Logic and Philosophy of Logic

Edited by Aleksandra Samonek (Université Catholique de Louvain, Jagiellonian University, Catholic University of Louvain)
Assistant editors: Jared Richards, Sadegh Balal Niaki
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  1. Coarse Groups, and the Isomorphism Problem for Oligomorphic Groups.André Nies, Philipp Schlicht & Katrin Tent - forthcoming - Journal of Mathematical Logic.
    Let S∞ denote the topological group of permutations of the natural numbers. A closed subgroup G of S∞ is called oligomorphic if for each n, its natural action on n-tuples of natural numbers has onl...
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  2. Sobre a Formalização Lógica de Mudança de Teorias e Anomalias Científicas.Ricardo Silvestre - 2017 - ARGUMENTOS - Revista de Filosofia 1 (17):72-91.
    Neste trabalho, é apresentada uma investigação do que poderia ser chamado de formalização lógica do processo de mudança de teorias devido a anomalias. Por anomalia entende-se um fato observado que faz parte do escopo explanatório de uma teoria, mas que vai de encontro à previsão da mesma. Uma abordagem clássica para restaurar o poder explicativo de uma teoria ameaçada por uma anomalia é a postulação de hipóteses novas e provisórias que, em conjunto com as demais hipóteses auxiliares originais, sejam capazes (...)
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  3. Supervaluations and the Strict-Tolerant Hierarchy.Brian Porter - forthcoming - Journal of Philosophical Logic:1-20.
    In a recent paper, Barrio, Pailos and Szmuc show that there are logics that have exactly the validities of classical logic up to arbitrarily high levels of inference. They suggest that a logic therefore must be identified by its valid inferences at every inferential level. However, Scambler shows that there are logics with all the validities of classical logic at every inferential level, but with no antivalidities at any inferential level. Scambler concludes that in order to identify a logic, we (...)
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  4. How Mathematics Isn't Logic.Roger Wertheimer - 1999 - Ratio 12 (3):279-295.
    View more Abstract If logical truth is necessitated by sheer syntax, mathematics is categorially unlike logic even if all mathematics derives from definitions and logical principles. This contrast gets obscured by the plausibility of the Synonym Substitution Principle implicit in conceptions of analyticity: synonym substitution cannot alter sentence sense. The Principle obviously fails with intercepting: nonuniform term substitution in logical sentences. ‘Televisions are televisions’ and ‘TVs are televisions’ neither sound alike nor are used interchangeably. Interception synonymy gets assumed because logical (...)
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  5. 19th Brazilian Logic Conference: Book of Abstracts.Cezar A. Mortari & Ricardo Silvestre (eds.) - 2019 - João Pessoa, PB, Brasil: EDUFCG.
    This is the book of abstracts of the 19th Brazilian Logic Conferences. The Brazilian Logic Conferences (EBL) is one of the most traditional logic conferences in South America. Organized by the Brazilian Logic Society (SBL), its main goal is to promote the dissemination of research in logic in a broad sense. It has been occurring since 1979, congregating logicians of different fields — mostly philosophy, mathematics and computer science — and with different backgrounds — from undergraduate students to senior researchers. (...)
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  6. One Step is Enough.David Ripley - forthcoming - Journal of Philosophical Logic:1-27.
    The recent development and exploration of mixed metainferential logics is a breakthrough in our understanding of nontransitive and nonreflexive logics. Moreover, this exploration poses a new challenge to theorists like me, who have appealed to similarities to classical logic in defending the logic ST, since some mixed metainferential logics seem to bear even more similarities to classical logic than ST does. There is a whole ST-based hierarchy, of which ST itself is only the first step, that seems to become more (...)
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  7. Aristoteles – Schopenhauer – Erdmann. Basistexte Zur Eristik. [REVIEW]Jens Lemanski - 2021 - History and Philosophy of Logic 42 (3):297-299.
    In recent years, previously unknown aspects of Arthur Schopenhauer's œuvre have increasingly become the focus of various research efforts. Examples of this are Schopenhauer's philosophy of language...
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  8. Paraconsistent Logic: Consistency, Contradiction and Negation.Abilio Rodrigues - 2021 - History and Philosophy of Logic 42 (3):300-306.
    The book Paraconsistent Logic: Consistency, Contradiction and Negation by Walter Carnielli and Marcelo Coniglio is the most thorough study of Logics of Formal Inconsistency...
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  9. Empty Logics.Federico Pailos - forthcoming - Journal of Philosophical Logic:1-29.
    TS is a logic that has no valid inferences. But, could there be a logic without valid metainferences? We will introduce TSω, a logic without metainferential validities. Notwithstanding, TSω is not as empty—i.e., uninformative—as it gets, because it has many antivalidities. We will later introduce the two-standard logic [TSω, STω], a logic without validities and antivalidities. Nevertheless, [TSω, STω] is still informative, because it has many contingencies. The three-standard logic [\] that we will further introduce, has no validities, no antivalidities (...)
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  10. Derivability and Metainferential Validity.Bruno Da Ré, Damian Szmuc & Paula Teijeiro - forthcoming - Journal of Philosophical Logic:1-27.
    The aim of this article is to study the notion of derivability and its semantic counterpart in the context of non-transitive and non-reflexive substructural logics. For this purpose we focus on the study cases of the logics ST and TS. In this respect, we show that this notion doesn’t coincide, in general, with a nowadays broadly used semantic approach towards metainferential validity: the notion of local validity. Following this, and building on some previous work by Humberstone, we prove that in (...)
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  11. Erratum: Equations in Oligomorphic Clones and the Constraint Satisfaction Problem for Ω-Categorical Structures.Libor Barto, Michael Kompatscher, Miroslav Olšák, Trung Van Pham & Michael Pinsker - 2021 - Journal of Mathematical Logic 21 (2):2192001.
    Journal of Mathematical Logic, Ahead of Print.
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  12. Inner Models From Extended Logics: Part 1.Juliette Kennedy, Menachem Magidor & Jouko Väänänen - 2020 - Journal of Mathematical Logic 21 (2):2150012.
    If we replace first-order logic by second-order logic in the original definition of Gödel’s inner model L, we obtain the inner model of hereditarily ordinal definable sets [33]. In this paper...
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  13. From Noncommutative Diagrams to Anti-Elementary Classes.Friedrich Wehrung - 2020 - Journal of Mathematical Logic 21 (2):2150011.
    Anti-elementarity is a strong way of ensuring that a class of structures, in a given first-order language, is not closed under elementary equivalence with respect to any infinitary language of the...
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  14. Pseudofinite Groups and VC-Dimension.Gabriel Conant & Anand Pillay - 2020 - Journal of Mathematical Logic 21 (2):2150009.
    We develop “local NIP group theory” in the context of pseudofinite groups. In particular, given a sufficiently saturated pseudofinite structure G expanding a group, and left invariant NIP formula δ...
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  15. Interpolative Fusions.Alex Kruckman, Chieu-Minh Tran & Erik Walsberg - 2020 - Journal of Mathematical Logic 21 (2):2150010.
    We define the interpolative fusion T∪∗ of a family i∈I of first-order theories over a common reduct T∩, a notion that generalizes many examples of random or generic structures in the model-theo...
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  16. Generic Derivations on o-Minimal Structures.Antongiulio Fornasiero & Elliot Kaplan - 2020 - Journal of Mathematical Logic 21 (2):2150007.
    Let T be a complete, model complete o-minimal theory extending the theory RCF of real closed ordered fields in some appropriate language L. We study derivations δ on models ℳ⊧T. We introduce the no...
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  17. Forcing Axioms and Coronas of C∗-Algebras.Paul McKenney & Alessandro Vignati - 2020 - Journal of Mathematical Logic 21 (2):2150006.
    We prove rigidity results for large classes of corona algebras, assuming the Proper Forcing Axiom. In particular, we prove that a conjecture of Coskey and Farah holds for all separable C∗-algebras...
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  18. On the Existence of Small Antichains for Definable Quasi-Orders.Raphaël Carroy, Benjamin D. Miller & Zoltán Vidnyánszky - 2021 - Journal of Mathematical Logic 21 (2):2150005.
    We generalize Kada’s definable strengthening of Dilworth’s characterization of the class of quasi-orders admitting an antichain of a given finite cardinality.
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  19. Model-Theoretic Elekes–Szabó in the Strongly Minimal Case.Artem Chernikov & Sergei Starchenko - 2020 - Journal of Mathematical Logic 21 (2):2150004.
    We prove a generalization of the Elekes–Szabó theorem [G. Elekes and E. Szabó, How to find groups?, Combinatorica 32 537–571 ] for relations defina...
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  20. Guessing Models and the Approachability Ideal.Rahman Mohammadpour & Boban Veličković - 2020 - Journal of Mathematical Logic 21 (2):2150003.
    Starting with two supercompact cardinals we produce a generic extension of the universe in which a principle that we call GM+ holds. This principle implies ISP and ISP, and hence th...
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  21. Logic and Religion: Special Issue of Logica Universalis.Jean-Yves Beziau & Ricardo Silvestre (eds.) - 2017 - Londres, Reino Unido: Springer.
    This special issue of Logica Universalis (Springer) deals with the relations between logic and religion, broadly conceived. It contains the following articles: Logic and Religion, by Jean-Yves Beziau and Ricardo Silvestre; Thinking Negation in Early Hinduism and Classical Indian Philosophy, by Purushottama Bilimoria; Karma Theory, Determinism, Fatalism and Freedom of Will, by Ricardo Sousa Silvestre; From Logic in Islam to Islamic Logic, by Musa Akrami; Leibniz’s Ontological Proof of the Existence of God and the Problem of Impossible Objects, by Wolfgang (...)
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  22. A Philosophical Argument for the Beginning of Time.Laureano Luna & Jacobus Erasmus - 2020 - Prolegomena 19 (2):161-176.
    A common argument in support of a beginning of the universe used by advocates of the kalām cosmological argument (KCA) is the argument against the possibility of an actual infinite, or the “Infinity Argument”. However, it turns out that the Infinity Argument loses some of its force when compared with the achievements of set theory and it brings into question the view that God predetermined an endless future. We therefore defend a new formal argument, based on the nature of time (...)
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  23. Proving Cleanthes Wrong.Laureano Luna - 2021 - Journal of Applied Logic 8 (3):707-736.
    Hume’s famous character Cleanthes claims that there is no difficulty in explaining the existence of causal chains with no first cause since in them each item is causally explained by its predecessor. Relying on logico-mathematical resources, we argue for two theses: (1) if the existence of Cleanthes’ chain can be explained at all, it must be explained by the fact that the causal law ruling it is in force, and (2) the fact that such a causal law is in force (...)
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  24. Counterlogicals as Counterconventionals.Alexander W. Kocurek & Ethan J. Jerzak - 2021 - Journal of Philosophical Logic 50 (4):673-704.
    We develop and defend a new approach to counterlogicals. Non-vacuous counterlogicals, we argue, fall within a broader class of counterfactuals known as counterconventionals. Existing semantics for counterconventionals, 459–482 ) and, 1–27 ) allow counterfactuals to shift the interpretation of predicates and relations. We extend these theories to counterlogicals by allowing counterfactuals to shift the interpretation of logical vocabulary. This yields an elegant semantics for counterlogicals that avoids problems with the usual impossible worlds semantics. We conclude by showing how this approach (...)
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  25. Lattice Logic, Bilattice Logic and Paraconsistent Quantum Logic: a Unified Framework Based on Monosequent Systems.Norihiro Kamide - 2021 - Journal of Philosophical Logic 50 (4):781-811.
    Lattice logic, bilattice logic, and paraconsistent quantum logic are investigated based on monosequent systems. Paraconsistent quantum logic is an extension of lattice logic, and bilattice logic is an extension of paraconsistent quantum logic. Monosequent system is a sequent calculus based on the restricted sequent that contains exactly one formula in both the antecedent and succedent. It is known that a completeness theorem with respect to a lattice-valued semantics holds for a monosequent system for lattice logic. A completeness theorem with respect (...)
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  26. Basic Quasi-Boolean Expansions of Relevance Logics.Gemma Robles & José M. Méndez - 2021 - Journal of Philosophical Logic 50 (4):727-754.
    The basic quasi-Boolean negation expansions of relevance logics included in Anderson and Belnap’s relevance logic R are defined. We consider two types of QB-negation: H-negation and D-negation. The former one is of paraintuitionistic or superintuitionistic character, the latter one, of dual intuitionistic nature in some sense. Logics endowed with H-negation are paracomplete; logics with D-negation are paraconsistent. All logics defined in the paper are given a Routley-Meyer ternary relational semantics.
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  27. Elusive Propositions.Gabriel Uzquiano - 2021 - Journal of Philosophical Logic 50 (4):705-725.
    David Kaplan observed in Kaplan that the principle \\) cannot be verified at a world in a standard possible worlds model for a quantified bimodal propositional language. This raises a puzzle for certain interpretations of the operator Q: it seems that some proposition p is such that is not possible to query p, and p alone. On the other hand, Arthur Prior had observed in Prior that on pain of contradiction, ∀p is Q only if one true proposition is Q (...)
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  28. Completeness: From Husserl to Carnap.Víctor Aranda - forthcoming - Logica Universalis:1-27.
    In his Doppelvortrag, Edmund Husserl introduced two concepts of “definiteness” which have been interpreted as a vindication of his role in the history of completeness. Some commentators defended that the meaning of these notions should be understood as categoricity, while other scholars believed that it is closer to syntactic completeness. A detailed study of the early twentieth-century axiomatics and Husserl’s Doppelvortrag shows, however, that many concepts of completeness were conflated as equivalent. Although “absolute definiteness” was principally an attempt to characterize (...)
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  29. Imperative Inference and Practical Rationality.Daniel W. Harris - 2021 - Philosophical Studies.
    Some arguments include imperative clauses. For example: ‘Buy me a drink; you can’t buy me that drink unless you go to the bar; so, go to the bar!’ How should we build a logic that predicts which of these arguments are good? Because imperatives aren’t truth apt and so don’t stand in relations of truth preservation, this technical question gives rise to a foundational one: What would be the subject matter of this logic? I argue that declaratives are used to (...)
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  30. Islamic Contradictory Theology . . . Is There Any Such Thing?Abbas Ahsan - 2021 - Logica Universalis 15 (2):1-39.
    The application of paraconsistent logics to theological contradictions is a fascinating move. Jc Beall’s (J Anal Theol, 7(1): 400–439, 2019) paper entitled ‘Christ—A Contradiction: A Defense of ‘Contradictory Christology’ is a notable example. Beall proposes a solution to the fundamental problem of Christology. His solution aims at making the case, and defending the viability of, what he has termed, ‘Contradictory Christology’. There are at least two essential components of Beall’s ‘Contradictory Christology’. These include the dogmatic statements of Chalcedon and FDE (...)
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  31. Logical Maximalism in the Empirical Sciences.Brîncuș Constantin C. - 2021 - In Parusniková Zuzana & Merritt David (eds.), Karl Popper's Science and Philosophy. Springer. pp. 171-184.
    K. R. Popper distinguished between two main uses of logic, the demonstrational one, in mathematical proofs, and the derivational one, in the empirical sciences. These two uses are governed by the following methodological constraints: in mathematical proofs one ought to use minimal logical means (logical minimalism), while in the empirical sciences one ought to use the strongest available logic (logical maximalism). In this paper I discuss whether Popper’s critical rationalism is compatible with a revision of logic in the empirical sciences, (...)
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  32. Correction to: The Hahn Embedding Theorem for a Class of Residuated Semigroups.Sándor A. Jenei - 2021 - Studia Logica 109 (4):887-901.
    Let be the class of odd involutive even the notion of partial lex products is not sufficiently general. One more tweak is needed, a slightly even more complex construction, called partial sublex product, introduced here.
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  33. Positive Monotone Modal Logic.Jim de Groot - 2021 - Studia Logica 109 (4):829-857.
    Positive monotone modal logic is the negation- and implication-free fragment of monotone modal logic, i.e., the fragment with connectives and. We axiomatise positive monotone modal logic, give monotone neighbourhood semantics based on posets, and prove soundness and completeness. The latter follows from the main result of this paper: a duality between so-called \-spaces and the algebraic semantics of positive monotone modal logic. The main technical tool is the use of coalgebra.
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  34. Relational Representation Theorems for Extended Contact Algebras.Philippe Balbiani & Tatyana Ivanova - 2021 - Studia Logica 109 (4):701-723.
    In topological spaces, the relation of extended contact is a ternary relation that holds between regular closed subsets A, B and D if the intersection of A and B is included in D. The algebraic counterpart of this mereotopological relation is the notion of extended contact algebra which is a Boolean algebra extended with a ternary relation. In this paper, we are interested in the relational representation theory for extended contact algebras. In this respect, we study the correspondences between point-free (...)
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  35. Belnap–Dunn Modal Logic with Value Operators.Yuanlei Lin & Minghui Ma - 2020 - Studia Logica 109 (4):759-789.
    The language of Belnap–Dunn modal logic \ expands the language of Belnap–Dunn four-valued logic with the modal operator \. We introduce the polarity semantics for \ and its two expansions \ and \ with value operators. The local finitary consequence relation \ in the language \ with respect to the class of all frames is axiomatized by a sequent system \ where \. We prove by using translations between sequents and formulas that these languages under the polarity semantics have the (...)
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  36. Labelled Sequent Calculi for Lewis’ Non-normal Propositional Modal Logics.Matteo Tesi - 2020 - Studia Logica 109 (4):725-757.
    C. I. Lewis’ systems were the first axiomatisations of modal logics. However some of those systems are non-normal modal logics, since they do not admit a full rule of necessitation, but only a restricted version thereof. We provide G3-style labelled sequent calculi for Lewis’ non-normal propositional systems. The calculi enjoy good structural properties, namely admissibility of structural rules and admissibility of cut. Furthermore they allow for straightforward proofs of admissibility of the restricted versions of the necessitation rule. We establish completeness (...)
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  37. Inductive Plausibility, and Certainty.Ricardo Sousa Silvestre - 2021 - In Marcin Trepczyński (ed.), Philosophical Approaches to the Foundations of Logics and Mathematics. Leiden, Países Baixos: pp. 193-210.
    Is it possible to combine different logics into a coherent system with the goal of applying it to specific problems so that it sheds some light on foundational aspects of those logics? These are two of the most basic issues of combining logics. Paranormal modal logic is a combination of paraconsistent logic and modal logic. In this paper, I propose two further combinatory developments, focusing on each one of these two issues. On the foundational side, I combine paranormal modal logic (...)
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  38. Philosophical Logic = Philosophy + Logic?Ricardo Sousa Silvestre - 2021 - In J.-Y. Beziau, J.-P. Desclés, A. Moktefi & A. Pascau (eds.), Logic-in-Question (Workshop at the Sorbonne 2011-2019). Basiléia, Suíça: pp. 299-327.
    My purpose in this paper is to shed some light on two questions: In what sense is logic philosophical? And what is philosophical logic? I take these two questions as co-extensive: an answer to one of them is also (or can easily be converted into) an answer to the other. I approach the problem from three perspectives: a conceptual, a descriptive and a prescriptive perspective. In other words, I try to answer the following questions: (i) In what sense can logic (...)
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  39. Paraconsistent Logic as Model Building.Ricardo Sousa Silvestre - 2018 - South American Journal of Logic 1 (4):195-217.
    The terms “model” and “model-building” have been used to characterize the field of formal philosophy, to evaluate philosophy’s and philosophical logic’s progress and to define philosophical logic itself. A model is an idealization, in the sense of being a deliberate simplification of something relatively complex in which several important aspects are left aside, but also in the sense of being a view too perfect or excellent, not found in reality, of this thing. Paraconsistent logic is a branch of philosophical logic. (...)
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  40. Two Pretabular Linear Extensions of Relevance Logic R.Asadollah Fallahi - 2021 - Journal of Applied Non-Classical Logics 31 (2):154-179.
    Pretabularity is the attribute of logics that are not characterised by finite matrices, but all of whose proper extensions are. Two of the first-known pretabular logics were Dummett’s famous super-...
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  41. Natural Implicative Expansions of Variants of Kleene's Strong 3-Valued Logic with Gödel-Type and Dual Gödel-Type Negation.Gemma Robles & José M. Méndez - 2021 - Journal of Applied Non-Classical Logics 31 (2):130-153.
    Let MK3 I and MK3 II be Kleene's strong 3-valued matrix with only one and two designated values, respectively. Next, let MK3 G be defined exactly as MK3 I, except th...
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  42. A Note on the Complexity of S4.2.Aggeliki Chalki, Costas D. Koutras & Yorgos Zikos - 2021 - Journal of Applied Non-Classical Logics 31 (2):108-129.
    S4.2 is the modal logic of directed partial pre-orders and/or the modal logic of reflexive and transitive relational frames with a final cluster. It holds a distinguished position in philosophical...
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  43. Measuring Inconsistency in Some Branching Time Logics.John Grant - 2021 - Journal of Applied Non-Classical Logics 31 (2):85-107.
    Branching time logics have been studied in computer science since the 1980s primarily to model the tree of computations for discrete transition systems. Inconsistency measures for propositional log...
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  44. On Inclusions Between Quantified Provability Logics.Taishi Kurahashi - forthcoming - Studia Logica:1-24.
    We investigate several consequences of inclusion relations between quantified provability logics. Moreover, we give a necessary and sufficient condition for the inclusion relation between quantified provability logics with respect to \ arithmetical interpretations.
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  45. Grounding, Quantifiers, and Paradoxes.Francesco A. Genco, Francesca Poggiolesi & Lorenzo Rossi - forthcoming - Journal of Philosophical Logic:1-32.
    The notion of grounding is usually conceived as an objective and explanatory relation. It connects two relata if one—the ground—determines or explains the other—the consequence. In the contemporary literature on grounding, much effort has been devoted to logically characterize the formal aspects of grounding, but a major hard problem remains: defining suitable grounding principles for universal and existential formulae. Indeed, several grounding principles for quantified formulae have been proposed, but all of them are exposed to paradoxes in some very natural (...)
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  46. Advances in Experimental Philosophy of Logic and Mathematics.Yuri Sato - forthcoming - History and Philosophy of Logic:1-2.
    This book is a collection of articles on research that attempts to connect logic and mathematics with empirical and cognition. There have been various such a...
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  47. Péter on Church's Thesis, Constructivity and Computers.Mate Szabo - 2021 - In Liesbeth De Mol, Andreas Weiermann, Florin Manea & David Fernández-Duque (eds.), Connecting with Computability. Proceedings of Computability in Europe. pp. 434-445.
    Abstract The aim of this paper is to take a look at Péter's talk "Rekursivität und Konstruktivität" delivered at the Constructivity in Mathematics Colloquium in 1957, where she challenged Church's Thesis from a constructive point of view. The discussion of her argument and motivations is then connected to her earlier work on recursion theory as well as her later work on theoretical computer science.
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  48. A Consistency Result on Long Cardinal Sequences.Juan Carlos Martinez & Lajos Soukup - forthcoming - Annals of Pure and Applied Logic:103017.
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  49. Ming 名 in the Laozi Daodejing 老子道德經: Interpretations and Translations of the Opening Verse.Yumi Suzuki - 2021 - Philosophy East and West 71 (3):747-766.
    This paper revisits one of the most celebrated verses on dao and ming in the Opening Chapter of the received Laozi Daodejing. I shall clarify two types of English interpretations which are possibly applicable to the verse and demonstrate that they are equally sustainable. It follows that a commitment to either one of these interpretations may thereby spoil the meta-perspective effect which the verse skillfully creates.
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  50. Thicket Density.Siddharth Bhaskar - 2021 - Journal of Symbolic Logic 86 (1):110-127.
    We define a new type of “shatter function” for set systems that satisfies a Sauer–Shelah type dichotomy, but whose polynomial-growth case is governed by Shelah’s two-rank instead of VC dimension. We identify the least exponent bounding the rate of growth of the shatter function, the quantity analogous to VC density, with Shelah’s $\omega $ -rank.
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