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  1. Counterparts and Actuality.Michael Fara & Timothy Williamson - 2005 - Mind 114 (453):1-30.
    Many philosophers, following David Lewis, believe that we should look to counterpart theory, not quantified modal logic, as a means of understanding modal discourse. We argue that this is a mistake. Significant parts of modal discourse involve either implicit or explicit reference to what is actually the case, raising the question of how talk about actuality is to be represented counterpart-theoretically. By considering possible modifications of Lewis's counterpart theory, including actual modifications due to Graeme Forbes and Murali Ramachandran, we argue (...)
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  • On modal logics which enrich first-order S5.Harold T. Hodes - 1984 - Journal of Philosophical Logic 13 (4):423 - 454.
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  • Some theorems on the expressive limitations of modal languages.Harold T. Hodes - 1984 - Journal of Philosophical Logic 13 (1):13 - 26.
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  • Completeness and decidability results for some propositional modal logics containing “actually” operators.Dominic Gregory - 2001 - Journal of Philosophical Logic 30 (1):57-78.
    The addition of "actually" operators to modal languages allows us to capture important inferential behaviours which cannot be adequately captured in logics formulated in simpler languages. Previous work on modal logics containing "actually" operators has concentrated entirely upon extensions of KT5 and has employed a particular modeltheoretic treatment of them. This paper proves completeness and decidability results for a range of normal and nonnormal but quasi-normal propositional modal logics containing "actually" operators, the weakest of which are conservative extensions of K, (...)
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  • Reference, contingency, and the two-dimensional framework.Martin Davies - 2004 - Philosophical Studies 118 (1-2):83-131.
    I review and reconsider some of the themes of ‘Two notions of necessity’ (Davies and Humberstone, 1980) and attempt to reach a deeper understanding and appreciation of Gareth Evans’s reflections (in ‘Reference and contingency’, 1979) on both modality and reference. My aim is to plot the relationships between the notions of necessity that Humberstone and I characterised in terms of operators in two-dimensional modal logic, the notions of superficial and deep necessity that Evans himself described, and the epistemic notion of (...)
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  • Freedom, Omniscience and the Contingent A Priori.Fabio Lampert - forthcoming - Mind:fzae058.
    One of the major challenges in the philosophy of religion is theological fatalism—roughly, the claim that divine omniscience is incompatible with free will. In this article, I present new reasons to be skeptical of what I consider to be the strongest argument for theological fatalism. First, I argue that divine foreknowledge is not necessary for an argument against free will if we take into account divine knowledge of contingent a priori truths. Second, I show that this argument can be generalized (...)
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  • Can a dialetheist stay regular?Peter Eldridge-Smith & Jeremiah Joven Joaquin - forthcoming - Journal of Applied Non-Classical Logics:1-20.
    For a dialetheist, it is rational to believe that true contradictions exist. However, we argue that a dialetheist faces a complex dilemma given some bridge principles for rational beliefs that connect possibility and probability, including the so-called ‘Regularity Principle’. Either her belief is not doxastically possible even for her, or she must assign positive credence to the proposition that dialetheia exists. The former makes her belief prima facie self-defeating. The latter seems to compel her to choose between several more fine-grained (...)
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  • The Logic of Sequence Frames.Fabio Lampert - 2022 - Review of Symbolic Logic 15 (1):101-132.
    This paper investigates and develops generalizations of two-dimensional modal logics to any finite dimension. These logics are natural extensions of multidimensional systems known from the literature on logics for a priori knowledge. We prove a completeness theorem for propositional n-dimensional modal logics and show them to be decidable by means of a systematic tableau construction.
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  • Counterfactuals, counteractuals, and free choice.Fabio Lampert & Pedro Merlussi - 2020 - Philosophical Studies 178 (2):445-469.
    In a recent paper, Pruss proves the validity of the rule beta-2 relative to Lewis’s semantics for counterfactuals, which is a significant step forward in the debate about the consequence argument. Yet, we believe there remain intuitive counter-examples to beta-2 formulated with the actuality operator and rigidified descriptions. We offer a novel and two-dimensional formulation of the Lewisian semantics for counterfactuals and prove the validity of a new transfer rule according to which a new version of the consequence argument can (...)
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  • A Defense of Hume's Dictum.Cameron Gibbs - 2019 - Dissertation, University of Massachusetts Amherst
    Is the world internally connected by a web of necessary connections or is everything loose and independent? Followers of David Hume accept the latter by upholding Hume’s Dictum, according to which there are no necessary connections between distinct existences. Roughly put, anything can coexist with anything else, and anything can fail to coexist with anything else. Hume put it like this: “There is no object which implies the existence of any other if we consider these objects in themselves.” Since Hume’s (...)
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  • In Defense of the Possibilism–Actualism Distinction.Christopher Menzel - 2020 - Philosophical Studies 177 (7):1971-1997.
    In Modal Logic as Metaphysics, Timothy Williamson claims that the possibilism-actualism (P-A) distinction is badly muddled. In its place, he introduces a necessitism-contingentism (N-C) distinction that he claims is free of the confusions that purportedly plague the P-A distinction. In this paper I argue first that the P-A distinction, properly understood, is historically well-grounded and entirely coherent. I then look at the two arguments Williamson levels at the P-A distinction and find them wanting and show, moreover, that, when the N-C (...)
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  • Actuality and the a priori.Fabio Lampert - 2018 - Philosophical Studies 175 (3):809-830.
    We consider a natural-language sentence that cannot be formally represented in a first-order language for epistemic two-dimensional semantics. We also prove this claim in the “Appendix” section. It turns out, however, that the most natural ways to repair the expressive inadequacy of the first-order language render moot the original philosophical motivation of formalizing a priori knowability as necessity along the diagonal.
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  • On the expressive power of first-order modal logic with two-dimensional operators.Alexander W. Kocurek - 2018 - Synthese 195 (10):4373-4417.
    Many authors have noted that there are types of English modal sentences cannot be formalized in the language of basic first-order modal logic. Some widely discussed examples include “There could have been things other than there actually are” and “Everyone who is actually rich could have been poor.” In response to this lack of expressive power, many authors have discussed extensions of first-order modal logic with two-dimensional operators. But claims about the relative expressive power of these extensions are often justified (...)
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  • The Problem of Cross-world Predication.Alexander W. Kocurek - 2016 - Journal of Philosophical Logic 45 (6):697-742.
    While standard first-order modal logic is quite powerful, it cannot express even very simple sentences like “I could have been taller than I actually am” or “Everyone could have been smarter than they actually are”. These are examples of cross-world predication, whereby objects in one world are related to objects in another world. Extending first-order modal logic to allow for cross-world predication in a motivated way has proven to be notoriously difficult. In this paper, I argue that the standard accounts (...)
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  • Can the constructive empiricist be a nominalist? Quasi-truth, commitment and consistency.Paul Dicken - 2006 - Studies in History and Philosophy of Science Part A 37 (2):191-209.
    In this paper, I explore Rosen’s ‘transcendental’ objection to constructive empiricism—the argument that in order to be a constructive empiricist, one must be ontologically committed to just the sort of abstract, mathematical objects constructive empiricism seems committed to denying. In particular, I assess Bueno’s ‘partial structures’ response to Rosen, and argue that such a strategy cannot succeed, on the grounds that it cannot provide an adequate metalogic for our scientific discourse. I conclude by arguing that this result provides some interesting (...)
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  • The Logic of Contingent Existence.Daniel Michael Kervick - 1997 - Dissertation, University of Massachusetts Amherst
    Among modal claims, claims that involve the notions of broadly logical possibility and necessity, one that seems almost trivial is this: that if some proposition is possible, then it is possibly true. However, there is an argument, due in its essentials to the medieval philosopher and logician Jean Buridan, to the effect that this seemingly trivial claim is, in fact, untrue. ;Briefly put, the argument is this. Let Q be the proposition that Quine does not exist. Since Quine's existence is (...)
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  • Actuality for Counterpart Theorists.Jeffrey Sanford Russell - 2013 - Mind 122 (485):85-134.
    The counterpart theorist has a problem: there is no obvious way to understand talk about actuality in terms of counterparts. Fara and Williamson have charged that this obstacle cannot be overcome. Here I defend the counterpart theorist by offering systematic interpretations of a quantified modal language that includes an actuality operator. Centrally, I disentangle the counterpart relation from a related notion, a ‘representation relation’. The relation of possible things to the actual things they represent is variable, and an adequate account (...)
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  • Possible Worlds for Modal Primitivists.Louis deRosset - 2014 - Journal of Philosophical Logic 43 (1):109-131.
    Among the most remarkable developments in metaphysics since the 1950’s is the explosion of philosophical interest in possible worlds. This paper proposes an explanation of what possible worlds are, and argues that this proposal, the interpreted models conception, should be attractive to anyone who thinks that modal facts are primitive, and so not to be explained in terms of some non-modal notion of “possible world.” I articulate three constraints on any acceptable primitivist explanation of the nature of possible worlds, and (...)
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  • Modal Ontology and Generalized Quantifiers.Peter Fritz - 2013 - Journal of Philosophical Logic 42 (4):643-678.
    Timothy Williamson has argued that in the debate on modal ontology, the familiar distinction between actualism and possibilism should be replaced by a distinction between positions he calls contingentism and necessitism. He has also argued in favor of necessitism, using results on quantified modal logic with plurally interpreted second-order quantifiers showing that necessitists can draw distinctions contingentists cannot draw. Some of these results are similar to well-known results on the relative expressivity of quantified modal logics with so-called inner and outer (...)
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  • Assessment Sensitivity: Relative Truth and its Applications.John MacFarlane - 2014 - Oxford: Oxford University Press.
    John MacFarlane explores how we might make sense of the idea that truth is relative. He provides new, satisfying accounts of parts of our thought and talk that have resisted traditional methods of analysis, including what we mean when we talk about what is tasty, what we know, what will happen, what might be the case, and what we ought to do.
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  • ‘Now’ and ‘Then’ in Tense Logic.Ulrich Meyer - 2009 - Journal of Philosophical Logic 38 (2):229-247.
    According to Hans Kamp and Frank Vlach, the two-dimensional tense operators “now” and “then” are ineliminable in quantified tense logic. This is often adduced as an argument against tense logic, and in favor of an extensional account that makes use of explicit quantification over times. The aim of this paper is to defend tense logic against this attack. It shows that “now” and “then” are eliminable in quantified tense logic, provided we endow it with enough quantificational structure. The operators might (...)
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  • Counterpart Theory and Actuality.James Milford - 2024 - Journal of Philosophical Logic 53 (3):679-694.
    Lewis (The Journal of Philosophy, 65(5), 113–126, 1968) attempts to provide an account of modal talk in terms of the resources of counterpart theory, a first-order theory that eschews transworld identity. First, a regimentation of natural language modal claims into sentences of a formal first-order modal language L is assumed. Second, a translation scheme from L-sentences to sentences of the language of the theory is provided. According to Hazen (The Journal of Philosophy, 76(6), 319–338, 1979) and Fara & Williamson (Mind, (...)
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  • From modal fallacies to a new argument for fatalism.Pedro Merlussi - 2019 - Manuscrito 42 (3):86-107.
    Do incompatibilist arguments, like some fatalist arguments, rest on modal fallacies? If Westphal (2012) is right, then one popular argument for incompatibilism van Inwagen’s “First Formal Argument” does rest on a modal fallacy. Similarly, Warfield (2000) claims that the standard modal formulation of the master argument for incompatibilism is a modal fallacy. Here, I refute both claims. Contra Westphal, I show that the mistake in van Inwagen’s "First Formal Argument" is no modal fallacy. After that, I argue that Warfield’s charge (...)
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  • Quantifying over Possibilities.John Mackay - 2013 - Philosophical Review 122 (4):577-617.
    A person of average height would assert a truth by the conditional ‘if I were seven feet tall, I would be taller than I am,’ in which an indicative clause ‘I am’ is embedded in a subjunctive conditional. By contrast, no one would assert a truth by ‘if I were seven feet tall, I would be taller than I would be’ or ‘if I am seven feet tall, I am taller than I am’. These examples exemplify the fact that whether (...)
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  • Counterpart Theory and the Actuality Operator.Ulrich Meyer - 2013 - Mind 122 (485):27-42.
    Fara and Williamson (Mind, 2005) argue that counterpart theory is unable to account for modal claims that use an actuality operator. This paper argues otherwise. Rather than provide a different counterpart translation of the actuality operator itself, the solution presented here starts out with a quantified modal logic in which the actuality operator is redundant, and then translates the sentences of this logic into claims of counterpart theory.
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  • Actuality in Propositional Modal Logic.Allen P. Hazen, Benjamin G. Rin & Kai F. Wehmeier - 2013 - Studia Logica 101 (3):487-503.
    We show that the actuality operator A is redundant in any propositional modal logic characterized by a class of Kripke models (respectively, neighborhood models). Specifically, we prove that for every formula ${\phi}$ in the propositional modal language with A, there is a formula ${\psi}$ not containing A such that ${\phi}$ and ${\psi}$ are materially equivalent at the actual world in every Kripke model (respectively, neighborhood model). Inspection of the proofs leads to corresponding proof-theoretic results concerning the eliminability of the actuality (...)
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  • Indispensability arguments and instrumental nominalism.Richard Pettigrew - 2012 - Review of Symbolic Logic 5 (4):687-709.
    In the philosophy of mathematics, indispensability arguments aim to show that we are justified in believing that abstract mathematical objects exist. I wish to defend a particular objection to such arguments that has become increasingly popular recently. It is called instrumental nominalism. I consider the recent versions of this view and conclude that it has yet to be given an adequate formulation. I provide such a formulation and show that it can be used to answer the indispensability arguments. -/- There (...)
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  • In the mood.Kai Frederick Wehmeier - 2004 - Journal of Philosophical Logic 33 (6):607-630.
    The purpose of the present paper is to challenge some received assumptions about the logical analysis of modal English, and to show that these assumptions are crucial to certain debates in current philosophy of language. Specifically, I will argue that the standard analysis in terms of quantified modal logic mistakenly fudges important grammatical distinctions, and that the validity of Kripke's modal argument against description theories of proper names crucially depends on ensuing equivocations.
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  • First-order expressivity for s5-models: Modal vs. two-sorted languages.Holger Sturm & Frank Wolter - 2001 - Journal of Philosophical Logic 30 (6):571-591.
    Standard models for model predicate logic consist of a Kripke frame whose worlds come equipped with relational structures. Both modal and two-sorted predicate logic are natural languages for speaking about such models. In this paper we compare their expressivity. We determine a fragment of the two-sorted language for which the modal language is expressively complete on S5-models. Decidable criteria for modal definability are presented.
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  • The ersatz pluriverse.Theodore Sider - 2002 - Journal of Philosophy 99 (6):279-315.
    While many are impressed with the utility of possible worlds in linguistics and philosophy, few can accept the modal realism of David Lewis, who regards possible worlds as sui generis entities of a kind with the concrete world we inhabit.1 Not all uses of possible worlds require exotic ontology. Consider, for instance, the use of Kripke models to establish formal results in modal logic. These models contain sets often regarded for heuristic reasons as sets of “possible worlds”. But the “worlds” (...)
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  • How to Lewis a Kripke–Hintikka.Alessandro Torza - 2013 - Synthese 190 (4):743-779.
    It has been argued that a combination of game-theoretic semantics and independence-friendly (IF) languages can provide a novel approach to the conceptual foundations of mathematics and the sciences. I introduce and motivate an IF first-order modal language endowed with a game-theoretic semantics of perfect information. The resulting interpretive independence-friendly logic (IIF) allows to formulate some basic model-theoretic notions that are inexpressible in the ordinary quantified modal logic. Moreover, I argue that some key concepts of Kripke’s new theory of reference are (...)
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  • Coming True: A Note on Truth and Actuality.Richard Dietz & Julien Murzi - 2013 - Philosophical Studies 163 (2):403-427.
    John MacFarlane has recently presented a novel argument in support of truth- relativism. According to this, contextualists fail to accommodate retrospective reassessments of propositional contents, when it comes to languages which are rich enough to express actuality. The aim of this note is twofold. First, it is to argue that the argument can be effectively rejected, since it rests on an inadequate conception of actuality. Second, it is to offer a more plausible account of actuality in branching time, along the (...)
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  • Béziau's Translation Paradox.Lloyd Humberstone - 2005 - Theoria 71 (2):138-181.
    Jean-Yves Béziau (‘Classical Negation can be Expressed by One of its Halves’, Logic Journal of the IGPL 7 (1999), 145–151) has given an especially clear example of a phenomenon he considers a sufficiently puzzling to call the ‘paradox of translation’: the existence of pairs of logics, one logic being strictly weaker than another and yet such that the stronger logic can be embedded within it under a faithful translation. We elaborate on Béziau’s example, which concerns classical negation, as well as (...)
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  • Against modalism.Joseph Melia - 1992 - Philosophical Studies 68 (1):35 - 56.
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  • (1 other version)Abstract objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
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  • Physicalism, instrumentalism and the semantics of modal logic.Graeme Forbes - 1983 - Journal of Philosophical Logic 12 (3):271 - 298.
    The delicate point in the formalistic position is to explain how the non-intuitionistic classical mathematics is significant, after having initially agreed with the intuitionists that its theorems lack a real meaning in terms of which they are true (S. C. Kleene, 1952).
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  • A Modal Approach to Intentional Identity.Ephraim Glick - 2012 - Noûs 46 (3):386-399.
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  • Times in Tense Logic.Ulrich Meyer - 2009 - Notre Dame Journal of Formal Logic 50 (2):201--19.
    This paper explains how to obtain quantification over times in a tense logic in which all temporal distinctions are ultimately spelled out in terms of the two simple tense operators “it was the case that” and “it will be the case that.” The account of times defended here is similar to what is known as “linguistic ersatzism” about possible worlds, but there are noteworthy differences between these two cases. For example, while linguistic ersatzism would support actualism, the view of times (...)
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  • Scope and subjunctivity.I. L. Humberstone - 1982 - Philosophia 12 (1-2):99-126.
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  • On Equivalence Relations Between Interpreted Languages, with an Application to Modal and First-Order Language.Kai F. Wehmeier - 2021 - Erkenntnis 88 (1):193-213.
    I examine notions of equivalence between logics (understood as languages interpreted model-theoretically) and develop two new ones that invoke not only the algebraic but also the string-theoretic structure of the underlying language. As an application, I show how to construe modal operator languages as what might be called typographical notational variants of _bona fide_ first-order languages.
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  • Nothing But d‐Truth.Kai F. Wehmeier - 2014 - Analytic Philosophy 55 (1):114-117.
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  • 'Identity' without Identity.Alessandro Torza - 2012 - Mind 121 (481):67-95.
    I introduce and defend the semantic notion of counterfactual identity, distinguishing it from the metaphysical notion of transworld identity. After showing that Lewis's counterpart theory misconstrues counterfactual identity facts, I outline and motivate a ‘Leibnizian counterpart theory’ where the notion of counterfactual identity is adequately modelled. Finally, I show that counterfactual identity can be characterized without relying on some implausible features of Lewis's theory of conditionals.
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  • Two-dimensional adventures.Lloyd Humberstone - 2004 - Philosophical Studies 118 (1-2):17--65.
    This paper recalls some applications of two-dimensional modal logic from the 1980s, including work on the logic of Actually and on a somewhat idealized version of the indicative/subjunctive distinction, as well as on absolute and relative necessity. There is some discussion of reactions this material has aroused in commentators since. We also survey related work by Leslie Tharp from roughly the same period.
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  • Still in the Mood: The Versatility of Subjunctive Markers in Modal Logic.Kai F. Wehmeier & Helge Rückert - 2019 - Topoi 38 (2):361-377.
    We investigate and compare two major approaches to enhancing the expressive capacities of modal languages, namely the addition of subjunctive markers on the one hand, and the addition of scope-bearing actuality operators, on the other. It turns out that the subjunctive marker approach is not only every bit as versatile as the actuality operator approach, but that it in fact outperforms its rival in the context of cross-world predication.
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  • Some Limitations to the Psychological Orientation in Semantic Theory.Richmond H. Thomason - 2011 - Journal of Philosophical Logic 40 (1):1 - 14.
    The psychological orientation treats semantics as a matter of idealized computation over symbolic structures, and semantic relations like denotation as relations between linguistic expressions and these structures. I argue that results similar to Gödel's incompleteness theorems and Tarski's theorem on truth create foundational difficulties for this view of semantics.
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  • The Logic of Counterpart Theory with Actuality.Adam Rigoni & Richmond H. Thomason - 2012 - Journal of Philosophical Logic 43:1-31.
    It has been claimed that counterpart theory cannot support a theory of actuality without rendering obviously invalid formulas valid or obviously valid formulas invalid. We argue that these claims are not based on logical flaws of counterpart theory itself, but point to the lack of appropriate devices in first-order logic for “remembering” the values of variables. We formulate a mildly dynamic version of first-order logic with appropriate memory devices and show how to base a version of counterpart theory with actuality (...)
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  • Modality, mood, and descriptions.Kai F. Wehmeier - 2005 - In Reinhard Kahle (ed.), Intensionality: An Interdisciplinary Discussion. AK Peters.
    §1. Introduction. By means of what semantic features is a proper name tied to its bearer? This is a puzzling question indeed: proper names — like “Aristotle” or “Paris” — are syntactically simple, and it therefore does not seem possible to reduce their meanings, by means of a principle of compositionality, to the meanings of more basic, and hence perhaps more tractable, linguistic elements.
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  • Axiomatizing relativistic dynamics using formal thought experiments.Attila Molnár & Gergely Székely - 2015 - Synthese 192 (7):2183-2222.
    Thought experiments are widely used in the informal explanation of Relativity Theories; however, they are not present explicitly in formalized versions of Relativity Theory. In this paper, we present an axiom system of Special Relativity which is able to grasp thought experiments formally and explicitly. Moreover, using these thought experiments, we can provide an explicit definition of relativistic mass based only on kinematical concepts and we can geometrically prove the Mass Increase Formula in a natural way, without postulates of conservation (...)
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  • The question of moral ontology.Daniel Nolan - 2014 - Philosophical Perspectives 28 (1):201-221.
    Our ordinary moral practices not only suppose that some people ought to perform some actions, and that some outcomes are morally better or worse than others, but also that there are rights, duties, goodness, and other apparently abstract moral entities. What should we make of these entities, and the talk of these entities? It is not straighforward to account for these entities in other terms. On the other hand, this paper will argue that talk of such entities is not easily (...)
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