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Summary The interplay of essentialism and modal logic is a major topic in the logic and metaphysics of modality. Quine 1953 argued that quantified modal logic (QML) entails essentialism, the view that an object can have a property essentially, independently of how it is referred to. Since he found essentialism to be unintelligible, Quine concluded by modus tollens that QML should be rejected. Kripke 1963 and Marcus 1967 have contributed to the rehabilitation of QML by showing how it can be made sense of within a suitable semantic framework. Others, such as Parsons 1969 and McKay 1975, have argued that QML is not committed to the thesis of essentialism in the way Quine thought. Now that the intelligibility of QML is no longer at issue, a central problem in the contemporary debate is whether the notion of essence can be understood in modal terms. A classical modalist analysis of essence is due to Moore 1919: x is essentially P iff x is necessarily P (or, in conditional form: iff x is necessarily P, if existent). This reduction of essence to pure QML has been found wanting by Fine 1994. A general argument against modal characterizations of essence has been proposed by Torza 2015. As a consequence, the Moorean definition has been mostly abandoned (but see Cowling 2013). Some proposals have emerged that attempt to understand essence by means of revisions or extensions of standard QML. Zalta 2006 and Wildman 2013 have proposed to reduce essence to a combination of modal and non-modal notions. Correia 2007 has put forward an analysis of essence carried out in a modal logic which is more fine-grained that standard QML.  Fine 1995, 2000 has formulated a quantified intensional logic for the notion of essence.
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  1. John Robert Baker (1978). Essentialism and the Modal Semantics of J. Hintikka. Notre Dame Journal of Formal Logic 19 (1):81-91.
  2. John Robert Baker (1973). Quantified Modal Logic and the Problem of Essentialism. Dissertation, Vanderbilt University
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  3. Ruth Barcan Marcus & Shaughan Lavine (1995). Modalities: Philosophical Essays. British Journal for the Philosophy of Science 46 (2):267-274.
    Based on her earlier ground-breaking axiomatization of quantified modal logic, the papers collected here by the distinguished philosopher Ruth Barcan Marcus cover much ground in the development of her thought, including influential essays on moral conflict, on belief and rationality, and on some historical figures.
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  4. Cleverson Bastos & Paulo de Oliveira (2011). Quine E O “pecado” Da Lógica Modal. Episteme NS: Revista Del Instituto de Filosofía de la Universidad Central de Venezuela 31 (1):1-17.
    O presente trabalho pretende analisar as objeções de Quine à ló­gica modal. O trabalho evidencia que tais objeções dirigem-se às formas proposicionais e também às formas quantificadas. Como o próprio Quine faz, não se pretende aqui apresentar soluções, mas apenas levantar os pro­blemas que o seu trabalho identificou. Este texto apóia-se, sobretudo, no importante estudo de Jaime Nubiola, intitulado El Compromisso Esencialista de La Lógica Modal: Estudio de Quine y Kripke. Inicialmente, serão apresen­tadas as seis objeções de Quine e, em (...)
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  5. Nuel Belnap & Thomas Müller, CIFOL: Case-Intensional First Order Logic. Toward a Theory of Sorts.
    This is Part I of a two-part essay introducing case-intensional first-order logic, an easy-to-use, uniform, powerful, and useful combination of first order logic with modal logic resulting from philosophical and technical modifications of Bressan’s General interpreted modal calculus. CIFOL starts with a set of cases; each expression has an extension in each case and an intension, which is the function from the cases to the respective case-relative extensions. Predication is intensional; identity is extensional. Definite descriptions are context-independent terms, and lambda-predicates (...)
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  6. Alexander Bird (2006). Potency and Modality. Synthese 149 (3):447-52.
    Let us call a property that is essentially dispositional a potency.1 David Armstrong thinks that potencies do not exist. All sparse properties are essentially categorical, where sparse properties are the explanatory properties of the type science seeks to discover. An alternative view, but not the only one, is that all sparse properties are potencies or supervene upon them. In this paper I shall consider the differences between these views, in particular the objections Armstrong raises against potencies.
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  7. Andrea Borghini (ed.) (2010). Il Genio Compreso: La Filosofia di Saul Kripke. Carocci.
  8. Baruch A. Brody (1972). De Re and de Dicto Interpretations of Modal Logic or a Return to an Aristotelean Essentialism. Philosophia 2 (1-2):117-136.
  9. Mark A. Brown (1990). "The Metaphysics of Modality" by Graeme Forbes. [REVIEW] Philosophy and Phenomenological Research 50 (3):615.
  10. Howard Burdick (1993). Non-Essentialistic Modal Logic or Meaning and Necessity Revisited. Philosophia 22 (1-2):87-93.
    Using the method of ordered pairs proposed in my 'A Logical Form for the Propositional Attitudes', a non-essentialistic modal logic is possible which avoids these oddities.
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  11. Howard Burdick (1982). A Logical Form for the Propositional Attitudes. Synthese 52 (2):185 - 230.
    The author puts forth an approach to propositional attitude contexts based upon the view that one does not have beliefs of ordinary extensional entitiessimpliciter. Rather, one has beliefs of such entities as presented in various manners. Roughly, these are treated as beliefs of ordered pairs — the first member of which is the ordinary extensional entity and the second member of which is a predicate that it satisfies. Such an approach has no difficulties with problems involving identity, such as of (...)
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  12. John P. Burgess (2013). Kripke. Polity.
    Saul Kripke has been a major influence on analytic philosophy and allied fields for a half-century and more. His early masterpiece, _Naming and Necessity_, reversed the pattern of two centuries of philosophizing about the necessary and the contingent. Although much of his work remains unpublished, several major essays have now appeared in print, most recently in his long-awaited collection _Philosophical Troubles_. In this book Kripke’s long-time colleague, the logician and philosopher John P. Burgess, offers a thorough and self-contained guide to (...)
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  13. V. C. C. (1957). Meaning and Necessity. Review of Metaphysics 10 (3):536-536.
  14. Richard Campbell (1964). Modality de Dicto and de Re. Australasian Journal of Philosophy 42 (3):345 – 359.
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  15. Fabrice Correia (2007). (Finean) Essence and (Priorean) Modality. Dialectica 61 (1):63–84.
    In Fine 1994, Kit Fine challenges the view that the notion of essence is to be understood in terms of the metaphysical modalities, and he argues that it is not essence which reduces to metaphysical modality, but rather metaphysical modality which reduces to essence. In this paper I put forward a modal account of essence and argue that it is immune from Fine’s objections. The account presupposes a non‐standard, independently motivated conception of the metaphysical modalities which I dub Priorean. Arthur (...)
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  16. Horacio Costa (2012). Quantified Modal Logic. Journal of the Indian Council of Philosophical Research 2.
    The chapter is divided in two parts. The first part gives an introduction to issues in quantified modal logic . We provide an overview of recent work in QML and we presuppose the use of a relational semantics. We discuss models for constant domains, increasing domains and varying domains and present axiomatizations for the corresponding logics. We also discuss philosophical issues related to the interpretation of the quantifiers, terms and identity and we present a first-order quantified intensional logic. A crucial (...)
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  17. M. J. Cresswell (2010). Predicate Wormism a Quinean Account of de Re Modality. Logique Et Analyse 212:449-464.
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  18. M. J. Cresswell (1973). Physical theories and possible worlds. Logique Et Analyse 16 (63):495.
    Formalized physical theories are not, as a rule, stated in intensional languages. Yet in talking about them we often treat them as if they were. We say for instance: 'Consider what would happen if instead of p's being true q were. In such a case r would be likely.' If we say this sort of thing, p, q and r appear to stand for the meanings of sentences of the theory, but meanings in some intensional sense. Now it is very (...)
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  19. M. J. Cresswell & G. E. Hughes (1996). A New Introduction to Modal Logic. Routledge.
    This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic: _An Introduction to Modal Logic_ and _A Companion to Modal Logic_. _A New Introduction to Modal Logic_ is an entirely new work, completely re-written by the authors. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing tha clarity of exposition and approachability that were essential features of their earlier works. The book takes (...)
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  20. Max Cresswell (1991). In Defence of the Barcan Formula. Logique Et Analyse 135 (136):271-282.
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  21. S. Croddy (1985). Quine and de Dicto Modal Substitution. Logique Et Analyse 28 (112):395-402.
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  22. W. S. Croddy (1985). Quine and de dicto modal substitution. Logique Et Analyse 28 (12):395.
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  23. W. Stephen Croddy (1988). Quine Against Essentialism and Quantified Modal Logic. Logique Et Analyse 31 (123-124):317-328.
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  24. John Divers (2014). Modal Reality and (Modal) Logical Space. Philosophy and Phenomenological Research 88 (3):726-733.
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  25. John Divers (1997). The Analysis of Possibility and the Possibility of Analysis. Proceedings of the Aristotelian Society 97 (2):141–160.
  26. Kit Fine (2000). Semantics for the Logic of Essence. Journal of Philosophical Logic 29 (6):543-584.
    This paper provides a possible worlds semantics for the system of the author's previous paper 'The Logic of Essence '. The basic idea behind the semantics is that a statement should be taken to be true in virtue of the nature of certain objects just in case it is true in any possible world compatible with the nature of those objects. It is shown that a slight variant of the original system is sound and complete under the proposed semantics.
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  27. Kit Fine (1995). The Logic of Essence. Journal of Philosophical Logic 24 (3):241 - 273.
  28. Kit Fine (1994). Essence and Modality. Philosophical Perspectives 8:1-16.
    It is my aim in this paper to show that the contemporary assimilation of essence to modality is fundamentally misguided and that, as a consequence, the corresponding conception of metaphysics should be given up. It is not my view that the modal account fails to capture anything which might reasonably be called a concept of essence. My point, rather, is that the notion of essence which is of central importance to the metaphysics of identity is not to be understood in (...)
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  29. Kit Fine (1989). The Problem of de Re Modality. In John Perry, J. Almog & Howard K. Wettstein (eds.), Themes From Kaplan. Oxford University Press 197--272.
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  30. Frederic B. Fitch (1967). A Theory of Logical Essences. The Monist 51 (1):104-109.
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  31. Vicky Ruth Vicklund Franks (1982). The Definite Description and Quine's Formal Attack on Quantified Modal Logic. Dissertation, University of Washington
    Quine's formal challenge to quantified modal logic involves the dual problems of referential opacity and extensional transparency. Quine's position is that the modal logician is faced with an inescapable dilemma: modal logic is either referentially opaque or extensionally transparent, and, hence, either "quantification into" modal contexts is illegitimate or the distinctions between the necessary, the possible and the actual collapse. Quine himself was convinced that the first horn of the dilemma is true, that modal logic is referentially opaque; however, I (...)
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  32. Dagfinn Føllesdal (2004). Referential Opacity and Modal Logic. Routledge.
    This landmark work provides a systematic introduction to systems of modal logic and stands as the first presentation of what have become central ideas in philosophy of language and metaphysics, from the "new theory of reference" and non-linguistic necessity and essentialism to "Kripke semantics.".
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  33. Dagfinn Føllesdal (1968). Quine on Modality. Synthese 19 (1-2):147 - 157.
    An appraisal of the current status of the modalities and of quine's arguments against them. The author accepts "quine's thesis," that one cannot quantify into referentially opaque contexts, And argues that nobody has succeeded in making sense of such quantification. However, It is shown that modal constructions, Being constructions on general terms and sentences, Can be referentially transparent and extensionally opaque and that consequently the collapse of modal distinctions warned against by quine in "word and object" can be avoided. This (...)
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  34. Alessandro Giordani (2013). A New Semantics for Systems of Logic of Essence. Studia Logica 102 (3):411-440.
    The purpose of the present paper is to provide a way of understanding systems of logic of essence by introducing a new semantic framework for them. Three central results are achieved: first, the now standard Fitting semantics for the propositional logic of evidence is adapted in order to provide a new, simplified semantics for the propositional logic of essence; secondly, we show how it is possible to construe the concept of necessary truth explicitly by using the concept of essential truth; (...)
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  35. Dominic Gregory (2011). Iterated Modalities, Meaning and A Priori Knowledge. Philosophers' Imprint 11 (3).
    Recent work on the philosophy of modality has tended to pass over questions about iterated modalities in favour of constructing ambitious metaphysical theories of possibility and necessity, despite the central importance of iterated modalities to modal logic. Yet there are numerous unresolved but fundamental issues involving iterated modalities: Chandler and Salmon have provided forceful arguments against the widespread assumption that all necessary truths are necessarily necessary, for example. The current paper examines a range of ways in which one might seek (...)
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  36. Lars Gundersen (1995). The Problem of Transworld Identity. Danish Yearbook of Philosophy 30.
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  37. Reina Hayaki (2006). Contingent Objects and the Barcan Formula. Erkenntnis 64 (1):75 - 83.
    It has been argued by Bernard Linsky and Edward Zalta, and independently by Timothy Williamson, that the best quantified modal logic is one that validates both the Barcan Formula and its converse. This requires that domains be fixed across all possible worlds. All objects exist necessarily; some – those we would usually consider contingent – are concrete at some worlds and non-concrete (but still existent) at others. Linsky and Zalta refer to such objects as ‘contingently non-concrete’. I defend the standard (...)
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  38. Reina Hayaki (2002). Actualism and Quantified Modal Logic. Dissertation, Princeton University
    It has been alleged that actualism and quantified modal logic are incompatible. My aim in this dissertation is twofold: to defend thoroughgoing actualism with respect to possible objects, and to present a modified semantics for quantified modal logic that is compatible with such a position. The basic strategy is to draw on the parallels between fictions and possible worlds to develop a hierarchical system of worlds-within-worlds ;Actualists usually take first-order modal statements as being about the right objects, by stipulation. Any (...)
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  39. Arata Ishimoto & Yoshimi Fujikawa (1968). The Construction of a Subcalculus of Lewis' S1 and a Solution of its Decision Problem. Kagaku Tetsugaku 1:9-22.
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  40. Nicholas K. Jones (2016). Object as a Determinable. In Mark Jago (ed.), Reality Making. OUP 121-151.
    This paper outlines a heterodox and largely unexplored conception of objecthood according to which the notion of an individual object is a determinable. §1 outlines the view. §2 argues that the view is incompatible with a natural analysis of kind membership and, as a consequence, undermines the Quinean distinction between ontology and ideology. The view is then used to alleviate one source of Quinean hostility towards non-trivial restrictions on de re possibility in §3, and to elucidate Fine’s neo-Aristoteltian, non-modal conception (...)
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  41. Philip V. Kargopoulos (1984). Realism, Relativism and Reference. University Microfilms International.
    The central thesis of this dissertation is that the recently proposed Causal Theories of Reference by K. Donnellan, H. Putnam, and especially S. Kripke provide support for Scientific Realism as developed in the theories of J. J. C. Smart, H. Putnam, and especially R. Boyd, on the face of the most serious challenge to scientific objectivity contained in the writings of the Relativists S. Toulmin, N. R. Hanson, T. S. Kuhn, and P. Feyerabend. I have argued accordingly that all the (...)
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  42. Daniel Michael Kervick (1997). The Logic of Contingent Existence. 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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  43. Antti Keskinen (2013). Quine on Objects and De Re Modality. European Journal of Analytic Philosophy 8 (2):4-17.
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  44. S. Knuuttila (ed.) (1980). Reforging the Great Chain of Being: Studies of the History of Modal Theories. Reidel.
    JAAKKO HINTIKKA GAPS IN THE GREAT CHAIN OF BEING: AN EXERCISE IN THE METHODOLOGY OF THE HISTORY OF IDEAS* For some historians, to understand everything is to pardon everything. For others, like Lord Acton, history is not only a judge, ...
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  45. Saul A. Kripke (2015). Quantified Modality and Essentialism. Noûs 50 (2).
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  46. Leonard Linsky (1971). Reference and Modality. London,Oxford University Press.
    1. Reference and modality by W. V. O. Quine.--2. Modality and description by A. F. Smullyan.--3. Extensionality by R. B. Marcus.--4. Quantification into causal contexts by D. Føllesdal.--5. Semantical considerations on modal logic by S. A. Kripke.--6. Essentialism and quantified modal logic by T. Parsons.--7. Reference, essentialism, and modality by L. Linsky.--8. Quantifiers and propositional attitudes by W. V. O. Quine.--9. Quantifying in by D. Kaplan.--10. Semantics for propositional attitudes by J. Hintikka.--11. On Carnap's analysis of statements of assertion and (...)
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  47. Joao Marcos (2005). Logics of Essence and Accident. Bulletin of the Section of Logic 34 (1):43-56.
    We say that things happen accidentally when they do indeed happen, but only by chance. In the opposite situation, an essential happening is inescapable, its inevitability being the sine qua non for its very occurrence. This paper will investigate modal logics on a language tailored to talk about essential and accidental statements. Completeness of some among the weakest and the strongest such systems is attained. The weak expressibility of the classical propositional language enriched with the non-normal modal operators of essence (...)
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  48. Ruth Barcan Marcus (1967). Essentialism in Modal Logic. Noûs 1 (1):91-96.
  49. Ruth Barcan Marcus (1961). Modalities: Philosophical Essays. Oxford University Press.
    Based on her earlier ground-breaking axiomatization of quantified modal logic, the papers collected here by the distinguished philosopher Ruth Barcan Marcus cover much ground in the development of her thought, spanning from 1961 to 1990. The first essay here introduces themes initially viewed as iconoclastic, such as the necessity of identity, the directly referential role of proper names as "tags", the Barcan Formula about the interplay of possibility and existence, and alternative interpretations of quantification. Marcus also addresses the putative puzzles (...)
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  50. Ruth Barcan Marcus, Walter Sinnott-Armstrong, Diana Raffman & Nicholas Asher (eds.) (1995). Modality, Morality, and Belief: Essays in Honor of Ruth Barcan Marcus. Cambridge University Press.
    Modality, morality and belief are among the most controversial topics in philosophy today, and few philosophers have shaped these debates as deeply as Ruth Barcan Marcus. Inspired by her work, a distinguished group of philosophers explore these issues, refine and sharpen arguments and develop new positions on such topics as possible worlds, moral dilemmas, essentialism, and the explanation of actions by beliefs. This 'state of the art' collection honours one of the most rigorous and iconoclastic of philosophical pioneers.
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