Names and Context

A Use-Sensitive Philosophical Account

Dolf Rami

• Publisher: Bloomsbury Academic
• Year: 2021
• ISBN:
  9781350180642
• Edition: 1
• Topic: Philosophy
• Subtopic: Language in Philosophy

Dolf Rami contributes to contemporary debates about the meaning and reference of proper names by providing an overview of the main challenges and developing a new contextualist account of names. Questions about the use and semantic features of proper names are at the centre of philosophy of language. How does a single proper name refer to the same thing in different contexts of use? What makes a thing a bearer of a proper name? What is their meaning? Guided by these questions, Rami discusses Saul Kripke's main contributions to the debate and introduces two new ways to capture the rigidity of names, proposing a pluralist version of the causal chain picture. Covering popular contextualist accounts of names, both indexical and variabilist, he presents a use-sensitive alternative based on a semantic comparison between names, pronouns and demonstratives. Extending and applying his approach to a wide variety of uses, including names in fiction, this is a comprehensive explanation of why we should interpret proper names as use-sensitive expressions.

1

Proper Names and Rigidity¹

In this chapter I will show that typical formal semantic representations of the rigidity of proper names neglect an essential aspect of the rigidity of ordinary names, namely that their rigidity is determined by our ordinary use of a name relative to the actual world. This fact was already clearly pointed out by Kripke but ignored by the subsequent formal discussion of this topic. Firstly, I will introduce on this basis two different new varieties of known versions of rigidity; namely, actualized persistent and actualized obstinate rigidity. Secondly, I will introduce two new and overlooked versions of rigidity, which I will call actualized restricted rigidity and actualized accessible 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, as I will show. This chapter also contains a modified version of Kripke’s test for the rigidity of proper names.

Setting the stage: Kripke and his followers on different notions of rigidity

Kripke famously introduced the notion of a rigid designator in his essay ‘Identity and Necessity’ and in the second of a series of lectures published under the title Naming and Necessity in the following way:

What do I mean by ‘rigid designator’? I mean a term that designates the same object in all possible worlds.²

Let’s call something a rigid designator if in every possible world it designates the same object, a nonrigid or accidental designator if that is not the case.³

Different interpretations of what exactly is meant by an expression that designates the same object in every possible world seem to be possible. Firstly, we will clarify what it means that an expression designates something in a possible world. Secondly, we will clarify what exactly Kripke means by all possible worlds. As we will see, an unrestricted understanding of this generalization requires certain background assumptions, and given these assumptions, there are also different options on how to spell out the details.

Prima facie there are different explanatory roles that possible worlds can play in the formal framework of (possible) world semantics. In connection with the topic of rigidity, possible worlds are mainly conceived of as semantic points of evaluation that are sensitive to modal or temporal operators and can be shifted by these operators. Hence, in the quoted passages, Kripke implicitly makes use of the conceptual resources of his famous model-theoretic possible world semantics for modal logic.

According to this semantics, every formula is evaluated relative to a possible world and, hence, every formula has truth-values relative to possible worlds. This world-relative evaluation of formulas is based on a world-relative interpretation function that assigns world-relative extensions to predicates and individual constants. Furthermore, it can also be based on a world-relative denotation function that unifies the semantics of singular terms. Hence, every singular term receives a denotation relative to a possible world. Against this background, we can now first try to formulate Kripke’s thesis concerning the rigidity of certain referring expressions in a more precise way if we conceive of ‘Den (…, …)’ as an expression for the world-relative denotation function:

(RID)

φ is a rigid designator iff for every possible world w and w*: Den(φ, w) = Den(φ, w*).

It is not clear whether Kripke himself endorses a conception of rigidity for referring terms that accepts (RID) in its full generality. Which kinds of restriction of (RID) are possible and meaningful? Why should one restrict (RID) at all? What are the background assumptions that are required to accept (RID) in its full generality?

Obstinate and persistent rigidity

The world-relative interpretation function of model-theoretic possible world semantics presupposes the existence of a so-called domain of discourse. Such a domain of discourse basically has two different functions. Firstly, the domain of discourse specifies the possible range of the (first-order) quantifiers. Secondly, it determines the range of possible values of the interpretation or denotation function. There are two fundamentally different conceptions regarding the relations between the domain of discourse, on the one hand, and quantifiers and the interpretation function, on the other hand: a so-called constant domain conception and a variable domain conception. According to the first conception, there is a single constant domain that determines the range of the quantifiers and the interpretation function relative to all possible worlds.⁴ According to the second conception, domains of discourse are also relativized to possible worlds. Hence, there is a domain function that assigns exactly one domain of discourse to each possible world. On this basis, quantifiers and the interpretation or denotation function are bound to world-relative domains.⁵

If we introduce a world-relative denotation function to unify the semantics of singular terms and to allow the formulation of a thesis like (RID) as we did, we also have the option either to use a single constant domain of discourse as a possible range of values for this function or to use world-relative variable possible ranges of values. Hence, we can distinguish a constant domain and a variable domain interpretation of the denotation function. Before we focus on the details and possible variants of both interpretations, let us see whether there are clear indications of which of these different possibilities are contained in Kripke’s work.

Kripke seems to endorse different views on this issue in ‘Identity and Necessity’ and in Naming and Necessity. In the first work, he makes the following remarks concerning the details of his conception of rigidity:

[I]n talking about the notion of a rigid designator, I do not mean to imply that the object referred to has to exist in all possible worlds, that is, that it has to necessarily exist. […]

All I mean is that in any possible world where the object in question does exist, in any situation where the object would exist, we use the designator in question to designate that object. In a situation where the object does not exist, then we should say that the designator has no referent and that the object in question so designated does not exist.⁶

This quote shows that another important issue for a correct understanding of the notion of a rigid designator is the exact nature of the relation between the extension of the existence predicate and the single constant or different variable domains of reference respectively.

Against the background of a constant domain semantics, there seem to be two possible options to determine this relation. Firstly, one might conceive of the existence predicate as a predicate with a constant extension relative to all possible worlds, which is identical to the single domain of discourse. Let us call this view the necessity variant of the constant domain view. Secondly, one might conceive of the existence predicate as a world-relative predicate and identify the extension of the existence predicate with different subsets of our single domain of discourse. Let us call this view the contingency variant of the constant domain view.

According to the first view, existence is a first-order non-discriminating property. A prima facie implausible consequence of this view is that every object exists according to this view relative to every possible world and hence every object is a necessarily existing object.⁷ According to the second view, existence is a first-order discriminating property. This view can account for the intuitive possibility that there are things that exist only contingently.⁸

Against the background of a variable domain semantics, there only seems to be one prima facie plausible view concerning the relation between the extension of the existence predicate and the domain of discourse. This view holds that the extension of the world-relative existence predicate is identical with the respective world-relative domain of discourse. In this sense, the third view can be seen as a compromise between the other two views. According to this view, existence is a first-order non-discriminating property, but it can also account for the distinction between necessarily and contingently existing objects.

Which of these three views does Kripke presuppose in the quote mentioned above? The answer very much depends on how we interpret the following last part of the quote: ‘we should say that the designator has no referent and that the object in question so designated does not exist’. Superficially, this claim sounds contradictory, because Kripke speaks both about a term without a referent and about an object that is designated by this very term and that does not exist. Here we must be careful; there is a consistent interpretation of Kripke’s claim. According to the third conception of existence, referential terms can designate an object relative to som...