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ModalityMetaphysics, Logic, and Epistemology$
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Bob Hale and Aviv Hoffmann

Print publication date: 2010

Print ISBN-13: 9780199565818

Published to Oxford Scholarship Online: September 2010

DOI: 10.1093/acprof:oso/9780199565818.001.0001

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Logical Necessity *

Logical Necessity *

(p.35) 2 Logical Necessity*

Ian Rumfitt (Contributor Webpage)

Oxford University Press

This chapter explains the notion of broadly logical necessity via the principle that ‘It is logically necessary that A’ is equivalent to ‘It is logically contradictory that not A’. The relevant notion of logical contradiction is cognate to that of absolute logical consequence: a conclusion is an absolute consequence of some premisses if it follows from them no matter what ancillary or background assumptions are made. The notion of logical necessity (so understood) is defended against sceptics (notably Russell). The relationship between logical and metaphysical necessity is explored, and Ian McFetridge's thesis that logical necessity is the strongest form of non-epistemic necessity is defended. The account of logical necessity is then deployed in elucidating Gareth Evans's distinction between deep and superficial forms of necessity, and that distinction is in turn employed to rebut Dummett's argument that the logic of metaphysical necessity cannot include the Brouwerian axiom.

Keywords:   logical necessity, logical consequence, metaphysical necessity, deep versus superficial necessity, Brouwerian axiom, Dummett, Evans, McFetridge, Russell

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