Syntactical Treatments of Interacting Modalities

我们的目标是提供一个系统的框架，相互作用的方式。与将模态作为算子的主流方法相反，我们设想将它们作为谓词对待。我们的方法采纳了卡尔纳普和奎因的建议，这些建议更符合我们的一些语言或哲学直觉。此外，有证据表明，将模态作为谓词处理比运营商的方法更普遍。虽然已经研究了作为谓词的单个模态，但还没有系统地考虑到联合处理的多个模态。主要目标是开发作为谓词的交互模态系统。提供这样一个框架的主要障碍之一是避免自我指涉悖论，例如~说谎者悖论或知者悖论威胁着谓词性解释。受真理理论的启发，我们希望发展语义方法以及公理理论，所有这些都是在几个相互作用的模态被形式化为谓词的设置制定。形式系统和工具将被证明是有用的，当应用于哲学论证时，采用几种模态，例如~我们有信心提供新的见解与激烈争论的惠誉悖论，因此也为现实主义/反现实主义的辩论。

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.