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Being ForEvaluating the Semantic Program of Expressivism$
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Mark Schroeder

Print publication date: 2008

Print ISBN-13: 9780199534654

Published to Oxford Scholarship Online: September 2008

DOI: 10.1093/acprof:oso/9780199534654.001.0001

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Composition and Logic

Composition and Logic

Chapter:
(p.65) 5 Composition and Logic
Source:
Being For
Author(s):

Mark Schroeder (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199534654.003.0005

This chapter shows that once we have accepted the solution to the negation problem from Chapter 4, this leads immediately to solutions to analogous problems about conjunction and disjunction, and in fact to a constructive semantics for a very simple normative language with the expressive power of propositional logic. The semantics for this simple language is outlined, and inconsistency, entailment, and validity are defined. It is proven, given very simple assumptions, that the semantics yields the correct results about which sentences are inconsistent with which. Logical inconsistency is distinguished from ordinary inconsistency and given a precise definition, and it is shown why Geach's original moral modus ponens argument is logically valid. Finally, a loose end about the inconsistency of ‘murdering is wrong’ and ‘not murdering is wrong’ is set aside.

Keywords:   conjunction, disjunction, propositional logic, inconsistency, entailment, validity, logical inconsistency, logical entailment, logical validity, Geach

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