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Modal LogicAn Introduction to its Syntax and Semantics$
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Nino B. Cocchiarella and Max A. Freund

Print publication date: 2008

Print ISBN-13: 9780195366587

Published to Oxford Scholarship Online: October 2011

DOI: 10.1093/acprof:oso/9780195366587.001.0001

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The Semantics of Quantified Modal Logic

The Semantics of Quantified Modal Logic

Chapter:
(p.152) (p.153) Chapter 8 The Semantics of Quantified Modal Logic
Source:
Modal Logic
Author(s):

Nino B. Cocchiarella

Max A. Freund

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780195366587.003.0008

The authors develop semantics for first-order modal predicate logic in terms of standard model theory, the models of which we take to be set-theoretic counterparts of possible worlds. A primary semantics for logical necessity as based on the notion of “all possible worlds” of a logical space is also described and shown to be essentially incomplete. The thesis that concepts that apply necessarily to some objects necessarily apply to all objects is the modal thesis of anti-essentialism and is valid in this semantics, however, which is as it should be for logical necessity. In other words, logical necessity does not discriminate between objects and the concepts they fall under.

Keywords:   first-order modal predicate logic, standard model theory, possible worlds, anti-essentialism, logical necessity

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