The aim of this paper is to make the case for the obstinacy thesis. This is the thesis that proper names like ‘Hitler’, demonstratives like ‘this’, pure indexicals like ‘I’, and natural kind terms like ‘water’ and ‘gold’, are obstinately rigid terms. An obstinately rigid term is one that refers to the object that is its actual referent with respect to every possible world (hence, a fortiori, even with respect to worlds where that object does not exist). This form of (...) rigidity is stronger than the usual Kripkean one and has been notoriously explored by David Kaplan (Kaplan 1989a: 492-3; Kaplan 1989b: 569-71). Yet, the obstinacy thesis seems implausible to many philosophers and is worth substantive argument. For convenience, we focus our attention on proper names; but most of our remarks could be easily generalized to other unstructured singular terms. We shall take for granted Saul Kripke’s semantical doctrine that proper names are rigid in the general sense of the term and argue that their rigidity should take the specific form of obstinacy rather than persistence. (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)

Some hold that proper names and indexicals are “Kaplan rigid”: they designate their designata even in worlds where the designata don’t exist. An argument they give for this is based on the analogy between time and modality. It is shown how this argument gains forcefulness at the expense of carefulness. Then the argument is criticized as forming a part of an inconsistent philosophical framework, the one with which David Kaplan and others operate. An alternative account of a certain class of (...) negative existentials is developed, one which eliminates both the inconsistency and the need for Kaplan rigidity. After all, mustn’t whatever is referred to exist? (shrink)

Names are rigid designators, but what kind of rigidity do they exhibit? Both “obstinately” and “persistently” rigid designators pick out O at every world at which they pick out anything at all. They differ in that obstinately rigid designators also pick out O at worlds at which O fails to exist; persistently rigid designators have no extension whatsoever at worlds at which O fails to exist. The question whether names are obstinate or persistent arises in two contexts: in arguments against (...) rigidified descriptivism (on the grounds that names and rigidified descriptions exhibit different kinds of rigidity) and in considerations about what it means for an expression to be “directly referential.” This paper contends that names are persistent, not obstinate. The position thus clarifies the relationship between Millian theories of names and rigid designation, in addition to undermining attempts to rehabilitate the modal argument against rigidified descriptivism. (shrink)

Joseph Almog says concerning “a certain locus where Quine doesn’t exist…qua evaluation locus, we take to it [singular] propositions involving Quine [as a constituent] which we have generated in our generation locus.” This seems to be either murder, or worse, self-contradiction. It presumes that certain designators designate their designata even at loci where the designata do not exist, i.e., the designators have “Kaplan rigidity.” Against this view, this paper argues that negative existentials such as “Quine does not exist” are true (...) only at ordered couples of loci (times or possible worlds) < l, l’ > such that the constituents of the truthmaker are the designatum itself from l and whatever corresponds to “does not exist” from l’. (shrink)

The main chapters of this thesis develop and defend a version of two-dimensional semantics that provides an account of Kripkean a posteriori necessity.