Composition and Logic
Composition and Logic
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
Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
Please, subscribe or login to access full text content.
If you think you should have access to this title, please contact your librarian.
To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .
