Rigid designators designate whatever they do in all possible worlds. Mathematical definite descriptions are usually considered paradigmatic examples of such expressions. The main aim of the present paper is to challenge this view. It is argued that mathematical definite descriptions cannot be rigid in the same sense as ordinary empirical definite descriptions because—assuming that mathematical facts are not determined by goings on in possible worlds—mathematical descriptions designate whatever they do independently of possible worlds. Nevertheless, there is a widespread practice of (...) treating mathematical definite descriptions as rigid. Apart from this, there might be theoretical reasons for admitting that they are rigid in some sense. The second part of the paper suggests a way out. Borrowing from ideas proposed by Kit Fine, it develops and defends an extended notion of rigidity, which can be applied to mathematical definite descriptions. Importantly, this notion is fully compatible with the claim that mathematical facts are independent of possible worlds. (shrink)

Kripke has argued that definitions of units of measurements provide examples of statements that are both contingent and a priori. In this paper I argue that definitions of units of measurement are intended to be stipulations of what Kripke calls "theoretical identities": a stipulation that two terms will have the same rigid designation. Hence such a definition is both a priori and necessary. The necessity arises because such definitions appeal to natural kind properties only, which on Kripke's account are necessary.

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)

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)

Summary of Anna Pilatova’s doctoral thesis A User’s Guide to Proper Names, Their Semantics And Pragmatics The origins of this work go all the way back to my reading of Kripke’s Naming and Necessity in 1993. It had left me with a feeling of dissatisfaction that lingered long enough to inspire my MA thesis (on Internalism and Externalism in the Theories of Reference), and finally inspired the current work. Over time, I became acquainted with other influential accounts of reference of (...) proper names, but my unease with essentialism and wariness of direct designation remained. In the User’s Guide to Proper Names, I seized the opportunity to analyse what I thought was problematic with the mainstream theories of reference of proper names. I tried to tease apart a number of related doctrines about the behaviour of proper names, and thus arrive at a better understanding of how the various parts of the theories of reference I chose to analyse are related. This helped me to develop my own proposal regarding both the semantics and the pragmatics of proper names. The Guide is organised around a particular approach to the tasks of a semantic theory. According to this view, proposed by Stalnaker, a semantic theory dealing with proper names should account for the descriptive semantics of names, their foundational semantics, and the semantics of modal statements in which they figure. Descriptive semantics focuses on the contribution a proper name makes to the truth-value of sentences in which it occurs. Based on such an analysis, a proper name is assigned a semantic value, which is supposed to provide us with an interpretation of that name. A crucial part of this task is to see just what kind of thing the semantic value of a proper name is. In interpreting sentences containing proper names, one can, and often does, use the notion of possible worlds. This is especially true if the sentences in question are modal. There are various approaches to modality, which carry with them different sets of presuppositions. An analysis of the systematic features and presuppositions of various possible-world frameworks is a part of the task of the semantics of modal statements. Another task of semantics of modal statements is to investigate whence the constraints on possible worlds used in analysing these statements should derive, that is, whether, and to what degree, they should derive from the descriptive or the foundational part of the semantic enterprise. Both of these parts of a semantic theory have the potential to make predictions about the foundational semantics of proper names, which deals with the speaker’s behaviour and communication. Foundational semantics aims at answering the following question: What makes it the case that the language spoken by a particular individual or community has the very descriptive semantics it has? In this investigation, one looks at the speaker, her intentions and communicative goals, and tries to look at the strategies she uses to get her (linguistic) point across. To show the usefulness of organising the User’s Guide to Proper Names around these distinctions, and to provide their proper characterisation, is the task of the first part of the introductory first chapter, Outlining the Field and Introducing Some of the Players. In the second part of the same chapter, Setting the Scene, I give a preliminary outline of some of the notions needed to describe the theories of reference that are later investigated, that is mainly the theories proposed by Kripke, Kaplan, Lewis, and Stalnaker. The second chapter, Descriptive Semantics, focuses on the descriptive semantics proposed by Kripke and Kaplan for proper names. In the first part of the chapter, I introduce several arguments in favour of rigid designation. A closer look reveals that none of the three arguments in question -- the modal, the epistemological, and the semantic one -- is actually an argument for rigid designation. They all just argue against some forms of descriptivism. Moreover, in the case of the modal and the epistemological argument, it is relatively easy to find forms of descriptivism that are immune to the lines of reasoning proposed in these arguments. The semantic argument seems to be the strongest of the three. An analysis of a direct argument for rigid designation highlights the connection between rigid designation and certain preconceptions about the identity of individuals. A further investigation of the notion of identity of individuals across possible worlds emerges at this point as an important issue to tackle. It also becomes clear that rigid designation alone cannot fully determine the Kripkean picture of names as non-descriptive entities referring without a mediation of any sort of conceptual content. In the second part of Chapter 2, I introduce the basic notions of Kaplan’s approach to the descriptive semantics of proper names. It turns out that in order to derive the familiar Kripkean picture of proper names, one has to presuppose direct reference for names and at least some version of haecceitism for the individuals in question. While, as we show, Kaplan’s framework does not work well for proper names, it gives us conceptual tools that help us in our undertaking. In the third chapter, Modal Statements, Individuals, and Essences, I analyse three different approaches to building a possible-world framework, Lewis’s, Kripke’s, and Stalnaker’s. In each case, the same questions are asked: What is the motivation and intended field of application of this framework? What are the ontological commitments of the approach? What form of essentialism, if any, does it imply? How does it deal with the notion of an individual? In Lewis’s case, the main problem turns out to be the theory of counterparts, which is, as I show, an integral part of his approach. The concept of an individual implied by it does not seem to correspond to any intuitive reading of counterfactual statements involving individuals. The investigation of Kripke’s framework focuses on describing the weakest form of essentialism that has to be presupposed to make the proposal work. Once that is concluded, I analyse the essentialism Kripke actually proposes, and the motivation and presuppositions on which it rests. I conclude that its motivation cannot be said to come from an analysis of language and that it presupposes a particular form of scientific realism. The rest of the chapter is devoted to a reconstruction and analysis of Stalnaker’s possible world framework, which turns out to be rather more cautious about metaphysical presuppositions and more suited for an analysis of natural language. As in the two previous proposals, I try to reconstruct the notion of actual world that is presupposed here. In the fourth chapter, Foundational Semantics, I investigate the notion of proposition implied by Lewis’s, Kripke’s, and Stalnaker’s approach. I focus on propositions containing proper names, and analyse the way in which each of the conceptions mentioned above is vulnerable to the problem of logical omniscience. An analysis of Lewis’s framework reveals that the concept of proposition implied by it is so weak as to be rather uninteresting. An investigation of Kripke’s concept of proposition deals not only with the systematic issues, but also with the Pierre puzzle and various attempts at solving it. I present a number of different approaches to the problem and compare their merits. Stalnaker is very worried about the problem of logical omniscience, and yet it turns out that his conception is less vulnerable to the adverse consequences of the problem of logical omniscience than other frameworks we investigate. I point out that various pragmatic features of Stalnaker’s framework (the epistemic nature of his possible-world framework, the Gricean principles built into the notion of assertion) help to counterbalance and mitigate the scope of the problem of logical omniscience within it. In Chapter 5, User-friendly Descriptive Semantics, I present and motivate my own proposal for the descriptive semantics of proper names and the treatment of modal statements in which they figure. Basically, the aim is to preserve the notion of names as rigidly designating expressions while admitting as little metaphysics as possible. Working with epistemic possible worlds whose domain is in each case co-determined by a particular context enables me to develop a very intuitive plausible notion of individual, to which a name can be said to refer rigidly. The interpretation of modal statements is then driven not by essentialist constraints in the common sense of the term, but by context-derived limitations, which seems to be a more natural approach. In the sixth and last chapter, Names, Indexicality, and Ambiguity, I develop a view of foundational semantics inspired by the pragmatic observation that in common parlance one can say that a name, `John Smith’ for instance, can refer to numerous individuals. A lot of attention is given to the ontology of names, and the question `What is a name?’ delivers answers which are then used in a discussion about whether names should be seen as indexical or ambiguous. I adopt the ambiguity view, and propose a way of using a Stalnakerian possible-world framework to derive intuitively plausible results for some difficult cases. The weight of the discussion all through the guide rests in an examination of different kinds of presuppositions implied by various possible-world frameworks and the notion of the individual used in accounts of the behaviour of proper names. In my own account of these issues, I do without any metaphysical assumptions and aim at describing communication in terms accessible to its participants. (shrink)