Results for 'trans-classical logic'

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  1.  57
    M. HEIDEGGER, Heraclitus. The Inception of Occidental Thinking and Logic: Heraclitus's Doctrine of the Logos, Trans. Julia Goesser Assaiante, S. Montgomery Ewegen. [REVIEW]Keith Begley - 2020 - Classics Ireland 26:163–166.
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  2. Conservatively Extending Classical Logic with Transparent Truth.David Ripley - 2012 - Review of Symbolic Logic 5 (2):354-378.
    This paper shows how to conservatively extend classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truth—involving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and complete. (One proof system allows (...)
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  3. Non-Classical Metatheory for Non-Classical Logics.Andrew Bacon - 2013 - Journal of Philosophical Logic 42 (2):335-355.
    A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical metatheory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena of higher order vagueness and the revenge liar are just two such examples. The aim (...)
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  4. Conceptual Structure of Classical Logic.John Corcoran - 1972 - Philosophy and Phenomenological Research 33 (1):25-47.
    One innovation in this paper is its identification, analysis, and description of a troubling ambiguity in the word ‘argument’. In one sense ‘argument’ denotes a premise-conclusion argument: a two-part system composed of a set of sentences—the premises—and a single sentence—the conclusion. In another sense it denotes a premise-conclusion-mediation argument—later called an argumentation: a three-part system composed of a set of sentences—the premises—a single sentence—the conclusion—and complex of sentences—the mediation. The latter is often intended to show that the conclusion follows from (...)
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  5. Reasoning with Imperatives Using Classical Logic.Joseph S. Fulda - 1995 - Sorites 3:7-11.
    As the journal is effectively defunct, I am uploading a full-text copy, but only of my abstract and article, and some journal front matter. -/- Note that the pagination in the PDF version differs from the official pagination because A4 and 8.5" x 11" differ. -/- Traditionally, imperatives have been handled with deontic logics, not the logic of propositions which bear truth values. Yet, an imperative is issued by the speaker to cause (stay) actions which change the state of (...)
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  6. Supervaluationism and Classical Logic.Pablo Cobreros - 2011 - In Rick Nouwen, Robert van Rooij, Hans-Christian Schmitz & Uli Sauerland (eds.), Vagueness in Communication, Lecture Notes in Computer Science, Vol. 6517. Springer.
    This paper is concerned with the claim that supervaluationist consequence is not classical for a language including an operator for definiteness. Although there is some sense in which this claim is uncontroversial, there is a sense in which the claim must be qualified. In particular I defend Keefe's position according to which supervaluationism is classical except when the inference from phi to Dphi is involved. The paper provides a precise content to this claim showing that we might provide (...)
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  7. Making Sense of Paraconsistent Logic: The Nature of Logic, Classical Logic and Paraconsistent Logic.Koji Tanaka - 2013 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. pp. 15--25.
    Max Cresswell and Hilary Putnam seem to hold the view, often shared by classical logicians, that paraconsistent logic has not been made sense of, despite its well-developed mathematics. In this paper, I examine the nature of logic in order to understand what it means to make sense of logic. I then show that, just as one can make sense of non-normal modal logics (as Cresswell demonstrates), we can make `sense' of paraconsistent logic. Finally, I turn (...)
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  8.  88
    Judgement Aggregation in Non-Classical Logics.Daniele Porello - 2017 - Journal of Applied Non-Classical Logics 27 (1-2):106-139.
    This work contributes to the theory of judgement aggregation by discussing a number of significant non-classical logics. After adapting the standard framework of judgement aggregation to cope with non-classical logics, we discuss in particular results for the case of Intuitionistic Logic, the Lambek calculus, Linear Logic and Relevant Logics. The motivation for studying judgement aggregation in non-classical logics is that they offer a number of modelling choices to represent agents’ reasoning in aggregation problems. By studying (...)
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  9.  76
    A Poetics of Designing.Claudia Westermann - 2019 - In Thomas Fischer & Christiane M. Herr (eds.), Design Cybernetics: Navigating the New. Basel, Switzerland: Springer. pp. 233-245.
    The chapter provides an overview on what it means to be in a world that is uncertain, e.g., how under conditions of limited understanding any activity is an activity that designs and constructs, and how designing objects, spaces, and situations relates to the (designed) meta-world of second-order cybernetics. Designers require a framework that is open, but one that supplies ethical guidance when ‘constructing’ something new. Relating second-order design thinking to insights in philosophy and aesthetics, the chapter argues that second-order cybernetics (...)
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  10.  81
    The (Greatest) Fragment of Classical Logic That Respects the Variable-Sharing Principle (in the Fmla-Fmla Framework).Damian E. Szmuc - forthcoming - Bulletin of the Section of Logic.
    We examine the set of formula-to-formula valid inferences of Classical Logic, where the premise and the conclusion share at least a propositional variable in common. We review the fact, already proved in the literature, that such a system is identical to the first-degree entailment fragment of R. Epstein's Relatedness Logic, and that it is a non-transitive logic of the sort investigated by S. Frankowski and others. Furthermore, we provide a semantics and a calculus for this (...). The semantics is defined in terms of a Rp-matrix built on top of a 5-valued extension of the 3-element weak Kleene algebra, whereas the calculus is defined in terms of a Gentzen-style sequent system where the left and right negation rules are subject to linguistic constraints. (shrink)
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  11. A Non-Classical Logical Foundation for Naturalised Realism.Emma Ruttkamp-Bloem, Giovanni Casini & Thomas Meyer - 2015 - In P. & M. Danćak Arazim (ed.), Logica Yearbook 2014. College Publications. pp. 249-266.
    In this paper, by suggesting a formal representation of science based on recent advances in logic-based Artificial Intelligence (AI), we show how three serious concerns around the realisation of traditional scientific realism (the theory/observation distinction, over-determination of theories by data, and theory revision) can be overcome such that traditional realism is given a new guise as ‘naturalised’. We contend that such issues can be dealt with (in the context of scientific realism) by developing a formal representation of science based (...)
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  12.  70
    Normalisation for Bilateral Classical Logic with Some Philosophical Remarks.Nils Kürbis - 2021 - Journal of Applied Logics 2 (8):531-556.
    Bilateralists hold that the meanings of the connectives are determined by rules of inference for their use in deductive reasoning with asserted and denied formulas. This paper presents two bilateral connectives comparable to Prior's tonk, for which, unlike for tonk, there are reduction steps for the removal of maximal formulas arising from introducing and eliminating formulas with those connectives as main operators. Adding either of them to bilateral classical logic results in an incoherent system. One way around this (...)
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  13. Logical Entropy: Introduction to Classical and Quantum Logical Information Theory.David Ellerman - 2018 - Entropy 20 (9):679.
    Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions of a partition. All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose of (...)
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  14. Formal Logic: Classical Problems and Proofs.Luis M. Augusto - 2019 - London, UK: College Publications.
    Not focusing on the history of classical logic, this book provides discussions and quotes central passages on its origins and development, namely from a philosophical perspective. Not being a book in mathematical logic, it takes formal logic from an essentially mathematical perspective. Biased towards a computational approach, with SAT and VAL as its backbone, this is an introduction to logic that covers essential aspects of the three branches of logic, to wit, philosophical, mathematical, and (...)
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  15.  52
    Resonances of the Unknown.Claudia Westermann - 2011 - Kybernetes 40 (7/8):1189-1195.
    Purpose – The purpose of this paper is to discuss the relevance of second-order cybernetics for a theory of architectural design and related discourse. -/- Design/methodology/approach – First, the relation of architectural design to the concept of “poiesis” is clarified. Subsequently, selected findings of Gotthard Günther are revisited and related to an architectural poetics. The last part of the paper consists of revisiting ideas mentioned previously, however, on the level of a discourse that has incorporated the ideas and offers a (...)
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  16. A Hierarchy of Classical and Paraconsistent Logics.Eduardo Alejandro Barrio, Federico Pailos & Damian Szmuc - 2020 - Journal of Philosophical Logic 49 (1):93-120.
    In this article, we will present a number of technical results concerning Classical Logic, ST and related systems. Our main contribution consists in offering a novel identity criterion for logics in general and, therefore, for Classical Logic. In particular, we will firstly generalize the ST phenomenon, thereby obtaining a recursively defined hierarchy of strict-tolerant systems. Secondly, we will prove that the logics in this hierarchy are progressively more classical, although not entirely classical. We will (...)
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  17. Computational Logic. Vol. 1: Classical Deductive Computing with Classical Logic. 2nd Ed.Luis M. Augusto - 2020 - London: College Publications.
    This is the 2nd edition of Computational logic. Vol. 1: Classical deductive computing with classical logic. This edition has a wholly new chapter on Datalog, a hard nut to crack from the viewpoint of semantics when negation is included.
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  18.  69
    Many-Valued And Fuzzy Logic Systems From The Viewpoint Of Classical Logic.Ekrem Sefa Gül - 2018 - Tasavvur - Tekirdag Theology Journal 4 (2):624 - 657.
    The thesis that the two-valued system of classical logic is insufficient to explanation the various intermediate situations in the entity, has led to the development of many-valued and fuzzy logic systems. These systems suggest that this limitation is incorrect. They oppose the law of excluded middle (tertium non datur) which is one of the basic principles of classical logic, and even principle of non-contradiction and argue that is not an obstacle for things both to exist (...)
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  19.  94
    On the Notion of Validity for the Bilateral Classical Logic.Ukyo Suzuki & Yoriyuki Yamagata - manuscript
    This paper considers Rumfitt’s bilateral classical logic (BCL), which is proposed to counter Dummett’s challenge to classical logic. First, agreeing with several authors, we argue that Rumfitt’s notion of harmony, used to justify logical rules by a purely proof theoretical manner, is not sufficient to justify coordination rules in BCL purely proof-theoretically. For the central part of this paper, we propose a notion of proof-theoretical validity similar to Prawitz for BCL and proves that BCL is sound (...)
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  20. Computational Logic. Vol. 1: Classical Deductive Computing with Classical Logic.Luis M. Augusto - 2018 - London: College Publications.
    This is the first of a two-volume work combining two fundamental components of contemporary computing into classical deductive computing, a powerful form of computation, highly adequate for programming and automated theorem proving, which, in turn, have fundamental applications in areas of high complexity and/or high security such as mathematical proof, software specification and verification, and expert systems. Deductive computation is concerned with truth-preservation: This is the essence of the satisfiability problem, or SAT, the central computational problem in computability and (...)
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  21.  27
    Normalisation and Subformula Property for a System of Classical Logic with Tarski’s Rule.Nils Kürbis - forthcoming - Archive for Mathematical Logic:1-25.
    This paper considers a formalisation of classical logic using general introduction rules and general elimination rules. It proposes a definition of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system, and gives reduction procedures for them. It is then shown that deductions in the system convert into normal form, i.e. deductions that contain neither maximal formulas nor maximal segments, and that deductions in normal form satisfy the subformula property. Tarski’s Rule is treated as a general introduction rule (...)
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  22. Strong Normalization of a Symmetric Lambda Calculus for Second-Order Classical Logic.Yoriyuki Yamagata - 2002 - Archive for Mathematical Logic 41 (1):91-99.
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  23. Bilateralist Detours: From Intuitionist to Classical Logic and Back.Nils Kürbis - 2017 - Logique Et Analyse 60 (239):301-316.
    There is widespread agreement that while on a Dummettian theory of meaning the justified logic is intuitionist, as its constants are governed by harmonious rules of inference, the situation is reversed on Huw Price's bilateralist account, where meanings are specified in terms of primitive speech acts assertion and denial. In bilateral logics, the rules for classical negation are in harmony. However, as it is possible to construct an intuitionist bilateral logic with harmonious rules, there is no formal (...)
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  24.  69
    Theories of Truth for Countable Languages Which Conform to Classical Logic.Seppo Heikkilä - forthcoming - Nonlinear Studies.
    Every countable language which conforms to classical logic is shown to have an extension which has a consistent definitional theory of truth. That extension has a consistent semantical theory of truth, if every sentence of the object language is valuated by its meaning either as true or as false. These theories contain both a truth predicate and a non-truth predicate. Theories are equivalent when sentences of the object lqanguage are valuated by their meanings.
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  25. Complementary Logics for Classical Propositional Languages.Achille C. Varzi - 1992 - Kriterion - Journal of Philosophy 4 (1):20-24.
    In previous work, I introduced a complete axiomatization of classical non-tautologies based essentially on Łukasiewicz’s rejection method. The present paper provides a new, Hilbert-type axiomatization (along with related systems to axiomatize classical contradictions, non-contradictions, contingencies and non-contingencies respectively). This new system is mathematically less elegant, but the format of the inferential rules and the structure of the completeness proof possess some intrinsic interest and suggests instructive comparisons with the logic of tautologies.
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  26.  19
    Note on 'Normalisation for Bilateral Classical Logic with Some Philosophical Remarks'.Nils Kürbis - 2021 - Journal of Applied Logics 7 (8):2259-2261.
    This brief note corrects an error in one of the reduction steps in my paper 'Normalisation for Bilateral Classical Logic with some Philosophical Remarks' published in the Journal of Applied Logics 8/2 (2021): 531-556.
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  27.  23
    G. Priest's An Introduction to Non-Classical Logic (2001). [REVIEW]Hans-Peter Leeb - 2003 - History and Philosophy of Logic 24:65-66.
    The review gives a short description of the content of the book and discusses the treatment of conditionals in it.
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  28.  59
    "Theoretical Logic in Sociology", Volume 2: "The Antinomies of Classical Thought: Marx and Durkheim" by Jeffrey C. Alexander.Stephen P. Turner - 1985 - Philosophy of the Social Sciences 15 (2):211-216.
    The four volume work of which this book is a part has been praised as one of the great monuments of theoretical scholarship in sociology of the century. The praise has come largely from the older generation of students of Parsons and Merton. A great deal of dispraise has come from Alexander's own generation. Alan Sica's (1983) brilliant, biting review of Volume I speaks for many of Alexander's peers. Volume II is likely to be even more controversial. This volume begins (...)
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  29. Why a Logical-Pragmatic Perspective on Validity in Mental Health is Not Sufficient: Introduction to the Principle of Convergent Trans-Disciplinary Crossvalidity.Drozdstoj St Stoyanov - 2010 - Dialogues in Philosophy, Mental and Neuro Sciences 3 (1):25-26.
    The logical-pragmatic perspective on the psychiatric diagnosis, presented by Rodriguez and Banzato contributes to and develops the existing conventional taxonomic framework. The latter is regarded as grounded on the epistemological prerequisites proponed by Carl Gustav Hempel in the late 1960s, adopted by the DSM task force of R. Spitzer in 1973.
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  30. On Classical and Quantum Logical Entropy.David Ellerman - manuscript
    The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean logic is usually mis-specified as "propositional" logic). The notion of an element of a subset has as its dual the notion of a distinction of a partition (a pair of elements in different blocks). Boole developed finite logical probability as the normalized counting (...)
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  31. Non‐Classical Knowledge.Ethan Jerzak - 2019 - Philosophy and Phenomenological Research 98 (1):190-220.
    The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely-held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single-premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a consistent (...)
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  32.  86
    Logic of Paradoxes in Classical Set Theories.Boris Čulina - 2013 - Synthese 190 (3):525-547.
    According to Cantor (Mathematische Annalen 21:545–586, 1883 ; Cantor’s letter to Dedekind, 1899 ) a set is any multitude which can be thought of as one (“jedes Viele, welches sich als Eines denken läßt”) without contradiction—a consistent multitude. Other multitudes are inconsistent or paradoxical. Set theoretical paradoxes have common root—lack of understanding why some multitudes are not sets. Why some multitudes of objects of thought cannot themselves be objects of thought? Moreover, it is a logical truth that such multitudes do (...)
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  33. An Introduction to Partition Logic.David Ellerman - 2014 - Logic Journal of the IGPL 22 (1):94-125.
    Classical logic is usually interpreted as the logic of propositions. But from Boole's original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (nonempty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoretic duality--which is reflected in the duality between quotient objects and subobjects throughout algebra. (...)
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  34. The Logic of Opacity.Andrew Bacon & Jeffrey Sanford Russell - 2019 - Philosophy and Phenomenological Research 99 (1):81-114.
    We explore the view that Frege's puzzle is a source of straightforward counterexamples to Leibniz's law. Taking this seriously requires us to revise the classical logic of quantifiers and identity; we work out the options, in the context of higher-order logic. The logics we arrive at provide the resources for a straightforward semantics of attitude reports that is consistent with the Millian thesis that the meaning of a name is just the thing it stands for. We provide (...)
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  35. Logic for Exact Entailment.Kit Fine & Mark Jago - 2018 - Review of Symbolic Logic:1-21.
    An exact truthmaker for A is a state which, as well as guaranteeing A’s truth, is wholly relevant to it. States with parts irrelevant to whether A is true do not count as exact truthmakers for A. Giving semantics in this way produces a very unusual consequence relation, on which conjunctions do not entail their conjuncts. This feature makes the resulting logic highly unusual. In this paper, we set out formal semantics for exact truthmaking and characterise the resulting notion (...)
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  36. From Classical to Intuitionistic Probability.Brian Weatherson - 2003 - Notre Dame Journal of Formal Logic 44 (2):111-123.
    We generalize the Kolmogorov axioms for probability calculus to obtain conditions defining, for any given logic, a class of probability functions relative to that logic, coinciding with the standard probability functions in the special case of classical logic but allowing consideration of other classes of "essentially Kolmogorovian" probability functions relative to other logics. We take a broad view of the Bayesian approach as dictating inter alia that from the perspective of a given logic, rational degrees (...)
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  37. Paraconsistency: Logic and Applications.Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.) - 2013 - Dordrecht, Netherland: Springer.
    A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems (...)
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  38. What is a Paraconsistent Logic?Damian Szmuc, Federico Pailos & Eduardo Barrio - 2018 - In Jacek Malinowski & Walter Carnielli (eds.), Contradictions, from Consistency to Inconsistency. Springer Verlag.
    Paraconsistent logics are logical systems that reject the classical principle, usually dubbed Explosion, that a contradiction implies everything. However, the received view about paraconsistency focuses only the inferential version of Explosion, which is concerned with formulae, thereby overlooking other possible accounts. In this paper, we propose to focus, additionally, on a meta-inferential version of Explosion, i.e. which is concerned with inferences or sequents. In doing so, we will offer a new characterization of paraconsistency by means of which a (...) is paraconsistent if it invalidates either the inferential or the meta-inferential notion of Explosion. We show the non-triviality of this criterion by discussing a number of logics. On the one hand, logics which validate and invalidate both versions of Explosion, such as classical logic and Asenjo–Priest’s 3-valued logic LP. On the other hand, logics which validate one version of Explosion but not the other, such as the substructural logics TS and ST, introduced by Malinowski and Cobreros, Egré, Ripley and van Rooij, which are obtained via Malinowski’s and Frankowski’s q- and p-matrices, respectively. (shrink)
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  39. LP, K3, and FDE as Substructural Logics.Lionel Shapiro - 2017 - In Pavel Arazim & Tomáš Lavička (eds.), The Logica Yearbook 2016. London: College Publications.
    Building on recent work, I present sequent systems for the non-classical logics LP, K3, and FDE with two main virtues. First, derivations closely resemble those in standard Gentzen-style systems. Second, the systems can be obtained by reformulating a classical system using nonstandard sequent structure and simply removing certain structural rules (relatives of exchange and contraction). I clarify two senses in which these logics count as “substructural.”.
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  40. Quantificational Logic and Empty Names.Andrew Bacon - 2013 - Philosophers' Imprint 13.
    The result of combining classical quantificational logic with modal logic proves necessitism – the claim that necessarily everything is necessarily identical to something. This problem is reflected in the purely quantificational theory by theorems such as ∃x t=x; it is a theorem, for example, that something is identical to Timothy Williamson. The standard way to avoid these consequences is to weaken the theory of quantification to a certain kind of free logic. However, it has often been (...)
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  41.  99
    Classical Form or Modern Scientific Rationalization? Nietzsche on the Drive to Ordered Thought as Apollonian Power and Socratic Pathology.Eli I. Lichtenstein - 2021 - Journal of Nietzsche Studies 52 (1):105-134.
    Nietzsche sometimes praises the drive to order—to simplify, organize, and draw clear boundaries—as expressive of a vital "classical" style, or an Apollonian artistic drive to calmly contemplate forms displaying "epic definiteness and clarity." But he also sometimes harshly criticizes order, as in the pathological dialectics or "logical schematism" that he associates paradigmatically with Socrates. I challenge a tradition that interprets Socratism as an especially one-sided expression of, or restricted form of attention to, the Apollonian: they are more radically disparate. (...)
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  42. Aristotle, Logic, and QUARC.Jonas Raab - 2018 - History and Philosophy of Logic 39 (4):305-340.
    The goal of this paper is to present a new reconstruction of Aristotle's assertoric logic as he develops it in Prior Analytics, A1-7. This reconstruction will be much closer to Aristotle's original text than other such reconstructions brought forward up to now. To accomplish this, we will not use classical logic, but a novel system developed by Ben-Yami [2014. ‘The quantified argument calculus’, The Review of Symbolic Logic, 7, 120–46] called ‘QUARC’. This system is apt for (...)
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  43. The Logicality of Language: A New Take on Triviality, “Ungrammaticality”, and Logical Form.Guillermo Del Pinal - 2019 - Noûs 53 (4):785-818.
    Recent work in formal semantics suggests that the language system includes not only a structure building device, as standardly assumed, but also a natural deductive system which can determine when expressions have trivial truth-conditions (e.g., are logically true/false) and mark them as unacceptable. This hypothesis, called the `logicality of language', accounts for many acceptability patterns, including systematic restrictions on the distribution of quantifiers. To deal with apparent counter-examples consisting of acceptable tautologies and contradictions, the logicality of language is often paired (...)
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  44.  67
    Normality Operators and Classical Recapture in Extensions of Kleene Logics.Ciuni Roberto & Massimiliano Carrara - forthcoming - Logic Journal of the IGPL.
    In this paper, we approach the problem of classical recapture for LP and K3 by using normality operators. These generalize the consistency and determinedness operators from Logics of Formal Inconsistency and Underterminedness, by expressing, in any many-valued logic, that a given formula has a classical truth value (0 or 1). In particular, in the rst part of the paper we introduce the logics LPe and Ke3 , which extends LP and K3 with normality operators, and we establish (...)
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  45. Substructural Logics, Pluralism and Collapse.Eduardo Alejandro Barrio, Federico Pailos & Damian Szmuc - 2018 - Synthese 198 (Suppl 20):4991-5007.
    When discussing Logical Pluralism several critics argue that such an open-minded position is untenable. The key to this conclusion is that, given a number of widely accepted assumptions, the pluralist view collapses into Logical Monism. In this paper we show that the arguments usually employed to arrive at this conclusion do not work. The main reason for this is the existence of certain substructural logics which have the same set of valid inferences as Classical Logic—although they are, in (...)
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  46. The Logicality of Language: A New Take on Triviality, `Ungrammaticality', and Logical Form.Guillermo Del Pinal - 2019 - Noûs 53 (4):785-818.
    Recent work in formal semantics suggests that the language system includes not only a structure building device, as standardly assumed, but also a natural deductive system which can determine when expressions have trivial truth‐conditions (e.g., are logically true/false) and mark them as unacceptable. This hypothesis, called the ‘logicality of language’, accounts for many acceptability patterns, including systematic restrictions on the distribution of quantifiers. To deal with apparent counter‐examples consisting of acceptable tautologies and contradictions, the logicality of language is often paired (...)
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  47. Logic in the Tractatus.Max Weiss - 2017 - Review of Symbolic Logic 10 (1):1-50.
    I present a reconstruction of the logical system of the Tractatus, which differs from classical logic in two ways. It includes an account of Wittgenstein’s “form-series” device, which suffices to express some effectively generated countably infinite disjunctions. And its attendant notion of structure is relativized to the fixed underlying universe of what is named. -/- There follow three results. First, the class of concepts definable in the system is closed under finitary induction. Second, if the universe of objects (...)
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  48. Truthmaker Semantics for Relevant Logic.Mark Jago - 2020 - Journal of Philosophical Logic 49 (4):681-702.
    I develop and defend a truthmaker semantics for the relevant logic R. The approach begins with a simple philosophical idea and develops it in various directions, so as to build a technically adequate relevant semantics. The central philosophical idea is that truths are true in virtue of specific states. Developing the idea formally results in a semantics on which truthmakers are relevant to what they make true. A very natural notion of conditionality is added, giving us relevant implication. I (...)
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  49. On an Intuitionistic Logic for Pragmatics.Gianluigi Bellin, Massimiliano Carrara & Daniele Chiffi - 2018 - Journal of Logic and Computation 50 (28):935–966..
    We reconsider the pragmatic interpretation of intuitionistic logic [21] regarded as a logic of assertions and their justi cations and its relations with classical logic. We recall an extension of this approach to a logic dealing with assertions and obligations, related by a notion of causal implication [14, 45]. We focus on the extension to co-intuitionistic logic, seen as a logic of hypotheses [8, 9, 13] and on polarized bi-intuitionistic logic as a (...)
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  50. Impossible Worlds and the Logic of Imagination.Francesco Berto - 2017 - Erkenntnis 82 (6):1277-1297.
    I want to model a finite, fallible cognitive agent who imagines that p in the sense of mentally representing a scenario—a configuration of objects and properties—correctly described by p. I propose to capture imagination, so understood, via variably strict world quantifiers, in a modal framework including both possible and so-called impossible worlds. The latter secure lack of classical logical closure for the relevant mental states, while the variability of strictness captures how the agent imports information from actuality in the (...)
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