caa a22 4500 605539014 CHVBK 20210128100904.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10992-014-9319-5 doi (NATIONALLICENCE)springer-10.1007/s10992-014-9319-5 Paradoxes of Interaction? [Elektronische Daten] [Johannes Stern, Martin Fischer] 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. Springer Science+Business Media Dordrecht, 2014 Modal paradox nationallicence Multimodal paradoxes nationallicence Paradoxes of interaction nationallicence Syntactical treatments of modalities nationallicence Modal logic nationallicence Liar paradox nationallicence Theories of truth nationallicence Fixed-points nationallicence Fixed-point logic nationallicence Stern Johannes Munich Center for Mathematical Philosophy, LMU Munich, Fakultät für Philosophie, Wissenschaftstheorie und Religionswissenschaft, Geschwister-Scholl-Platz 1, 80539, München, Germany aut Fischer Martin Munich Center for Mathematical Philosophy, LMU Munich, Fakultät für Philosophie, Wissenschaftstheorie und Religionswissenschaft, Geschwister-Scholl-Platz 1, 80539, München, Germany aut Journal of Philosophical Logic Springer Netherlands 44/3(2015-06-01), 287-308 0022-3611 44:3<287 2015 44 10992 https://doi.org/10.1007/s10992-014-9319-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10992-014-9319-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Stern Johannes Munich Center for Mathematical Philosophy, LMU Munich, Fakultät für Philosophie, Wissenschaftstheorie und Religionswissenschaft, Geschwister-Scholl-Platz 1, 80539, München, Germany aut NATIONALLICENCE 700 1- Fischer Martin Munich Center for Mathematical Philosophy, LMU Munich, Fakultät für Philosophie, Wissenschaftstheorie und Religionswissenschaft, Geschwister-Scholl-Platz 1, 80539, München, Germany aut NATIONALLICENCE 773 0- Journal of Philosophical Logic Springer Netherlands 44/3(2015-06-01), 287-308 0022-3611 44:3<287 2015 44 10992