in the scholarly circles of the early 17th century. In particular, Barry Smith's (2022) analysis of the birth of ontology provides a springboard for some further remarks on the author of the work with the first known occurrence of the word “ontologia”, Jacob Lorhard, including an analysis of his relationship with earlier philosophers Petr…Read more
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485John Eliot's Logick Primer: A Bilingual English-Massachusett Logic TextbookHistory and Philosophy of Logic 45 (3): 1-24. 2023.In 1672 John Eliot, English Puritan educator and missionary to New England, published The Logick Primer: Some Logical Notions to initiate the INDIANS in the knowledge of the Rule of Reason; and to know how to make use thereof (Eliot 1672) The Logick Primer: Some Logical Notions to Initiate the INDIANS in the Knowledge of the Rule of Reason; and to Know How to Make Use Thereof, Cambridge, MA: Marmaduke Johnson]. This roughly 80 page pamphlet introduces syllogistic vocabulary and reasoning so that…Read more
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248Logic as Liberation, or, Logic, Feminism, and Being a Feminist in LogicIn Igor Sedlár (ed.), Logica Yearbook 2023, College Publications. forthcoming.There has been a long history of tension between feminists and feminist philosophy, on the one hand, and logic, on the other hand. This tension expresses itself in many ways, including claims that logic is a tool of the patriarchy, that logic/rationality/analytical tools in philosophy need to be rejected if women are to fully participate, that women = body and man = mind, that to do feminist philosophy one must do it as a situated, embodied person, not as an impersonal, disembodied mind, that lo…Read more
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166Prior on an Insolubilium of Jean BuridanSynthese 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
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142Complete Symposium on Jc Beall's Christ – A Contradiction: A Defense of Contradictory ChristologyJournal of Analytic Theology 7 (1): 400-577. 2019.The fundamental problem of Christology is the apparent contradiction of Christ as recorded at Chalcedon. Christ is human and Christ is divine. Being divine entails being immutable. Being human entails being mutable. Were Christ two different persons there’d be no apparent contradiction. But Chalcedon rules as much out. Were Christ only partly human or only partly divine there’d be no apparent contradiction. But Chalcedon rules as much out. Were the very meaning of ‘mutable’ and/or ‘immutable’ ot…Read more
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139Medieval Disputationes de obligationibus as Formal Dialogue SystemsArgumentation 27 (2): 143-166. 2013.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
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126Logic and the Condemnations of 1277Journal 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
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125Against Truth-Conditional Theories of Meaning: Three Lessons from the Language(s) of FictionRes Philosophica 93 (2): 441-459. 2016.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
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117Arthur Prior and Medieval LogicSynthese 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
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116A Curious Dialogical Logic and its Composition ProblemJournal 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
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109The logic of categorematic and syncategorematic infinitySynthese 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
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93Against the Theistic MultiverseKriterion - Journal of Philosophy 34 (4): 1-14. 2020.We argue that Kraay's "theistic multiverse" response to the objections to theism [Kraay 2011] is unsuccessful as it simply shifts the problems leveled against theism from the level of possible worlds to the level of possible universes. Furthermore, when we restate the objections at the level of possible universes, we can show how Kraay's conclusion about the uniqueness of the theistic multiverse is undermined.
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87Modal 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): 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
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86A Quantified Temporal Logic for Ampliation and RestrictionVivarium 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
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63John Buridan’s Sophismata and Interval Temporal SemanticsHistory of Philosophy & Logical Analysis 13 (1): 131-147. 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, 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 analysis differs from…Read more
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61The ontological argument and Russell's antinomyLogic 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
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61Sit Verum Obligationes and Counterfactual ReasoningVivarium 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
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54What Problem Did Ladd-Franklin (Think She) Solve(d)?Notre Dame Journal of Formal Logic 62 (3): 527-552. 2021.Christine Ladd-Franklin is often hailed as a guiding star in the history of women in logic—not only did she study under C. S. Peirce and was one of the first women to receive a PhD from Johns Hopkins, she also, according to many modern commentators, solved a logical problem which had plagued the field of syllogisms since Aristotle. In this paper, we revisit this claim, posing and answering two distinct questions: Which logical problem did Ladd-Franklin solve in her thesis, and which problem did …Read more
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51Interactive Logic in the Middle AgesLogic 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
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50Deceit and indefeasible knowledge: the case of dubitatioJournal 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
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43Contradictions, Impossibility, and Triviality: A Response to Jc BeallJournal of Analytic Theology 7 (1): 544-559. 2019.ㅤ
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43A simple semantics for Aristotelian apodeictic syllogisticsAdvances 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.
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32Castagnoli, Luca. 2010. Ancient Self-Refutation: The Logic and History of the Self-Refutation Argument from Democritus to Augustine. Cambridge: Cambridge University Press (394 pages, ISBN 978-0-521-89631-3 (hardback)) (review)History of Philosophy & Logical Analysis 16 (1): 398-402. 2013.
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28What Logical Consequence Could, Could Not, Should, and Should Not BeAristotelian Society Supplementary Volume 98 (1): 255-275. 2024.In ‘Logical Consequence (Slight Return)’, Gillian Russell asks ‘What is logical consequence?’, a question which has vexed logicians since at least the twelfth century, when people first began to wonder what it meant for one sentence (or proposition) to follow from another sentence (or proposition, or set of sentences, or set of propositions), or whether it was possible to put down rules determining when the relation of ‘follows from’ (or ‘is antecedent to’) holds. Her aim is threefold: (1) to ex…Read more
University of Amsterdam
PhD, 2009
Areas of Specialization
Logic and Philosophy of Logic |
Medieval and Renaissance Philosophy |