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2Consistency-Sensitive Epistemic Modalities in Information-Based SemanticsStudia Logica 1-39. forthcoming.The paper extends a framework of information-based semantics for intuitionistic logic with a paraconsistent negation and consistency-sensitive epistemic modalities. In this framework information states represent information collected from various sources and as such they can be inconsistent because they receive contradictory information either from a single inconsistent source or from various mutually incompatible sources. The modalities reflect only those sources that are consistent and trusted…Read more
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13Topic-Theoretic Extensions of Analytic ImplicationNotre Dame Journal of Formal Logic 64 (4): 471-493. 2023.Like many intensional logics, William Parry’s logic of analytic implication PAI admits extensions determined by imposing semantic conditions on its account of modality. PAI is unique, however, in its allowing a second dimension—a topic-theoretic dimension—along which extensions can be defined. The recent introduction by Francesco Berto of topic-sensitive intentional modals (TSIMs)—which disagree with PAI on this type of condition—provide further motivations to examine such topic-theoretic extens…Read more
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117Topic Transparency and Variable Sharing in Weak Relevant LogicsErkenntnis 1-28. forthcoming.In this paper, we examine a number of relevant logics’ variable sharing properties from the perspective of theories of topic or subject-matter. We take cues from Franz Berto’s recent work on topic to show an alignment between families of variable sharing properties and responses to the topic transparency of relevant implication and negation. We then introduce and defend novel variable sharing properties stronger than strong depth relevance—which we call cn-relevance and lossless cn-relevance—sho…Read more
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38Subject-Matter and Intensional Operators II: Applications to the Theory of Topic-Sensitive Intentional ModalsJournal of Philosophical Logic 52 (6): 1673-1701. 2023.In frameworks in which _topic-__theoretic_ considerations—_e.g._, tracking _subject-matter_ or _topic_—are given equal importance with _veridical_ considerations, assigning topics to formulae in a satisfactory way is of critical importance. While intuitions are more-or-less solid for _extensional_ formulae in a propositional language, arriving at a compelling account of the subject-matter of _intensional_ formulae, _i.e._, formulae including intensional operators, is more challenging. This paper…Read more
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5Structural Completeness and Superintuitionistic Inquisitive LogicsIn Helle Hvid Hansen, Andre Scedrov & Ruy J. G. B. De Queiroz (eds.), Logic, Language, Information, and Computation: 29th International Workshop, WoLLIC 2023, Halifax, NS, Canada, July 11–14, 2023, Proceedings, Springer Nature Switzerland. pp. 194-210. 2023.In this paper, the notion of structural completeness is explored in the context of a generalized class of superintuitionistic logics involving also systems that are not closed under uniform substitution. We just require that each logic must be closed under D-substitutions assigning to atomic formulas only ∨\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\od…Read more
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28Subject-Matter and Intensional Operators III: State-Sensitive Subject-Matter and Topic SufficiencyReview of Symbolic Logic 1-27. forthcoming.Logical frameworks that are sensitive to features of sentences’ subject-matter—like Berto’s topic-sensitive intentional modals (TSIMs)—demand a maximally faithful model of the topics of sentences. This is an especially difficult task in the case in which topics are assigned to intensional formulae. In two previous papers, a framework was developed whose model of intensional subject-matter could accommodate a wider range of intuitions about particular intensional conditionals. Although resolving …Read more
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19From Excluded Middle to Homogenization in Plumwood’s Feminist Critique of LogicAustralasian Journal of Logic 20 (2): 243-277. 2023.A key facet of Valerie Plumwood’s feminist critique of logic is her analysis of classical negation. On Plumwood’s reading, the exclusionary features of classical negation generate hierarchical dualisms, i.e., dichotomies in which dominant groups’ primacy is reinforced while underprivileged groups are oppressed. For example, Plumwood identifies the system collapse following from ex contradictione quodlibet—that a theory including both φ and ∼φ trivializes—as a primary source of many of these feat…Read more
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12Executability and Connexivity in an Interpretation of GrissStudia Logica 112 (1): 459-509. 2023.Although the work of G.F.C. Griss is commonly understood as a program of negationless mathematics, close examination of Griss’s work suggests a more fundamental feature is its executability, a requirement that mental constructions are possible only if corresponding mental activity can be actively carried out. Emphasizing executability reveals that Griss’s arguments against negation leave open several types of negation—including D. Nelson’s strong negation—as compatible with Griss’s intuitionism.…Read more
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10Robert Meyer's Publications on Relevant ArithmeticAustralasian Journal of Logic 18 (5): 146-149. 2021.This is a bibliography of R.K. Meyer's published articles on relevant arithmetic.
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6IntroductionAustralasian Journal of Logic 18 (5): 132-145. 2021.This is the introduction to the special issue on Robert K. Meyer and the philosophy of arithmetic.
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7Episodes in Model-Theoretic Xenology: Rationals as Positive Integers in R#Australasian Journal of Logic 18 (5): 428-446. 2021.Meyer and Mortensen’s Alien Intruder Theorem includes the extraor- dinary observation that the rationals can be extended to a model of the relevant arithmetic R♯, thereby serving as integers themselves. Al- though the mysteriousness of this observation is acknowledged, little is done to explain why such rationals-as-integers exist or how they operate. In this paper, we show that Meyer and Mortensen’s models can be identified with a class of ultraproducts of finite models of R♯, providing insight…Read more
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43Subject-matter and intensional operators I: conditional-agnostic analytic implicationPhilosophical Studies 180 (7): 1849-1879. 2023.Although logical settings are typically concerned with tracking alethic considerations, frameworks exist in which topic-theoretic considerations—e.g., tracking subject-matter or topic—are given equal importance. Intuitions about extending topic through a propositional language are generally straightforward for extensional cases. For a number of reasons, arriving at a compelling account of the subject-matter of intensional operators—such as intensional conditionals—is a more difficult task. In pa…Read more
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30Negation in Negationless Intuitionistic MathematicsPhilosophia Mathematica 31 (1): 29-55. 2023.The mathematician G.F.C. Griss is known for his program of negationless intuitionistic mathematics. Although Griss’s rejection of negation is regarded as characteristic of his philosophy, this is a consequence of an executability requirement that mental constructions presuppose agents’ executing corresponding mental activity. Restoring Griss’s executability requirement to a central role permits a more subtle characterization of the rejection of negation, according to which D. Nelson’s strong con…Read more
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200Logics Based on Linear Orders of Contaminating ValuesJournal of Logic and Computation 29 (5). 2019.A wide family of many-valued logics—for instance, those based on the weak Kleene algebra—includes a non-classical truth-value that is ‘contaminating’ in the sense that whenever the value is assigned to a formula φ, any complex formula in which φ appears is assigned that value as well. In such systems, the contaminating value enjoys a wide range of interpretations, suggesting scenarios in which more than one of these interpretations are called for. This calls for an evaluation of systems with mu…Read more
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27Monstrous Content and the Bounds of DiscourseJournal of Philosophical Logic 52 (1): 111-143. 2022.Bounds consequence provides an interpretation of a multiple-conclusion consequence relation in which the derivability of a sequent is understood as the claim that it is conversationally out-of-bounds to take a position in which each member of Γ is asserted while each member of Δ is denied. Two of the foremost champions of bounds consequence—Greg Restall and David Ripley—have independently indicated that the shape of the bounds in question is determined by conversational practice. In this paper, …Read more
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Correia Semantics RevisitedIn Thomas Macaulay Ferguson (ed.), Meaning and Proscription in Formal Logic: Variations on the Propositional Logic of William T. Parry, Springer Verlag. 2017.
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Concluding RemarksIn Thomas Macaulay Ferguson (ed.), Meaning and Proscription in Formal Logic: Variations on the Propositional Logic of William T. Parry, Springer Verlag. 2017.
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A Computational Interpretation of ConceptivismIn Thomas Macaulay Ferguson (ed.), Meaning and Proscription in Formal Logic: Variations on the Propositional Logic of William T. Parry, Springer Verlag. 2017.
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7Secrecy, Content, and QuantificationAnálisis Filosófico 41 (2): 285-302. 2021.While participating in a symposium on Dave Ripley’s forthcoming book Uncut, I had proposed that employing a strict-tolerant interpretation of the weak Kleene matrices provided a content-theoretical conception of the bounds of conversational norms that enjoyed advantages over Ripley’s use of the strong Kleene matrices. During discussion, I used the case of sentences that are taken to be out-of-bounds for being secrets as an example of a case in which the setting of conversational bounds in practi…Read more
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63Deep STJournal of Philosophical Logic 51 (6): 1261-1293. 2021.Many analyses of notion of _metainferences_ in the non-transitive logic ST have tackled the question of whether ST can be identified with classical logic. In this paper, we argue that the primary analyses are overly restrictive of the notion of metainference. We offer a more elegant and tractable semantics for the strict-tolerant hierarchy based on the three-valued function for the LP material conditional. This semantics can be shown to easily handle the introduction of _mixed_ inferences, _i.e.…Read more
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345Modeling the interaction of computer errors by four-valued contaminating logicsIn Rosalie Iemhoff, Michael Moortgat & Ruy de Queiroz (eds.), Logic, Language, Information, and Computation, Folli Publications On Logic, Language and Information. pp. 119-139. 2019.Logics based on weak Kleene algebra (WKA) and related structures have been recently proposed as a tool for reasoning about flaws in computer programs. The key element of this proposal is the presence, in WKA and related structures, of a non-classical truth-value that is “contaminating” in the sense that whenever the value is assigned to a formula ϕ, any complex formula in which ϕ appears is assigned that value as well. Under such interpretations, the contaminating states represent occurrences of…Read more
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607Meaningless DivisionsNotre Dame Journal of Formal Logic 62 (3): 399-424. 2021.In this article we revisit a number of disputes regarding significance logics---i.e., inferential frameworks capable of handling meaningless, although grammatical, sentences---that took place in a series of articles most of which appeared in the Australasian Journal of Philosophy between 1966 and 1978. These debates concern (i) the way in which logical consequence ought to be approached in the context of a significance logic, and (ii) the way in which the logical vocabulary has to be modified (…Read more
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9Variations on the Collapsing LemmaIn Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency, Springer Verlag. pp. 249-270. 2019.Graham Priest has frequently employed a construction in which a classical first-order model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {A}$$\end{document} may be collapsed into a three-valued model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage…Read more
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11Introduction to Graham Priest on Dialetheism and ParaconsistencyIn Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency, Springer Verlag. pp. 1-2. 2019.
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60Correia Semantics RevisitedStudia Logica 104 (1): 145-173. 2016.Despite a renewed interest in Richard Angell’s logic of analytic containment ), the first semantics for \ introduced by Fabrice Correia has remained largely unexamined. This paper describes a reasonable approach to Correia semantics by means of a correspondence with a nine-valued semantics for \. The present inquiry employs this correspondence to provide characterizations of a number of propositional logics intermediate between \ and classical logic. In particular, we examine Correia’s purported…Read more
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1967Finding middle ground between intellectual arrogance and intellectual servility: Development and assessment of the limitations-owning intellectual humility scalePersonality and Individual Differences 124 184-193. 2018.Recent scholarship in intellectual humility (IH) has attempted to provide deeper understanding of the virtue as personality trait and its impact on an individual's thoughts, beliefs, and actions. A limitations-owning perspective of IH focuses on a proper recognition of the impact of intellectual limitations and a motivation to overcome them, placing it as the mean between intellectual arrogance and intellectual servility. We developed the Limitations-Owning Intellectual Humility Scale to assess …Read more
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22Corrigendum: The Keisler—Shelah theorem for QmbC through semantical atomizationLogic Journal of the IGPL 27 (6): 933-933. 2019.
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31The Keisler–Shelah theorem for $\mathsf{QmbC}$ through semantical atomizationLogic Journal of the IGPL 28 (5): 912-935. 2020.In this paper, we consider some contributions to the model theory of the logic of formal inconsistency $\mathsf{QmbC}$ as a reply to Walter Carnielli, Marcelo Coniglio, Rodrigo Podiacki and Tarcísio Rodrigues’ call for a ‘wider model theory.’ This call demands that we align the practices and techniques of model theory for logics of formal inconsistency as closely as possible with those employed in classical model theory. The key result is a proof that the Keisler–Shelah isomorphism theorem holds…Read more
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29This book aids in the rehabilitation of the wrongfully deprecated work of William Parry, and is the only full-length investigation into Parry-type propositional logics. A central tenet of the monograph is that the sheer diversity of the contexts in which the mereological analogy emerges – its effervescence with respect to fields ranging from metaphysics to computer programming – provides compelling evidence that the study of logics of analytic implication can be instrumental in identifying conne…Read more
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Cut-Down Operations on MultilatticesIn Thomas Macaulay Ferguson (ed.), Meaning and Proscription in Formal Logic: Variations on the Propositional Logic of William T. Parry, Springer Verlag. 2017.