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  1.  12
    Modular Semantics for Theories: An Approach to Paraconsistent Reasoning.Holger Andreas - 2018 - Journal of Philosophical Logic 47 (5):877-912.
    Some scientific theories are inconsistent, yet non-trivial and meaningful. How is that possible? The present paper aims to show that we can analyse the inferential use of such theories in terms of consistent compositions of the applications of universal axioms. This technique will be represented by a preferred models semantics, which allows us to accept the instances of universal axioms selectively. For such a semantics to be developed, the framework of partial structures by da Costa and French will be extended (...)
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  2.  37
    Correction To: The Broadest Necessity.Andrew Bacon - 2018 - Journal of Philosophical Logic 47 (5):785-785.
    The original version of this article unfortunately contains mistakes.
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  3. The Broadest Necessity.Andrew Bacon - 2018 - Journal of Philosophical Logic 47 (5):733-783.
    In this paper the logic of broad necessity is explored. Definitions of what it means for one modality to be broader than another are formulated, and it is proven, in the context of higher-order logic, that there is a broadest necessity, settling one of the central questions of this investigation. It is shown, moreover, that it is possible to give a reductive analysis of this necessity in extensional language. This relates more generally to a conjecture that it is not possible (...)
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  4.  11
    Minimal Complete Propositional Natural Deduction Systems.Amr Elnashar & Wafik Boulos Lotfallah - 2018 - Journal of Philosophical Logic 47 (5):803-815.
    For each truth-functionally complete set of connectives, we construct a sound and complete natural deduction system containing no axioms and the smallest possible number of inference rules, namely one.
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  5.  13
    Learning Conditional Information by Jeffrey Imaging on Stalnaker Conditionals.Mario Günther - 2018 - Journal of Philosophical Logic 47 (5):851-876.
    We propose a method of learning indicative conditional information. An agent learns conditional information by Jeffrey imaging on the minimally informative proposition expressed by a Stalnaker conditional. We show that the predictions of the proposed method align with the intuitions in Douven, 239–263 2012)’s benchmark examples. Jeffrey imaging on Stalnaker conditionals can also capture the learning of uncertain conditional information, which we illustrate by generating predictions for the Judy Benjamin Problem.
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  6.  23
    Rosy with Sider? The Case of the Metaphysical Liar.Simon Hewitt - 2018 - Journal of Philosophical Logic 47 (5):787-801.
    An important trend in contemporary metaphysics denies that the structure of natural language is an important datum for investigating fundamental structure. Ted Sider proceeds on this basis to propose a metaphysical semantics for natural language. Within this framework he argues that natural language and a fundamental, ‘jointcarving’, language could be subject to distinct logics. Developing an argument of Hartry Field’s, I show that Sider’s preferred option of fundamental classicality combined with non-fundamental non-classicality trivialises within the framework of Siderian metaphysical semantics. (...)
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  7.  10
    Supervaluation-Style Truth Without Supervaluations.Johannes Stern - 2018 - Journal of Philosophical Logic 47 (5):817-850.
    Kripke’s theory of truth is arguably the most influential approach to self-referential truth and the semantic paradoxes. The use of a partial evaluation scheme is crucial to the theory and the most prominent schemes that are adopted are the strong Kleene and the supervaluation scheme. The strong Kleene scheme is attractive because it ensures the compositionality of the notion of truth. But under the strong Kleene scheme classical tautologies do not, in general, turn out to be true and, as a (...)
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  8.  3
    On Sahlqvist Formulas in Relevant Logic.Guillermo Badia - 2018 - Journal of Philosophical Logic 47 (4):673-691.
    This paper defines a Sahlqvist fragment for relevant logic and establishes that each class of frames in the Routley-Meyer semantics which is definable by a Sahlqvist formula is also elementary, that is, it coincides with the class of structures satisfying a given first order property calculable by a Sahlqvist-van Benthem algorithm. Furthermore, we show that some classes of Routley-Meyer frames definable by a relevant formula are not elementary.
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  9.  38
    Contraction, Infinitary Quantifiers, and Omega Paradoxes.Bruno Da Ré & Lucas Rosenblatt - 2018 - Journal of Philosophical Logic 47 (4):611-629.
    Our main goal is to investigate whether the infinitary rules for the quantifiers endorsed by Elia Zardini in a recent paper are plausible. First, we will argue that they are problematic in several ways, especially due to their infinitary features. Secondly, we will show that even if these worries are somehow dealt with, there is another serious issue with them. They produce a truth-theoretic paradox that does not involve the structural rules of contraction.
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  10.  72
    Williamson on Counterpossibles.Berto Francesco, French Rohan, Priest Graham & Ripley David - 2018 - Journal of Philosophical Logic 47 (4):693-713.
    A counterpossible conditional is a counterfactual with an impossible antecedent. Common sense delivers the view that some such conditionals are true, and some are false. In recent publications, Timothy Williamson has defended the view that all are true. In this paper we defend the common sense view against Williamson’s objections.
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  11.  30
    Higher-Order Contingentism, Part 3: Expressive Limitations.Peter Fritz - 2018 - Journal of Philosophical Logic 47 (4):649-671.
    Two expressive limitations of an infinitary higher-order modal language interpreted on models for higher-order contingentism – the thesis that it is contingent what propositions, properties and relations there are – are established: First, the inexpressibility of certain relations, which leads to the fact that certain model-theoretic existence conditions for relations cannot equivalently be reformulated in terms of being expressible in such a language. Second, the inexpressibility of certain modalized cardinality claims, which shows that in such a language, higher-order contingentists cannot (...)
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  12.  10
    Obligation as Optimal Goal Satisfaction.Robert Kowalski & Ken Satoh - 2018 - Journal of Philosophical Logic 47 (4):579-609.
    Formalising deontic concepts, such as obligation, prohibition and permission, is normally carried out in a modal logic with a possible world semantics, in which some worlds are better than others. The main focus in these logics is on inferring logical consequences, for example inferring that the obligation O q is a logical consequence of the obligations O p and O. In this paper we propose a non-modal approach in which obligations are preferred ways of satisfying goals expressed in first-order logic. (...)
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  13.  7
    The Representation of Belief.Isaac Wilhelm - 2018 - Journal of Philosophical Logic 47 (4):715-732.
    I derive a sufficient condition for a belief set to be representable by a probability function: if at least one comparative confidence ordering of a certain type satisfies Scott’s axiom, then the belief set used to induce that ordering is representable. This provides support for Kenny Easwaran’s project of analyzing doxastic states in terms of belief sets rather than credences.
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  14.  39
    Emptying a Paradox of Ground.Jack Woods - 2018 - Journal of Philosophical Logic 47 (4):631-648.
    Sometimes a fact can play a role in a grounding explanation, but the particular content of that fact make no difference to the explanation—any fact would do in its place. I call these facts vacuous grounds. I show that applying the distinction between-vacuous grounds allows us to give a principled solution to Kit Fine and Stephen Kramer’s paradox of ground. This paradox shows that on minimal assumptions about grounding and minimal assumptions about logic, we can show that grounding is reflexive, (...)
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  15.  17
    A Rational Way of Playing: Revision Theory for Strategic Interaction.Riccardo Bruni & Giacomo Sillari - 2018 - Journal of Philosophical Logic 47 (3):419-448.
    Gupta has proposed a definition of strategic rationality cast in the framework of his revision theory of truth. His analysis, relative to a class of normal form games in which all players have a strict best reply to all other players’ strategy profiles, shows that game-theoretic concepts have revision-theoretic counterparts. We extend Gupta’s approach to deal with normal form games in which players’ may have weak best replies. We do so by adapting intuitions relative to Nash equilibrium refinements to the (...)
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  16.  84
    Agreement and Updating For Self-Locating Belief.Michael Caie - 2018 - Journal of Philosophical Logic 47 (3):513-547.
    In this paper, I argue that some plausible principles concerning which credences are rationally permissible for agents given information about one another’s epistemic and credal states have some surprising consequences for which credences an agent ought to have in light of self-locating information. I provide a framework that allows us to state these constraints and draw out these consequences precisely. I then consider and assess the prospects for rejecting these prima facie plausible principles.
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  17.  28
    Higher-Order Contingentism, Part 2: Patterns of Indistinguishability.Peter Fritz - 2018 - Journal of Philosophical Logic 47 (3):407-418.
    The models of contingency in what propositions, properties and relations there are developed in Part 1 are related to models of contingency in what propositions there are due to Robert Stalnaker. It is shown that some but not all of the classes of models of Part 1 agree with Stalnaker’s models concerning the patterns of contingency in what propositions there are they admit. Further structural connections between the two kinds of models are explored.
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  18.  14
    Handling Inconsistencies in the Early Calculus.Jesse Heyninck, Peter Verdée & Albrecht Heeffer - 2018 - Journal of Philosophical Logic 47 (3):481-511.
    The early calculus is a popular example of an inconsistent but fruitful scientific theory. This paper is concerned with the formalisation of reasoning processes based on this inconsistent theory. First it is shown how a formal reconstruction in terms of a sub-classical negation leads to triviality. This is followed by the evaluation of the chunk and permeate mechanism proposed by Brown and Priest in, 379–388, 2004) to obtain a non-trivial formalisation of the early infinitesimal calculus. Different shortcomings of this application (...)
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  19.  11
    Principles for Object-Linguistic Consequence: From Logical to Irreflexive.Carlo Nicolai & Lorenzo Rossi - 2018 - Journal of Philosophical Logic 47 (3):549-577.
    We discuss the principles for a primitive, object-linguistic notion of consequence proposed by ) that yield a version of Curry’s paradox. We propose and study several strategies to weaken these principles and overcome paradox: all these strategies are based on the intuition that the object-linguistic consequence predicate internalizes whichever meta-linguistic notion of consequence we accept in the first place. To these solutions will correspond different conceptions of consequence. In one possible reading of these principles, they give rise to a notion (...)
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  20.  13
    Uncertainty and Persistence: A Bayesian Update Semantics for Probabilistic Expressions.Deniz Rudin - 2018 - Journal of Philosophical Logic 47 (3):365-405.
    This paper presents a general-purpose update semantics for expressions of subjective uncertainty in natural language. First, a set of desiderata are established for how expressions of subjective uncertainty should behave in dynamic, update-based semantic systems; then extant implementations of expressions of subjective uncertainty in such models are evaluated and found wanting; finally, a new update semantics is proposed. The desiderata at the heart of this paper center around the contention that expressions of subjective uncertainty express beliefs which are not persistent, (...)
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  21.  12
    Some Notes on Truths and Comprehension.Thomas Schindler - 2018 - Journal of Philosophical Logic 47 (3):449-479.
    In this paper we study several translations that map models and formulae of the language of second-order arithmetic to models and formulae of the language of truth. These translations are useful because they allow us to exploit results from the extensive literature on arithmetic to study the notion of truth. Our purpose is to present these connections in a systematic way, generalize some well-known results in this area, and to provide a number of new results. Sections 3 and 4 contain (...)
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  22.  33
    There is More to Negation Than Modality.Michael De & Hitoshi Omori - 2018 - Journal of Philosophical Logic 47 (2):281-299.
    There is a relatively recent trend in treating negation as a modal operator. One such reason is that doing so provides a uniform semantics for the negations of a wide variety of logics and arguably speaks to a longstanding challenge of Quine put to non-classical logics. One might be tempted to draw the conclusion that negation is a modal operator, a claim Francesco Berto, 761–793, 2015) defends at length in a recent paper. According to one such modal account, the negation (...)
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  23.  6
    Combinatorial Bitstring Semantics for Arbitrary Logical Fragments.Lorenz Demey & Hans Smessaert - 2018 - Journal of Philosophical Logic 47 (2):325-363.
    Logical geometry systematically studies Aristotelian diagrams, such as the classical square of oppositions and its extensions. These investigations rely heavily on the use of bitstrings, which are compact combinatorial representations of formulas that allow us to quickly determine their Aristotelian relations. However, because of their general nature, bitstrings can be applied to a wide variety of topics in philosophical logic beyond those of logical geometry. Hence, the main aim of this paper is to present a systematic technique for assigning bitstrings (...)
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  24.  30
    On the Costs of Nonclassical Logic.Volker Halbach & Carlo Nicolai - 2018 - Journal of Philosophical Logic 47 (2):227-257.
    Solutions to semantic paradoxes often involve restrictions of classical logic for semantic vocabulary. In the paper we investigate the costs of these restrictions in a model case. In particular, we fix two systems of truth capturing the same conception of truth: of the system KF of Feferman formulated in classical logic, and the system PKF of Halbach and Horsten, formulated in basic De Morgan logic. The classical system is known to be much stronger than the nonclassical one. We assess the (...)
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  25.  8
    Proof Theory of Paraconsistent Quantum Logic.Norihiro Kamide - 2018 - Journal of Philosophical Logic 47 (2):301-324.
    Paraconsistent quantum logic, a hybrid of minimal quantum logic and paraconsistent four-valued logic, is introduced as Gentzen-type sequent calculi, and the cut-elimination theorems for these calculi are proved. This logic is shown to be decidable through the use of these calculi. A first-order extension of this logic is also shown to be decidable. The relationship between minimal quantum logic and paraconsistent four-valued logic is clarified, and a survey of existing Gentzen-type sequent calculi for these logics and their close relatives is (...)
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  26.  42
    Axiomatic Theories of Partial Ground I.Johannes Korbmacher - 2018 - Journal of Philosophical Logic 47 (2):161-191.
    This is part one of a two-part paper, in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. This allows us to connect theories of partial ground with axiomatic theories of truth. In this part of the paper, we develop an axiomatization of the relation of partial ground over the truths of arithmetic and show that (...)
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  27.  26
    Axiomatic Theories of Partial Ground II.Johannes Korbmacher - 2018 - Journal of Philosophical Logic 47 (2):193-226.
    This is part two of a two-part paper in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. In this part of the paper, we extend the base theory of the first part of the paper with hierarchically typed truth-predicates and principles about the interaction of partial ground and truth. We show that our theory is (...)
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  28.  17
    An Axiomatic System and a Tableau Calculus for STIT Imagination Logic.Grigory K. Olkhovikov & Heinrich Wansing - 2018 - Journal of Philosophical Logic 47 (2):259-279.
    We formulate a Hilbert-style axiomatic system and a tableau calculus for the STIT-based logic of imagination recently proposed in Wansing. Completeness of the axiom system is shown by the method of canonical models; completeness of the tableau system is also shown by using standard methods.
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  29.  19
    Second-Order Logic and the Power Set.Ethan Brauer - 2018 - Journal of Philosophical Logic 47 (1):123-142.
    Ignacio Jane has argued that second-order logic presupposes some amount of set theory and hence cannot legitimately be used in axiomatizing set theory. I focus here on his claim that the second-order formulation of the Axiom of Separation presupposes the character of the power set operation, thereby preventing a thorough study of the power set of infinite sets, a central part of set theory. In reply I argue that substantive issues often cannot be separated from a logic, but rather must (...)
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  30.  12
    Order-Dual Relational Semantics for Non-Distributive Propositional Logics: A General Framework.Chrysafis Hartonas - 2018 - Journal of Philosophical Logic 47 (1):67-94.
    The contribution of this paper lies with providing a systematically specified and intuitive interpretation pattern and delineating a class of relational structures and models providing a natural interpretation of logical operators on an underlying propositional calculus of Positive Lattice Logic and subsequently proving a generic completeness theorem for the related class of logics, sometimes collectively referred to as Generalized Galois Logics.
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  31.  27
    Relational Semantics and Domain Semantics for Epistemic Modals.Dilip Ninan - 2018 - Journal of Philosophical Logic 47 (1):1-16.
    The standard account of modal expressions in natural language analyzes them as quantifiers over a set of possible worlds determined by the evaluation world and an accessibility relation. A number of authors have recently argued for an alternative account according to which modals are analyzed as quantifying over a domain of possible worlds that is specified directly in the points of evaluation. But the new approach only handles the data motivating it if it is supplemented with a non-standard account of (...)
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  32.  44
    Modeling Unicorns and Dead Cats: Applying Bressan’s ML Ν to the Necessary Properties of Non-Existent Objects.Tyke Nunez - 2018 - Journal of Philosophical Logic 47 (1):95–121.
    Should objects count as necessarily having certain properties, despite their not having those properties when they do not exist? For example, should a cat that passes out of existence, and so no longer is a cat, nonetheless count as necessarily being a cat? In this essay I examine different ways of adapting Aldo Bressan’s MLν so that it can accommodate an affirmative answer to these questions. Anil Gupta, in The Logic of Common Nouns, creates a number of languages that have (...)
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  33.  25
    Subjunctive Conditional Probability.Wolfgang Schwarz - 2018 - Journal of Philosophical Logic 47 (1):47-66.
    There seem to be two ways of supposing a proposition: supposing “indicatively” that Shakespeare didn’t write Hamlet, it is likely that someone else did; supposing “subjunctively” that Shakespeare hadn’t written Hamlet, it is likely that nobody would have written the play. Let P be the probability of B on the subjunctive supposition that A. Is P equal to the probability of the corresponding counterfactual, A □→B? I review recent triviality arguments against this hypothesis and argue that they do not succeed. (...)
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  34.  52
    Probabilistic Opinion Pooling with Imprecise Probabilities.Rush T. Stewart & Ignacio Ojea Quintana - 2018 - Journal of Philosophical Logic 47 (1):17-45.
    The question of how the probabilistic opinions of different individuals should be aggregated to form a group opinion is controversial. But one assumption seems to be pretty much common ground: for a group of Bayesians, the representation of group opinion should itself be a unique probability distribution, 410–414, [45]; Bordley Management Science, 28, 1137–1148, [5]; Genest et al. The Annals of Statistics, 487–501, [21]; Genest and Zidek Statistical Science, 114–135, [23]; Mongin Journal of Economic Theory, 66, 313–351, [46]; Clemen and (...)
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  35.  7
    Approximating Cartesian Closed Categories in NF-Style Set Theories.Morgan Thomas - 2018 - Journal of Philosophical Logic 47 (1):143-160.
    I criticize, but uphold the conclusion of, an argument by McLarty to the effect that New Foundations style set theories don’t form a suitable foundation for category theory. McLarty’s argument is from the fact that Set and Cat are not Cartesian closed in NF-style set theories. I point out that these categories do still have a property approximating Cartesian closure, making McLarty’s argument not conclusive. After considering and attempting to address other problems with developing category theory in NF-style set theories, (...)
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