Syntactical Treatments of Interacting Modalities

点击翻译按钮获取中文摘要

We aim at providing a systematic framework for interacting modalities. In contrast to the mainstream approach of modalities as operators we envisage treating them as predicates. Our approach takes up proposals by Carnap and Quine that agree better with some of our linguistic or philosophical intuitions. Furthermore, there is evidence that treating modalities as predicates is more general than the operator approach. Whereas single modalities treated as predicates have been investigated, there is no systematic account of multiple modalities treated jointly.The principal objective is to develop systems for interacting modalities treated as predicates. One of the main obstacles of providing such a framework is to avoid self-referential paradoxes as e.g.~the liar paradox or the paradox of the knower which threaten the predicate accounts. Inspired by theories of truth we wish to develop semantic approaches as well as axiomatic theories where all of these are formulated in a setting of several interacting modalities being formalized as predicates. The formal systems and tools will prove useful when applied to philosophical arguments employing several modalities, e.g.~we are confident to provide new insights in connection with the hotly debated Fitch paradox and therefore also for the realist/anti-realist debate.