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Logical Pluralism$
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JC Beall and Greg Restall

Print publication date: 2005

Print ISBN-13: 9780199288403

Published to Oxford Scholarship Online: October 2011

DOI: 10.1093/acprof:oso/9780199288403.001.0001

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Classical Logic

Classical Logic

(p.34) (p.35) Chapter 4 Classical Logic
Logical Pluralism

JC Beall

Oxford University Press

Logical pluralism addresses the following conditions. First, the settled core of consequence is given in the Generalised Tarski Thesis (GTT). Second, an instance of GTT is obtained by a specification of the cases in GTT, and a specification of the relation is true in a case. Such a specification can be seen as a way of spelling out truth conditions. Third, an instance of GTT is admissible if it satisfies the settled role of consequence, and if its judgements about consequence are necessary, normative, and formal. Fourth, a logic is given by an admissible instance of GTT. Lastly, there are at least two different admissible instances of GTT. Logic is a matter of preservation of truth in all cases, which lies at the heart of logical consequence, the settled core of follows from. This chapter considers two well-known specifications of cases x : possible worlds and models for classical predicate logic. It notes the extent to which the canvassed accounts of consequence are admissible: the extent to which their respective judgements are necessary, normative, and formal.

Keywords:   logical pluralism, classical predicate logic, admissibility, plurality, Generalised Tarski Thesis, judgements, logical consequence

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