Results for 'partition logic'

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  1. 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. Hence the (...)
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  2. Partitioning Logical Space.Jeroen Groenendijk & Martin Stokhof - manuscript
    In the present version of these lecture notes only a number of typos and a few glaring mistakes have been corrected. Thanks to Paul Dekker for his help in this respect. No attempt has been been made to update the original text or to incorporate new insights and approaches. For a more recent overview, see our ‘Questions’ in the Handbook of Logic and Language (edited by Johan van Benthem and Alice ter Meulen, Elsevier, 1997).
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  3. The logic of partitions: Introduction to the dual of the logic of subsets: The logic of partitions.David Ellerman - 2010 - Review of Symbolic Logic 3 (2):287-350.
    Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary “propositional” logic should in general be the logic of subsets of a given universe set. Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms—which is reflected in the duality between quotient objects and subobjects throughout algebra. If “propositional” logic is thus seen as (...)
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  4. The logic of systems of granular partitions.Thomas Bittner, Barry Smith & Maureen Donnelly - 2005 - IFOMIS Reports.
    The theory of granular partitions is designed to capture in a formal framework important aspects of the selective character of common-sense views of reality. It comprehends not merely the ways in which we can view reality by conceiving its objects as gathered together not merely into sets, but also into wholes of various kinds, partitioned into parts at various levels of granularity. We here represent granular partitions as triples consisting of a rooted tree structure as first component, a domain satisfying (...)
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  5. Partitions and Objective Indefiniteness.David Ellerman - manuscript
    Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of reality. The problem of interpreting quantum mechanics (QM) is essentially the problem of making sense out of an objectively indefinite reality. These two types of reality can be respectively associated with the two mathematical concepts of subsets and quotient sets (or partitions) which are category-theoretically dual (...)
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  6. Follow the Math!: The Mathematics of Quantum Mechanics as the Mathematics of Set Partitions Linearized to (Hilbert) Vector Spaces.David Ellerman - 2022 - Foundations of Physics 52 (5):1-40.
    The purpose of this paper is to show that the mathematics of quantum mechanics is the mathematics of set partitions linearized to vector spaces, particularly in Hilbert spaces. That is, the math of QM is the Hilbert space version of the math to describe objective indefiniteness that at the set level is the math of partitions. The key analytical concepts are definiteness versus indefiniteness, distinctions versus indistinctions, and distinguishability versus indistinguishability. The key machinery to go from indefinite to more definite (...)
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  7. 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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  8. An introduction to logical entropy and its relation to Shannon entropy.David Ellerman - 2013 - International Journal of Semantic Computing 7 (2):121-145.
    The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the partition. The logical concept of entropy based on partition logic is the normalized counting measure of the set of distinctions of a partition on a finite set--just as the usual logical notion (...)
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  9. 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 (...)
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  10. 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 (...)
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  11. On the logic of common belief and common knowledge.Luc Lismont & Philippe Mongin - 1994 - Theory and Decision 37 (1):75-106.
    The paper surveys the currently available axiomatizations of common belief (CB) and common knowledge (CK) by means of modal propositional logics. (Throughout, knowledge- whether individual or common- is defined as true belief.) Section 1 introduces the formal method of axiomatization followed by epistemic logicians, especially the syntax-semantics distinction, and the notion of a soundness and completeness theorem. Section 2 explains the syntactical concepts, while briefly discussing their motivations. Two standard semantic constructions, Kripke structures and neighbourhood structures, are introduced in Sections (...)
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  12. 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 (...)
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  13. Semantic Information G Theory and Logical Bayesian Inference for Machine Learning.Chenguang Lu - 2019 - Information 10 (8):261.
    An important problem with machine learning is that when label number n>2, it is very difficult to construct and optimize a group of learning functions, and we wish that optimized learning functions are still useful when prior distribution P(x) (where x is an instance) is changed. To resolve this problem, the semantic information G theory, Logical Bayesian Inference (LBI), and a group of Channel Matching (CM) algorithms together form a systematic solution. MultilabelMultilabel A semantic channel in the G theory consists (...)
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  14. On the duality between existence and information.David Ellerman - manuscript
    Recent developments in pure mathematics and in mathematical logic have uncovered a fundamental duality between "existence" and "information." In logic, the duality is between the Boolean logic of subsets and the logic of quotient sets, equivalence relations, or partitions. The analogue to an element of a subset is the notion of a distinction of a partition, and that leads to a whole stream of dualities or analogies--including the development of new logical foundations for information theory (...)
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  15. Universality, topic-neutrality, monism, and pluralism in logic.Luis F. Bartolo Alegre - forthcoming - South American Journal of Logic.
    The concept of topic-neutrality, though central to contemporary characterisations of logic, lacks a standard formal definition. I propose a formal reconstruction of topic-neutrality in terms of a topical partition of atoms and its applicability across consequence relations. I explore the implications of this reconstruction for logical pluralism and monism, distinguishing between topic-neutral and topic-specific variants of each. I argue that while topic-neutral pluralism posits various applicable consequence relations across domains, topic-specific pluralism holds that some relations are applicable only (...)
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  16. A Judgmental Reconstruction of some of Professor Woleński’s logical and philosophical writings.Fabien Schang - 2020 - Studia Humana 9 (3):72-103.
    Roman Suszko said that “Obviously, any multiplication of logical values is a mad idea and, in fact, Łukasiewicz did not actualize it.” The aim of the present paper is to qualify this ‘obvious’ statement through a number of logical and philosophical writings by Professor Jan Woleński, all focusing on the nature of truth-values and their multiple uses in philosophy. It results in a reconstruction of such an abstract object, doing justice to what Suszko held a ‘mad’ project within a generalized (...)
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  17. COMPLEXITY VALUATIONS: A GENERAL SEMANTIC FRAMEWORK FOR PROPOSITIONAL LANGUAGES.Juan Pablo Jorge, Hernán Luis Vázquez & Federico Holik - forthcoming - Actas Del Xvii Congreso Dr. Antonio Monteiro.
    A general mathematical framework, based on countable partitions of Natural Numbers [1], is presented, that allows to provide a Semantics to propositional languages. It has the particularity of allowing both the valuations and the interpretation Sets for the connectives to discriminate complexity of the formulas. This allows different adequacy criteria to be used to assess formulas associated with the same connective, but that differ in their complexity. The presented method can be adapted potentially infinite number of connectives and truth values, (...)
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  18. A Fundamental Duality in the Exact Sciences: The Application to Quantum Mechanics.David Ellerman - 2024 - Foundations 4 (2):175-204.
    There is a fundamental subsets–partitions duality that runs through the exact sciences. In more concrete terms, it is the duality between elements of a subset and the distinctions of a partition. In more abstract terms, it is the reverse-the-arrows of category theory that provides a major architectonic of mathematics. The paper first develops the duality between the Boolean logic of subsets and the logic of partitions. Then, probability theory and information theory (as based on logical entropy) are (...)
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  19. Counting distinctions: on the conceptual foundations of Shannon’s information theory.David Ellerman - 2009 - Synthese 168 (1):119-149.
    Categorical logic has shown that modern logic is essentially the logic of subsets (or "subobjects"). Partitions are dual to subsets so there is a dual logic of partitions where a "distinction" [an ordered pair of distinct elements (u,u′) from the universe U ] is dual to an "element". An element being in a subset is analogous to a partition π on U making a distinction, i.e., if u and u′ were in different blocks of π. (...)
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  20. How Category Theory Works.David Ellerman - manuscript
    The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and functions. The analysis extends directly to other concrete categories (groups, rings, vector spaces, etc.) where the objects are sets with a certain type of structure and the morphisms are functions that preserve that structure. Then the elements & distinctions-based definitions can be (...)
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  21. Another Side of Categorical Propositions: The Keynes–Johnson Octagon of Oppositions.Amirouche Moktefi & Fabien Schang - 2023 - History and Philosophy of Logic 44 (4):459-475.
    The aim of this paper is to make sense of the Keynes–Johnson octagon of oppositions. We will discuss Keynes' logical theory, and examine how his view is reflected on this octagon. Then we will show how this structure is to be handled by means of a semantics of partition, thus computing logical relations between matching formulas with a semantic method that combines model theory and Boolean algebra.
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  22. Praise, blame, obligation, and DWE: Toward a framework for classical supererogation and kin.Paul McNamara - 2011 - Journal of Applied Logic 9 (2):153-170.
    Continuing prior work by the author, a simple classical system for personal obligation is integrated with a fairly rich system for aretaic (agent-evaluative) appraisal. I then explore various relationships between definable aretaic statuses such as praiseworthiness and blameworthiness and deontic statuses such as obligatoriness and impermissibility. I focus on partitions of the normative statuses generated ("normative positions" but without explicit representation of agency). In addition to being able to model and explore fundamental questions in ethical theory about the connection between (...)
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  23. Question-relative knowledge for minimally rational agents.Francisca Silva - 2024 - Inquiry: An Interdisciplinary Journal of Philosophy:1-31.
    Agents know some but not all logical consequences of what they know. Agents seem to be neither logically omniscient nor logically incompetent. Yet finding an intermediate standard of minimal rationality has proven difficult. In this paper, I take suggestions found in the literature (Lewis, 1988; Hawke, Özgün and Berto, 2020; Plebani and Spolaore, 2021) and join the forces of subject matter and impossible worlds approaches to devise a new solution to this quandary. I do so by combining a space of (...)
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  24. Two Kinds of Mental Conflict in Republic IV.Galen Barry & Edith Gwendolyn Nally - 2021 - History of Philosophy & Logical Analysis 25 (2):255-281.
    Plato’s partition argument infers that the soul has parts from the fact that the soul experiences mental conflict. We consider an ambiguity in the concept of mental conflict. According to the first sense of conflict, a soul is in conflict when it has desires whose satisfaction is logically incompatible. According to the second sense of conflict, a soul is in conflict when it has desires which are logically incompatible even when they are unsatisfied. This raises a dilemma: if the (...)
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  25. (1 other version)GOL: A general ontological language.Wolfgang Degen, Barbara Heller, Heinrich Herre & Barry Smith - 2001 - In Barry Smith & Christopher Welty (eds.), Formal Ontology in Information Systems (FOIS). ACM Press. pp. 34-46.
    Every domain-specific ontology must use as a framework some upper-level ontology which describes the most general, domain-independent categories of reality. In the present paper we sketch a new type of upper-level ontology, which is intended to be the basis of a knowledge modelling language GOL (for: 'General Ontological Language'). It turns out that the upper- level ontology underlying standard modelling languages such as KIF, F-Logic and CycL is restricted to the ontology of sets. Set theory has considerable mathematical power (...)
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  26. Million Dollar Questions: Why Deliberation is More Than Information Pooling.Daniel Hoek & Richard Bradley - 2024 - Social Choice and Welfare 63:581-600.
    Models of collective deliberation often assume that the chief aim of a deliberative exchange is the sharing of information. In this paper, we argue that an equally important role of deliberation is to draw participants’ attention to pertinent questions, which can aid the assembly and processing of distributed information by drawing deliberators’ attention to new issues. The assumption of logical omniscience renders classical models of agents’ informational states unsuitable for modelling this role of deliberation. Building on recent insights from psychology, (...)
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  27. Deductive Reasoning Under Uncertainty: A Water Tank Analogy.Guy Politzer - 2016 - Erkenntnis 81 (3):479-506.
    This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability bounds (...)
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  28. Un problema abierto de independencia en la teoría de conjuntos relacionado con ultrafiltros no principales sobre el conjunto de los números naturales N, y con Propiedades Ramsey.Franklin Galindo - manuscript
    En el ámbito de la lógica matemática existe un problema sobre la relación lógica entre dos versiones débiles del Axioma de elección (AE) que no se ha podido resolver desde el año 2000 (aproximadamente). Tales versiones están relacionadas con ultrafiltros no principales y con Propiedades Ramsey (Bernstein, Polarizada, Subretículo, Ramsey, Ordinales flotantes, etc). La primera versión débil del AE es la siguiente (A): “Existen ultrafiltros no principales sobre el conjunto de los números naturales (ℕ)”. Y la segunda versión débil del (...)
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  29. MacColl’s Modes of Modalities.Fabien Schang - 2011 - Philosophia Scientiae 15:149-188.
    Hugh MacColl is commonly seen as a pioneer of modal and many-valued logic, given his introduction of modalities that go beyond plain truth and falsehood. But a closer examination shows that such a legacy is debatable and should take into account the way in which these modalities proceeded. We argue that, while MacColl devised a modal logic in the broad sense of the word, he did not give rise to a many-valued logic in the strict sense. Rather, (...)
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  30. The Automated Discovery of Universal Theories.Kevin T. Kelly - 1986 - Dissertation, University of Pittsburgh
    This thesis examines the prospects for mechanical procedures that can identify true, complete, universal, first-order logical theories on the basis of a complete enumeration of true atomic sentences. A sense of identification is defined that is more general than those which are usually studied in the learning theoretic and inductive inference literature. Some identification algorithms based on confirmation relations familiar in the philosophy of science are presented. Each of these algorithms is shown to identify all purely universal theories without function (...)
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  31. Maxwell–boltzmann statistics and the metaphysics of modality.Bruce L. Gordon - 2002 - Synthese 133 (3):393 - 417.
    Two arguments have recently been advanced that Maxwell-Boltzmann particles areindistinguishable just like Bose–Einstein and Fermi–Dirac particles. Bringing modalmetaphysics to bear on these arguments shows that ontological indistinguishabilityfor classical (MB) particles does not follow. The first argument, resting on symmetryin the occupation representation for all three cases, fails since peculiar correlationsexist in the quantum (BE and FD) context as harbingers of ontic indistinguishability,while the indistinguishability of classical particles remains purely epistemic. The secondargument, deriving from the classical limits of quantum statistical (...) functions,embodies a conceptual confusion. After clarifying the doctrine of haecceitism, a thirdargument is considered that attempts to deflate metaphysical concerns altogether byshowing that the phase-space and distribution-space representations of MB-statisticshave contrary haecceitistic import. Careful analysis shows this argument to fail as well,leaving de re modality unproblematically grounding particle identity in the classicalcontext while genuine puzzlement about the underlying ontology remains for quantumstatistics. (shrink)
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  32. Type-2 Fuzzy Sets and Newton’s Fuzzy Potential in an Algorithm of Classification Objects of a Conceptual Space.Adrianna Jagiełło, Piotr Lisowski & Roman Urban - 2022 - Journal of Logic, Language and Information 31 (3):389-408.
    This paper deals with Gärdenfors’ theory of conceptual spaces. Let S{\mathcal {S}} be a conceptual space consisting of 2-type fuzzy sets equipped with several kinds of metrics. Let a finite set of prototypes P~1,,P~nS\tilde{P}_1,\ldots,\tilde{P}_n\in \mathcal {S} be given. Our main result is the construction of a classification algorithm. That is, given an element A~S,{\tilde{A}}\in \mathcal {S}, our algorithm classifies it into the conceptual field determined by one of the given prototypes P~i.\tilde{P}_i. The construction of our algorithm uses some physical analogies (...)
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  33. A Constructive Critique of the Foundations of Philosophy.Ramesh Nath Patel - 1970 - Dissertation, The University of New Mexico
    A CONSTRUCTIVE CRITIQUE OF THE FOUNDATIONS OF PHILOSOPHY: Abstract of the Ph.D. Dissertation By Ramesh N. Patel June, 1970 -/- Philosophy pursues a rational explication of our understanding, experiences, and values in terms of objective truth and reality. Conspicuously, its view of rationality has been rigid and preconceived. Application of the preconceived reason in the explication of the essential features of our world fails and issues in a network of dialectical tangles. These artificially created tangles pose a unique intellectual challenge, (...)
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  34. End of the square?Fabien Schang - 2018 - South American Journal of Logic 4 (2):485-505.
    It has been recently argued that the well-known square of opposition is a gathering that can be reduced to a one-dimensional figure, an ordered line segment of positive and negative integers [3]. However, one-dimensionality leads to some difficulties once the structure of opposed terms extends to more complex sets. An alternative algebraic semantics is proposed to solve the problem of dimensionality in a systematic way, namely: partition (or bitstring) semantics. Finally, an alternative geometry yields a new and unique pattern (...)
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  35. Departed Souls? Tripartition at the Close of Plato’s Republic.Nathan Bauer - 2017 - History of Philosophy & Logical Analysis 20 (1):139-157.
    Plato’s tripartite soul plays a central role in his account of justice in the Republic. It thus comes as a surprise to find him apparently abandoning this model at the end of the work, when he suggests that the soul, as immortal, must be simple. I propose a way of reconciling these claims, appealing to neglected features of the city-soul analogy and the argument for the soul’s division. The original true soul, I argue, is partitioned, but in a finer manner (...)
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  36. On Why Thumos will Rule by Force.Nathan Rothschild - 2017 - History of Philosophy & Logical Analysis 20 (1):120-138.
    I argue that Republic presents thumos as a limited, or flawed, principle of psychic unity. My central claim is that Plato both makes this assertion about the necessary limitations of thumos, and can defend it, because he understands thumos as the pursuit of to oikeion, or one’s own. So understood, the thumoetic part divides the world into self and other and pursues the defense of the former from the latter. As a result, when confronted with a conflicting desire, the thumoetic (...)
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  37. Pluralism in Logic: The Square of Opposition, Leibniz'Principle of Sufficient Reason and Markov's Principle.Antonino Drago - 2012 - In Jean-Yves Béziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. New York: Springer Verlag. pp. 175--189.
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  38. Hume On Is and Ought: Logic, Promises and the Duke of Wellington.Charles Pigden - 2016 - In Paul Russell (ed.), The Oxford Handbook of David Hume. Oxford: Oxford University Press.
    Hume seems to contend that you can’t get an ought from an is. Searle professed to prove otherwise, deriving a conclusion about obligations from a premise about promises. Since (as Schurz and I have shown) you can’t derive a substantive ought from an is by logic alone, Searle is best construed as claiming that there are analytic bridge principles linking premises about promises to conclusions about obligations. But we can no more derive a moral obligation to pay up from (...)
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  39. Modeling Deep Disagreement in Default Logic.Frederik J. Andersen - 2024 - Australasian Journal of Logic 21 (2):47-63.
    Default logic has been a very active research topic in artificial intelligence since the early 1980s, but has not received as much attention in the philosophical literature thus far. This paper shows one way in which the technical tools of artificial intelligence can be applied in contemporary epistemology by modeling a paradigmatic case of deep disagreement using default logic. In §1 model-building viewed as a kind of philosophical progress is briefly motivated, while §2 introduces the case of deep (...)
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  40. Higher-order logic as metaphysics.Jeremy Goodman - 2024 - In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press.
    This chapter offers an opinionated introduction to higher-order formal languages with an eye towards their applications in metaphysics. A simply relationally typed higher-order language is introduced in four stages: starting with first-order logic, adding first-order predicate abstraction, generalizing to higher-order predicate abstraction, and finally adding higher-order quantification. It is argued that both β-conversion and Universal Instantiation are valid on the intended interpretation of this language. Given these two principles, it is then shown how we can use pure higher-order (...) to ask, and begin to answer, metaphysical questions with non-trivial implications. In particular, while we must reject the popular idea that structural differences between sentences correspond to parallel distinctions in the logical structure of extra-linguistic reality, it may still be possible to give a purely logical characterization of objectual aboutness and related notions. (shrink)
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  41. Adaptationism and the Logic of Research Questions: How to Think Clearly About Evolutionary Causes.Elisabeth A. Lloyd - 2015 - Biological Theory 10 (4):DOI: 10.1007/s13752-015-0214-2.
    This article discusses various dangers that accompany the supposedly benign methods in behavioral evoltutionary biology and evolutionary psychology that fall under the framework of "methodological adaptationism." A "Logic of Research Questions" is proposed that aids in clarifying the reasoning problems that arise due to the framework under critique. The live, and widely practiced, " evolutionary factors" framework is offered as the key comparison and alternative. The article goes beyond the traditional critique of Stephen Jay Gould and Richard C. Lewontin, (...)
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  42. Truthmaker Semantics for Epistemic Logic.Peter Hawke & Aybüke Özgün - 2023 - In Federico L. G. Faroldi & Frederik Van De Putte (eds.), Kit Fine on Truthmakers, Relevance, and Non-classical Logic. Springer Verlag. pp. 295-335.
    We explore some possibilities for developing epistemic logic using truthmaker semantics. We identify three possible targets of analysis for the epistemic logician. We then list some candidate epistemic principles and review the arguments that render some controversial. We then present the classic Hintikkan approach to epistemic logic and note—as per the ‘problem of logical omniscience’—that it validates all of the aforementioned principles, controversial or otherwise. We then lay out a truthmaker framework in the style of Kit Fine and (...)
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  43. 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 for Cut—elimination, but (...)
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  44. Future Contingents and the Logic of Temporal Omniscience.Patrick Todd & Brian Rabern - 2019 - Noûs 55 (1):102-127.
    At least since Aristotle’s famous 'sea-battle' passages in On Interpretation 9, some substantial minority of philosophers has been attracted to the doctrine of the open future--the doctrine that future contingent statements are not true. But, prima facie, such views seem inconsistent with the following intuition: if something has happened, then (looking back) it was the case that it would happen. How can it be that, looking forwards, it isn’t true that there will be a sea battle, while also being true (...)
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  45. (A Little) Quantified Modal Logic for Normativists.Mark Povich - forthcoming - Analysis.
    Burgess (1997), building on Quine (1953), convincingly argued that claims in quantified modal logic cannot be understood as synonymous with or logically equivalent to claims about the analyticity of certain sentences. According to modal normativism, metaphysically necessary claims instead express or convey our actual semantic rules. In this paper, I show how the normativist can use Sidelle’s (1992a, 1995) neglected work on rigidity to account for two important phenomena in quantified modal logic: the necessity of identity and the (...)
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  46. Countering Justification Holism in the Epistemology of Logic: The Argument from Pre-Theoretic Universality.Frederik J. Andersen - 2023 - Australasian Journal of Logic 20 (3):375-396.
    A key question in the philosophy of logic is how we have epistemic justification for claims about logical entailment (assuming we have such justification at all). Justification holism asserts that claims of logical entailment can only be justified in the context of an entire logical theory, e.g., classical, intuitionistic, paraconsistent, paracomplete etc. According to holism, claims of logical entailment cannot be atomistically justified as isolated statements, independently of theory choice. At present there is a developing interest in—and endorsement of—justification (...)
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  47. New foundations for imperative logic I: Logical connectives, consistency, and quantifiers.Peter B. M. Vranas - 2008 - Noûs 42 (4):529-572.
    Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: "kiss me and hug me" is the conjunction of "kiss me" with "hug me". This example may suggest that declarative and imperative logic are isomorphic: just as the conjunction of two declaratives is true exactly if both conjuncts are true, the conjunction of two imperatives is satisfied exactly if both conjuncts are satisfied—what more is there to say? Much (...)
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  48. A Semantics for the Impure Logic of Ground.Louis deRosset & Kit Fine - 2023 - Journal of Philosophical Logic 52 (2):415-493.
    This paper establishes a sound and complete semantics for the impure logic of ground. Fine (Review of Symbolic Logic, 5(1), 1–25, 2012a) sets out a system for the pure logic of ground, one in which the formulas between which ground-theoretic claims hold have no internal logical complexity; and it provides a sound and complete semantics for the system. Fine (2012b) [§§6-8] sets out a system for an impure logic of ground, one that extends the rules of (...)
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  49. Formality in Logic: From Logical Terms to Semantic Constraints.Gil Sagi - 2014 - Logique Et Analyse 57 (227).
    In this paper I discuss a prevailing view by which logical terms determine forms of sentences and arguments and therefore the logical validity of arguments. This view is common to those who hold that there is a principled distinction between logical and nonlogical terms and those holding relativistic accounts. I adopt the Tarskian tradition by which logical validity is determined by form, but reject the centrality of logical terms. I propose an alternative framework for logic where logical terms no (...)
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  50. 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, (...)
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