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  1. Proof Invariance.Blane Worley - forthcoming - Australasian Journal of Logic.
    We explore depth substitution invariance, or hyperformalism, and extend known results in this realm to justification logics extending weak relevant logics. We then examine the surprising invariance of justifications over formulas and restrict our attention to the substitution of proofs in the original relevant logic. The results of this paper indicate that depth invariance is a recalcitrant feature of the logic and that proof structures in hyperformal logics are quite inflexible.
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  2. A New Logic, a New Information Measure, and a New Information-Based Approach to Interpreting Quantum Mechanics.David Ellerman - 2024 - Entropy Special Issue: Information-Theoretic Concepts in Physics 26 (2).
    The new logic of partitions is dual to the usual Boolean logic of subsets (usually presented only in the special case of the logic of propositions) in the sense that partitions and subsets are category-theoretic duals. The new information measure of logical entropy is the normalized quantitative version of partitions. The new approach to interpreting quantum mechanics (QM) is showing that the mathematics (not the physics) of QM is the linearized Hilbert space version of the mathematics of partitions. Or, putting (...)
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  3. Fine on the Possibility of Vagueness.Andreas Ditter - 2023 - In Federico L. G. Faroldi & Frederik Van De Putte (eds.), Kit Fine on Truthmakers, Relevance, and Non-classical Logic. Springer Verlag. pp. 715-734.
    In his paper ‘The possibility of vagueness’ (Fine in Synthese 194(10):3699–3725, 2017), Kit Fine proposes a new logic of vagueness, CL, that promises to provide both a solution to the sorites paradox and a way to avoid the impossibility result from Fine (Philos Perspect 22(1):111–136, 2008). The present paper presents a challenge to his new theory of vagueness. I argue that the possibility theorem stated in Fine (Synthese 194(10):3699–3725, 2017), as well as his solution to the sorites paradox, fail in (...)
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  4. The Paradox Paradox Non-Paradox and Conjunction Fallacy Non-Fallacy.Noah Greenstein - 2023 - Australasian Journal of Logic 20 (3):478-489.
    Brock and Glasgow recently introduced a new definition of paradox and argue that this conception of paradox itself leads to paradox, the so-called Paradox Paradox. I show that they beg the questions during the course of their argument, but, more importantly, do so in a philosophically interesting way: it reveals a counterexample to the equivalence between being a logical truth and having a probability of one. This has consequences regarding norms of rationality, undermining the grounds for the Conjunction Fallacy.
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  5. Yamauchi Tokuryū (1890-1982). Philosophie occidentale et pensée bouddhique.Romaric Jannel - 2023 - Paris: Éditions Kimé.
    Philosophe japonais polyglotte au savoir encyclopédique, Yamauchi Tokuryū est à n’en point douter l’un des auteurs les moins étudiés de l’école de Kyōto. La présente étude vient corriger ce qui ne constitue rien d’autre qu’un accident de l’histoire, tant l’ampleur du projet philosophique de Yamauchi est à même de susciter l’intérêt du philosophe, du savant et de l’amateur cultivé. La démarche de ce penseur japonais, disciple de Nishida Kitarō, est remarquable en ce qu’il chercha à proposer un dépassement englobant de (...)
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  6. Against Classical Paraconsistent Metatheory.Koji Tanaka & Patrick Girard - 2023 - Analysis 83 (2):285-294.
    There was a time when 'logic' just meant classical logic. The climate is slowly changing and non-classical logic cannot be dismissed off-hand. However, a metatheory used to study the properties of non-classical logic is often classical. In this paper, we will argue that this practice of relying on classical metatheories is problematic. In particular, we will show that it is a bad practice because the metatheory that is used to study a non-classical logic often rules out the very logic it (...)
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  7. Empty validity all the way up: an easy road (Proceedings) (12th edition).Estrada-González Luis & Romero-RodrÍguez Christian (eds.) - 2022 - Moscow: Lomonosov Moscow State University.
    There is a tension between the definition of empty logic as a logic with no valid arguments and no valid meta-arguments, on the one hand, and the way in which we have usually interpreted the validity of meta-arguments, on the other. Here we argue that one way to eliminate the tension is understanding the “If. . . then. . . ” in a meta-argument, at least in the case of an empty logic, as a transplication (aka the de Finetti conditional) (...)
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  8. Refining Labelled Systems for Modal and Constructive Logics with Applications.Tim Lyon - 2021 - Dissertation, Technischen Universität Wien
    This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic paradigms: labelled and nested sequent calculi. The formalism of labelled sequents has been successful in that cut-free calculi in possession of desirable proof-theoretic properties can be automatically generated for large classes of logics. Despite these qualities, labelled systems make use of a complicated syntax that explicitly incorporates the (...)
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  9. La contrastación de teorías inconsistentes no triviales.Luis Felipe Bartolo Alegre - 2020 - Dissertation, Universidad Nacional Mayor de San Marcos
    This dissertation offers a proof of the logical possibility of testing empirical/factual theories that are inconsistent, but non-trivial. In particular, I discuss whether or not such theories can satisfy Popper's principle of falsifiablility. An inconsistent theory Ƭ closed under a classical consequence relation implies every statement of its language because in classical logic the inconsistency and triviality are coextensive. A theory Ƭ is consistent iff there is not a α such that Ƭ ⊢ α ∧ ¬α, otherwise it is inconsistent. (...)
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  10. Três Vezes Não: Um Estudo Sobre as Negações Clássica, Paraconsistente e Paracompleta.Kherian Gracher - 2020 - Dissertation, Federal University of Santa Catarina
    Could there be a single logical system that would allow us to work simultaneously with classical, paraconsistent, and paracomplete negations? These three negations were separately studied in logics whose negations bear their names. Initially we will restrict our analysis to propositional logics by analyzing classical negation, ¬c, as treated by Classical Propositional Logic (LPC); the paraconsistent negation, ¬p, as treated through the hierarchy of Paraconsistent Propositional Calculi Cn (0 ≤ n ≤ ω); and the paracomplete negation, ¬q, as treated by (...)
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  11. Limits of Abductivism About Logic.Ulf Hlobil - 2020 - Philosophy and Phenomenological Research 103 (2):320-340.
    I argue against abductivism about logic, which is the view that rational theory choice in logic happens by abduction. Abduction cannot serve as a neutral arbiter in many foundational disputes in logic because, in order to use abduction, one must first identify the relevant data. Which data one deems relevant depends on what I call one's conception of logic. One's conception of logic is, however, not independent of one's views regarding many of the foundational disputes that one may hope to (...)
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  12. Star models and the semantics of infectiousness.Matthew W. G. McClure - 2020 - Undergraduate Philosophy Journal of Australasia 2 (2):35–57.
    The first degree entailment (FDE) family is a group of logics, a many-valued semantics for each system of which is obtained from classical logic by adding to the classical truth-values true and false any subset of {both, neither, indeterminate}, where indeterminate is an infectious value (any formula containing a subformula with the value indeterminate itself has the value indeterminate). In this paper, we see how to extend a version of star semantics for the logics whose many-valued semantics lack indeterminate to (...)
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  13. In the name of paraconsistency.Francisco Miró Quesada Cantuarias & Luis Felipe Bartolo Alegre - 2020 - South American Journal of Logic 6 (2):163-171.
    Logic systems that can handle contradictions were being used for some time without having a general technical name. One of the main proposers of these systems, Newton da Costa, asked Francisco Miró Quesada to suggest him a name for those systems. In the historical letter that here we translate into English for the first time, Miró Quesada suggests three names to da Costa for this purpose: ‘ultraconsistent’, ‘metaconsistent’, and ‘paraconsistent’; explaining their pros and cons. -/- Paper based on a letter (...)
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  14. Las Lógicas Mixtas como escape al Problema del Colapso y al Desafío de Quine.Joaquín Santiago Toranzo Calderón - 2020 - Análisis Filosófico 40 (2):247-272.
    En este trabajo presentaré una forma de evitar los problemas más recurrentes en cierta versión del pluralismo lógico, aquella que defiende que incluso considerando un lenguaje fijo existen múltiples sistemas lógicos legítimos. Para ello, será necesario considerar los puntos de partida del programa pluralista y explicitar los problemas que de ellos surgen, principalmente el Desafío de Quine y el Problema del Colapso. Luego, propondré una modificación respecto de lo que se entiende por consecuencia lógica, para poder considerar una familia de (...)
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  15. Apontamentos em Filosofia da Lógica.Gilson Maicá de Oliveira - 2019 - Basilíade - Revista de Filosofia 1 (1):101-120.
    Neste artigo discutimos alguns aspectos da lógica nos dias atuais. O propósito central é mostrar a evolução dessa disciplina. Começamos com uma breve introdução onde especificamos o que queremos dizer com o termo “lógica”. A seguir, exporemos e discutiremos o que consideramos ser algumas das principais áreas de investigação da lógica atual. Concluímos o artigo com algumas observações sobre lógicas não clássicas e seus impactos sobre a filosofia. Ao final do texto se encontram mais detalhes que apontam para um aprofundamento (...)
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  16. A Graph-theoretic Method to Define any Boolean Operation on Partitions.David Ellerman - 2019 - The Art of Discrete and Applied Mathematics 2 (2):1-9.
    The lattice operations of join and meet were defined for set partitions in the nineteenth century, but no new logical operations on partitions were defined and studied during the twentieth century. Yet there is a simple and natural graph-theoretic method presented here to define any n-ary Boolean operation on partitions. An equivalent closure-theoretic method is also defined. In closing, the question is addressed of why it took so long for all Boolean operations to be defined for partitions.
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  17. Formalizing Kant’s Rules.Richard Evans, Andrew Stephenson & Marek Sergot - 2019 - Journal of Philosophical Logic 48:1-68.
    This paper formalizes part of the cognitive architecture that Kant develops in the Critique of Pure Reason. The central Kantian notion that we formalize is the rule. As we interpret Kant, a rule is not a declarative conditional stating what would be true if such and such conditions hold. Rather, a Kantian rule is a general procedure, represented by a conditional imperative or permissive, indicating which acts must or may be performed, given certain acts that are already being performed. These (...)
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  18. A Neutral Temporal Deontic STIT Logic.Kees van Berkel & Tim Lyon - 2019 - In P. Blackburn, E. Lorini & M. Guo (eds.), Logic, Rationality, and Interaction. Springer. pp. 340-354.
    In this work we answer a long standing request for temporal embeddings of deontic STIT logics by introducing the multi-agent STIT logic TDS . The logic is based upon atemporal utilitarian STIT logic. Yet, the logic presented here will be neutral: instead of committing ourselves to utilitarian theories, we prove the logic TDS sound and complete with respect to relational frames not employing any utilitarian function. We demonstrate how these neutral frames can be transformed into utilitarian temporal frames, while preserving (...)
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  19. Conjunto plitogénico, una extensión de los conjuntos crisp, difusos, conjuntos difusos intuicionistas y neutrosóficos revisitado.Florentin Smarandache - 2018 - Neutrosophic Computing and Machine Learning 3 (1):1-19.
    En el presente artículo, introducimos el conjunto plitogénico (como generalización de conjuntos nítidos, borrosos, intuicionistas, borrosos y neutrosóficos), que es un conjunto cuyos elementos se caracterizan por los valores de muchos atrib utos. Un valor de atributo v tiene un grado correspondiente (difuso, intuicionista difuso o neutrosófico) de pertenencia d (x, v) del elemento x, al conjunto P, con respecto a algunos criterios dados. Para obtener una mejor precisión para los operadores d e agregación plitogénica en el conjunto plitogénico, y (...)
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  20. Modal Logic Kalish-and-Montague Style.Nathan Salmon - 2005 - In _Metaphysics, Mathematics, and Meaning: Philosophical Papers I_. New York: Oxford University Press. pp. 111-118.
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  21. A cut-free sequent calculus for the bi-intuitionistic logic 2Int.Sara Ayhan - manuscript
    The purpose of this paper is to introduce a bi-intuitionistic sequent calculus and to give proofs of admissibility for its structural rules. The calculus I will present, called SC2Int, is a sequent calculus for the bi-intuitionistic logic 2Int, which Wansing presents in [2016a]. There he also gives a natural deduction system for this logic, N2Int, to which SC2Int is equivalent in terms of what is derivable. What is important is that these calculi represent a kind of bilateralist reasoning, since they (...)
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