David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Journal of Philosophical Logic 34 (5/6):621-649 (2005)
Quantified modal logic has reputation for complexity. Completeness results for the various systems appear piecemeal. Different tactics are used for different systems, and success of a given method seems sensitive to many factors, including the specific combination of choices made for the quantifiers, terms, identity, and the strength of the underlying propositional modal logic. The lack of a unified framework in which to view QMLs and their completeness properties puts pressure on those who develop, apply, and teach QML to work with the simplest systems, namely those that adopt the Barcan Formulas and predicate logic rules for the quantifiers. In these systems, the quantifier ranges over a fixed domain of possible individuals, so advocates of these logics are sometimes called possibilists. A literature has grown up rationalizing the choice of possibilist logics despite ordinary intuitions that the resulting theorems are too strong.Williamson even takes the view that the complications to be faced within the weaker logics “are a warning sign of philosophical error”. It is the purpose of this paper to show that abandonment of the weaker QMLs is excessively fainthearted, since most QMLs can be given relatively simple formulations within one general framework. Given the straightforward nature of the systems and their completeness results, the purported complications evaporate, along with any philosophical warnings one might have associated with them.
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References found in this work BETA
Timothy Williamson (1998). Bare Possibilia. Erkenntnis 48 (2/3):257--73.
Melvin Fitting, R. Mendelsohn & Roderic A. Girle (2002). First-Order Modal Logic. Bulletin of Symbolic Logic 8 (3):429-430.
Melvin Fitting (2004). First-Order Intensional Logic. Annals of Pure and Applied Logic 127 (1-3):171-193.
Max Cresswell (1991). In Defence of the Barcan Formula. Logique Et Analyse 135 (136):271-282.
Citations of this work BETA
Nuel Belnap & Thomas Müller (2013). BH-CIFOL: Case-Intensional First Order Logic. Journal of Philosophical Logic (2-3):1-32.
Horacio Arló-Costa & Eric Pacuit (2006). First-Order Classical Modal Logic. Studia Logica 84 (2):171 - 210.
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