1 The dispute about proper names

There is a long lasting dispute about proper names. From Frege (1892), Russell (1905) and Quine (1953) the anti-referentialist tradition includes Burge (1973), Lewis (1984), Jackson (1998), Kroon (2004), and Geurts (1997), and finds its most recent development in Matushansky (2008), Elbourne (2005), and Fara (2015). Kripke’s (1980) outstanding work, however, gave way to an equally strong tradition including Longobardi (1994), Kaplan (1989), Salmon (1986), Soames (2002) with its most recent development in García-Carpintero (2017), Schoubye (2017), Saab & Lo Guercio (2020), and Saab (2021).

The data put forward involve a variegated set of uses of proper names:

Substitution failures:

    1. (1)
    1. a.
    1.   Aristotle could not have been the teacher of Alexander.
    1.  
    1. b.
    1. *Aristotle could not have been Aristotle.
    1. (2)
    1. a.
    1.   King Charles does not believe that Samuel Clemens is the author of Huckleberry Finn.
    1.  
    1. b.
    1. *King Charles does not believe that Samuel Clemens is Samuel Clemens.

Differences of Informativeness:

    1. (3)
    1. a.
    1.   Giorgione is Barbarelli.
    1.  
    1. b.
    1. *Giorgione is Giorgione.
    1. (4)
    1. a.
    1.   Paderewski is the great polish pianist.
    1.  
    1. b.
    1.   Paderewski is the president of Poland.
    1.  
    1. c.
    1.   I didn’t know Paderewski is Paderewski.

Rigid uses:

    1. (5)
    1. a.
    1.   Nixon might not have been the president.
    1.  
    1. b.
    1.   The president might not have been the president.
    1.  
    1. c.
    1. *Nixon might not have been Nixon.

Predicative uses:

    1. (6)
    1. a.
    1. Lauras are usually smart.
    1.  
    1. b.
    1. The Laura that wrote the book is a great philosopher.
    1.  
    1. c.
    1. The department made an offer to a Laura and a Martha.
    1.  
    1. d.
    1. Every Martha in the seminar is a biologist.
    1.  
    1. e.
    1. There are three Marthas in the seminar.

Predicative inferences:

    1. (7)
    1. a.
    1. No Wally is smart.
    1.  
    1. b.
    1. ∴ Wally is not smart.
    1.  
    1. c.
    1. Martha is a genius.
    1.  
    1. d.
    1. ∴ At least one Martha is a genius.

Anti-referentialists defend that proper names are type < e,t > expressions —but see below for Matushansky’s sophisticated view—, while referentialists insist they are of type e. Both sides claim their preferred type can account for all uses.

Predicativists (see Elbourne 2005; Matushansky 2008; and Fara 2015) claim that referentialists cannot satisfactorily account for (6) and (7), that only predicativism can offer a single non-ambiguous semantics of the data. Such is the case of Matushansky’s naming convention account whereby proper names are two-place predicates that take arguments for an individual and a naming convention —a relation between referents and phonological strings. Thus, ‘Alice’ will have the semantics described in (8), where R is a specific naming convention.

    1. (8)
    1. ⟦ Alice ⟧ = λx ∈ De . λR<e,<n,t>> . R(x) (/ælis/)

This directly explains (6) and (7) as unproblematic uses of a predicate, accounting as well for the syntactic complexity of constructions such as ‘The Laura’. When used in argument position of a predicate the name takes a null definite article and the naming convention slot is saturated by an indexical convention R0 —in force between hearer and speaker— related to a single individual. This also explains the constancy of the name since the convention “contains no argument slot for a possible world” (Matushansky 2008: 599). The resulting interpretive sequence of ‘Alice’ appears in (9).

    1. (9)
    1. ⟦ the Alice ⟧ = ıx . R0(x) (/ælis/)

1.1 The return of referentialism

Matushansky (2006) claims that, even though some languages like Spanish and English take null articles with proper names in argument position —and can be accounted for as expletives (see Longobardi, 1994)— it is at least clear that “languages such as Catalan and Pima require a definite article with proper names” (2006: 303). Philosophers in the referential tradition have taken this claim at face value and accepted the data as requiring changes to the referentialist semantics. García-Carpintero (2017) claims names carry a reference-fixing metalinguistic presupposition making no semantic contribution, while Schoubye (2017; 2020) takes names to be like pronouns, with no given value but a partial function from variable assignments to individuals.

Matushansky’s claims must be taken with caution, however. In multiple opportunities Longobardi (1991; 1994; 1996; 2005) has shown an essential syntactic feature of Romance proper names. Unlike Germanic Languages like English, Italian requires N-to-D raising for proper names. Italian proper names may be preceded by determiners and adjectives as in (10a), but adjectives can never take the D position as in (10b), forcing the proper name to move to D whenever the determiner is missing, as in (10c).1

    1. (10)
    1. a.
    1.   L’antica
    2.   the-ancient
    1. Roma
    2. Rome
    1. fu
    2. was
    1. la
    2. the
    1. città
    2. city
    1. più
    2. most
    1. importante
    2. important
    1. del
    2. of-the
    1. Mediterraneo.
    2. Mediterranean.
    1.   ‘Ancient Rome was the most important city of the Mediterranean’.
    1.  
    1. b.
    1. *Antica
    2.   ancient
    1. Roma
    2. Rome
    1. fu
    2. was
    1. la
    2. the
    1. città
    2. city
    1. più
    2. most
    1. importante
    2. important
    1. del
    2. of-the
    1. Mediterraneo.
    2. Mediterranean.
    1.  
    1. c.
    1.   Roma
    2.   Rome
    1. antica
    2. ancient
    1. fu
    2. was
    1. la
    2. the
    1. città
    2. city
    1. più
    2. most
    1. importante
    2. important
    1. del
    2. of-the
    1. Mediterraneo.
    2. Mediterranean.
    1.   ‘Ancient Rome was the most important city of the Mediterranean’.

It follows that Italian proper names cannot be preceded by a null or unexpressed determiner, for otherwise (10b) would be syntactically equivalent to (10a) and, thus, acceptable. There is substantial cross-linguistic evidence (see Longobardi, 2005) showing that N-to-D raising for proper names is required by the derivational nature of Romance languages in general. Like their Italian cousins, when accompanied by an adjective, Spanish proper names must be preceded by an overt determiner —an expletive, as Longobardi (1994) shows— or lack one and, thus, cross over to D position. This casts serious doubts over the truth-conditional relevance of Matushansky’s (2006) claims about personal articles modifying proper names in Catalan.

The complete raising pattern for Romance nouns offers further theoretical challenges as it differs substantially between proper names and pronouns (see Longobardi, 2005). Both must be raised to D when accompanied by an adjective while lacking a determiner, as in (11a) and (11b), but only proper names may be preceded by an overt determiner, as in (11c), while pronouns are ungrammatical, as in (11d).2

    1. (11)
    1. a.
    1.   Padova
    2.   Padua
    1. sola
    2. only(fem.sg.)
    1. è
    2. has
    1. stata
    2. been
    1. prescelta
    2. selected
    1. tra
    2. among
    1. le
    2. the
    1. città
    2. cities
    1. italiane.
    2. Italian.
    1.   ‘Only Padua was selected among Italian cities’.
    1.  
    1. b.
    1.   Tu
    2.   you
    1. sola
    2. only(fem.sg.)
    1. sei
    2. have
    1. stata
    2. been
    1. prescelta
    2. selected
    1. tra
    2. among
    1. le
    2. the
    1. concorrenti
    2. applicants
    1. italiane.
    2. Italian.
    1.   ‘Only you were selected among Italian applicants’.
    1.  
    1. c.
    1.   La
    2.   the
    1. sola
    2. only(fem.sg.)
    1. Padova
    2. Padua
    1. è
    2. has
    1. stata
    2. been
    1. prescelta
    2. selected
    1. tra
    2. among
    1. le
    2. the
    1. città
    2. cities
    1. italiane.
    2. Italian.
    1.   ‘Only Padua was selected among Italian cities’.
    1.  
    1. d.
    1. *La
    2.   the
    1. sola
    2. only(fem.sg.)
    1. tu
    2. you
    1. sei
    2. have
    1. stata
    2. been
    1. prescelta
    2. selected
    1. tra
    2. among
    1. le
    2. the
    1. concorrenti
    2. applicants
    1. italiane.
    2. Italian.

These N-raising patterns strongly suggest that Schoubye’s (2020) variabilist view of proper names as pronouns is not the best way to account for the data presented by Matushansky (2006).

Saab (2021) offers further evidence in the same direction.3 Against Matushansky (2006), Saab (2021) points out that personal articles in Catalan (e.g. ‘en’, ‘na’) and honorifics in Spanish (e.g., ‘don’, ‘doña’) interact in similar ways with proper names (see also Bernstein & Ordóñez & Roca, 2019). The evidence also shows that personal articles in Catalan and honorifics in Spanish do not allow for pluralization (12), must be adjacent to the name (13), and do not allow for restrictive modification (14). These results are equally problematic for Schoubye’s (2020) view which takes proper names to be capable of behaving just like predicates. If such were the case, then ‘Don’ and ‘Doña’ should be applicable to predicates and, thus, pluralizable.

    1. (12)
    1. a.
    1. en (masc.sg.), *ens (masc.pl.)
    1.  
    1. b.
    1. na (fem.sg.), *nes (fem.pl.)
    1.  
    1. c.
    1. don (masc.sg.), *dones (masc.pl.).
    1.  
    1. d.
    1. doña (fem.sg.)., *doñas (fem. pl.)
    1. (13)
    1. a.
    1. *en propi Pere.
    1.  
    1. b.
    1. *don mismo Luis.
    1. (14)
    1. a.
    1. *en Pere que va arribar ahir.
    1.  
    1. b.
    1. *don Luis que llegó ayer.

Saab’s (2021) data from Catalan also shows (pace Matushansky, 2006) that the expressions in question are not definite articles, either diachronically or synchronically. In fact, the evidence presents a further puzzle for < e,t >-type theorists since both ‘en’/‘na’ in Catalan and ‘Don’/‘Doña’ in Spanish may be used with proper names but cannot be used with common nouns that are syntactically predicates, such as ‘Professor’ or ‘Doctor’ in (15).

    1. (15)
    1. a.
    1. *Llegó el don médico.
    1.  
    1. b.
    1. *Va arribar en profesor.

Such problematic features sorrounding the predicativist evidence have led some linguists into Gutzmann’s (2019) rehashing of Potts’ (2005) idea of expressive meaning to question the truth-conditional relevance of the data. Taken together, the data from Catalan and Spanish strongly suggest that, when interacting with referential uses of proper names, personal articles are expletives. Saab (2021) argues that to best account for the data in (12)–(15) we must take personal articles and honorifics as pure expressives.

This is further supported by Oggiani & Aguilar-Guevara (2024), who consider the case of proper names preceded by a definite article in Rioplatense Spanish. Evidence shows the definite article may precede a proper name when there is affective proximity between speaker and referent, but may not do so when there is no such relation either because the referent is unfamiliar (16)–(17), because it is unknown (18)–(19), or simply because the conversation has a formal register (20).

    1. (16)
    1. a.
    1.   Hoy
    2.   today
    1. viene
    2. come
    1. a
    2. to
    1. mi
    2. my
    1. casa
    2. house
    1. Julia,
    2. Julia,
    1. una
    2. a
    1. prima
    2. cousin
    1. de
    2. of
    1. mi
    2. my
    1. padre
    2. father
    1. que
    2. that
    1. nunca
    2. never
    1. vimos.
    2. saw.
    1.   ‘Julia, a cousin of my father’s that we have never seen, is coming to my house today.’
    1.  
    1. b.
    1. *Hoy
    2.   today
    1. viene
    2. come
    1. a
    2. to
    1. mi
    2. my
    1. casa
    2. house
    1. la
    2. the
    1. Julia,
    2. Julia,
    1. una
    2. a
    1. prima
    2. cousin
    1. de
    2. of
    1. mi
    2. my
    1. padre
    2. father
    1. que
    2. that
    1. nunca
    2. never
    1. vimos.
    2. saw.
    1. (17)
    1. a.
    1.   La
    2.   the
    1. Julia
    2. Julia
    1. Roberts
    2. Roberts
    1. sí
    2. yes
    1. que
    2. that
    1. actúa
    2. act
    1. bien.
    2. good.
    1.   ‘Julia Roberts is a good actress.’
    1.  
    1. b.
    1. *La
    2.   the
    1. Julia
    2. Julia
    1. González
    2. Gonzalez
    1. es
    2. is
    1. la
    2. the
    1. nueva
    2. new
    1. profesora.
    2. professor.
    1. (18)
    1. a.
    1.   Hoy
    2.   today
    1. conocí
    2. met
    1. a
    2. to
    1. Carla.
    2. Carla.
    1.   ‘I met Carla today’.
    1.  
    1. b.
    1. *Hoy
    2.   today
    1. conocí
    2. met
    1. a
    2. to
    1. la
    2. the
    1. Carla.
    2. Carla.
    1. (19)
    1. a.
    1.   Ayer
    2.   yesterday
    1. fui
    2. went
    1. a
    2. to
    1. la
    2. the
    1. casa
    2. house
    1. del
    2. of-the
    1. Carlos
    2. Carlos
    1. y
    2. and
    1. no
    2. not
    1. me
    2. me
    1. abrió
    2. open
    1. la
    2. the
    1. puerta.
    2. door.
    1. ¿Podés
    2. Can-you
    1. creerlo?
    2. believe?
    1.   ‘I went to Carlos’ house yesterday and he didn’t open the door. Can you believe it?’
    1.  
    1. b.
    1.   Es
    2.   is
    1. que
    2. that
    1. no
    2. not
    1. sé
    2. know
    1. quién
    2. who
    1. es
    2. is
    1. Carlos.
    2. Carlos.
    1.   ‘The thing is I do not know who Carlos is’.
    1.  
    1. c.
    1.   Es
    2.   is
    1. que
    2. that
    1. no
    2. not
    1. sé
    2. know
    1. quién
    2. who
    1. es
    2. is
    1. “el
    2. “the
    1. Carlos”.
    2. Carlos”.
    1.   ‘The thing is I do not know who “the Carlos” is’.
    1.  
    1. d.
    1. *Es
    2.   is
    1. que
    2. that
    1. no
    2. not
    1. sé
    2. know
    1. quién
    2. who
    1. es
    2. is
    1. el
    2. the
    1. Carlos.
    2. Carlos.
    1. (20)
    1. a.
    1.   Hoy
    2.   today
    1. le
    2. to
    1. hicimos
    2. did
    1. una
    2. one
    1. entrevista
    2. interview
    1. de
    2. of
    1. trabajo
    2. job
    1. a
    2. to
    1. Carlos.
    2. Carlos.
    1.   ‘We gave Carlos a job interview today.’
    1.  
    1. b.
    1. *Hoy
    2.   today
    1. le
    2. to
    1. hicimos
    2. did
    1. una
    2. one
    1. entrevista
    2. interview
    1. de
    2. of
    1. trabajo
    2. work
    1. al
    2. to-the
    1. Carlos
    2. Carlos.

Oggiani & Aguilar-Guevara (2024) show that the definite article merely conveys affective proximity, lacking truth-conditional relevance. This proximity is not discourse familiarity, used by Saab & Lo Guercio (2020), but it meets all the standards for a secondary expressive meaning. It is not at issue; it projects under negation, conditionals, and questions; it is non-displaceable; it is speaker dependent; and it is not substitutable by similar descriptive content. Saab (2021) shows these same results hold for Catalan.

Like Saab & Lo Guercio (2020), Oggiani & Aguilar-Guevara (2024) take proper names to be e type expressions with contextual sensitivity triggered by the syntax. The definite article is an expletive (Longobardi, 1994) syntactically allowing proper names to take an argument function. Oggiani & Aguilar-Guevara (2024) follow Tsiakmakis & Espinal (2022) in claiming that the definite article in the above constructions is a semantic expletive, in virtue of introducing a piece of meaning that is already present (i.e., being semantically redundant). More especifically, Oggiani & Aguilar-Guevara (2024) understand the definite article as an identity function of type < e, e >, taking an item as value and delivering the same item as result. This is how meaning is enriched at the expressive level. However, this enrichment precludes any truth-conditionally non-redundant enrichment, such as the one envisaged by predicativist views.

This may be illustrated by the semantics in (21).

    1. (21)
    1. a.
    1. ⟦the⟧ = λxe. Familiar(Ic, xe)
    1.  
    1. b.
    1. ⟦ Maria ⟧ = m
    1.  
    1. c.
    1. ⟦ the⟧ ⟦ Maria ⟧ = λxe. Familiar(Ic, xe)(m) = m
    1.  
    1. d.
    1. ⟦ the Maria ⟧ = m

Together these views deliver the same picture according to which proper names have:

    1. (22)
    1. a.
    1. Simple semantics: ⟦ N ⟧ = ι ; and
    1.  
    1. b.
    1. Modifiable syntax: for expressive or predicative meaning.

1.2 Constancy: a common commitment

If we focus on their account of referential uses, there is one noticeable commonality between e and < e, t >-type theories. According to both, bare singular uses in argument position are always modally constant (rigid). As Heim & Kratzer (1998) put it:

    1. (23)
    1. “Their reference is picked out in the actual world, and they denote the same individual that was so picked out in every possible world.” [1998: 304]

Heim & Kratzer (1998) endorse an e-type view, yet (23) is accepted by both e and < e, t >-type theorists. On the one hand, e-type theories deliver constancy directly, as a constitutive part of the semantics. There simply is the referent assigned in the actual world and no functions or modal operators that may allow for inconstancy. On the other hand, < e, t >-type theories guarantee constancy in absentia, so to speak. Even though the semantics includes slots for functions, they are saturated by modally insensitive ones. In the absence of such sensitivity, the actual individual assignment becomes constant. This is clearly the case with Matushansky (2008) positing an indexical convention with “no argument slot for a possible world”.

Elbourne (2005) offers a different account, yet claims that “any use of a proper name in which the speaker does have some specific person in mind and intends to refer to that person is ipso facto a use which employs one of the non-trivial indices.” (Elbourne 2005: 174) Such indices cannot be affected by modal operators and are, thus, constant. Elbourne (2005) considers this a virtue of his theory, in light of which “the rigidity of proper names is not a problem” (Ibid: 175). He further adds “we do not conceive of actual objects or people changing their identity in any relevant way when we imagine them figuring in different sets of circumstances” (Ibid: 175). Of course, as Lewis (1986) shows, and as I will too in section 2, objects need not change their identity —they cannot— for there to be inconstancy. It will suffice to show that referential uses of proper names may shift their referent from one self-identical object to another in modal scenarios.

Now, Elbourne (2005) does consider the possibility of inconstant proper names in argument position when considering a version of Geurts’ (1997) Bambi cases (24).

    1. (24)
    1. a.
    1. Every woman who has a husband called John and a lover called Gerontius takes only Gerontius to the Rare Names Convention.
    1.  
    1. b.
    1. If John insists on calling his next son Gerontius, then his wife will be annoyed and Gerontius will get made fun of because of his name.

The second ocurrence of ‘Gerontius’ in (24a) does not have a non-trivial assignment, since there is no particular individual that is being referred to. The same goes for the second ocurrence of ‘Gerontius’ in (24b).4 Yet, Elbourne (2005) also makes clear that these are not referential uses.

    1. (25)
    1. a.
    1. “Presumably this D-type proper name will have index 0 (since it cannot be bound or referential) and will behave like any other D-type definite description” (2005: 181).
    1.  
    1. b.
    1. “The descriptive content of Gerontius must enter into the proposition […], since we need to find the person with the property of being called Gerontius in each of a set of previously defined situations” (Ibidem).

Briefly put, examples like (24a) and (24b) show that proper names can have descriptive, non-referential uses in argument position. It naturally follows that they are not constant, as descriptions typically are not. Descriptive uses of names aside, Elbourne (2005) is also committed to modal constancy for referential uses of proper names. In Elbourne’s (2005) terms, ‘Gerontius’ gets a 0-index assignment in (24a) and (24b), as no particular object is referred to across modal scenarios. Referential inconstancy, in contrast, demands a non-trivial index in the actual world and different non-trivial indeces across possible worlds, as multiple particular objects are referred to (see sections 2 and 3).

Fara (2015) offers a predicativist view that differs from those of Matushansky (2006) and Elbourne (2005) and where the commitment to constancy is straightforward. According to this view proper names in argument position are incomplete definite descriptions. The latter are considered to be always constant; thus keeping a commitment to constancy for the former.

Geurts (1997) is the only predicativst to avoid such commitment. He claims constancy is just an appearance, product of correferential indexing between the presuppositions of the speaker and the antecedent information of the hearer. This account is, unfortunately, too flexible. As Geurts himself puts it, “a name will practically always be used to refer to an individual that was already given to the hearer beforehand, and if a name is thus used it will appear to be rigid”(Geurts 1997: 340).

Geurts’ criterion is problematic in both directions. On the one hand, it predicts no constancy where there is such, since there can be constant uses that do not meet the coreferential criterion. If I say to you “Massa could have won the election” and you have no idea who Massa is, the criterion will not be met. Still, my use of ‘Massa’ will appear to be constant. On the other hand, this same criterion also predicts constancy where there is none. As I will show in the following section —see (27), (32), and (34)— the correferential indexing criterion is met even in cases of inconstancy.5 Briefly put, Geurts (1997) avoids the common commitment to constancy by way of avoiding constancy altogether. That seems like a hefty price.

Extant theories are bound to modal constancy in virtue of their proposed semantics, as they predict that all bare singular (referential) uses of proper names in argument position of a predicate will be modally constant.

2 Modal Inconstancy

Modal inconstancy is a well known phenomenon discussed at least since Quine (1953). There is modal inconstancy whenever speakers’ truth-value assessments of de re modal claims and judgments vary as a function of changes in contextual interests.6 Prior to Lewis’ (1986), modal inconstancy was only associated with predicates and/or properties. To illustrate consider (26) —see also Cray (2012; 2014) for further examples and analysis.

    1. (26)
    1. Lio Messi could have been taller.

In a conversation where human size distributions are salient, speakers may be inclined to accept (26) as true. After all, it is humanly possible to be as tall as, say, Cristiano Ronaldo. But if Messi’s specific growth hormone defficiency is salient, speakers may be inclined to reject (26) as false. If it were not for the medical supply of growth hormone Messi would have rather been shorter, not taller. At 5’7” Messi is as tall as he could be. Given the shift of interest on what it takes to be taller, the inconstancy is owed to some or other shift in the predicate or its associated property.7 It is the inconstancy of the predicate (or the property) that accounts for the shift in truth values of (28), to which competent speakers are sensitive in their assessments.

2.1 Referential Inconstancy

Lewis (1986) taught us that modal contexts observe “a rule of accommodation: what you say makes itself true, if at all possible, by creating a context that selects the relevant features so as to make it true” [Lewis, 1986: 251]. Could we create a context that selects the relevant features to allow for a shift in referential interests?

We need a context that makes more than one object referentially salient. Lewis offers one himself:

The Great Western Railway ought to have absorbed two other railways early on: the Bristol and Gloucester, and the Birmingham and Gloucester. But it tried to drive too hard a bargain. In 1845 the line from Bristol to Gloucester to Birmingham fell into rival hands. Therefore, after the grouping of railways in 1923, the post-grouping Great Western lacked a part that it might have had. What we know as the Great Western, without the missing line, was the whole of the Great Western; not, as it so easily might have been, a part of a still Greater Western (Lewis 1986: 248).

Now consider a de re modal statement about GWR, as the railway is usually called.

    1. (27)
    1. GWR could have been greater in size.8

The truth value assessment of (27) depends on the referent of ‘GWR’ in the relevant counterfactual scenario and its non-modal properties. (28) presents some such scenario.

    1. (28)
    1. Let GWR– be the Great Western as it actually was without the missing line. Let GWR be the Great Western. Let GWR+ be the sum of GWR– and the missing line. Here is GWR, in other words GWR–; they are identical. But the plural is a nonsense of grammar: ‘they’ are one thing, and it is self-identical (Lewis 1986: 249).

We have two different railways GWR–and GWR+ in w. They differ in length, shape, and geographical location. GWR– runs to and from South West England and South Wales, excluding the line from Bristol to Gloucester to Birmingham. GWR+ also runs to and from South West England and South Wales, but it includes the line from Bristol to Gloucester to Birmingham. Clearly, GWR, the actual railway, could have been either one of them. It could have added the extra Bristol-Gloucester-Birmingham line, thus being identical to GWR+. Thus, if GWR+ referential interests are salient, (27) is assessed to be true. Yet, GWR is GWR–, and GWR– could not have been identical to GWR+. If GWR– referential interests are salient, (27) is assessed to be false.

This much is known to both, you and me. Geurts’ (1997) correferential indexing criterion is met. ‘GWR’ is directly referential and has a bare singular use in argument position in (27). Yet, It also varies its reference in w following a shift of referential interests in (28). Contemporary theories of proper names, however, predict its interpretive sequence in (27) will be either (29a) or (29b) —for e-type and < e, t >-type theories respectively.

    1. (29)
    1. a.
    1. ⟦ GWR ⟧ = GWR
    1.  
    1. b.
    1. ⟦ the GWR ⟧ = ιx . R0(x) (/dӡi ‘d∧bǝlju ɑ: /)

2.2 A puzzle about names

Unfortunately, both (29a) and (29b) are false predictions, they fail to account for the shift in reference/truth values of (27). True predictions would look like (30a) or (30b).

    1. (30)
    1. a.
    1.  
    1. b.

Now, the problem is not merely that theories aimed at modal constancy fail to account for inconstancy. The problem is that, even if they wanted to, these theories could not succeed in doing so, given the resources and restrictions they take themselves to have.

Referential inconstancy is triggered by extra-linguistic contextual variations, there is no syntactic trigger involved. And the shift has an effect on truth-conditional meaning. Whatever the semantics of, say, ‘GWR’ turns out to be it must be compatible with constant and inconstant referential uses. Extant theories of proper names are incompatible with the latter and if they make themselves so compatible they will end up being incompatible with the former.

On the < e, t >-type view bare singular uses in argument position receive a non-trivial assignment yet lack argument slots for possible worlds. This is the case with Matushansky (2008) for whom variable assignments cannot be affected by modal operators. As I described earlier (see section 1.2) Elbourne (2005) offers an account according to which proper names may be either referential —non-trivial index unaffected by modal operators— or descriptive —0-index. Though inconstant, the latter is not referential and, thus, fails to account for the phenomena at hand. When shifting from GWR+ to GWR−, ‘GWR’ must shift between particular objects, and Elbourne (2005) can only offer descriptive content with no particular object. Further evidence that Elbourne’s (2005) descriptive inconstancy has little to do with referential inconstancy is Elbourne’s (2005) own recognition that even with an inconstant (0-index) assignment a proper name will still pass Kripke’s constancy test —i.e., they are still referentially constant.9 As I will show in section 4.3, (27) and (28) do not pass Kripke’s test.

Things differ for Fara (2015), who takes proper names to be incomplete definite descriptions which are, in turn, constant designators by fiat. Suppose we add an argument slot for possible worlds. This would account for the inconstancy in (27). But it would also undercut the constancy originally given, since the referential value assignment would depend on that of the possible world slot. Heim & Kratzer’s (1998) definition of constancy in (31) could not be met.

    1. (31)
    1. “Their reference is picked out in the actual world, and they denote the same individual that was so picked out in every possible world” (1998: 304).

Mutatis mutandis for e-type theories. Suppose we follow Schoubye (2020) and posit a (partial) function in the semantics. Unlike him,10 we can have an index taking a modally sensitive function that delivers an individual relative to a possible world only if such individual meets certain requirements —e.g., being called N in w; being the referent of N in w. This would potentially account for the inconstancy in (27). Yet it would also entail that for any use of a proper name there may be multiple objects meeting the relevant requirements relative to any given w, thus contradicting (31).

A different issue arises for Saab & Lo Guercio (2020). On their anti-predicativist view, referential uses of proper names depend on a particular syntax lacking slots for predicates. Whether this view is committed to constancy depends on the semantic consequences of the said view. Yet Saab & Lo Guercio (2020) merely claim a type e value must be assigned without adding details on how a particular value gets so assigned. Saab & Lo Guercio (2020) do claim that referential uses are assigned a numberless DP, assuming that the value assignment for e is insensitive to extra-linguistic context, such as varying modal scenarios. Now, since the view assumes modal constancy is related to the said syntax, it is not obvious how to modify the view to accommodate for inconstancy, short of cutting off the assumed syntax-type e semantics relation.

The puzzle is clear. All current semantic theories of proper names entail that no proper name may be inconstant in bare singular uses in argument position. Lewis’ (1986) example in (27) proves this to be wrong. Therefore, these theories must be modified to no longer entail such prohibition of inconstancy. However, if they explicitly give place to inconstancy within semantics they wind up prohibiting constancy. Briefly put, we cannot have both constancy and inconstancy to be directly or indirectly prescribed by the semantics of referential uses of proper names. Yet, we need both.

Lewis’ (1986) own account of referential inconstancy underscores the puzzling nature of the phenomenon. On his view we should give up on constancy and not “expect an ordinary proper name of a person or a thing —of a railway, say— to be strictly [constant].” Instead, we should expect a name to be quasi-constant if it “names at another world the counterpart there of what it names here” (Lewis 1986: 256). The problem with quasi-constancy is not that it requires a lavish ontology.11 The problem is simply that it does not solve the puzzle since constancy is also a genuine phenomenon. There are bare singular referential uses of proper names in argument position that are constant. In fact most typical uses of names in argument position are such. Mere quasi-constancy will not account for them.12

3 Generalizing Lewis

As Kripke (1980) explicitly notes, constancy/inconstancy is directly related to identity across possible worlds and, thereby, to the metaphysics of objects. To show that we are dealing with a linguistic phenomenon related to competent use of proper names —and not a metaphysical issue with respect to the nature of inanimate objects such as railways; or with not-so-ordinary names such as names of railway companies— it will be important to consider other kinds of names, e.g., names of persons, countries, etc.

3.1 Which David Lewis?

David Lewis was born in Oberlin, Ohio, in 1941. His parents, John D. Lewis and Ruth Ewart Kellogg Lewis, were professors of government and medieval history at Oberlin College. His influential contributions include the philosophy of language, philosophy of mathematics, metaphysics, philosophy of science, epistemology, meta-ethics, decision theory, and aesthetics. David Lewis could have been taller and with a bigger musculature, enough for him to become a professional basketball player with an extraordinary intellectual capacity. So consider the following de re modal statement.

    1. (32)
    1. David Lewis could have won the NBA Finals.

Now, consider a counterfactual scenario (33) with two salient individuals.

    1. (33)
    1. There is Lewis+, a 6’9” tall and 250lb individual born to John D. Lewis and Ruth Ewart Kellogg Lewis, both academics at Oberlin College. Lewis+ was born and raised to be an academic. He was fond of philosophy in his early college years, but he also loved athletics and quickly became a basketball star. And there is Lewis–, a 6’0” tall and 200 lb individual looking just like David Lewis, who shares all his beliefs, desires and philosophical ideas.

Lewis+ and Lewis– differ in height, weight and spatiotemporal location in w. The former is a power forward for the Cleveland Cavaliers, the latter a philosophy professor at Princeton. David Lewis could have been either in w, not both. He could have been taller and more muscular, potentially one of the best players in NBA’s (possible) history. He could have been identical to Lewis+, thus granting an assessment of (32) as true. Yet David Lewis is Lewis– and he could not have been identical to Lewis+ in w. If our referential interests point to Lewis–, then (32) is assessed as false.

As with ‘GWR’ in (27), ‘David Lewis’ shifts its reference in (32) from Lewis+ to Lewis–. Consequently there is a shift in truth-conditional content that cannot be accounted for by extant semantic theories of proper names (see 2.2).

3.2 Any name whatever

This same procedure can be extended to names of animate and innanimate objects in general. All we need is a modal context including multiple salient individuals as referential alternatives. Given that “what you say makes itself true, if at all possible, by creating a context that selects the relevant features so as to make it true” (Lewis 1986: 251), the contextual requirement for referential inconstancy will always be met.

As a final example consider the case of ‘America’. Prior to the annexation of Texas in the 1850s, America did not include what are now the states of Alaska, Arizona, California, Nevada, New Mexico, Utah and, of course, Texas. There is a possible world w with two countries, America1 and America2, with the former lacking the above mentioned states and the latter including only those states. The truth-value inconstancy of (34) relative to w should be evident.

    1. (34)
    1. America could have lacked Texas as a member state.

4 Objections and Replies

Let me now consider three objections and why they fail.

4.1 Predicative Inconstancy?

The first objection claims the relevant change in conversational interests in (27), (36) below, has an effect on the predicate and not its argument, as is the case with (26), (35) below.

    1. (35)
    1. Lio Messi could have been taller.
    1. (36)
    1. GWR could have been greater in size.

In the case of (35) the inconstancy is owed to variations on what it takes for the predicate ‘to be taller’ to apply to an object. These variations explicitly go from the property of being a taller human being to that of being a taller Messi with growth hormone defficiency. If the inconstancy of (36) were to be another case of predicative inconstancy there should be varying interests on what it takes for the predicate ‘to be greater in size’ to apply to a railway. For example, a railway may be greater in virtue of having more train cars running through it or perhaps by having a more extended railway.

This is precisely what does not happen with (36). The shifting conversational interests are not about what it takes for the predicate to be truly applied to the object assigned as argument; they are about which is the object so assigned, about which railway could be the referent of ‘GWR’ in w.

4.2 Proper Language Use

Kripke (1980) complaints about cases of language change as theoretically misleading.

    1. (37)
    1. It might also, if people gave the names ‘Hesperus’ and ‘Phosphorus’ to [distinct planets other than Venus], be a situation in which some planet other than Hesperus was called ‘Hesperus’. But even so, it would not be a situation in which Hesperus itself was not Phosphorus (Kripke 1980: 109).

To avoid sowing confusion, Kripke (1980) recommends that one

    1. (38)
    1. Describe the situation in our language, not the language that the people in that situation would have used. Hence, one must use the terms […] with the same reference as in the actual world (1980: 109, ft.51).

The second objection I want to consider claims there is improper language change in (27)–(32). To find out if this is so, we must ask if the actual referent of ‘GWR’ and ‘David Lewis’ has changed? ‘GWR’ is used in (27) and (28), below (39) and (40), with the British railway as its actual referent as Kripke demands.

    1. (39)
    1. GWR could have been greater in size.
    1. (40)
    1. Let GWR– be the Great Western as it actually was without the missing line. Let GWR be the Great Western. Let GWR+ be the sum of GWR– and the missing line. Here is GWR, in other words GWR–; they are identical. But the plural is a nonsense of grammar: ‘they’ are one thing, and it is self-identical (Lewis 1986: 249).

The same goes for ‘David Lewis’, which refers to the father of modal realism in (32) and (33) above, (41) and (42) below.

    1. (41)
    1. David Lewis could have won the NBA Finals.
    1. (42)
    1. There is Lewis+, a 6’9” tall and 250lb individual born to John D. Lewis and Ruth Ewart Kellogg Lewis, both academics at Oberlin College. Lewis+ was born and raised to be an academic. He was fond of philosophy in his early college years, but he also loved athletics and quickly became a basketball star. And there is Lewis–, a 6’0” tall and 200 lb individual looking just like David Lewis, who shares all his beliefs, desires and philosophical ideas.

The case of freshly introduced names — ‘GWR–’;‘GWR+’; etc.— is clearer. There is no prior use of them, much less one with some other reference. So, the answer to our query is no. The names used in contexts of referential inconstancy have not changed their actual referent. There is no improper use of language.

4.3 The Intuitive Test

Kripke (1980) argues that ordinary names pass the “intuitive test” of constancy illustrated in (43) and (44).

    1. (43)
    1. Although someone other than the U.S. President in 1970 might have been the U.S. President in 1970 (e.g., Humphrey might have), no one other than Nixon might have been Nixon.
    1. (44)
    1. Although [Nixon] might not have been the President, it is not the case that he might not have been Nixon (Kripke 1980: 48–49).

If ‘GWR’ and ‘David Lewis’ are truly inconstant in (39) and (41), the objection goes, it should be possible to come up with true statements that do not pass Kripke’s test. Indeed, to find some such statement one need only read more from Lewis (1986).

    1. (45)
    1. Let GWR– be the Great Western as it actually was without the missing line. Let GWR be the Great Western. Let GWR+ be the sum of GWR– and the missing line. Here is GWR, in other words GWR–; they are identical. But the plural is a nonsense of grammar: ‘they’ are one thing, and it is self-identical. What might have happened to it? It is GWR; so it would have been greater, in fact it would have been identical to GWR+. It is GWR–, so it would have been only a part of GWR, not the whole, and hence not identical to GWR, which would instead be identical to GWR+ (Lewis 1986: 249).

In (45) Lewis begins by presenting two salient objects as referential alternatives in w. Once this is accommodated, he goes on to claim (46a) and (46b), from which he infers (46c). In conjunction, (46a)–(46c) entail (46d), a statement that does not pass Kripke’s intuitive test.

    1. (46)
    1. a.
    1. “GWR […] would have been identical to GWR+.”
    1.  
    1. b.
    1. “It would have been only part of GWR.”
    1.  
    1. c.
    1. “Hence [it would have been] not identical to GWR.”
    1.  
    1. d.
    1. GWR would not have been GWR.

The first ocurrence of ‘GWR’ in (46d) has a different referent from that of the second ocurrence, embedded in the scope of the modal. Which is as it should be, since ‘GWR’ is inconstant in (45).

5 Final remarks: Kripke on constancy and semantics

Proper names are puzzling. When used in argument position, constancy is one of their most salient features, with effects on truth-conditional content (section 1). Yet, they may also be inconstant within such uses. And accounting for either one from within the semantics goes against explaining the other (sections 2 and 3). How should we proceed?

It is common in linguistics to follow Heim & Kratzer’s (1998) definition of a constant (rigid) designator —(23) and (31) above, (47) below — and to assume that it is nothing over and above Kripke’s (1980) intuitive thesis.

    1. (47)
    1. “Their reference is picked out in the actual world, and they denote the same individual that was so picked out in every possible world” (1998: 304).

However, all Kripke (1980) says about proper names — (48) and (49)— is that they intuitively designate the same object in every possible world and that this is connected with the truth conditions of the relevant statement (50).

    1. (48)
    1. “Let’s call something a rigid designator if in every possible world it designates the same object” (1980: 48).
    1. (49)
    1. “I will argue, intuitively, that proper names are rigid designators” (1980: 49).
    1. (50)
    1. “The rule that there is a single individual and a single property such that, with respect to every counterfactual situation, the truth conditions of the proposition are the possession of the property by that individual in that situation” (1980: 10).

Kripke (1980) does not say whether constancy is a semantic feature of names and what he does say, (51) and (52), suggests it is not since it may be the result of speaker stipulation. Semantics, of course, is not something speakers can meddle with while considering possible scenarios.

    1. (51)
    1. “The distinction between ‘de jure’ rigidity, where the reference of a designator is stipulated to be a single object, whether we are speaking of the actual world or a counterfactual situation, and mere ‘de facto’ rigidity, where a description ‘the x such that Fx’ happens to use a predicate ‘F’ that in each possible world is true of one and the same unique object. Clearly my thesis about names is that they are rigid de jure (1980: 21, ft.21)
    1. (52)
    1. “There is no reason why we cannot stipulate that, in talking about what would have happened to Nixon in a certain counterfactual situation, we are talking about what would have happened to him” (1980: 44).

Strikingly perhaps, Kripke (1980) rejects the idea that the only truth-conditional contribution of a name in argument position is its referential assignment. This becomes clearer with the use of correferential proper names (53), about which Kripke claims that even constant ones may nonetheless put together different truth-conditional contributions, further suggesting that constancy is not semantic.

    1. (53)
    1. My view that the English sentence ‘Hesperus is Phosphorus’ could sometimes be used to raise an empirical issue while ‘Hesperus is Hesperus’ could not shows that I do not treat the sentences as completely interchangeable (Ibid: 20).

In addition, Kripke suggests that the way in which the referential assignment is fixed may be truth-conditionally relevant, (54), and recognizes there are multiple such ways (55).

    1. (54)
    1. “[T]he mode of fixing the reference is relevant to our epistemic attitude towards the sentences expressed. How this relates to the question what ‘propositions’ are expressed by these sentences […is a] vexing [one]. […] Hence, I sidestepped [it]; no firm doctrine regarding the point should be read into my words” (Ibid: 21).
    1. (55)
    1. “In the case of proper names, the reference can be fixed in various ways. In an initial baptism it is typically fixed by an ostension or a description. Otherwise, the reference is usually determined by a chain, passing the name from link to link” (Ibid: 135).

Briefly put, it seems as though for Kripke (1980) there are two truth-conditionally relevant dimensions for proper names, one of them being the referential assignment, without them being interchangeable.

    1. (56)
    1. “The present view asserts, in the case of species terms as in that of proper names, that one should bear in mind the contrast between the a priori but perhaps contingent properties carried with a term, given by the way its reference was fixed, and the analytic (and hence necessary) properties a term may carry, given by its meaning. For species, as for proper names, the way the reference of a term is fixed should not be regarded as a synonym for the term” (Ibidem).

Offering the exact details of Kripke’s (1980) view is neither simple nor brief. Yet, with respect to semantics Kripke (1980) is known for claiming both that proper names have no meaning (57) and no connotation (58).

    1. (57)
    1. “There are writers, I think, who explicitly deny that names have meaning at all even more strongly than I would. […] A good case in point is Paul Ziff, who says, very emphatically, that names don’t have meaning at all, [that] they are not a part of language” (Ibid: 32).13
    1. (58)
    1. “Names have denotation but not connotation […] it is not part of the meaning of the name ‘Dartmouth’ that the town so named lies at the mouth of the Dart”(Ibid: 26).

Following this non-semantic —in times stipulative— lead may prove fruitful when it comes to solving the puzzle surrounding the constancy/inconstancy of bare singular, referential uses of proper names in argument position. The puzzle is clear (see section 2.2). We cannot let constancy or inconstancy be prescribed by semantics. This suggests a Kripke-friendly way out of the puzzle: let neither one be prescribed or predetermined by semantics.

Typically, referential uses of proper names in argument position are modally constant. Still, they may be turned inconstant. This is a puzzling phenomenon distancing proper names from other nouns. Furthermore, unlike other nouns, proper names are not easily pluralizable (see Saab, 2021). I have argued that no extant theory, whether referentialist or predicativist, can account for the data since it admits no semantic explanation. Proper names appear to be unique, and may be better understood from a syntactic viewpoint that accommodates for syntax-pragmatics interactions. Nonetheless, proper names may still observe Longobardi’s (2005) generalization that the referential capacity of an expression is determined by its connection to D position. Further empirical consideration is desirable in this direction.

Abbreviations

‘GWR’: Great Western Railway.

‘NBA’: National Basketball Association.

Funding information

Thanks for the financial support from PIBAA-CONICET 28720210101265CO and PAPIIT IN400823 research projects.

Acknowledgements

This paper has been in the works for several years now. I am grateful to many friends and colleagues for valuable discussions of the material in it: to to Zoltán Szabó for his poignant comments at the 2016 Philosophy of Language workshop at MIT; to the members of the Language Theory and Linguistics Department at the Linguistics Institute of the School of Humanitities, Universidad de la República, Uruguay, specially to Ana Clara Polakof and Carolina Oggiani; and to my colleagues, past and present, Ana Aguilar-Guevara, Eduarda Calado Barbosa, Axel Barceló, Fernando Carranza, Ramiro Caso, Sofía Checchi, Leandro Cherñavsky, Maite Ezcurdia, Federico Jaimes, Jorge Le-dezma, Nicolás Lo Guercio, Alfonso Losada, Ricardo Mena, Eleonora Orlando, Andrés Saab, Florencia Silva, Alessandro Torza, Matías Verdecchia, and Pablo Zdrojewski.

Separate and special thanks are owed to Agata Renans for her extraordinary editorial work. I am also grateful to three anonymous reviewers for their valuable objections and suggestions.

Competing interests

The author has no competing interests to declare.

Notes

  1. Examples are taken from Longobardi (2005). I am thankful to an anonymous referee for putting this forward. [^]
  2. Examples taken from Longobardi (2005). [^]
  3. I am indebted to an anonymous referee for presenting this issue. [^]
  4. Based on these data Elbourne claims that ‘Gerontius’ does not seem “to be directly referential or rigid” and that “the widespread position that claims that proper names have these qualities as an essential part of their semantics has encountered a serious problem” (2005: 183). It is doubtful, however, that this is a serious problem. Kripke (1980), for example, would not be surprised as he admits descriptive, and thus non-rigid, uses of names in argument position. “Another case, if you want to call this a name, might be when the police in London use the name ‘Jack’ or ‘Jack the Ripper’ to refer to the man, whoever he is, who committed all these murders, or most of them” (Kripke, 1980: 79). As Kripke (1980) puts it, “There may be some cases where the description picture is true.” (Ibid: 94). [^]
  5. Thanks to an anonymous referee for this remark. [^]
  6. In de re modal claims and judgments the modal operator has scope over the values assigned to predicates and/or singular terms. Whereas in de dicto ones they have scope over the proposition expressed by the whole sentence. Thus, ‘Aristotle could have become a politician’ is considered de re with respect to Aristotle whereas ‘It could have been that Aristotle became a politician’ is considered de dicto. [^]
  7. The literature presents two alternative ways of sorting this out. So called “shallow” views blame the inconstancy upon the expressions, claiming that the predicate shifts its meaning from one property to another —e.g., from being a taller human being to being a taller Messi with growth hormone defficiency. Alternatively, in a way reminiscent of McFarlane’s (2009) nonindexical contextualism, so called “deep” views take the propositions expressed to be inconstant. More specifically, the property expressed by the predicate changes its application conditions alongside variations in contextual interests —e.g., from applying to taller unspecified humans to applying only to taller possible Messi counterparts with growth hormone defficiency. [^]
  8. It is important to note that ‘GWR’ is not, as a matter of historical fact, an abbreviation of ‘the Great Western Railway’. Back in 1833 a British railway was founded with the name ‘Great Western Railway’. Competent uses allow for both ‘GWR’ and ‘the Great Western Railway’ as proper names for the same railway as in “Buy GWR tickets” or “GWR is nicknamed ‘God’s Wonderful Railway”. It is not the most western railway in the UK and, as Lewis (1986) cares to point out, it could have been greater. As with ‘the Holy Roman Empire’ and ‘the United Nations’, we could follow Kripke (1980) and claim that “Here it would seem that since these things can be so-called even though they are not Holy Roman United Nations, these phrases should be regarded not as definite descriptions, but as names” (Kripke 1980: 26). For further examples using ordinary proper names —e.g., ‘David Lewis’ or ‘America’— see section 3 below, examples (32) and (34). Thanks to an anonymous referee for raising this worry. [^]
  9. Or, as Elbourne (2005) puts it “we still predict that people will judge that there are no circumstances in which [“Nixon was not Nixon”] would be true. The reason is as follows. We are supposing that the semantic content of Nixon is just ‘the entity called “Nixon”.’ Then, for each circumstance of evaluation w, [“Nixon was not Nixon”] says that the entity called Nixon in w was not the entity called Nixon in w; if we suppose that it is indeed possible to locate a maximally salient entity called Nixon in each circumstance w, the sentence is still an obvious falsehood” (2005: 175). [^]
  10. “Since the semantic value of a name relative to an assignment is simply an individual, modal operators cannot shift its extension. Consequently, it is never going to be the case that the extension of a name can shift simply as a result of shifting the world of evaluation” (Schoubye 2020: 68). [^]
  11. On Lewis’ (1986) view, relations of comparative similarity are natural relations among concrete real objects. Henceforth, counterpart relations presuppose the existence of a plurality of concrete possible worlds and individuals. [^]
  12. Quasi-constancy depends on relations of comparative similarity among individuals across modal scenarios. Comparative similarity is inconstant. ‘Lewis’ may refer to different individuals in different worlds, but also in the same world, depending on which similarity relation is evoked by the use of the name, and still be a quasi-constant designator. [^]
  13. Interestingly, Ziff (1960) does not only argue that proper names are not part of the lexicon, he insists they may have connotation even though they lack any linguistic meaning. See (Ziff 1960: 85–115). [^]

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