Embracing intensionality: Paradoxicality and semi-truth operators in fixed point models

The Embracing Revenge account of semantic paradox avoids the expressive limitations of previous approaches based on the Kripkean fixed point construction by replacing a single language with an indefinitely extensible sequence of languages, each of which contains the resources to fully characterize the semantics of the previous languages. In this paper we extend the account developed in Cook (2008), Cook (2009), Schlenker (2010), and Tourville and Cook (2016) via the addition of intensional operators such as "is paradoxical". In this extended framework we are able to characterize the difference between sentences, such as the Liar and the Truth-teller, that receive the same semantic value in minimal fixed points yet seem to involve distinct semantic phenomena.