Paradoxes of Interaction?

Journal of Philosophical Logic 44 (3):287-308 (2015)
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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 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



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Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
The Logic of Provability.George Boolos - 1993 - Cambridge and New York: Cambridge University Press.
A paradox regained.D. Kaplan & R. Montague - 1960 - Notre Dame Journal of Formal Logic 1 (3):79-90.

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