Chapter

Semantics for Logical Necessity

Nino B. Cocchiarella and Max A. Freund

in Modal Logic

Published in print August 2008 | ISBN: 9780195366587
Published online October 2011 | e-ISBN: 9780199851898 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780195366587.003.0004
Semantics for Logical Necessity

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This chapter initially describes possible-worlds semantics, which was first introduced by Rudolf Carnap in 1946 in terms of his state-description semantics, for sentential modal logic. Carnap was not concerned with different notions of necessity and possibility, but only with logical necessity and logical possibility. He proposed a criterion of adequacy that any formal semantics for these notions must satisfy in his account of logical necessity and logical possibility. The authors construct a formal semantics and modal logic that satisfies Carnap's criterion in terms of the ontology of logical atomism — an ontology that was implicit in Carnap's state-description semantics.

Keywords: possible-worlds semantics; Rudolf Carnap; logical necessity; logical possibility; semantics; modal logic; logical atomism

Chapter.  5123 words. 

Subjects: Philosophy of Language

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