Worlds and Models in Bayart and Carnap

  • Max Cresswell Victoria University


In the early days of the semantics for modal logic the `possible worlds' were thought of as models or interpretations. This was particularly so when the interpretation was of \emph{logical} necessity or possibility, where this was understood in terms of validity. Arnould Bayart in 1958 may have been the first modal logician to argue explicitly against the identification of necessity and validity. This note contrasts his semantics with that provided by Rudolf Carnap in 1946, and examines Bayart's proof that if you identify necessity with validity then certain theorems of S5 are not valid. The proof is then examined using Carnap's semantics.


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How to Cite
CRESSWELL, Max. Worlds and Models in Bayart and Carnap. The Australasian Journal of Logic, [S.l.], v. 13, n. 1, jan. 2016. ISSN 1448-5052. Available at: <>. Date accessed: 02 july 2020. doi: