NAMES AND OBSTINATE RIGIDITY
Brendan Murday
Ithaca College
For the finished version of this paper, please see The Southern Journal of Philosophy, volume 51
(2), June 2013
ABSTRACT
Names are rigid designators, but what kind of rigidity do they exhibit? Both “obstinate” 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.
Names are rigid designators. While that thesis is no longer controversial, multiple
debates about the meaning of names continue. There is first the skirmish between rigidified
descriptivists and their Kripkean opponents. Secondly, anti-descriptivists disagree amongst
themselves about the meaning of names. In both of these debates, one sometimes hears the claim
that names are obstinately rigid as opposed to being merely rigid. This paper argues that such a
claim is erroneous; whether descriptivism is true or not, names (like rigid descriptions) are
merely persistently rigid.
The paper will proceed as follows: §1 defines ‘obstinacy’ and explains the relevance to
Kripke’s modal argument. §2 reviews David Kaplan’s content/extension distinction, which is
presupposed throughout the paper. §3 and §4 address and rebut arguments alleging a direct
connection between obstinate rigidity and direct reference and/or Millian theories of names.
Finally, §5 returns to the debate between rigidified descriptivism and its opponents, rebutting
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three anti-descriptivist arguments for obstinacy. No stance is taken here on the debate between
Millianism and rigidified descriptivism; the aim is to show that both parties should accept that
names are persistently rigid, and to observe as a corollary that the modal argument against
descriptivism fails.
§1.
The Revised Modal Argument
The distinction between rigid and non-rigid designators will be familiar to most readers;
that distinction is illustrated by contrasting the descriptions ‘the sum of 2 and 3’ and ‘the first
person to walk on the moon’. The former expression designates the number 5 in every possible
world, and hence it rigidly designates the number 5. ‘The first person to walk on the moon’,
however, designates different individuals in different possible worlds; the expression in fact
designates Neil Armstrong, but had events progressed differently, the expression would have
designated someone else. The expression ‘the first person to walk on the moon’ thus non-rigidly
designates Armstrong. With the distinction between rigid and non-rigid designators in place, we
can shift our focus from definite descriptions to names. “Descriptivists” are those who think that
the names are semantically equivalent (in some fashion) to definite descriptions. “Naïve
descriptivists” identify the meanings of names with definite descriptions that are typically nonrigid.
Saul Kripke (1980) deployed a modal argument (among others) against naïve
descriptivism. The argument observes that natural language names are rigid1 while definite
descriptions are [typically] non-rigid. This difference is taken to constitute their semantic
nonequivalence.
Some descriptivists have countered that natural language names are equivalent to
1
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Stanley (1997) discusses the case for the rigidity of names.
rigidified descriptions. Perhaps ‘Aristotle’ is semantically equivalent to a rigid description such
as ‘the actual teacher of Alexander the Great’. The extension of ‘the actual teacher of Alexander
the Great’ is Aristotle for any world of evaluation, because we evaluate that content by looking
for the extension of ‘the teacher of Alexander the Great’ at the actual world @. Since names and
rigid descriptions have the same modal profile, rigidified descriptivism undermines a crucial
premise in Kripke’s modal argument.
A revised modal argument,2 however, attacks rigidified descriptivism. The argument
suggests that while actualized descriptions are rigid designators, they are not rigid in the same
way that names are rigid, and therefore names and actualized descriptions are not semantically
equivalent.
How do rigid names and rigid descriptions differ? Nathan Salmon [1981: 32-36]
suggests the following: an obstinate (or “obstinately rigid”) designator is “insensitive to the
question of whether [its designatum exists] in a given possible world; [it designates] the same
thing with respect to every possible world, whether that thing exists there or not”. 3 In contrast, a
persistent (or “persistently rigid”) designator is “an expression which designates the same thing
with respect to every possible world in which that thing exists, and which designates nothing
with respect to possible worlds in which that thing does not exist”. 4 Thus the difference between
an obstinate and a persistent designator of O depends on whether the expression designates O
when evaluated at worlds where O does not exist.
Crucially, we are not asking whether the word as used in an O-less world designates O;
2
See Salmon (1981), Almog (1986), Branquinho (2003), and Brock (2004).
3
Salmon (1981: 34).
4
Salmon (1981: 33-4).
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all parties in this debate agree that such a use would fail to designate. But if a term is obstinate,
then our use of the term, when evaluated at an O-less world, will designate O; if a term is
persistent, then our use of the term when evaluated at an O-less world will fail to designate
anything. The distinction between obstinacy and persistence emerges only when we inquire
whether evaluating the term at a world where O does not exist will determine a [non-degenerate]
extension. The obstinacy theorist holds that the extension is O, because she does not require that
O exists in world w in order to be the extension of a term evaluated at w. The persistence
theorist, on the other hand, holds that the evaluation fails to determine a [non-degenerate]
extension, because she requires that O exists in w in order to be the extension of a term evaluated
at w.
The revised modal argument against rigidified descriptivism is thus: names are
obstinately rigid 5, but rigidified descriptions are persistently rigid. Since they have different
modal profiles, names are not semantically equivalent to rigidified descriptions.
Why think that rigidified descriptions are persistently rigid? Given the Russellian
treatment of descriptions and an actualist interpretation of the existential quantifier, then in
evaluating ‘the actual F’ at w, we determine an individual O so long as O is the unique individual
at w who is actually F. 6 If there is no unique individual at w who is actually F, the description
5
See Kaplan (1973) and (1989) (both reprinted in Davidson (2007)), Salmon
(1981), Almog (1986), and Smith (1984) and (1987) in favor of obstinacy. Plumer (1989),
Steinman (1985), and Stanley (1997: 567) express reservations about some arguments for
obstinacy.
6
Perhaps instead we determine an individual O so long as O exists at w and is the
one and only individual who is F-at-the-actual-world-@; the difference between these two
formulations consists in where the uniqueness is required to obtain, but that question need not
trouble us here; see Soames (2005: 30n22).
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fails to denote. Thus, the rigid description will be persistent, not obstinate. 7
We have in this section characterized the obstinacy/persistence distinction, while
additionally observing the first way in which obstinacy matters to debates about the meaning of
names. The second way in which obstinacy arises in the literature on names is in Kaplan’s
explanation of the notion of direct reference. To present the alleged connection between
obstinacy and direct reference, we should first review Kaplan’s distinction between content and
extension.
§2.
Content and Rigidity
Millians and actualized descriptivists disagree about the semantic content of a name. An
actualized descriptivist might represent the semantic content of ‘Obama’ as:
7
Carter (1983) argues that rigidified descriptions are in fact obstinate; Kaplan
might also think that actualized descriptions are obstinate (though not directly referential).
Kaplan says “one who believes that a name is connected to its referent by a description ... can
achieve rigidity, even obstinate rigidity, through the use of rigidifying operators. Thus, a
Fregean ... need only add something like actuality to the content in order to account for the
rigidity of proper names. We then have .... rigid designation without direct reference.” [Kaplan
(1989: 577), reprinted in Davidson (2007: 790); italics in original, underlining added for
emphasis]. It is unclear whether Kaplan meant that any description can be thus modified to
create an obstinately rigid designator, or merely that some descriptions can become obstinate
when rigidified. The latter claim is true in virtue of a description which contingently designates
a necessary entity, since upon rigidification the resulting description would be both obstinate and
persistent; the former claim would be more controversial.
Contrast Carter’s view with the more common treatment of actualized descriptions
presented in Salmon (1981: 35): “if a definite description ... denotes a contingent individual i,
then even the rigid designator (x)A(x), i.e., the unique individual who is, in actuality, such
that , where ‘A’ is the sentential actuality operator, only persistently designates i.” (Italics in
original, underlining added for emphasis). Soames (2002: 41; 2005: 27n18) agrees with Salmon
that actualized descriptions are persistent; however, Soames also holds (2002: 49; 2005: 28-29)
that descriptions rigidified with Kaplan’s ‘dthat’ operator would be obstinate.
Carter’s (1983) position differs from the one taken in this paper concerning the modal
profile of rigidified descriptions, but it is interesting to note that both positions provide the
rigidified descriptivist with a response to the revised modal objection – names and actualized
descriptions would have the same modal profile, and so modal arguments against descriptivism
would fail.
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<being the unique bearer of (44th President of the United States) at @, and ...>
On the Millian view, the content of ‘Aristotle’ is simply the individual, so a Millian might
represent the content as:
<Obama>
Millianism and actualized descriptivism are thus two views about the content of a name. By
contrast, the rigidity of an expression concerns the expression’s extension.
Let us step back for a moment. An expression generates a content when it is uttered in a
particular context, so we can construe a content as the product of an expression paired with a
context of utterance:
Expression

Content
Context-of-Utterance
Once a content has been generated, we evaluate that content to determine an extension.
The extension of a name or a definite description is an individual; we find the extension by
evaluating the content at a world:
Content

Extension
World-of-Evaluation
If the extension of a singular term changes when we change the evaluation-world, the
term is non-rigid. 8 Salmon’s distinction between obstinacy and persistence is a distinction
8
This is a terse but imprecise definition of rigidity. An incautious definition of
rigidity such as this will entail that persistent “rigid” designation is not rigid designation at all,
since at some worlds the extension is the individual in question while at other worlds there is no
extension at all. A more nuanced definition of rigidity allows that both obstinate and persistent
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between types of rigidity; that distinction concerns extension, not content.
The contrast between obstinacy and persistence matters only when the world of
evaluation is one at which the relevant individual does not exist – it is only in that situation that
obstinacy and persistence predict different results.9 The results differ with respect to the
extension of the expression. Nothing in the definitions of these two types of rigidity commits to
one or the other view about content – the definitions of ‘obstinacy’ and ‘persistence’ make no
explicit commitments to Millianism or actualized descriptivism.
This point is sometimes blurred. Kaplan [1978a] employs the term ‘direct reference’,
distinguishing it from ‘rigid designation’. Kaplan [1989] clarifies that in calling a term ‘directly
referential’ he means both that it has a Millian content 10 and is obstinately rigid. 11 Kaplan seems
to assume that any term expressing a Millian content is obstinate, and this assumption seems to
be commonly accepted (though rarely discussed). This assumption will be challenged in §3 and
§4.
§3
Names as Persistently Rigid
As noted above, if names are equivalent to rigidified descriptions, we have good reason
to think that they will be obstinately rigid. The claim that names would be persistently rigid on a
designators count as rigid; for instance: “A rigid designator designates the same object in all
possible worlds in which that object exists and never designates anything else” (LaPorte, 2006).
9
An assumption in this paper is that some individuals are contingent beings; for a
contrary view, see Williamson (2002).
‘The “direct” of “direct reference” means unmediated by any propositional
component.... Whatever rules, procedures, or mechanisms there are that govern the search for
the referent, they are irrelevant to the propositional component, to content. When the individual
is determined ... it is loaded into the proposition.’ [Kaplan (1989: 569), reprinted in Davidson
(2007: 784), italics added for emphasis].
10
‘All directly referential terms will be obstinately rigid’ [Kaplan (1989: 571),
reprinted in Davidson (2007: 786)]. The converse does not hold, however, since rigid
descriptions denoting a necessary individual are obstinate.
11
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Millian view, however, is highly contentious. This section considers how one could formulate a
view that combines Millian semantics and persistent rigidity; §4 addresses the rival view that
Millianism demands obstinacy.
Consider the way we evaluate ‘the shortest spy’ – we generate a descriptive content, and
then look for the thing at the evaluation-world that satisfies that description. Consider too the
way we evaluate complete sentences – we find the content generated by the sentence at the
context of utterance, and then determine the truth-value of that proposition at the evaluationworld. Now consider proper names; suppose that Obama exists at our world @, but not at world
. What are we doing when we evaluate the Millian content <Obama> (which, let us stipulate, is
the content of @-utterances of ‘Obama’) at ?
Here is one proposal: we are looking for the individual at  corresponding to this content.
What thing at  is Obama? Nothing. Obama does not exist at , so our search comes up empty.
Since no individual in  is the extension determined by < Obama> at , there is no extension at
.
The search for an extension at  has been characterized in terms of looking for the right
sort of individual at . Whether the expression is a description, a sentence, or a name, the
content is generated at the context of utterance, and we then look in the evaluation world to see
what extension is determined by that content. The proposal thus suggests that the evaluation of
Millian contents resembles the evaluation of any other content in this respect – that content is
generated at the world of utterance, and the extension is then determined by using the content to
find the appropriate object/truth-value in the evaluation world. Of course, a Millian insists on a
crucial difference between the ways that Millian and non-Millian contents designate; Kaplan
[(1977: 485-486), reprinted in Davidson (2007: 722)] takes pains to emphasize this point. Before
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we can accept the proposal at issue, then, we must be sure that it does not conflate the evaluation
of a name and the evaluation of a description.
The worry is that the proposal amounts to evaluating at  a Millian content < Obama> by
looking for something that satisfies a description in that world. But that worry can be dismissed;
we can pair Millianism with the view that names are persistently rigid without thereby conflating
Millianism and descriptivism. The descriptive content <being the unique bearer of 44th President
of the United States at the actual world> is evaluated by finding the unique exemplifier of that
property at the world of evaluation. To evaluate a Millian content at , on the other hand, we are
simply asking which individual at  is that guy. Who at  is Obama – who at  is that guy? No
one. If anyone at  were Obama, it would surely be Obama. But there is no such person at , so
no one at  is Obama. Evaluating <Obama> in this way differs from the evaluation of <being
the unique bearer of 44th President of the United States at the actual world> or even <being the
unique bearer of identical with Obama >, though the difference in the latter case is subtle. An
individual exemplifies the property identical with Obama just in case that individual is Obama,
so the evaluations of <being the unique bearer of identical with Obama> and < Obama> will be
extensionally equivalent. But one should not take that extensional equivalence to demonstrate
that we are conflating the two contents; when we evaluate the Millian content we are not asking
which individual exemplifies a property.
There is therefore a coherent view which pairs Millianism and persistent rigidity; it is a
further claim, however, that Millians should adopt this view. The following section identifies a
difficulty for the orthodox view that Millianism entails obstinacy.
§4
Severing the Link between Millianism and Obstinacy
Why might a Millian think that names are obstinate? Consider Kaplan’s comments about
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direct reference:
I intend to use ‘directly referential’ for an expression whose referent, once determined, is taken as
fixed for all possible circumstances, i.e., is taken as being the propositional component.
(Kaplan [1978a: 493], reprinted in Davidson [2007: 727]; italics in original)
The claim that the referent is fixed for all possible circumstances suggests that the term
has that referent at every point of evaluation, whether or not the referent exists there.12 To say
that the referent just is the propositional component is to endorse Millianism. The use of “i.e.”
might suggest that Kaplan is taking obstinacy and Millianism to be two sides of the same coin. 13
Kaplan (1989) characterizes direct reference as the pairing of Millianism and obstinacy. 14
He suggests further that obstinacy is a consequence of Millianism:
If the individual is loaded into the proposition (to serve as the propositional component) before the
proposition begins its round-the-worlds journey, it is hardly surprising that the proposition
manages to find that same individual at all of its stops, even those in which the individual had no
prior, native presence. The proposition conducted no search for a native who meets propositional
specifications; it simply ‘discovered’ what it had carried in.
(Kaplan [1989: 569], reprinted in Davidson [2007: 784])
Kaplan employs here the “carrying in” metaphor; he uses it again later:
I see ... a central distinction ... between what exists at a given point and what can be ‘carried in’ to
be evaluated at that point, though it may exist only elsewhere. My ‘circumstances of evaluation’
evaluate contents that may have no native existence at the circumstances but can be expressed
elsewhere and carried in for evaluation.
(Kaplan [1989: 613], reprinted in Davidson [2007: 820])
Why would the evaluation of Millian content entail obstinacy? One proposal can be
considered and quickly dismissed: one could interpret Kaplan’s talk of ‘carrying in’ to mean that
When Kaplan says “all” possible circumstances of evaluation, he means “all” -he is not overlooking circumstances of evaluation at which the individual fails to exist. The
quoted passage directly follows a distinction between obstinate and persistent rigidity.
12
It is surprising that Kaplan writes “i.e.” here; as noted above, he recognizes that a
rigid description of a necessary individual is obstinately rigid without thereby expressing a
Millian content.
13
14
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See notes 10 and 11 for the original passages.
in evaluating a proposition containing Obama as a constituent at , Obama becomes an eligible
extension in virtue of arriving with the content. But we certainly should not think that evaluating
a singular content at  adds to the domain of  in any way. The content tells us what extension
we are looking for in the evaluation world, but it does not increase the stock of individuals
eligible to serve as extensions.
Another attempt to derive obstinacy from Millianism might seize on the suggestion that
the individual has been determined prior to the evaluation; Kaplan (1989: 569) says something
like this, as does Scott Soames:
“the content … is identified with [the] referent…. Since an object has already been determined,
there is no further object determination to be done with respect to [the world of evaluation].”
(Soames [2005: 27n18])
One might attempt to construct from this turn of phrase an argument that Millianism
entails obstinacy: to evaluate a Millian content, we must first construct that content, and we
cannot construct the content unless we already have the individual. 15 Content-generation
precedes determination of an extension, since the latter is executed by carrying the content to a
world of evaluation. Thus in the case of singular propositions, we have the individual before we
evaluate that content to determine an extension. Since we have the individual already, regardless
whether the individual exists at the world of evaluation, why not think that the extension
determined will be that individual, no matter what the world of evaluation is like? We already
have the individual, so there is no reason to say that for some points of evaluation the Millian
content fails to determine any individual.
Plantinga defines ‘existentialism’ as the view that a singular proposition cannot
exist at w unless the relevant individual exists at w. If singular propositions are set-theoretic
entities, existentialism is plausible, since it is natural to think that a set is built up out of its
members, such that if the members did not exist the set would not exist either. Although
Plantinga (1979) and (1983) rejects existentialism, the thesis bears some plausibility.
15
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This argument is clearly flawed. A content is generated at a context of utterance; to
express a Millian content, we must have the individual in that context [at least given certain
assumptions]. But the fact that we have the individual in the context of utterance does not entail
that we have the individual in the world of evaluation. It is a mistake to reason that if we have
the individual before content-generation, and we generate the content before extensiondetermination, then we have the individual before extension-determination, and therefore that
individual is always available to be the extension. The mistake trades on an ambiguity in the
‘then’ clause; we have the individual at the context of utterance before we evaluate the singular
content at a circumstance of evaluation, but that is no reason to think that the individual is
eligible to serve as the extension determined at that circumstance of evaluation. Rather, the
world of evaluation provides the individuals eligible to serve as the extension, and thus in
evaluating a content at the Obama-less world , Obama is not available to be the extension.
Perhaps we can find another way to formulate the thought that seems to motivate those
who think that obstinacy goes hand-in-hand with Millianism. When one evaluates a singular
content at a world, the individual determined is simply the constituent of the singular content; the
thought may be that unlike the case of descriptive contents, for which one must go looking in the
world of evaluation for an individual who satisfies the description, the extension determined by a
singular content is simply the constituent of that content.16
If the Millian endorses this, however, she will encounter some of the problems already
canvassed. On this characterization, the determination of the extension takes place
independently of the world of evaluation. If the extension is determined by the content alone, in
16
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Thanks to an anonymous referee for suggesting this formluation.
what sense are we determining extensions by evaluation at a possible world at all? The proposal
here seems to break with the priority of content to extension reviewed in §2.
Direct reference theorists might embrace this; Kaplan says of direct reference that it
“makes the referent prior to the propositional component” and that it “reverses the arrow from
propositional content to individual” [(1989: 569), reprinted in Davidson (2007: 784)] So
Millians might say that the extension of a name is determined not by finding an individual at the
evaluation-world who corresponds to the content, but rather that the extension is determined
logically prior to the evaluation-world.
That suggestion, however, is needlessly revolutionary. The Millian needs to say that the
individual is identified and “loaded into” the proposition directly, but there is no reason to say
that this counts as the determination of the extension. The evaluation of every other lexical item
proceeds by finding the content generated at the context of utterance, taking that content to an
evaluation-world, and finding the extension determined by that pairing of content and world. As
noted in §3, we can say the same thing about singular contents – a proposition containing Obama
as a constituent is generated at the context of utterance, and we evaluate that proposition by
finding the individual at the evaluation-world who is Obama (if he is there) and determining
whether that individual exemplifies the property attributed to him by the singular proposition. In
so doing, we allow that a name, like any other term, generates a content, which then determines
an extension at the evaluation-world. But the counter-proposal on the table is that the extension
of ‘Obama’ is Obama even at worlds where the individual does not exist, because Obama is a
constituent of the proposition – because we have that individual when we generate the content.
We find the extension of the sentence at β by seeing whether that individual has the right
property at β, but we find the extension of the name at β without looking at β at all. One could
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adopt that view about the evaluation of Millian contents, but it is a radically different picture of
evaluation than we adopt about other terms, and there is no reason to adopt it. The key principle
motivating Millianism is that names latch onto an extension directly, not by mediation through
some description. Singular propositions give us that; we satisfy the Millian by formulating a
theory about the content of names. There is no need to additionally offer a novel theory about
how such a content determines an extension. The extension of ‘Obama’ is determined not by
finding an individual who satisfies the right description; it is determined by finding the
individual who is Obama. The extension of a description is determined by finding an individual,
whomever she may be, who has the right properties; the extension of a name is determined by
the particular individual we are looking for. Millians need a novel picture of the content of
names. But they do not need a novel picture of the evaluation of that content, of the way that the
content determines an extension. When a novel picture is not needed, it should not be adopted.
There is still another place we might look for an argument that Millianism entails
obstinacy. Kaplan attributes the inspiration for direct reference to logic:
It is a striking and important feature of the possible world semantics for quantified intensional
logics, which Kripke did so much to create and popularize, that variables, those paradigms of rigid
designation, designate the same individual in all possible worlds whether the individual ‘exists’ or
not.
(Kaplan [1978a: 493], reprinted in Davidson [2007: 727])
This conception of direct reference takes the variable under an assignment of value as its
paradigm. In evaluating ‘Fx’ at a world w, we do not ask whether its value exists in w, we only
ask what value was assigned to the variable before the process of evaluation at w began. Until a
value is assigned we have nothing to evaluate.
(Kaplan [1989: 571], reprinted in Davidson [2007: 786])
Significantly, in the latter passage Kaplan proceeds to explain that direct reference is a
theory featuring Millian contents. Millianism seems to form the core of Kaplan’s notion of
direct reference – the appeal to variables in logic is meant to emphasize that the assignment of an
individual to a variable is unlike the way a descriptive content determines an extension. But as
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argued in §3, we do not get obstinate rigidity simply from Millianism – we can accept that a term
has Millian content, yet explain the evaluation of that content in a way such that the term is
persistently rigid rather than obstinate.
Smith [1987] appeals to the analogy with logic in a slightly different way that may help
the case for obstinacy:
With names, designata are specified in the base-clauses of our semantic theory antecedently to the
running of the possible-worlds machinery. It is for this reason that names can be uniformly
assigned designata with respect to worlds independently of the issue of whether those designata
exist in those worlds – since this latter issue will be relevant only to the working out of satisfaction
at worlds that is irrelevant to names.
(Smith [1987: 87-88]; underlining added for emphasis).
Smith, unlike Kaplan, emphasizes the suggestion that the extension (the designation) of a
name is determined prior to the possible worlds machinery. But as argued in this section, it is
more compelling to take the relationship between content and extension articulated by Kaplan
and apply it to names as well – allow that the name generates a Millian content at the context of
utterance, but still maintain Kaplan’s view that contents are evaluated at a world, and that the
extension is determined through that evaluation. Understood this way, we can endorse
Millianism while also holding that extensions are determined by evaluating contents at worlds. 17
17
There is one other thought we might pursue. We could generate an argument for
obstinacy that does not attempt to derive that view from direct reference if we distinguish
between existence-at-W and membership-in-the-domain-of-W, and supposed further that every
individual is a member of every world’s domain. We could then say that an extension is
determined at W by finding the appropriate individual in the domain of W (whether or not the
individual exists at that world). Now the extension of ‘Obama’ will be that guy at every
evaluation-world, since Obama (like every individual) is a member of every world’s domain.
This move, however, would trivialize the obstinacy thesis. This tactic would make both
names and rigidified descriptions count as obstinate, and the Millian wants to say that names are
special in virtue of being obstinate. So divorce existing-at-W from membership-in-the-domainof-W will be of no interest to the obstinacy theorist.
The tactic might nevertheless be of interest in providing an argument that both names and
rigidified descriptions are obstinate. But divorcing existence-at-W and membership-in-thedomain-of-W is a radical move in its own right, and it is hard to see any compelling motivation in
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§5.
Arguments for Obstinacy
The previous section argues that Millianism does not entail obstinate designation, but one
might come to believe that names are obstinate by a different route – by arguing that the truth of
certain sentences can only be explained by obstinacy. Those who deploy the revised modal
argument against rigidified descriptivism, for instance, adopt precisely this tactic; this section
argues that the truth of the sentences in question can be explained without any appeal to
obstinacy.
§5.1. The Negative Existential Argument for Obstinacy
One argument for obstinacy is motivated by negative existentials. Consider the
proposition expressed by @-denizens in uttering
(1)
Obama does not exist.
The proposition is false when evaluated at @, but true when evaluated at .
Nathan Salmon suggests that (1) expresses the singular proposition attributing
nonexistence to Obama:
(2)
<Obama, nonexistence>
The argument for obstinacy now runs as follows: (2) is true when evaluated at , and this is
because the extension of <Obama> at  exemplifies nonexistence at . If ‘Obama’ were
persistently rigid, <Obama> would be extensionless at , so we would not have designated an
individual who would be exemplifying the property nonexistence. According to the argument, if
(2) is true at , <Obama> must determine an extension at ; the extension of <Obama> is Obama
its favor besides perhaps an attempt to explain how negative existentials can be true. §5.1 argues
that we do not need so radical a solution to negative existentials.
16 | P a g e
(even at ), and that individual exemplifies nonexistence at .18
Salmon’s argument is thus that we need some explanation of the truth of (2) at , and that
the best explanation of this truth requires the assumption that ‘Obama’ is obstinate – that Obama
is an element of the domain of all worlds, even worlds of which we want to say that Obama does
not exist.
This argument for obstinacy is not compelling; the persistence theorist can easily explain
the truth of (2) at  without giving up the benefits of persistence adduced in section 3; 19 consider
the singular proposition
(3)
<Obama, existence>
To say that (1) is true when evaluated at β is to say that (3) is false when so evaluated. The
persistence theorist can easily explain why (3) is false when evaluated at β – <Obama> fails to
determine an individual, and hence we have no individual to go looking for in the extension of
existence at β. Critically, this story does not require the claim that (3) exists at β, nor need we
say that (3) exemplifies a truth-value at β. We need only say that the proposition can be
evaluated at a world at which it does not exist, and this can be explained as above by asking
whether the individual determined by <Obama> at β falls in the extension of existence at
β.
We have focused here on the evaluation of (3) at β; what about the evaluation of (2) at
such a world? Salmon explains the truth of (1) by saying that Obama exemplifies the
property nonexistence at β. The persistence theorist ought to disagree. Nothing
exemplifies the property nonexistence, at this world or any other. We demand that
18
See Salmon (1981: 37-8) and (1998: 287).
19
See Plantinga (1974: chapter 8), Smiley (1960), and Stanley (1997), for instance.
17 | P a g e
negative existentials can turn out true; we do not demand (nor have we any intuitive
reason to think) that individuals can exemplify nonexistence. So the persistence theorist
will deny that (2) is true when evaluated at β, but this is not a cost of persistence, it is a
benefit. We can explain the truth-at-β of (1) without having to pay the price of saying that
individuals can exemplify nonexistence.
One might still worry that the persistence theorist cannot explain the truth at β of
(4)
<Negation, <Obama, existence> >
But this worry turns on a mistake. (4) does not exist at β, but that does not prevent us
from evaluating the proposition at β. Critically, the persistence theorist does not claim that
the nonexistence of Obama at β makes false every proposition that has Obama as a
constituent in some way. (4) is true at β for the same reason that (3) is false at β -<Obama> evaluated at β fails to determine an individual falling within the extension of
existence at β.
Having seen that the persistence theorist can explain these negative existentials
easily enough, there is no reason to agree with Salmon that they provide a reason to prefer
obstinacy.
§5.2. Modality and Time
There is a second argument for obstinacy; in broad strokes, the argument is that proper
names are temporally obstinate, and since modality and time are analogous, we should think that
names are modally obstinate as well. 20
20
(1981: 36-40).
18 | P a g e
See Kaplan [(1973: 503-505, reprinted in Davidson (2007: 247-9)] and Salmon
There are multiple examples used to motivate temporal obstinacy. Some of them are not
compelling; others may be compelling for temporal obstinacy, but have no obvious modal
analogues. The absence of modal analogues itself suggests that the analogy between time and
modality is insufficient to sustain an argument for modal obstinacy. Let us consider the
following examples:
(5)
Kripke was not yet born.
[uttered in 2011, evaluated at 1911.]
(6)
Kripke will still be influential. 21 [uttered in 2011, evaluated at 2111.]
(7)
Newman-1 will be famous.22
[uttered in 2011, evaluated at 2111.]
Because (5) features a negation, the temporal persistence theorist can interpret it as denying that
some claim about Kripke’s birth is true. Following the suggestion made at the end of §5.1, she
can argue that such a claim is true at 1911 simply in virtue of the fact that <Kripke, born> is not
true when evaluated at 1911.
(6) and (7) present more compelling cases for temporal obstinacy; they do not contain
negations, so the temporal persistence theorist cannot dispose of them the way she handles (5).
But while they [particularly (6)] may motivate temporal obstinacy, they do not have obvious
modal analogues that would provide a reason to endorse modal obstinacy. (6) expresses a
proposition that is true at 2111 only in virtue of the fact that Kripke’s actions have causal effects
on events in 2111. In the modal analogue, that does not obtain -- events at this world do not
cause events at other worlds. This disanalogy between time and modality – that temporal points
21
Both (5) and (6) are inspired by Branquinho (2003), though Branquinho puts
references to the past and future times into the utterances themselves. It is critical that 1911 and
2111 serve as the respective times of evaluation for (5) and (6); nothing turns on whether or not
1911 and 2111 also figure into the utterances and the propositions expressed.
Suppose ‘Newman-1’ is a label used by a 2011 speaker to designate the first
person born in the 22nd century; the example was introduced in Kaplan (1978b).
22
19 | P a g e
are causally interconnected, but modal points are not – thus undermines the argument that where
a reason to endorse temporal obstinacy exists, an analogous reason to endorse modal obstinacy
exists as well.
(7) may not even successfully motivate temporal obstinacy, since one might think that
2011-denizens cannot successfully refer using ‘Newman-1’. Regardless, in the modal analogue,
few of the parties active in the obstinacy/persistence debate are inclined to think that one can
refer to merely possible individuals; many have worries about positing merely possible
individuals in the first place. None of these three cases present a compelling case for modal
obstinacy. Perhaps (6) at least does motivate temporal obstinacy, but at issue here is the putative
modal obstinacy of names, and we have thus far found no reason to endorse that view. Reliance
on the analogy between time and modality will not help the obstinacy theorist, since the absence
of a compelling modal example precisely undermines the claim that the analogy obtains in the
relevant respect.
§5.3. World-Indexing Operators
Consider:
(8)
Obama is happy.
(9)
At @, Obama is happy.
and
The content of the @-utterance of (8) is
(10)
< Obama, happiness>
(10) is false when evaluated at . The persistence theorist has no difficulty here, since <Obama>
fails to determine an extension at .
(9), however, is troubling for modal persistence. If (8) expresses a proposition true at @,
20 | P a g e
(9) apparently expresses a truth at every world of evaluation. There is only one world @, so if p
is true at @, it is necessarily the case that at @, p. This poses a threat to persistence: (9)
expresses a non-negative proposition containing Obama as a constituent, and that proposition
seems to be true at . Obstinacy would solve the problem by allowing that when the content
<Obama> is evaluated at , the extension is Obama, and Obama is happy at @. Persistence
theorists cannot adopt so straightforward an explanation, so (9) seems to motivate obstinacy.
Whether (9) truly threatens persistence depends on the proposition @-denizens express in
uttering (9), however, and we have not specified yet what proposition that is. Consider the
rendering most likely to pose a problem for persistence:
(11)
< <Obama, happiness>, truth-at-@>
To say that this proposition is true when evaluated at , we must say that (10) exemplifies truthat-@ at . Because Obama does not exist at , and Obama is a constituent of (10), we should
deny that (10) exists at . If we denied serious actualism [i.e., if we denied that an
exemplification at w entails the existence of an exemplifier at w], then we could maintain that
(10) exemplifies truth-at-@ at . But the persistence theorist should not deny serious actualism,
since she objects to the obstinacy account of negative existentials precisely on the grounds that
such an account is forced to deny serious actualism. As a result, the persistence theorist is forced
to deny that (11) is true at ; hence, (11) is not true at all worlds. However, (9) apparently
expresses a necessity, and (9) seems to express (11). The persistence theorist must make some
sort of concession.
We should say that (11) is weakly necessary; that is, (11) is true at all worlds at which the
21 | P a g e
proposition exists. 23 (11) does not exist at , of course, since one of its constituents does not
exist at . So the persistence theorist concedes that (11) is not a necessary truth in the sense of
strong necessity (truth at every world), though it is weakly necessary.
This is not a significant theoretical cost. The operator ‘at @’ is not part of ordinary
language, so we have some flexibility in interpreting it as philosophical needs dictate. The
persistence theorist’s suggestion that (11) fails to be true at  is founded on plausible claims: the
constituent proposition (10) does not exist at  [assuming the ontological dependence thesis that
singular propositions cannot exist at a world unless their constituents exist at that world], and as
such (10) cannot exemplify properties at  given serious actualism. The philosophical
motivation for thinking that (11) is true at  turns on the thought that there is only one world @,
and hence regardless of the world of evaluation, (11) is true. To preserve serious actualism and
the ontological dependence thesis, we should accept that embedding a singular proposition24
under an operator like ‘At ’ produces a proposition that is merely weakly necessary. That is a
price we should be willing to pay.
One might wonder, however, whether other examples are less amenable to such a
response. ‘Actually’, unlike ‘At @’, is part of ordinary language, and hence if there are
sentences equally problematic for persistence that employ ‘actually’, we cannot be so cavalier
about proposing an analysis that violates ordinary intuition. Consider:
23
On the connection between serious actualism and weak necessity, see Caplan
(2007) and Plantinga (1979) [although Plantinga’s appeal to weak necessity arises only in
discussing a view he rejects, one which combines serious actualism with existentialism].
24
If a proposition exists non-contingently, the gap between weak necessity and
strong necessity is closed – the distinction obtains only if the proposition fails to exist at all
worlds. Let us suppose that the only contingent propositions are singular propositions.
22 | P a g e
(12)
Possibly Obama doesn’t exist even though actually he does.25
Intuitively, this expresses a truth; can the persistence theorist accommodate that intuition?
We should first clarify the scope of ‘possibly’. Suppose the modal operator takes narrow
scope:
(13)
(Obama doesn’t exist) ⋀ Actually (Obama does exist).
Since Obama is actual, there is no issue for a persistence theorist in accounting for the truth of
the second conjunct. We have already seen in §5.1 how the persistence theorist can explain the
truth of the first conjunct. (13) is thus unproblematic. But there is a genuine threat to a
persistence theorist if the modal operator takes wide scope:
(14)
[(Obama doesn’t exist) ⋀ Actually (Obama does exist)].
p is true when p is true at some accessible world, but given what we have said in this section, a
world that makes Obama doesn’t exist true is a world at which there are no de re non-negative
truths about Obama, and Actually, Obama does exist certainly seems to allege a de re nonnegative truth about Obama.
Persistence theorists have two options. On some views, ‘actually’ has (at least on some
occasions of use) the function of canceling a modal operator.26 Thus (14) would turn out to be
semantically equivalent to the unproblematic (13). Nothing about the persistence doctrine
requires this view of the semantics of ‘actually’, but one could adopt it as a way of dodging the
objection.
A second [and to my mind more compelling] option embraces the view that there are no
de re [non-negative] truths about merely possible individuals, and hence denies the intuition that
(14) is true. While denying such an intuition is a concession, there is already some pressure in
25
26
23 | P a g e
Thanks to an anonymous referee for suggesting this example.
See Bostock (1988: 360-363), Forbes (1989: 91-102), and Stephanou (2010).
this direction: as Bennett (2005) has argued,27 if we accept actualism and the possibility of aliens
(that is, the claim that there could have been individuals that do not actually exist), we have
reason to deny the truth of (14). Those two principles are compelling enough that we should be
prepared to sacrifice the intuition that (14) is true.
§6.
Conclusion
We have argued against the view that names are obstinately rigid on the grounds that (a)
Millianism does not require obstinate rigidity, (b) a natural way to think about evaluating Millian
contents is well-suited to persistent rigidity, and (c) the examples putatively motivating the
revised modal argument can be explained without resorting to obstinate rigidity. Denying
obstinacy has intuitive merit with little theoretical cost.28
27
See also Adams (1981) and Fitch (1996).
I would like to thank Andre Gallois, Tom McKay, and anonymous referees for
their comments and suggestions on prior drafts of this paper.
28
24 | P a g e
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