2005Unpublished venueRequires access

invention is the mother of necessity: modal logic, modal semantics, and modal metaphysics

Greg Restall

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Abstract

Modal logic is a well-established field, and the possible worlds se- mantics of modal logics is essential to our understanding of the logical features of modal concepts such as possibility and necessity. However, the signifi- cance of possible worlds models for a genuine theory of meaning—let alone for metaphysics—is less clear. In this paper I shall explain how and why the use of the concepts of necessity and possibility could arise (and why they have the logical behaviour charted out by standard modal logics) without either taking the notions of necessity or possibility as primitive, and without starting with possible worlds. Once modal logic is explained, we can give an account of possible worlds, and explain why possible worlds semantics is a natural fit for modal logic without being the source of modal concepts.

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Modal logic is a well-established field, and the possible worlds se- mantics of modal logics is essential to our understanding of the logical features of modal concepts such as possibility and necessity. However, the signifi- cance of possible worlds models for a genuine theory of meaning—let alone for metaphysics—is less clear. In this paper I shall explain how and why the use of the concepts of necessity and possibility could arise (and why they have the logical behaviour charted out by standard modal logics) without either taking the notions of necessity or possibility as primitive, and without starting with possible worlds. Once modal logic is explained, we can give an account of possible worlds, and explain why possible worlds semantics is a natural fit for modal logic without being the source of modal concepts.

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Available abstract

Modal logic is a well-established field, and the possible worlds se- mantics of modal logics is essential to our understanding of the logical features of modal concepts such as possibility and necessity. However, the signifi- cance of possible worlds models for a genuine theory of meaning—let alone for metaphysics—is less clear. In this paper I shall explain how and why the use of the concepts of necessity and possibility could arise (and why they have the logical behaviour charted out by standard modal logics) without either taking the notions of necessity or possibility as primitive, and without starting with possible worlds. Once modal logic is explained, we can give an account of possible worlds, and explain why possible worlds semantics is a natural fit for modal logic without being the source of modal concepts.

Key concepts: Accessibility relation, Modal logic, S5, Normal modal logic, Possible world, Modal, Multimodal logic, Modal μ-calculus

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