In this paper, I will defend a new compositional semantics for single-domain free logic. This semantics makes use of a distinction between the semantic value of a singular term and its semantic referent. The semantic value of a singular term is conceived of as a set that either contains the semantic referent or no element at all. The semantic referent is the object that the term designates. Before I will introduce this new semantics for single-domain predicate and an S5-type modal (...) logic in detail, I will present five related problems of compositionality of the standard semantics for these logical systems. After that I will show in detail how my new proposed alternative semantics can be used to solve nearly all of the outlined five problems. (shrink)

In this paper, I will show that typical formal semantic reconstructions of the rigidity of proper names neglect the important aspect that the rigidity of names is determined by our ordinary use of a name relative to the actual world. This fact was clearly pointed out by Kripke, but overlooked by the subsequent discussion concerning this topic. Based on this diagnosis, I will distinguish three different actualized notions of rigidity. Firstly, I will introduce two different new varieties of known versions (...) of rigidity; namely, actualized persistent and actualized obstinate rigidity. Secondly, I will make use of the tools provided by free logic and introduce a new and overlooked version of rigidity, which I will call actually restricted rigidity. Against this background, I will argue that we have different options to formally model the rigidity of proper names in natural languages. Which option we choose, mainly depends on our philosophical background assumptions. For someone who believes in non-existent objects and the possibility of naming such objects, it is the best choice to hold that proper names are actually obstinately rigid designators. For someone who rejects non-existent objects and the possibility of naming such objects, actually restricted rigidity is a better choice than actualized persistent rigidity. (shrink)

In this essay I will defend a novel version of the indexical view on proper names. According to this version, proper names have a relatively sparse truth-conditional meaning that is represented by their rigid content and indexical character, but a relatively rich use-conditional meaning, which I call the (contextual) constraint of a proper name. Firstly, I will provide a brief outline of my favoured indexical view on names in contrast to other indexical views proposed in the relevant literature. Secondly, two (...) general motivations for an indexical view on names will be introduced and defended. Thirdly, I will criticize the two most popular versions of the indexical view on names: formal variable accounts and salience-based formal constant accounts. In the fourth and final section, I will develop my own use-conditional indexical view on names in three different steps by confronting an initial version of this view with three different challenges. (shrink)