On Compulsive Talkers

Abstract

This paper reevaluates Kaplan’s (Themes from Kaplan, Oxford University Press, Oxford, pp 481–563, 1989b) infamous ‘compulsive talker’ objection to Reichenbach’s (Elements of symbolic logic, AQ1 Macmillan, New York, 1947 ) token-reflexive theory of indexicals. It argues that Kaplan’s objection depends on the modal status of Reichenbachian tokens. On one interpretation, Kaplan’s objection stands. But on another, equally plausible interpretation, the following points hold: (i) Reichenbach’s theory effectively preempts contemporary discussion of rigid definite descriptions, (ii) Kaplan’s own analysis of indexicals in terms of dthat-terms comes extremely close to Reichenbach’s own analysis, and (iii) Kaplan’s ‘compulsive talker’ objection should be rejected.

1 Introduction

Token-reflexive theories of indexicals hold that the semantic rules associated with any indexical-type determine the semantic contribution of properly produced tokens of such types relative to certain relational properties of such tokens. For example, Hans Reichenbach (1947) argues that the semantic contribution of properly produced tokens of the first person indexical-type I to tokens of sentences containing them should be analysed as in (1):¹$^{,}$²

• (1) ‘I’ means the same as ‘the person who utters this token’.

In his Demonstratives, David Kaplan famously rejected Reichenbach’s analysis with the following remark:

It is certainly true that

• I am the person who utters this token

But if [(1)] correctly asserted a synonymy, then it would be true that

• [(2)] If no one were to utter this token, I would not exist.

Beliefs such as [(2)] could make one a compulsive talker. (Kaplan, 1989b, 519–520; my numbering)

Despite its brevity, Kaplan’s remark can be reconstructed into a powerful objection. For if (1) correctly expresses a synonymy, then (2) expresses the same content as (3) as uttered by the same speaker in the same context:

• (3) If no one were to utter this token, the person who utters this token would not exist.

The trouble is that (3) seems plainly true; and so, if (1) correctly expresses a synonymy, then (2) should also be true. But (2) seems plainly false: as Kaplan notes, anyone who truly believed (2) would presumably become a compulsive talker for fear of popping out of existence. Thus, (2) and (3) do not express the same content. Kaplan’s verdict: Reichenbach’s analysis in (1) is incorrect.

Kaplan’s arguments against token-reflexive theories of indexicals have been highly influential, with philosophers generally accepting his arguments.³ Indeed, even proponents of token-reflexive theories of indexicals typically accept the general thrust of his ‘compulsive talker’ argument and instead offer alternative proposals to escape its conclusion.⁴ The aim of this paper is to show that such attitudes are unwarranted and such steps are unnecessary, since Kaplan’s objection trades on a certain understanding about Reichenbach’s notion of a token.⁵ As we shall see, Reichenbach has in mind a quasi-technical use of the term ‘token’, one which departs from ordinary use. On one interpretation of Reichenbach’s notion of a token, Kaplan’s objection stands. But on another interpretation, we see that Kaplan’s objection falters and Reichenbach’s own view is revealed to be much closer to Kaplan’s than it first seems.

2 Reichenbach’s Theory of Tokens

Let us begin by elucidating Reichenbach’s treatment of indexical terms. As we have seen in (1), indexical terms are explained with reference to tokens. To understand the role that tokens play in Reichenbach’s theory of indexicals, we must first understand the role that tokens play in his theory of language.

According to Reichenbach, language is fundamentally a system of signs. More specifically, he takes language to be a system of a certain class of physical things, such as “ink marks on paper, chalk marks on a board, sound waves produced in a human throat” (Reichenbach, 1947, 4). These physical things get their linguistic significance in virtue of the intermediary position between an object for which they are a substitute and their user, namely, that “[t]he person, in the presence of a sign, takes account of an object; the sign therefore appears as the substitute for the object with respect to the sign user” (Reichenbach, 1947, 4). For individual signs to serve their practicable purpose in a system of language — that is, to explain how we can take different individual sound waves, produced at different times by different people, to be tokenings of the same word — we must be able to use different individual physical signs for the same linguistic purposes: “linguistic signs must be reproducible” (Reichenbach, 1947, 4).

To explain how individual signs can serve this function, Reichenbach distinguishes between a token, which is to be understood as “the individual sign” used on a particular occasion, and a symbol, which is to be understood as “the class of similar tokens” bearing the same appropriate relation to one another (Reichenbach, 1947, 284).⁶ For example, there are eight instances of the letter ‘u’ in the preceding sentence-token, all of them distinct tokens belonging to the same class of similar tokens.⁷ For Reichenbach, tokens are unique physical entities located at a particular space-time region and different tokens are identified as being of the same type in virtue of their similarity with each other and their conformity to the type of symbol they instantiate, but different tokens of the same type are distinct entities.⁸

Using the token–symbol distinction in his treatment of indexical terms, Reichenbach explains that he will be interpreting the phrase ‘this token’ in (1) as a novel operation which he calls token-quotes, an operation similar to, but importantly different from, ordinary quotes. He elucidates this operation as follows:

Whereas the ordinary-quotes operation leads from a word to the name of that word, the token-quotes operation leads from a token to a token denoting that token. Let us use little arrows for the token quotes; then the sign:

• [(4)]

  $^{\searrow }a^{\swarrow }$

  represents, not a name for the token ‘a’ in [(4)], but a token for it. [(4)] is not a name because the token [(4)] is a reflexive token and cannot be repeated; thus

• [(5)] $^{\searrow }a^{\swarrow }$

  not only is a token different from [(4)], but also refers to a different token. (Reichenbach, 1947, 284–285; my numbering)

It is important to note that, for Reichenbach, the term ‘this token’ functions in the same way as token quotes in the sense that “[t]he different tokens, similar to one another, constituting the symbol ‘this token’, are not equisignificant to one another”, and so do not denote the same thing (Reichenbach, 1947, 286).⁹ For example, if we consider the token (6) below:

• (6) If no one were to utter this token, the person who utters this token would not exist,

we must observe that, while (3) and (6) are evidentially tokens of the same sentence-type, they are not the same token, and so their respective occurrences of ‘this token’ each denote something different. On Reichenbach’s understanding of the function of the phrase ‘this token’, the tokens of ‘this token’ in (6) denote the token (6) and the tokens of ‘this token’ in (3) denote the token (3).

3 Compulsive Talkers Revisited

Reichenbach is clear in his treatment of tokens that they are non-repeatable, physical entities. That is, on his account, tokens are temporally-bound in the sense that an utterance of a particular token occurs wholly at a specific space-time region and never appears at any other (non-overlapping) space-time region. But he says little about the modal status of tokens, and, in particular, whether they are world-bound in the sense that they occur wholly in a single possible world and do not appear at any other world.

The central contention of this paper is that the success of Kaplan’s compulsive talkers objection trades on the answer to this question. If Reichenbachian tokens are transworld entities—that is, if they appear in more than one world—then Kaplan’s argument goes through. But if Reichenbachian tokens are world-bound, then Kaplan’s argument falters.¹⁰

3.1 Kaplan Vindicated

First, let us suppose that tokens are transworld entities, that is, they appear in more than world. On this assumption, what follows about the truth of the sentence ‘If no one were to utter this token, the person who utters this token would not exist’?

To ground our discussion, let us assume the Lewis–Stalnaker account of counterfactuals, the view according to which subjunctive conditionals of the form $\ulcorner \text {If it were that }\phi \text {, then it would be that }\psi \urcorner$ have the following truth-conditions:

• (7) The sentence $\ulcorner \text {If it were that }\phi \text {, then it would be that }\psi \urcorner$ is true at a world w iff the closest-$\phi$ world relative to w is also a $\psi$-world,

where $\phi , \psi$ are indicative, declarative sentences and a $\phi$-world is a world in which $\phi$ is true (Stalnaker, 1968; Lewis, 1973).¹¹ It follows straightforwardly that (3) is true, on this account, just in case the closest world such that no one were to utter the token (3) is one in which the person who utters the token (3) would not exist.

Next, we must consider how to interpret the definite description in the sentence ‘the person who utters this token would not exist’. The key observation is that, while the token (3) is a transworld entity, and so can appear in different worlds, there is no guarantee that it must appear in every world. Consequently, we must ask ourselves what the definite description ‘the person who utters this token’ in (3) denotes in a world where (3) has not been uttered.

For concreteness, let us assume an intensionalised version of Russell’s theory of definite descriptions. According to this view, the sentence ‘the person who utters this token would not exist’ denotes the following proposition:

• (8) $\lambda w. \lnot \exists x [P(x, w) \wedge sp(x, \Theta , w) \wedge \forall y [P(y, w) \wedge sp(y, \Theta , w) \rightarrow x = y]]$,

where ‘P(x, w)’ formalises that x is a person in w, ‘$\Theta$’ is the name for the relevant token (3), and ‘$sp(x, \Theta , w)$’ formalises that x speaks the token $\Theta$ in w.

Combining the Lewis–Stalnaker theory of counterfactuals and the intensionalised Russellian theory of definite descriptions, we can see that Kaplan’s conclusion follows immediately. The closest world in which no one utters the token (3) is one in which the definite description ‘the person who utters this token’ fails to denote. And since the consequent as in (8) is true at a world just in case there is no one who satisfies the nominal material of the description at that world, it is true in the closest antecedent-satisfying world. In other words, (3) is true, even though (2) is false.¹²

3.2 Reichenbach Vindicated

Let us now turn to the second interpretation of Reichenbach’s notion of a token, the interpretation according to which tokens are temporally-bound and world-bound.¹³ On this interpretation, an utterance of a particular token could not have occurred at any other time than it actually did and it could not have been uttered in another circumstance or world than it actually was. Consequently, any given token could not have been uttered by any other person than it actually was.

Given this interpretation, how should we understand Reichenbach’s treatment of token-reflexives? In particular, how should we understand Reichenbach’s phrase ‘the person who utters this token’?¹⁴ To get clear on these questions, and to see how Reichenbach intends this device to be used, it is instructive to see how he himself symbolises tokens of sentences containing token-reflexives in Elements of Symbolic Logic.

Consider, for example, Reichenbach’s example of a man who utters the sentence ‘This boy is tall’ (Reichenbach, 1947, 286). Letting the token used by the man (i.e., the whole sentence-token he uttered) be named ‘$\Theta$’, Reichenbach symbolises the man’s utterance as follows:¹⁵

• (9) $t[(\upiota x)b(x).rf(x,\Theta )]$,

where ‘t’ means ‘tall’, ‘b’ means ‘boy’, and ‘rf’ means ‘referred to’. Importantly, the token denoted by ‘$\Theta$’ is not the token used for the above formulation (9), but rather the token uttered by the man just mentioned. Thus, on this symbolisation, ‘this boy’ means the same as ‘the boy to whom $\Theta$ refers’, namely, the boy to whom $\Theta$ actually refers.¹⁶

How do we extend this understanding to occurrences of token-reflexive phrases embedded under a tense or modal operators? How do we use token-reflexive phrases to pick out an individual at some time or world other than the one at which the token was uttered? Here, it is instructive to consider a solution that Reichenbach gives to one of the exercises in Elements of Symbolic Logic (Reichenbach, 1947, 414, Ex. 51-B-3.). Supposing a man utters ‘When Peter comes, I shall have seen John’, Reichenbach symbolises this utterance as follows:

where ‘$t < t_0$’ indicates time order, ‘$t_0$’ is the point of speech (i.e., $t_0 = (\upiota t)rf(t,\Theta )$), and the existential quantifiers scope over the whole expression.

As it stands, this example does not immediately help us understand how Reichenbach treats the phrase ‘the person who utters this token’; the primary purpose of this exercise concerns the symbolisation of tense, and so Reichenbach simplified his solution by symbolising ‘I’ as $y_1$, rather than giving it a full token-reflexive analysis. Nevertheless, we can expand ‘I’ by taking Reichenbach’s symbolisation of the token-reflexive in (9) as a guide. Letting ‘$\Theta$’ denote the token that the man uttered, we have the following:

• (11) $(\exists t)(\exists t')c(x_1,t).s((\upiota y_1)sp(y_1, \Theta ), z_1, t').(t_0< t' < t)$

This expanded symbolisation states that, when Peter comes, the person who uttered $\Theta$ — that is, the man — will have seen John. This is empirically adequate.

What if, instead, we were tempted to expand of ‘I’ in this example to involve a three-place relation between an individual, a token, and a time, rather than a two-place predicate between an individual and a token? There would be three ways to do so, but only one of which leads to a correct symbolisation. Consider the following:

• (12)

  • a. $(\exists t)(\exists t')c(x_1,t).s((\upiota y_1)sp(y_1, \Theta , t), z_1, t').(t_0< t' < t)$

  • b. $(\exists t)(\exists t')c(x_1,t).s((\upiota y_1)sp(y_1, \Theta , t'), z_1, t').(t_0< t' < t)$

  • c. $(\exists t)(\exists t')c(x_1,t).s((\upiota y_1)sp(y_1, \Theta , t_0), z_1, t').(t_0< t' < t)$

Only the last interpretation avoids attributing to Reichenbach a flawed and obviously false symbolisation. Since $\Theta$ was uttered at $t_0$, there is no one who utters $\Theta$ at t or $t'$, and so the definite descriptions in (12a) and (12b) fail to refer. On those interpretations, then, the utterance is guaranteed not to be true. Contrastingly, the definite description in (12c) does manage to refer, since it fixes its referent relative to the time of the utterance, and it refers to the man who actually uttered $\Theta$. If that man will have seen John, when Paul comes, then his utterance is true.

Similar remarks apply to token-reflexives embedded under modals. Suppose a woman says ‘I might have been happy’ and let ‘$\Theta$’ denote the token she uttered. As before, the most direct way to implement Reichenbach’s ideas within a standard semantic treatment of modality would symbolise her utterance as follows:

• (13) $(\exists w)h((\upiota x)sp(x, \Theta ), w).(w_0 < w)$

where ‘$w_0$’ is the world of speech, and ‘$w_0 < w$’ indicates that w is accessible from $w_0$. Here, the woman’s utterance is true iff there is some world accessible from the world of speech such that the person who uttered $\Theta$—that is, the woman—is happy. This, again, is empirically adequate.

Furthermore, if we thought that, under modal operators, ‘sp’ should be a three-place predicate between an individual, a token, and a world, there would be two ways to symbolise the woman’s utterance, but only one would be empirically adequate. Consider the following:

• (14)

  • a. $(\exists w)h((\upiota x)sp(x, \Theta , w), w).(w_0 < w)$

  • b. $(\exists w)h((\upiota x)sp(x, \Theta , w_0), w).(w_0 < w)$

Since $\Theta$ can only be uttered in $w_0$, only the definite description in (14b) refers; the definite description in (14a) fails to refer. and so the utterance is false on that symbolisation. But on (14b), the Reichenbachean definite description ‘the person who utters this token’ is interpreted as referring to the person who actually uttered that token, and so the utterance is true iff there is a possibility where that woman is tall.

What does this extended discussion tell us about how Reichenbach intended his theory of token-reflexives to work? Since Reichenbach himself never relativised the symbolisation of the predicate ‘utters’ in the definite descriptions discussed above to a time or world, this should be considered evidence that determining the referent of such phrases should be done independently from the tense or modal environment in which it is embedded. Furthermore, if we were to relativise the symbolisation to a time or world, the only way to do so that doesn’t attribute an obviously false view to Reichenbach is one that fixes the denotation to the time or world at which the token was uttered, that is, to the person who actually uttered the token then. Again, this is the only way we can understand Reichenbach’s treatment of token-reflexives that doesn’t attribute to him obviously false views.

There are three upshots to note from this interpretation. First, it allows us to usefully relate Reichenbach’s theory of indexicals to the theory of rigid designation. A rigid designator is a term which designates the same object in all possible worlds in which that object exists and only ever designates that object (Kripke, 1980). While standard definite descriptions are paradigm examples of non-rigid designators, some definite descriptions are rigid designators, such as ‘the successor of 2’. Their rigidity arises in virtue of facts about metaphysical reality; in the example just given, the definite description is de facto rigid in virtue of the mathematical necessity that 3 is the successor of 2.

Similarly, assuming that Reichenbachian tokens are world-bound and temporally-bound, and that the definite description ‘the person who utters this token’ is to be understood as I have argued above, any token of the definite description ‘the person who utters this token’ is de facto rigid, since it necessarily denotes whoever actually uttered that token (although, given the nature of tokens, one cannot necessarily use another token of the same type to denote the same person). Thus, we have the following necessary truth:

• (15) $\Box [ (\upiota x)sp(x, \Theta ) = (\upiota x)ANsp(x, \Theta )]$,

where ‘$\Box$’ denotes metaphysical necessity, ‘A’ is the actuality operator, ‘N’ is the now operator, and ‘$\Theta$’ is the name of the specific token similar to ‘the person who utters this token’. The first upshot, then, is that Reichenbach’s theory of indexicals can be read as foreshadowing recent work on rigid definite descriptions.

Second, once Reichenbach is interpreted on this way, Kaplan’s own analysis of the first-personal pronoun involving dthat-terms comes extremely close to Reichenbach’s own analysis.¹⁷ Kaplan introduces a special demonstrative operator ‘dthat’ which “requires completion by a description and which is treated as a directly referential term whose referent is the denotation of the associated description”, resulting in a dthat-term (Kaplan, 1989b, 521). A dthat-term is a term of the form ‘dthat[$\alpha$]’, where $\alpha$ is a singular term, such as a definite description or a proper name. The content of ‘dthat[$\alpha$]’ in a context c is the object to which the term $\alpha$ refers in c. For example, the content of ‘dthat[the horse that I see now]’ in a context c is Secretariat just in case there is exactly one horse in the world of c that the agent of c sees at the time of c in the world of c, and that horse is Secretariat.

Kaplan (1989b, 522) claims that “we can come much closer to providing genuine synonyms [than Reichenbach’s own view]” by using his dthat-operator with the following stipulation:

• (16) ‘I’ means the same as ‘dthat[the person who utters this token]’.

But, on the present interpretation, this analysis is essentially just that of Reichenbach’s. To see this, it is enough to observe that Kaplan remarks that dthat-terms are eliminable in favour of definite descriptions plus Actuality and Now operators:¹⁸$^{,}$¹⁹

Remark 13: If $\beta$ is a variable of the same sort as the term $\alpha$ but is not free in $\alpha$, then $\{\text {dthat}[\alpha ]\} = \{\text {the}\ \beta \ AN(\beta = \alpha )\}$. (Kaplan, 1989b, 552)

Given Reichenbach’s understanding of ‘this token’ as essentially a rigidifying operator to the actual and the now, Kaplan’s proposal here is just that of Reichenbach’s.²⁰$^{,}$²¹

Lastly, we can now see where Kaplan’s ‘compulsive talker’ argument falters. Given the notion of ‘this token’ under consideration, we can see that (3) is true at w iff the closest world $w'$ relative to w in which no one utters the token (3) is such that the person who actually uttered the token (3) in w does not exist at $w'$; otherwise, (3) is false at w. For given that the token (3) is world-bound and temporally-bound, the occurrence of the definite description ‘the person who utters this token’ in (3) rigidly refers to the person who actually uttered the token (3), and not anyone else who may or may not have uttered a similar token of the same sentence-type in any other possible world. Thus, the closest world $w'$ relative to w in which no one utters the token (3) is just the closest world in which the person who uttered the token (3) in w says nothing. And since that person certainly exists in that world $w'$, (3) is false at w. Consequently, on this interpretation of ‘this token’, we can see that Reichenbach’s analysis correctly predicts that (3) is false, agreeing with our intuitive verdict about the truth-value of (2).²²

I submit, therefore, that, under the right interpretation, Kaplan’s objection is ultimately incorrect and Reichenbach need not worry about compulsive talkers.