Reconciling Austinian and Russellian accounts of the liar paradox (Q1337509)

In Ch. 11 of \textit{J. Barwise} and \textit{J. Etchemendy's} book \textit{The liar} (1987; Zbl 0678.03001), the following, called the Reflection Theorem, is proved: for every maximal Russellian model, \(M\), there is a possible (Austinian) situation, such that \(M \models \text{Exp}_ R (\varphi)\) iff \(\text{Exp}_ A (\varphi,m)\) is true, where \(\varphi\) is any sentence in a language without the demonstrative operators, \textit{that}, and \(\text{Exp}_ R(\varphi)\) and \(\text{Exp}_ A (\varphi,m)\) are the Russellian and Austinian propositions expressed by \(\varphi\) (in \(m\)), respectively. This paper proves a generalisation of the Theorem according to which (in Barwise and Etchemendy's terms) \(M\) is a weak model, \(m\) is a partial model, and \(\varphi\) may contain the demonstratives. Definitions of various notions are not always the same as those given by Barwise and Etchemendy, but are proved equivalent in appendices.