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Thomas Ferguson
City University of New York
  1.  74
    Logics of Nonsense and Parry Systems.Thomas Macaulay Ferguson - 2015 - Journal of Philosophical Logic 44 (1):65-80.
    We examine the relationship between the logics of nonsense of Bochvar and Halldén and the containment logics in the neighborhood of William Parry’s A I. We detail two strategies for manufacturing containment logics from nonsense logics—taking either connexive and paraconsistent fragments of such systems—and show how systems determined by these techniques have appeared as Frederick Johnson’s R C and Carlos Oller’s A L. In particular, we prove that Johnson’s system is precisely the intersection of Bochvar’s B 3 and Graham Priest’s (...)
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  2.  7
    Meaning and Proscription in Formal Logic.Thomas Macaulay Ferguson - 2017 - Springer Verlag.
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  3. Relevant Logics Obeying Component Homogeneity.Roberto Ciuni, Damian Szmuc & Thomas Macaulay Ferguson - 2018 - Australasian Journal of Logic 15 (2):301-361.
    This paper discusses three relevant logics that obey Component Homogeneity - a principle that Goddard and Routley introduce in their project of a logic of significance. The paper establishes two main results. First, it establishes a general characterization result for two families of logic that obey Component Homogeneity - that is, we provide a set of necessary and sufficient conditions for their consequence relations. From this, we derive characterization results for S*fde, dS*fde, crossS*fde. Second, the paper establishes complete sequent calculi (...)
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  4.  48
    A Computational Interpretation of Conceptivism.Thomas Macaulay Ferguson - 2014 - Journal of Applied Non-Classical Logics 24 (4):333-367.
    The hallmark of the deductive systems known as ‘conceptivist’ or ‘containment’ logics is that for all theorems of the form , all atomic formulae appearing in also appear in . Significantly, as a consequence, the principle of Addition fails. While often billed as a formalisation of Kantian analytic judgements, once semantics were discovered for these systems, the approach was largely discounted as merely the imposition of a syntactic filter on unrelated systems. In this paper, we examine a number of prima (...)
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  5.  36
    Faulty Belnap Computers and Subsystems of FDE.Thomas Macaulay Ferguson - forthcoming - Journal of Logic and Computation.
    In this article, we consider variations of Nuel Belnap's "artificial reasoner". In particular, we examine cases in which the artificial reasoner is faulty, e.g. situations in which the reasoner is unable to calculate the value of a formula due to an inability to retrieve the values of its atoms. In the first half of the article, we consider two ways of modelling such circumstances and prove the deductive systems arising from these two types of models to be equivalent to Graham (...)
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  6.  5
    The Keisler–Shelah Theorem for $\Mathsf{QmbC}$ Through Semantical Atomization.Thomas Macaulay Ferguson - forthcoming - Logic Journal of the IGPL.
    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 for $\mathsf{QmbC}$, i.e. (...)
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  7. Extensions of Priest-da Costa Logic.Thomas Macaulay Ferguson - 2014 - Studia Logica 102 (1):145-174.
    In this paper, we look at applying the techniques from analyzing superintuitionistic logics to extensions of the cointuitionistic Priest-da Costa logic daC (introduced by Graham Priest as “da Costa logic”). The relationship between the superintuitionistic axioms- definable in daC- and extensions of Priest-da Costa logic (sdc-logics) is analyzed and applied to exploring the gap between the maximal si-logic SmL and classical logic in the class of sdc-logics. A sequence of strengthenings of Priest-da Costa logic is examined and employed to pinpoint (...)
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  8. Notes on the Model Theory of DeMorgan Logics.Thomas Macaulay Ferguson - 2012 - Notre Dame Journal of Formal Logic 53 (1):113-132.
    We here make preliminary investigations into the model theory of DeMorgan logics. We demonstrate that Łoś's Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case study we examine the fate of Cantor's Theorem that the classical theory of dense linear orderings without endpoints is $\aleph_{0}$-categorical, and we show that the taking of ultraproducts commutes with respect to previously established methods of constructing nonclassical structures, namely, Priest's Collapsing (...)
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  9.  16
    Dunn–Priest Quotients of Many-Valued Structures.Thomas Macaulay Ferguson - 2017 - Notre Dame Journal of Formal Logic 58 (2):221-239.
    J. Michael Dunn’s Theorem in 3-Valued Model Theory and Graham Priest’s Collapsing Lemma provide the means of constructing first-order, three-valued structures from classical models while preserving some control over the theories of the ensuing models. The present article introduces a general construction that we call a Dunn–Priest quotient, providing a more general means of constructing models for arbitrary many-valued, first-order logical systems from models of any second system. This technique not only counts Dunn’s and Priest’s techniques as special cases, but (...)
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  10.  15
    Inconsistent Models for Arithmetics with Constructible Falsity.Thomas Macaulay Ferguson - forthcoming - Logic and Logical Philosophy:1.
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  11.  4
    Axiom (Cc0) and Verifiability in Two Extracanonical Logics of Formal Inconsistency.Thomas Macaulay Ferguson - 2018 - Principia: An International Journal of Epistemology 22 (1):113-138.
    In the field of logics of formal inconsistency, the notion of “consistency” is frequently too broad to draw decisive conclusions with respect to the validity of many theses involving the consistency connective. In this paper, we consider the matter of the axiom 0—i.e., the schema ◦ ◦ϕ—by considering its interpretation in contexts in which “consistency” is understood as a type of verifiability. This paper suggests that such an interpretation is implicit in two extracanonical LFIs—Sören Halldén’s nonsense-logic C and Graham Priest’s (...)
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  12.  54
    Two Paradoxes of Semantic Information.Thomas Macaulay Ferguson - 2015 - Synthese 192 (11):3719-3730.
    Yehoshua Bar-Hillel and Rudolph Carnap’s classical theory of semantic information entails the counterintuitive feature that inconsistent statements convey maximal information. Theories preserving Bar-Hillel and Carnap’s modal intuitions while imposing a veridicality requirement on which statements convey information—such as the theories of Fred Dretske or Luciano Floridi—avoid this commitment, as inconsistent statements are deemed not information-conveying by fiat. This paper produces a pair of paradoxical statements that such “veridical-modal” theories must evaluate as both conveying and not conveying information, although Bar-Hillel and (...)
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  13.  2
    Introduction to Graham Priest on Dialetheism and Paraconsistency.Thomas Macaulay Ferguson & Can Başkent - 2019 - In Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency. Springer Verlag. pp. 1-2.
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  14.  24
    On Non-Deterministic Quantification.Thomas Macaulay Ferguson - 2014 - Logica Universalis 8 (2):165-191.
    This paper offers a framework for extending Arnon Avron and Iddo Lev’s non-deterministic semantics to quantified predicate logic with the intent of resolving several problems and limitations of Avron and Anna Zamansky’s approach. By employing a broadly Fregean picture of logic, the framework described in this paper has the benefits of permitting quantifiers more general than Walter Carnielli’s distribution quantifiers and yielding a well-behaved model theory. This approach is purely objectual and yields the semantical equivalence of both α-equivalent formulae and (...)
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  15.  9
    Corrigendum: The Keisler—Shelah Theorem for QmbC Through Semantical Atomization.Thomas Macaulay Ferguson - 2019 - Logic Journal of the IGPL 27 (6):933-933.
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  16.  15
    Remarks on Ontological Dependence in Set Theory.Thomas Macaulay Ferguson - 2016 - Australasian Journal of Logic 13 (3).
    In a recent paper, John Wigglesworth explicates the notion of a set's being grounded in or ontologically depending on its members by the modal statement that in any world, that a set exists in that world entails that its members exist as well. After suggesting that variable-domain S5 captures an appropriate account of metaphysical necessity, Wigglesworth purports to prove that in any set theory satisfying the axiom Extensionality this condition holds, that is, that sets ontologically depend on their members with (...)
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  17.  21
    Andreas Kapsner, Logics and Falsifications. A New Perspective on Constructivist Semantics, Cham: Springer International Publishing, 2014, 217 Pp., €103.99 , ISBN 9783319052052. [REVIEW]Thomas Macaulay Ferguson - 2016 - Dialectica 70 (1):119-124.
  18.  25
    Łukasiewicz Negation and Many-Valued Extensions of Constructive Logics.Thomas Macaulay Ferguson - 2014 - In Proc. 44th International Symposium on Multiple-Valued Logic. IEEE Computer Society Press. pp. 121-127.
    This paper examines the relationships between the many-valued logics G~ and Gn~ of Esteva, Godo, Hajek, and Navara, i.e., Godel logic G enriched with Łukasiewicz negation, and neighbors of intuitionistic logic. The popular fragments of Rauszer's Heyting-Brouwer logic HB admit many-valued extensions similar to G which may likewise be enriched with Łukasiewicz negation; the fuzzy extensions of these logics, including HB, are equivalent to G ~, as are their n-valued extensions equivalent to Gn~ for any n ≥ 2. These enriched (...)
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  19.  8
    Parity, Revelance, and Gentle Explosiveness in the Context of Sylvan's Mate Function.Thomas Macaulay Ferguson - 2018 - Australasian Journal of Logic 15 (2):381-406.
    The Routley star, an involutive function between possible worlds or set-ups against which negation is evaluated, is a hallmark feature of Richard Sylvan and Val Plumwood's set-up semantics for the logic of first-degree entailment. Less frequently acknowledged is the weaker mate function described by Sylvan and his collaborators, which results from stripping the requirement of involutivity from the Routley star. Between the mate function and the Routley star, however, lies an broad field of intermediate semantical conditions characterizing an infinite number (...)
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  20. Proc. 44th International Symposium on Multiple-Valued Logic.Thomas Macaulay Ferguson - 2014 - IEEE Computer Society Press.
  21. Variations on the Collapsing Lemma.Thomas Macaulay Ferguson - 2019 - In Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency. Springer Verlag. pp. 249-270.
    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{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {A}^{\sim }$$\end{document} suitable for interpretations in Priest’s logic of paradox. The source of this construction’s utility is Priest’s Collapsing Lemma, which guarantees that a formula true in the 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} (...)
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  22. Graham Priest on Dialetheism and Paraconsistency.Can Başkent & Thomas Macaulay Ferguson (eds.) - 2019 - Springer Verlag.