Sense, reference, and contemporary “ predicativism ”

: Contributing to the debate between referentialist and predicativist accounts of the semantics of proper names, this paper partly endorses a recent trend to reject unitary accounts of their semantics. It does so by restoring a Fregean version of the variety of use account. It criticizes alternative variety of use accounts for not clearly distinguishing pragmatic, syntactic, and semantic issues and argues that, once these are distinguished, the necessity of accepting that names have a variety of uses, and are sometimes logical singular terms and at others logical predicates shows that Frege ’ s claim, that we should recognize that names have both reference and sense, is vindicated.


Introduction
There are those who argue that names are directly referential expressions which pick out objects. Associated with Mill and advocated by Kripke and those convinced by his rejection of description theories of naming, the "Millian" asserts that the semantic function of a name is simply to pick out an object, so that something can be said about it (Kripke 1980). Millians claim that names don't have senses, at least, when the sense of a name is assumed to be a feature of its meaning which uniquely determines its reference and is known by anyone who understands it.
Alternatively, there are those who, writing both before Kripke's attack on description theories and more recently, urge us to accept that ordinary proper names, such as "Joan," "Arthur," "Christine," and "London," as they occur in natural language, should be interpreted predicatively (Bach 1981(Bach , 2002(Bach , 2015Burge 1973;Fara 2015a;Hornsby 1976;Katz 2001;Loar 1976;Matushansky 2008;Quine 1960Quine : 176-186, 1963Sloat 1969). Although there are substantial differences of detail among them, early advocates of the Millian position and their opponents offered unitary accounts of naming. Early Millians offered no account of the semantics of names when they behave syntactically like predicates, while early predicativists took the fact that names sometimes behave syntactically as predicates to show that they always have predicate-type semantic value (Fara 2015a: 60). Important recent papers have criticized unitary predicativism, and have instead proposed that some kind of polysemy, type-ambiguity, or variety of use account is necessary (Delgado 2019;Jeshion 2015Jeshion , 2018Leckie 2013;Rami 2014Rami , 2015Schoubye 2017). According to such a view, names, in some of their uses are directly referential, in others, predicative.
In this paper I argue that the moral we should draw from the rejection of unitary predicativism is that Frege's assumption that names have sense as well as reference is vindicated, for his semantics can be adapted to provide an attractive variety of use account. At the very least, proponents of non-unitary predicativism need to demonstrate why the position that they propose, according to which names both can refer to objects and have a predicative element, does not amount to a vindication of Frege's claim that we need to recognize both sense and reference for names. There is a caveat, however. Although, the account offered is Fregean, it denies that Frege was committed to the view that sense determines reference independently of context. Recent work on the history of the reception of Frege's semantics suggests that there is no reason to believe that the historical Frege was committed to that doctrine (Beaney 2019;Green 2020). Kripke refuted a hybrid that had resulted from that historical reception (Kripke 2013: 6-9). That hybrid, which he attributed to Frege and Russell, but was also influenced by Carnap, had grown up as a result of an incomplete and partial reading of Frege's texts. It glossed over the substantial differences between these three authors. Here it is argued that once Frege's actual views are distinguished from Russell's, Frege's two distinctions, that between concepts and objects and that between sense and reference can be put to work to account for both referentialist and predicativist intuitions.
The paper falls into the following sections. In the first I outline the methodological and semantic presuppositions of the Fregean position developed and the assumed relationship between syntax, semantics, and pragmatics. In the next section I rehearse the case for accepting that there are predicative uses of names. Next, I examine early, semantic versions of predicativism, associated with what I will call nominal descriptivism, and argue that only a Fregean can successfully rebut the standard objections to it. In the next section I turn to the more recent syntactic arguments for predicativism and agree with recent authors that they don't offer a compelling case for unitary predicativism. In the last section I develop the methodological and semantic presuppositions of the first section in order to argue for the preferability of the Fregean variety of use account over other available non-unitary accounts which, it is argued, fail to properly distinguish semantics from pragmatics.
Before launching into the main argument of the paper, it is worthwhile stating its methodological presuppositions. These involve the relationship between semantics, syntax, and pragmatics. These are rarely clearly articulated. Some treat the debate as though it is purely syntactic (Gray 2017;Hinzen 2016;Jeshion 2018;Matushansky 2008;Sloat 1969). In isolation, the syntactic observations are unquestionable, but not philosophically very interesting. They become interesting when taken to have implications for the semantic contribution made by proper names, as used in natural language, to utterances or inscriptions in which they occur. The semantic contribution that an expression makes to an utterance or inscription is the contribution it makes to the truth conditions of that utterance and hence to its logical content, that is to say, the circumstances in which it is true or false, and what it implies and is implied by. 1 I assume that a claim about the semantic contribution of a kind of natural language expression is, in effect, a claim as to the normal or usual contribution made by expressions of that kind to the semantic contents of utterances in which they occur. That is to say, what is at issue is linguistic meaning, not speaker's meaning, which is a matter of pragmatics. As Kripke argued in relation to definite descriptions, the fact that a person can use a description to refer to somebody to whom the description does not apply, does not detract from the fact that the usual semantic content of a definite description is to indicate an object to which the description does apply (Kripke 1977). An account of linguistic, semantic content implies a view as to how expressions of that kind should normally be represented in a formal language, in which the semantic contribution of signs has been clearly specified. 2 Since utterances in natural language can be both syntactically and lexically ambiguous, can involve ellipsis, often have content which is context dependent, and may be literal or metaphorical, a claim about the semantic contribution of a kind of natural language expression amounts to a claim about the contribution that it normally makes to a "cleaned up" representation of the semantic content of an utterance, as made in a context. Pragmatics I understand as concerning itself both with speech acts other than literal assertions, with conversational implicatures, and with the variety of 1 See also (Leckie 2013(Leckie : 1140. For short, I will henceforth use "utterance" to mean "utterance or inscription." 2 The formal language that I will assume is standard predicate logic, in which atomic sentences Ra1 . . . an are taken to be decomposable into n-adic predicates represented as incomplete expressions, Rx1 . . . xn and individual constants a1 . . . an. The semantic value of a complete sentence is a truth value, the semantic value of an individual constant is an object, the semantic value of a predicate is a function from objects to truth values (in the general case from n-tuples of objects to truth values, though here we will be concerned mostly with one-place predicates). Quantifiers are "higher order" functions which take predicates as values. Sense, reference, and "predicativism" heuristics which take us from utterances, made in communicative situations, to the semantic content that is conveyed, or intended to be conveyed, by a particular utterance, in a situation.
The dividing line between semantics and pragmatics has been contested and some of the issues that divide referentialists from predicativists hinge on where the line should be drawn. Kaplan's influential account of demonstratives, of indexicals such as "here," "now," and of pronouns, such as "she" and "they," is discussed in the Stanford Encyclopaedia of Philosophy under "Pragmatics," though the authors note that it was developed as a semantics for these expressions (Kaplan 1989;Kotra and Perry 2015). It involves the introduction of a distinction between character and content. Character can, on the one hand, be thought of as a kind of pragmatic rule for determining semantic content and as distinct from semantic content, or on the other, as being a specific type of semantic content (Kaplan 1989(Kaplan , 1990. A case for the second way of understanding the distinction is that we don't think of "she" or "now" as ambiguous. Another reason is that we might think of character as like Fregean sense, a way the object indicated is given, and so as a specification of the indexical's meaning. On this way of looking at the matter, sharing a character is sharing a meaning and to understand the meaning of an indexical is to grasp the fact that what it picks out is determined by context. But, "meaning" in its pre-theoretic use is a vague term. If we want semantic content to be determinate, that is if we want the semantic content of an expression to be that which contributes to the truth or falsity of the more complex expressions in which it occurs, then we will be inclined to think of character as specifying a pragmatic rule, and the content indicated in a situation as the subject of semantics. Similar issues arise for names, which like indexicals can indicate, pick out, different individuals in different contexts. Below we return to this issue, and it will be argued that, as with indexicals, there are two elements to the meaning of a name, a sense, analogous to character, and a content (reference), the individual named.
As Frege noted, surface syntax, which deals with grammaticality, is not a reliable indicator of semantic content. To take his example, content remains stable through the transformation from active to passive constructions (Frege 1970(Frege , 1972. More significantly, the sentences, "Fred is a footballer" and "Red is a color" both have a simple NP/VP syntactic structure, but the first involves applying the concept of being a footballer, to an individual Fred, whereas the second asserts the subordination of the concept of being red to the concept of being a color, and so, should be represented semantically as quantified, ∀x (x is red ⊃ x is coloured). 3 A third is the example of negative existentials. "Arthur does not exist" has similar surface grammar to "Arthur does not swim." But from the truth of the second we are entitled to infer that Arthur exists, whereas from the truth of the first we cannot. Because surface syntax and valid inference can come apart in this manner, the relationship between syntax and semantics is problematic.
One version of predicativism would claim that, as in the case above, the apparent singular term, "Fred" as it occurs in "Fred is a footballer," should be represented as making the semantic contribution usually made by a predicate. It might offer, ∃x (x is Fred and x is a footballer) as an analysis. But, since this only says "Something is Fred and a footballer," actual supporters of predicativism, have interpreted "Fred" in this sentence as having a predicative element and as being semantically equivalent to the definite description, "the bearer of 'Fred'," and syntactically equivalent to "the Fred," with a hidden or null determiner (Fara 2015a;Sloat 1969). 4 Whether this actually amounts to the claim that a name makes the same semantic contribution to a sentence as does a predicate will depend on one's account of the semantic contribution made by definite descriptions. If definite descriptions in such contexts are used to refer to objects, then so too will names, as Kent Bach concludes (Bach 2015: 773-774). From the point of view this paper, this will no longer be a genuinely unitary account of the semantic functioning of names, since pragmatics will allow us to use some "predicative" expressions as equivalent to singular terms, when assessed from the semantic perspective. Instead, it will amount to the claim that names are singular referring expressions that indicate the objects named, and that names achieve this in a particular way, through being the name that the object is conventionally called. This, I argue, amounts to names having senses.

Reasons for adopting a predicative strategy
There are many good reasons for accepting that names (in at least some of their uses) should be interpreted semantically as predicates. One that has gained considerable contemporary traction is that there are contexts in which names take an indefinite article or are subject to pluralisation. We can say,

1)
There is a London in Ontario, as well as in England.

2)
Not all Joans are saints.
A second is that extending the account of existence statements such as "Centaurs don't exist" to accommodate cases such as,

3)
Arthur did not exist plausibly requires us to treat "Arthur" as behaving predicatively (Green 2015;Quine 1963, 7-8). 5 These sentences invite analyses that involve treating the occurrences of names as predicates.
Our three examples can be roughly analyzedwhere the "is London," "is Joan," and "is Arthur" are predicatesas; There is something which is London and located in Ontario and something else which is London and located in England.

2′)
¬∀x (x is a Joan ⊃ x is a saint) It is not the case that everything is such that if it is a Joan then it is a saint.
It is not the case that something exists which is Arthur. It is important to note that the "is" here is not the "is" of identity. Rather, just as ". . . is pretty" is understood as predicating being pretty, and ". . . is a saint" predicates being a saint, so, ". . . is London" should be understood as predicating being London, ". . . is Arthur" as predicating being Arthur, and ". . . is a Joan" as predicating being a Joan. Nothing so far has been said as to what properties things have to have in order for these predications to be true. It would be possible to equate being Arthur with being identical with Arthur, as Quine was inclined to do, but since this reintroduces a name, it falls back into the problem of non-denoting names and does not offer a complete solution to the problem of negative existentials. We need to treat "being Arthur" as making the kind of semantic contribution to a sentence that is characteristically made by a logical predicate. If we follow Frege, this will be a function from objects to truth values. Frege's general account of negative existentials can then be extended to include those involving names, once an appropriate function is identified, as recently proposed (Green 2015).
A third, historical motivation, for a kind of predicativism had to do with Russell's treatment of definite descriptions and the resultant need to develop a logical analysis that eliminated ordinary proper names (Russell 1956). Although Russell was impressed by Frege's logical advances, he never understood the reasons that had led Frege, in the Grundgesetze, to complicate the semantical machinery he had developed in the Begriffsschrift, by supplementing the functional analysis offered there with the distinction between sense and reference (Frege 1970(Frege , 1972(Frege , 2013. Russell understood functions to be incomplete expressions, whose introduction allowed scope distinctions to be neatly represented, and he argued in "On Denoting" that all the puzzles that might be solved by using the distinction between sense and reference (which he called the distinction between meaning and denotation) could be dealt with by showing that denoting phrases, "never have any meaning in themselves, but that every proposition in whose verbal expression they occur has a meaning" (Russell 1956: 43). Denoting phrases, and in particular definite descriptions such as "the leader of the knights of the round table" were to be eliminated as distinct semantical units. Russell argued that this strategy could solve "Frege's puzzle," that is, the problem of the meaningfulness of identity statements. But, in order for the strategy to be extended to include proper names, they needed to be eliminated in favor of definite descriptions. Thus, a motivation for a kind of predicativism was introduced, where "predicativism" was the view that all occurrences of names should be eliminated as directly referring expressions and be analyzed as definite descriptions. Names, according to Russell, were not to be treated logically as distinct semantical units with reference.
As Delia Fara characterized it, to say that names are predicates, means that "they have a predicate-type semantic value, whatever that might turn out to be" (Fara 2015a: 60). This cavalier attitude assumes that the contrast between a Russellian and Fregean semantic analysis is irrelevant to predicativism. But, in fact, it is highly relevant. Frege's Bedeutung, which has been translated as 'reference' captured a generalized notion of semantic value and, in contrast to Russell, he took predicates as well as singular terms to have Bedeutungen (Beaney 1997: 149-150, 172-180). According to Frege, both names and predicates have reference, but they refer to different kinds of entity, objects and concepts (functions from objects to truth values), respectively. Russell tended to equate Frege's notion of referring with denoting. "Denoting" is something concepts do, when they are true of objects. The result was the hybrid Frege/Russell view criticized by Kripke. Russell's method of incomplete expressions eliminates direct reference to objects, in favor of the denotation of concepts. Frege's method does not. As Russell expresses his account, a denoting expression such as, "'the author of Waverley' has been analyzed away, and no longer appears as a constituent of the proposition" (Russell 1910(Russell -1911. This is quite different to Frege, who takes definite descriptions to have Bedeutungen, but who explicitly rejects the view that, when a single object falls under the concept involved, the object referred to should be identified with the extension of the concept. He says this would make the falling under that concept an essential property of the object, which conflicts with the fact that one object can be given in many ways (Frege 2013: 18-10, n. 17).
Historically, Russell's description theory of naming, which attempts to show that ordinary proper names can be eliminated in favor of definite descriptions, has tended to be conflated with Frege's theory, according to which names, like definite descriptions, both refer to objects and express senses, while, to add confusion, the distinction between sense and reference has been equated with Carnap's intension and extension. According to Russell, predicative phrases, such as "is a king of France" do not refer. 6 By contrast, Frege accepts that names, predicates, and sentences all have both a reference (something they indicate) and a sense as is made particularly clear in a letter that he wrote to Husserl (Beaney 1997: 149-150, 174-180;Dummett 1981: 148-181). Names indicate objects. N-ary predicates indicate n-ary functions from objects to truth values. Sentences indicate truth values. Names also have senses, as do n-ary predicates, though Frege never settled on an account of what we should take their senses to be, leaving aspects of his theory unclear. Carnap's influence resulted in Frege's claim that sense is a way in which reference is given being conflated with his other claim, that functions from objects to truth values are the referents of predicates. 7 Once the difference between Russell and Frege is restored, syntactic predicativism becomes ambiguous. The position that is most common in the literature, is that names are not simple singular terms, but are complex singular terms, like definite descriptions, constructed out of a predicate and a (null) determiner. This syntactic position is, at first brush, compatible with either a Russellian or Fregean semantics of definite descriptions. As we saw, the more radical view that names are never singular terms, but always indicate functions from objects to truth values, as do predicates is implausible and can be ignored. So, the question arises, if names are syntactically definite descriptions, are they to be treated semantically as Russellian or Fregean definite descriptions?
Most of the early advocates of predicativism approached the issue from a Russellian perspective. The aim was to eliminate names in favor of definite descriptions. Nevertheless, the most popular and plausible candidate for the target description, according to Russellian predicativists, was also the most plausible candidate for a theory of sense of proper names, encouraging the assimilation of these views. 8 The sense of a name, according to Frege, is a way of being given the object it picks out, and the most obvious candidate for the way in which an object is indicated by a name is that it is indicated as the object called (in this context, by us) by that name. 9 So, while the reference of "London" would be a town, the sense it expresses would be, "something called 'London'." Similarly, Russellians have been attracted to versions of what Bach calls the "Nominal Description Theory" which says that even "when a singular proper name 'N' occurs in a sentence as a complete noun phrase," as in,

4)
London is a city "it is semantically equivalent to the nominal description that mentions it, 'the bearer of "N"'" (Bach 2002(Bach : 75, 1981. So, 4) is analyzed as,

4′)
The bearer of "London" is a city.
Various slightly differing versions of the nominalizing strategy have been developed by Kneale, by Frege in some moods, by Burge, Geurts, Katz, Elbourne, and Segal, as usefully outlined recently by Bach (Bach 2015;Burge 1973;Elbourne 2005;Frege 1984: 282;Geurts 1997: Katz 2001Kneale 1962;Segal 2001). In what follows I argue that only a Fregean version of the nominalizing account can successfully counter the standard objections that have been levelled against nominal descriptivism. More precisely, I argue that while it is sometimes necessary to interpret names predicatively, as in 1)-3), there are other cases, such as 4) where 8 Katz represents his version of the nominalizing strategy as a "non-Fregean definition of sense" (Katz 2001: 139). However, since Frege was himself tempted by the nominalizing strategy it is misleading for Katz to call his, pure metalinguistic theory, "non-Fregean" (Frege 1979: 60). Bach also lumbers Frege with the view that the sense of a name is some contentfull description and fails to note that he was an early proposer of nominal descriptivism (Bach 2015: 773). 9 Various theses concerning sense have been attributed to Frege that are not warranted by anything he says. Frege did not take the sense of a name to specify a necessary property of the object named, a view deriving from the illegitimate identification of senses with Carnapian intensions. Nor did he say anything to imply that the sense of a name, independent of context of use, provides us with a recipe for determining which object, if any, is named by the name, as is assumed by (Devitt 2015). Sense, reference, and "predicativism" "London" should be analyzed semantically as simply referring to an object, and this variety of use option is open to a Fregean but not to a Russellian. The early advocates of nominalizing predicativism were engaged in semantical analysis and interested in revealing the logical structures underpinning inference. More recently, philosophers and linguists have breathed new life into nominalizing predicativism by arguing for it from the perspective of natural language syntax (Bach 2002;Fara 2015a;Matushansky 2008;Sloat 1969). In what follows, I first argue that, approached from the perspective of logical form, only a Fregean semantical analysis can successfully counter the standard objections to the nominalizing strategy. Subsequently, I argue that Frege's full semantics can be used to explain the syntactic phenomena observed, while respecting the distinction between pragmatics and semantics, abrogated by other variety of use accounts currently available in the literature.

Semantic, nominal descriptivism and its discontents
An early objection to the nominalizing strategy was that in sentences such as 1) and 2) above, and in negative existentials, names are used, not mentioned (Evans 1982: 344). This metalinguistic objection can be fairly quickly avoided by arguing that, in predicative uses of names, what is going on is that a predicate, which picks out the property, or concept, of being called by the name is in fact being used (Bach 2002: 75-76;Green 2015). 10 Possession of this relational property involves being called by, or bearing, the name. The claim is not that ordinary names, used predicatively, are simply quotational. Rather a predicative use of a name indicates the concept of being called by that name. This comes out particularly clearly in the case of statements of existence involving names. We can imagine a situation in which a child talks about her friend, Anna. We wonder whether this is just an imaginary friend or whether Anna exists. When we discover that, "Anna does exist" we discover that "Anna" does name a person, that the concept of being the contextually relevant person called "Anna" is not empty. It is true that instantiating the relational property of being called "Anna" involves a metalinguistic element, but this does not mean that what is being spoken about is merely the name. Rather what is being referred to is the concept of possessing the extrinsic property, that something may have, of being called by that name. Unlike many count nouns, when a proper name is a name of a person, there is no intrinsic property that an object must possess in order for it to be true of it that it is called by that name. Instead, the concept maps an object to true just in case it has the relational property of being called (in this context) by that name. While the metalinguistic objection can be fairly easily countered by either a Russellian or a Fregean, the circularity objection, I contend, poses insuperable difficulties for Russellian nominalizing predicativism. In its original form, Kripke's circularity objection was that one could not give an explanation of how a name refers, by saying that a name, N, refers to an individual just in case the individual is called "N." This presupposes that we know what it is for the individual to be called "N" or equally, what it is for "N" to refer to a particular individual (Gray 2014;Kripke 1980: 70). If one accepts the above response to the metalinguistic objection, the circularity objection can be put in a different way. If the concept of "being called 'N'" (or bearing "N") is grasped, we must already have some understanding of the relation that has to hold between a person (or other named thing) and an expression, in order for it to be true of that thing that it is called "N." There must be some names in order for it to be true of individuals that they bear those names. In order to avoid circularity, the nominalizing account of predicative uses of names requires that standard, referential names exist.
The point emerges particularly clearly from Geurts's Russellian strategy for avoiding the circularity objection. He attempts to go thoroughly Russellian and denies that names are referring expressions (Geurts 1997: 325). On a thoroughly Russellian view, names, being disguised definite descriptions, do not refer. So, in order to avoid the surprising conclusion that we never refer to objects at all using names, Geurts adopts Kripke's pragmatist response to Donnellan's introduction of the semantic distinction between referential and attributive definite descriptions (Kripke 1977). Geurts argues that, while names are semantically predicative, speakers can use descriptive phrases such as "is called 'N'," to refer to people, even though there are no expressions that are semantically singular referring expressions. But if there are no names, what is it to be called "N"? Kripke argued that, when a speaker succeeds in referring to an individual by using a definite description that does not actually apply to that individual, the speaker is using the description referentially. Such speaker's reference is to be explained by pragmatics. But this does not detract from the fact that the normal semantic contribution of a definite description, to a sentence, is to refer to an individual to which the description applies. This is quite different from saying that names never make the semantic contribution made by singular terms to sentences in which they occur, but that, nevertheless, we can, somehow, manage to refer to individuals by using them. That is to say that names don't refer, but speakers use them to refer. This is like saying that predicates don't indicate concepts, but we use them to indicate concepts. What it is, in general, for a kind of expression to have a semantic function is for it to be, in general, used to perform that semantic function. So, in order for us to grasp the concept of being called by a name, we have to presuppose that there are words that fulfil the semantic function of names.
In response to this, it has been argued that we can identify proper names, not in virtue of the semantic property of directly referring, but via a non-semantic social property associated with baptizing or dubbing. 11 But is this kind of nonsemantic identification of names really possible? Dog breeders might baptize a new breed of dog, derived from crossing a pug with a poodle, a "pugoodle," and this would involve the introduction of a new common noun, or predicate, applicable to all pugoodles, not the introduction of a new proper name. The same breeders might, alternatively, baptize the accidental spawn of a pug and a poodle, "Pugoodle," and then the word introduced would be a proper name. Baptism or dubbing occurs in both situations. What distinguishes the two different kinds of baptism is that the proper name is introduced to name the individual independently of any of its properties, apart from bearing the name, while the common noun applies to members of a kind and can be extended to truly apply to any other individual that shares the properties of that kind. Application of the name does not track the possession of any independently specifiable property. So, to have the concept of the social practice of naming, presupposes the practice of using words with the semantic properties of names. When we come to represent the semantic content of "Pugoodle is a pugoodle" the first occurrence of the homophone will be taken to pick out an object, given as "called 'Pugoodle'," the second, to pick out a concept ascribed truly to any dog that is the result of crossing a pug with a poodle.
It is worth noting, at this point, an objection raised by Dummett against Russellian descriptivism. Dummett argued that even if we had a language in which there were no proper names, but only definite descriptions, we would not have really eliminated proper names, since the standard understanding of the quantifiers presupposes an understanding of the semantic function of proper names, thought of as expressions which simply serve to pick out objects (Dummett 1973: 165). The truth of ∃x (Fx), which says that some object is F, depends on the truth of Fa, for some non-empty individual constant. In the standard formal language of predicate logic, in which we disallow non-denoting names, we may not have names of all the objects in the domain, but we assume that we can provide logical names for all the objects of the domain, in order to be able to ascribe properties to them. The representation of simple atomic sentences as containing singular terms and predicates is essential to the most basic forms of inference, such as, What is true of a formal language need not be true of natural language. However, if the point of a theory of the semantic properties of expressions of natural language is to explicate the validity of those natural language inferences which are valid, and to reveal the invalidity of those which are not, then we would expect to be able to identify those expressions in natural language that are fulfilling the semantic function of names. 12 Ordinary proper names in natural language often do function to pick out individuals. This is a good prima facie reason to think that they must at least sometimes function as singular terms, and not always as predicates. So long as there are names, the concept of being called by a name will also be available. If we inhabit a world in which tags (names) are used to pick out individuals in order to attribute properties to them, we will easily grasp the concept of being tagged by a tag orthographically identified. But if there were no such tags, that is, expressions which fulfil the semantic role of individual constants, from whence would we be able to acquire the concept of bearing, or being called by a name? 13 Bach's response to the circularity objection is that "bearing a name is not the same property as being referred to by that name" (Bach 2002: 83). He says, "It is no more essential to the property of bearing a certain name that one be referred to by that name than it is essential to the property of having a certain Social Security number that one be referred to by that number." But this obscures the fact that the reason why people bear names is so they can be referred to by name. It overlooks the connection between the act of referring (done by a person) and the semantic 12 In standard interpretations of the predicate calculus, the quantifiers are assumed to be objectual, and empty names are not allowed. I suspect that in natural language quantification is often substitutional, empty names abound, and the basic inferences discussed here often don't go through. 13 In a recent paper Aidan Gray argues that anyone who claims that names have both a primary referential use and can also be used as predicates, will have to specify a projection function connecting the two uses, which he equates with two meanings (Gray 2017: 437). He sees this as a significant challenge. But seeing this as a challenge depends on a very unrealistic view of the relation between a grasp of the appropriate use of words, and a grasp of the meta-linguistic concept of the normal use of the word. If one grasps the use of predicates, as expressions correctly used when an object has a certain property, one thereby grasps the metalinguistic concept, of applying to an object, that holds between the predicate and the objects to which it applies. Similarly, if one grasps that an expression is a name, one thereby grasps the meta-linguistic concept of naming that has to hold between an object and the expression, in order for the expression to be a name of the object (Jeshion 2018: 506). Sense, reference, and "predicativism" property of referring (possessed by a word). It also ignores the fact that, from the semantical point of view, Social Security numbers play the same role as names. They are tags which are assigned to people, the application conditions of which do not track intrinsic properties of those people. Although we don't usually think of numbers as names, they are sometimes used in place of names, most famously for streets and prisoners. And they can be used in similar constructions, as in competitions, where competitors are referred to by number.
So far, I have argued that, from a semantical point of view, explaining predicative uses of names as involving the concept of being called by a name requires the existence of names, understood non-predicatively. The eliminative strategy of the Russellian is incapable of giving a non-circular account of what it is to be called by a name. For that strategy to work, some expressions have to function referentially as names (in individual constant mode). Since Fregeans have no desire to eliminate names, they avoid this problem. Names in sentences like 4) (when they are functioning normally) serve the semantic function of introducing objects in order to say something about them. In 1)-3) they serve the derivative function of indicating, for each name, the concept of being called by that name. The syntactic arguments do not alter this situation.
It is an advantage of the Fregean approach, adopted here, that it employs a vocabulary appropriate for distinguishing different elements within the pretheoretic concept of meaning, which are often run together. Ordinary language proper nameslike indexicals, demonstratives, and non-individuating definite descriptionsonly pick out determinate objects when used in a context where it is clear, both that the name is being used as a singular term and which of the various individuals that bear the name is in question. When used in such a context the semantic contribution (the role that it can play in inferences) that a name makes to a sentence can be equated with that made by an individual constant in a formal language. Another element of meaning, the sense of the name, is the way the individual is presented. When referred to by name, the individual is presented as one of the entities called by the name used.
If one discards the distinction between sense and reference, it can seem as though there are two competing referentialist accounts of the semantics of proper names, one, which has been called "homonymist" would treat names as semantically ambiguous, the other, which has been called "contextualist" would treat them as context sensitive (Gray 2017: 439-450). The Fregean, by contrast, treats these as two distinct elements to be distinguished within the pre-theoretic notion of meaning. Uses of a single name, orthographically identified, to indicate different individuals share a sense, so in this sense are not ambiguous, but since names can have multiple referents, in another sense they are ambiguous. The distinction between sense and reference thus dispels the apparent conflict between homonymist and contextualist accounts of the meaning of names.
Nevertheless, we should not simply equate names with indexicals. Evidence for this is that, very early on, children learn the use of names to pick out distinct individuals in their environment, and after a time, they show that they grasp the distinction between names and general terms. Later, they acquire competence with indexicals, a skill which usually brings with it amused play with the new skill of shifting reference. 14 Formal languages don't include demonstratives or indexicals, just because their meanings are such that the truth or falsity of sentences in which they occur always depends on rapidly shifting elements of the non-linguistic context of utterance. Names, within a specific conversational context, typically have a fixed reference. Formal languages may, and usually do, include singular constants, so as to be able to capture inferences such as instantiation and generalization. The inferential role of non-empty, proper names in natural language is intended to be captured by singular constants in formal languages, so distinct uses of names should be analyzed, semantically, as singular terms. This will commit us to treating natural language names, when used as singular terms, as making a variable contribution to the truth conditions of the sentences in which they occur, but as united in so far as, in each case, the object is presented as called by the same name. There are many Johns. When we use the name "John" to indicate any one of them, they are each presented to us as called "John." Different tokens of "John" share a sense but differ in reference. According to this Fregean account, the sense of "John" does not uniquely determine its reference independently of context. But nothing that Frege said conflicts with this feature.
The Fregean can also allow that, in certain contexts, names function semantically as predicates, equivalent to "x called 'N'." So long as a language has the practice of naminga relationship which holds between individuals and words such that, for instance, "John" names Johnthe relational concept, "'John' names x" and two place relation, "'N' names x" or "x is named (called) 'N'" will be easily grasped by any competent language user. Following normal Gricean conversational principles enables listeners to determine whether a use of a name should be interpreted as functioning as a singular term or as a predicate. There are general principles of communication which guide our assignment of semantic content to utterances. If someone seriously utters 3) we will hear them as claiming that being Arthur is uninstantiated, which amounts to there being no individual named by the contextually relevant use of the name "Arthur." This connection between the singular referring uses and predicative uses of names also explains the intuitive acceptability of inferences such as, Arthur was a Welsh king.

____________________________
There was a Welsh king named "Arthur." 15 The use of the singular referring expression, "Arthur" in the premise, implies that there is someone being referred to by this name, and justifies the conclusion. The reasoning is not strictly valid, since the person being referred to, by our contemporary use of "Arthur," may not have been called by the name "Arthur," but by some earlier form of the name, no longer in use. Nevertheless, it is good enough reasoning.
The question of whether a name is being used as a singular term or being used as a predicate is not obvious from syntax. Syntactically, "Arthur existed" and "Arthur fought" are identical. The need to account for differential inferential import requires the assignment of the different semantic analyses, ∃x x is Arthur, and Fa to these utterances. The fact that "Arthur" plays a different semantic role in these sentences, is something required by more general, semantic features of use, connected to inference.

The syntactic case for predicativism
In essence the syntactic argument for predicativism goes as follows. Definite descriptions are noun phrases constructed out of the definite article and count nouns (or general terms). Everybody agrees that definite descriptions, although they are singular terms, are not names. But, syntactically, names behave almost like definite descriptions, and are subject to (nearly) the same grammatical transformations. Therefore, names must be (denuded) definite descriptions and be fundamentally predicative. So, even if one accepts that individual constants are ineliminable from a formal language, names in natural language cannot be assimilated to individual constants. Bach makes the point particularly clearly, saying: The relevant difference between ordinary proper names and individual constants is not that proper names are often shared and that individual constants are proprietary. Their difference is ultimately syntactic: whereas individual constants are inherently complete noun phrases (or at least the formal equivalent), proper names are not. As we have seen, although proper names generally do occur as complete noun phrases, that is not what they are inherently, since they can be introduced by determiners and quantifiers and be modified and pluralized. (Bach 2002: 90) According to Bach, proper names are not "inherently" complete noun phrases because they can be introduced by determiners, etc.
Although the syntax shows that names sometimes function predicatively, the syntactic case for a fully unified treatment is weak. 16 Evidence abounds that names and predicates don't always perform the same grammatical roles. "John is kind" is grammatical, whereas "Dog is kind" is not. "The John is kind" is not grammatical whereas "The dog is kind" is grammatical (King 2006). Fara responded that this only shows that names and common count nouns are different varieties of the category, count noun, just as count nouns and mass nouns are different varieties of the category noun. But this is not compelling, since it has been pointed out that natural language allows for many syntactic category shifts (Delgado 2019;Hinzen 2016: 597). Evidence is piling up in favor of a non-unified treatment.
We have seen that the Russellian strategy of eliminating definite descriptions as singular terms in favor of predicates and quantifiers fails the test of being a fully coherent semantic theory. We need some expressions to play the logical role of singular terms, if we are to give an account of the quantifiers. If

5)
Joan was the savior of France, involves a denuded definite description, we might assume a Fregean, rather than a Russellian account of definite descriptions. 17 In that case, definite descriptions are treated as singular referring expressions. But then the theory that names are always denuded definite descriptions has some odd consequences. For a Fregean,

6)
The savior of France was burnt, has the form F (the savior of France) where "the savior of France" is a complex singular term constructed out of a predicate, ". . . is a savior of France," and the definite article. The whole expression indicates the unique contextually 16 The issue is discussed in detail in Schoubye (2017: 741-761) and the case for a unified treatment criticized by Hinzen (2016) and Jeshion (2015). 17 Elbourne, who like Fara interprets proper names as definite descriptions adopts a Fregean analysis (Elbourne 2005: 99). Sense, reference, and "predicativism" determined savior of France, if there is one. 18 If ". . . Joan" is the predicative part of "the Joan" then

7)
The Joan was burnt should be grammatical, but it is usually not (at least in English) and, except in a distinct set of cases, we have to drop the definite article in order for "Joan" to function semantically as a singular term. Two recent papers have discussed cases where constructions like 7) are grammatical. For instance, we might precede an utterance of 7) by the following story. "There were three girls undertaking a chemistry experiment at school, two Katherines and a Joan. The Joan was burnt." Now the sentence is acceptable. This illustrates how circumstances of the context of utterance, which cannot be fully formalized, but belong to pragmatics, influence the interpretation of an utterance. In such a situation, because the name has been previously used as a predicate, "the Joan" is naturally read as picking out the specific individual mentioned, who falls under the predicate (Gray 2017;Jeshion 2018). Such cases do not invalidate the argument offered, but rather illustrate how it belongs to pragmatics to determine whether a specific use of a name indicates an object or a concept.
Furthermore, there are also cases where phrases, similar to definite descriptions, because they contain the definite article, are not best represented as playing the logical role of singular terms. Phrases with the structure, "the F" may be functioning as Fregean concept expressions, and their predicative character is made explicit when translated into the predicate calculus. In utterances of,

8)
The female is born to suffer "the female" may, occasionally, be functioning as a definite description, but it need not be. It may indicate a concept. Then the sentence would be analyzed, 8′) ∀x x is female ⊃ x is born to suffer.
If, "Joan"' were always fundamentally predicative, and was only transformed into a singular term by the addition of the definite article, then one ought to be able to express the relation of subordination between being born to suffer and being Joan using the sentence,

9)
Joan was born to suffer.
But this sentence only supports a reading which attributes being born to suffer to the individual Joan. 19 Even if one reinstates the definite article, as in,

10)
The Joan was born to suffer, a reading in which this says that being Joan is, in general, subordinate to being born to suffer does not appear to be available. "The Joan" remains resolutely singular. In order to get something similar to 8) we need to pluralize, getting 11) Joans are born to suffer in which, as in 2) Not all Joans are saints, mentioned above, "Joan" is best represented as playing the role of a predicate. If we read 11) as a universal claim we get, 11′) ∀x x is called "Joan" ⊃ x is born to suffer. This is like 2) which is rendered,
Since we have to pluralize in 2) and 11) order to get "Joan" to function as a logical predicate, whereas we don't have to pluralize "female" to get this effect, this strongly suggests that there is a primary use of the name as a singular term.

In defence of a Fregean non-uniform referentialism
Neither of the alternative uniform accounts of the semantics of proper names accounts for their behavior in all contexts. The predicativists are correct to point out that proper names often behave like predicates, but they fail to demonstrate that they never play the semantic role of direct, singular referring expressions. Papers by Robin Jeshion, Dolf Rami, Gail Leckie, Anders Schoubye, and Wolfran Hinzen suggest that a non-uniform account is needed (Jeshion 2015;Leckie 2013;Rami 2015;Schoubye 2017). In this last section, I argue that the positive nonuniform accounts developed fail to distinguish pragmatics from semantics, and that the resources of a Fregean semantics are already rich enough to account for all the observed phenomena. Rami treats occurrences of proper names as singular terms as manifesting their primary use and attempts to explain their use as predicates through the phenomenon of 'meaning transfer' calling his account, a use-conditional version of the polysemy view (Rami 2015: 408). Meaning transfer is one way of accounting for non-literal uses of expressions, such as metaphor and metonymy. Rami also sees it at play in cases like,

12)
The ham sandwich did not pay.
It is part of the methodological assumptions of my account that a semantic representation of what is conveyed by an utterance, in a context, is only available after we have applied pragmatic heuristics, which take us from natural language utterances to the content conveyed. Pragmatics suggests that what is involved in 12) is ellipsis, not polysemy. The sentence, being implausible, will be interpreted in a context of utterance as expressing a thought of the form,

12′)
The person who ordered the ham sandwich did not pay.
This (in a context) can then be assessed for truth or falsity. Much of what Rami argues is compelling, and the position that he ends up with allows that different uses can be made of names. But there is a question as to whether we should equate the kind of non-uniform behavior displayed by names with polysemy. We often have to undertake a process of pragmatic interpretation in order to determine from an utterance what thought is being expressed. Indexicals, are not usually thought of as having many meanings, rather they have a kind of incomplete meaning, which has to be filled out by contextual elements in order for truth or falsity to be assessed. Superficially, names, considered independently of the sentential and broader context of utterance, are similar. Proper names are shared and so, like indexicals and demonstratives, they only indicate a definite individual in a context of utterance. This similarity leads Schoubye to argue that they should be interpreted as functioning semantically like demonstratives or indexicals, despite the fact that identifying proper names with indexicals was a position that Kaplan explicitly rejected (Kaplan 1989: 558-563;Schoubye 2017: 727-740). As argued above, although similar, names are not quite the same as indexicals. In a successful context of use, a name serves to indicate a determinate individual, called by that name in the mouth of any speaker in that context. In a particular context of use, an indexical will continue to serve a shifting purpose that depends on the speaker. In a context, the reference of a name will be fixed, its sense will present an object as called by that name. A Fregean does not need to postulate meaning transfer in order to account for the different kinds of semantic contribution that names can make to sentences in which they occur. Rather, there are two different but connected semantic functions names can perform. Often, and paradigmatically, they function as singular referring expressions, and their introduction into natural language is explained by the usefulness of tags, which can be used to pick out individuals, as well as to call them, and to gain their attention. However, once the practice of using arbitrary tags as names is introduced, the concept of being called by a name will also be available. The availability of the concept provides both an account of the sense of names, and an explanation of how it is that names can function as predicates. Once words are used to talk about things, we get for free, as it were, the metalinguistic concept of a word's indicating a thing, and this is true for common nouns as well as proper names.
In the version of the polysemy view developed by Leckie, the meaning of the name, considered as a singular referring expression, and its meaning when used predicatively are connected by what she calls a lexical rule (Leckie 2013(Leckie : 1144(Leckie -1145. Her notion of a lexical rule is similar to Rami's notion of meaning transfer and is illustrated by the same example of the "ham sandwich" that he uses, as well as cases of metonymy such as the fact that, "walnut" can be used for a kind of tree, as well as for a part of it (Leckie 2013(Leckie : 1151. Once again, from the methodological perspective adopted here, this approach confuses pragmatics and semantics. Nevertheless, Leckie's version of the polysemy view, which states that a predicative use of a name "N," means "person called 'N'" where the second occurrence of "N" is a referential use, is close to the Fregean view I propose (Leckie 2013(Leckie : 1154). Leckie's articulation of it cannot be quite right, because, in the predicative uses of names, the name is mentioned, not used, what is used is the predicate, "is called 'N'." Nevertheless, being called "N" is being called by a tag, of the kind normally used as a singular referring expression.
Frege's introduction of the distinction between sense and reference was based on the observation that a word, or sentence, can make a different kind of semantic contribution to the various sentences in which it occurs, depending on features of the linguistic or wider context. As well as distinguishing Bedeutung from Sinn, he also distinguished singular terms, which have objects as their referents from predicates, which have concepts (functions from objects to truth values) as their referents. He introduced the distinction between reference and sense partly because he recognized that, whereas many patterns of inference can be adequately represented in terms of the truth values of sentences, the objects referred to by singular terms, and functions from objects to truth values, not all patterns of inference can be captured using these resources. In "On Sinn and Bedeutung" he pointed out that the way in which an object, truth value, or function is given can also impact, in certain sentential contexts, on the validity of inference (Beaney 1997: 172-180). We have come to differentiate the contexts in which reference is sufficient to capture inferential structure, from those in which it is not, by calling the first extensional and the second intensional. But Frege's recognition that there are varieties of semantic contribution that can be made by words can also be used to explain features of our use of expressions in contexts which are usually deemed extensional.
The variety of use account offered here is not a version of ordinary polysemy. A name applies to a thing just in case, in the context of use, that name is used as a name of that thing. Having the capacity to use a name implies grasping the concept of being called by that name. So, the different semantic contributions that a name can make to various sentences in which it occurs should not be thought of as two different meanings, but rather, as grounded in two different features meaning, the semantic value, or what is indicated, and the sense expressed, or the way in which what is indicated is presented. Recognizing these different elements within the meaning of a word is required to account for differences in semantic functioning in different contexts. A name, even when used in a context where it is unambiguous which individual it picks out, can nevertheless function either as a singular term or predicatively. Which function it is performing has to be determined in accord with Gricean communicative principles.
The dictionary is full of words that can belong to many semantic categories. "Cat" is generally used as a common noun. But in my family, and in Jeshion's, it has been used as the name of a cat (Jeshion 2018: 477-478). Many people call their dog, "Dog," while others give their pets names like "Faithful," using as names words which more often function as adjectives. "Dog is kind," "Cat left us," "Faithful is greedy" are ungrammatical if the lexemes "dog," "cat" and "faithful" are interpreted as being used as common nouns or adjectives. But there is nothing to stop us from using these words as names, in which case the sentences are grammatical. Words that are paradigmatically used as common nouns can also be used as names, and words paradigmatically used as names can also be used as common nouns.
Since competence in the use of a name involves grasp of the concept of naming, we can say that even when names are being used as singular terms, the way in which the object is given is as the thing called by that name, and this constitutes its sense. Introducing Frege's distinction between sense and reference, as well as that between singular terms and predicates, also allows us to explain why it is that names, even when they are operating as singular terms, can nevertheless share some syntactic features with predicates. In sentences like,

2)
Not all Joans are saints, we can say that "Joan" pluralized is fully predicative, that is, it is functioning semantically as a concept expression. In,

5)
Joan was the savior of France, "Joan" is functioning semantically as a singular term. Nevertheless, the object, Joan is given as "someone called 'Joan'," which explains why, in answer to the question, "Which Joan?" we will specify, "the Joan born in Domremy" using a complex singular term in which the predicative element, which is, as it were, semantically inert in 5), becomes explicit and semantically operative.
In this paper I have agreed with those who reject unifying predicativism, the view that all occurrences of names should be analyzed predicatively, or as Delia Fara characterizes it that "they have a predicate-type semantic value, whatever that might turn out to be" (Fara 2015a: 60). But it might be objected that, by allowing that names have sense as well as reference, I have, after all, conceded that all names do have a predicative element. In a sense, this is correct. But this fact does not imply that names never function semantically as singular terms. This is a view that I reject. Nevertheless, I accept that, even simple unstructured singular terms, by their very nature, present the object spoken of in a particular way, they present it as referred to by a name, and so have a kind of minimal sense. That sense involves the concept of being called by a name, and that concept can also be semantically operative in fully predicative uses of the name. It is only by recognizing that names can fulfil a variety of semantic functions that their linguistic behavior can be adequately represented, and unlike that adopted by Russell, the full Fregean semantics has the resources to represent the variety of uses to which names can be put. The necessity, in order to account for all these uses, of recognizing that they can function as different semantic types appears to vindicate Frege's use of two distinctions, that between concept and object and that between sense and reference. Or, at the very least, it suggests that an explanation is owed for why, once a variety of use predicativism is adopted, we should not think that Frege has been vindicated.