Quantifiers, Propositions and Identity: Admissi. Goldblatt<|

Quantifiers, Propositions and IdentityAdmissible Semantics for Quantified Modal and Substructural Logics\nAuthor(s): Robert Goldblatt\nFormat: Hardback\nPublisher: Cambridge University Press, United Kingdom\nImprint: Cambridge University Press\nISBN-13: 9781107010529, 978-1107010529\nSynopsis\nMany systems of quantified modal logic cannot be characterised by Kripke's well-known possible worlds semantic analysis. This book shows how they can be characterised by a more general 'admissible semantics', using models in which there is a restriction on which sets of worlds count as propositions. This requires a new interpretation of quantifiers that takes into account the admissibility of propositions. The author sheds new light on the celebrated Barcan Formula, whose role becomes that of legitimising the Kripkean interpretation of quantification. The theory is worked out for systems with quantifiers ranging over actual objects, and over all possibilia, and for logics with existence and ide.