The Completeness of Carnap's Predicate Logic

  • Max Cresswell Victoria University of Wellington


The paper first proves the completeness of the (non-modal) first-order predicate logic presented in Carnap’s 1946 article ‘Modalities and quantification’. By contrast the modal logic defined by the semantics Carnap produces is unaxiomatisable. One can though adapt Carnap’s semantics so that a standard completeness proof for a Carnapian version of predicate S5 turns out to be available.


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Author Biography

Max Cresswell, Victoria University of Wellington
Emeritus Professor of the University Professor of Philosophy
How to Cite
CRESSWELL, Max. The Completeness of Carnap's Predicate Logic. The Australasian Journal of Logic, [S.l.], v. 11, n. 1, apr. 2014. ISSN 1448-5052. Available at: <>. Date accessed: 02 july 2020. doi: