Paradoxes of Interaction?

Johannes Stern, Martin Fischer

Research output: Contribution to journalArticle (Academic Journal)

Abstract

Since Montague’s work it is well known that treating a single modality as a predicate may lead to paradox. In their paper “No Future”, Horsten and Leitgeb (2001) show that if the two temporal modalities are treated as predicates paradox might arise as well. In our paper we investigate whether paradoxes of multiple modalities, such as the No Future paradox, are genuinely new paradoxes or whether they “reduce” to the paradoxes of single modalities. In order to address this question we develop a notion of reducibility based on a version of Smoryński Diagonalized Operator Logic. We show that there are reducible multimodal paradoxes as well as irreducible paradoxes of interaction. In particular, we show the No Future paradox to be an irreducible paradox according to our notion of reducibility.
Original languageEnglish
Pages (from-to)287-308
Number of pages22
JournalJournal of Philosophical Logic
Volume44
Issue number3
Early online date7 Jun 2014
DOIs
Publication statusPublished - 2015

Keywords

  • Modal paradox Multimodal paradoxes Paradoxes of interaction Syntactical treatments of modalities Modal logic Liar paradox Theories of truth Fixed-points Fixed-point logic

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