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Predicate Reference

Abstract and Keywords

Whether a predicate is a referential expression depends upon what reference is conceived to be. Even if it is granted that reference is a relation between words and worldly items, the referents of expressions being the items to which they are so related, this still leaves considerable scope for disagreement about whether predicates refer. One of Frege's great contributions to the philosophy of language was to introduce an especially liberal conception of reference relative to which it is unproblematic to suppose that predicates are referring expressions. According to this liberal conception, each significant expression in a language has its own distinctive semantic role or power, a power to effect the truth-value of the sentences in which it occurs.

Keywords: referential expression, predicate, wordly items, philosophy of language, liberal conception, truth-value, sentences

A verb … is a sign of something said of something else


Can we put the problem of philosophy thus? Let us write out all we think; then part of this will contain meaningless terms only there to connect (unify) the rest. I.e., some is there on its own account, the rest for the sake of the first. Which is that first, and how far does it extend?


The tendency to construe predication as a kind of, or analogous to, reference is one of the most persistent mistakes in the history of western philosophy


Are predicates referring expressions? If only a convincing answer to this question could be found and put in place, so many other pieces of the philosophical puzzle might fit together: the objectivity of judgement, the unity of the sentence, the status of higher‐order logic, the problem of universals. But what is the question asking? That all depends on what we mean by “predicate”, and what we mean by “referring expression”.

(p. 423)

It is in the fundamental union of predication that names and predicates find their contrasting but correlative roles. In the simplest form of sentence a name serves to pick out an object while the predicate supplies what the sentence says about the object so named. More generally, where a sentence consists of two or more names the predicate supplies what the sentence says about the objects thereby picked out (if they are different). Conceived in this way, predication may be represented by the neutral logical forms “Fa”, “Fab” and “Fabc” (etc.); forms that depict predicate expressions with an upper case letter “F”, and names with lower case “a”, “b”, “c”. Our question then becomes whether the expressions that the “F” represents in “Fa” or “Fab” or “Fabc” refer.

This picture of predication operates at a high level of abstraction. Predicates are conceived as what the rest of sentence says about the object or objects named. But the rest of a sentence (in natural languages at least) may exhibit considerable complexity that a mere “F” is beggared to represent. It is true that some sentences contain only a name and an intransitive verb in finite form (“Socrates walks”), but these are far from being the rule. There are others that conjoin a name with an adjective or a substantive prefaced by the copula “is” or “is a” (“Socrates is wise”, “Socrates is a man”). Then there are sentences that conjoin a name with another via a transitive verb (“Socrates loves Plato”). And there are sentences in which an adjective or a substantive is framed by the copula and a preposition or conjunction to relate one name to another (“Socrates is wiser than Plato”, “Socrates is a teacher of Plato”). There are also more complex constructions in which (e.g.) an adjective is placed in attributive position to a substantive (“Socrates is a wise man”) or an adverb is joined to a verb (“Socrates walks slowly”).

In abstracting away from these and other contrasting differences between verbs, adjectives and substantives—in depicting the different predicative constructions to which they contribute as mere grammatical variations on what is logically represented by “Fa” or “Fab” or “Fabc”—the practice of picturing a predicate with a simple “F” risks neglecting semantically significant structure. Quine has sought to justify the practice of operating at this high level of abstraction, declaring these grammatical contrasts to have “little bearing on questions of reference” (see his 1960: 96). But Quine offers no argument for this claim, and it is difficult to avoid the suspicion that operating at such a high level of abstraction seems acceptable to Quine only because the formal languages that logicians have found fruitful to study lack the grammatical paraphernalia of verb, adjective and substantive. It may be that it is only by attending to differences among the more complex constructions of natural language—differences concealed beneath the coat tails of an “F”—that it is possible to settle (at least) some questions of reference. Simplicity and generality in a theory are nevertheless to be prized and what is often difficult to make out at ground level may be seen clearly in outline from a loftier perspective. Let us therefore begin our investigations by entertaining the hypothesis that predication is adequately represented by the neutral forms “Fa”, “Fab”, “Fabc” while remaining ready to test out and if necessary discard it.

(p. 424)

Whether a predicate is a referential expression depends upon what reference is conceived to be. Even if it is granted that reference is a relation between words and worldly items, the referents of expressions being the items to which they are so related, this still leaves considerable scope for disagreement about whether predicates refer. One of Frege's great contributions to the philosophy of language was to introduce an especially liberal conception of reference relative to which it is unproblematic to suppose that predicates are referring expressions. According to this liberal conception, each significant expression in a language has its own distinctive semantic role or power, a power to effect the truth‐value of the sentences in which it occurs. Frege took the semantic power of an expression to be determined by the presence of an extra‐linguistic correlate or semantic value, a value to which the expression refers. So conceived, each significant expression in a language—whether a name, a predicate, a sentence or an expression of some other category—is a device for referring to its semantic value. Frege introduced this conception of reference because the systematic assignment of semantic values to expressions in a language provides the basis for a recursive determination of the truth‐values of sentences in the language. In doing so, Frege anticipated the modern logician's notion of an interpretation, an assignment of entities to expressions that enables the logician to track and code the truth‐sensitive features of a language, features vital to an appreciation of logical consequence and validity.

However, Frege also employed a far more demanding conception of reference—inchoate but still exerting of a powerful theoretical attraction of its own—that renders it far more problematic to suppose that predicates are referring expressions.1 There are prototypical cases of referring expressions: “that mountain”, “this river”, “Alexander”. What makes such expressions prototypical is the fact that—from an intuitive point of view—they are evidently used to identify the things about which we think and talk; they isolate and focus our attention upon features of the world drawn forth from the environmental backdrop. The prototypical cases, demonstratives, and names, thus provide a (provisional) model for conceiving of reference, reference being initially (at least) explained as the relation that obtains between a prototypical expression and the thing in the world it picks outs.2 Since predicates do not belong to the class of prototypical cases it needs to be argued, rather than assumed, that the conception of reference that arises from considering the prototypical cases should be extended to cover predicates. Whether predicates belong to a more general category of referring expressions therefore depends upon the extent to which predicates are to be compared rather than contrasted with the prototypes, akin or analogous in their functioning to demonstratives or names where (p. 425) these are conceived as referring devices. Are predicates referring expressions in this more demanding sense?

A Road Map

At first blush it may appear that a relational construal of predication—that likens predicates to names—is scarcely credible. For, from an intuitive point of view, it appears that a speaker of English can perfectly well understand “x is wise” or “y runs” without there being something that these predicates refer to. To understand “x is wise” and “y runs” the speaker need merely know when these predicates may be truly applied. He or she need merely know that “x is wise” applies to wise individuals, “y runs” to running things. This suggests that the semantic role of predicates consists in simply being true (or false) of objects picked out by names—predicates perform no additional role that demands them to have referents of their own. This conception of predication is introduced and developed in Section 19.1. Whether predication can be satisfactorily understood in such terms ultimately depends upon whether there are features of the use of predicates that are adequately explained if predicates are conceived as merely true (or false) of objects. Succeeding sections therefore explore whether there are such features of use. Section 19.2 considers whether the interaction between predicates and quantifiers forces the construal of predicates as referring expressions picking out elements of a domain over which quantifiers of the relevant form range. Section 19.3 discusses whether there are analogues of the notions of identity and identification familiarly associated with names that apply to predicates and supply analogous reasons for construing predicates as referring expressions. Finally, Section 19.4 investigates whether the prevalence of nominalizations in natural language, expressions like “wisdom” and “courage”, provide evidence that the predicates from which these expressions are derived are referring. It is illuminating to begin our exploration of these issues from a consideration of the historical point of entry for analytic philosophy into the debate about predication.

19.1 Objectivity without Objects

It is now routine to separate the question whether a given stretch of discourse is objective—whether the statements of the discourse express truths that are independent of cognition in some fitting sense—from the question whether the discourse in question describes a domain of objects.3 This separation of questions relies upon the (p. 426) veracity of the insight that objectivity does not require to be anchored in the existence of objects. But if this is an insight, it is hard won; for without the benefit of some of the most spectacular advances of analytic philosophy it might never have been achieved. And had these advances never been made, the question whether predicates are referring expressions might never have been a subject of controversy for us.

How can it be possible to make a statement about an objective reality true or false depending upon the character of that reality? One plausible answer is that it is possible because the different words that make up such a statement stand for different elements of reality, the whole true or false depending upon whether the elements of reality are arranged as stated. By so affirming the possibility of statements about a mind‐independent reality the founders of analytic philosophy—Frege, Moore and Russell—sought to undermine the different forms of idealism that prevailed among their contemporaries. The doctrine that predicates are referring expressions (alongside others) thus became key to their revolt against idealism.

The significance of subsequent developments is thrown into relief against the backdrop of Russell evolving views upon reference.4 In his Principles of Mathematics Russell had staunchly advocated a realist theory of meaning: “Words all have meaning, in the simple sense that they are symbols which stand for something other than themselves” (see his 1903: §51). This led Russell to admit a profligate ontology—that included “Numbers, the Homeric gods, relations, chimeras, and four‐dimensional spaces”—to correspond to the many different words of our language. By holding to the being, if not the existence, of these different objects Russell was able to maintain the objectivity of statements about them; for “whatever can be thought of has being, and its being is a precondition, not a result, of its being thought of” (1903: §427).

Russell was to become sceptical of this ultra‐realist theory because of the ontological excesses to which it gave rise. But he could not act upon such scruples to deny that many words have reference until some other means had been found of ensuring the objectivity of the statements to which these words contributed. Famously, the decisive breakthrough came when Russell discovered his theory of descriptions. Surface appearances suggest that phrases of the form “the ϕ” are referring expressions; the theory of descriptions shows that such appearances deceive us. This is because, according to the theory, contexts in which definite descriptions occur admit of eliminative paraphrase: “F(the ϕ) ” is equivalent to “Exactly one thing is ϕ and whatever is ϕ is also F”, a context in which “the ϕ” does not occur, referring or otherwise. In an echo of Russell's discovery, the early Wittgenstein was later to argue that the logical constants (“→”, “∼” etc.) do not refer either, their role taken up and discharged by a truth‐table notation from which the logical constants are absent (see Wittgenstein, 1922: 4.0312, 4.4414).

Despite these advances Russell continued to maintain that predicates are referring expressions. His reasons become evident in The Problems of Philosophy. There discussion is focused upon whether the preposition “in” is a referring expression: (p. 427)

Suppose, for instance, that I am in my room. I exist, and my room exists; but does ‘in’ exist? Yet obviously the word ‘in’ has a meaning; it denotes a relation which holds between me and my room. (Russell 1912: 50)

Why is it obvious that the word “in” refers to a relation? Russell invites us to entertain an alternative account of “in”, an account whereby the preposition reflects the synthesizing activity of the mind:

Many philosophers, following Kant, have maintained that relations are the work of the mind, that things in themselves have no relations, but that the mind brings them together in one act of thought and thus produces the relations which it judges them to have. (1912: 51)

But to suppose that the use of the word “in” reflects the activity of the mind would be—absurdly—to undermine the objectivity of what Russell uses the sentence “I am in my room” to express:

It seems plain that it is not thought which produces the truth of the proposition ‘I am in my room’. It may be true that an earwig is in my room, even if neither I nor the earwig nor any one else is aware of this truth; for this truth concerns only the earwig and the room, and does not depend upon anything else. (1912: 51)

Russell so arrives at the conclusion that “relations … must be placed in a world which is neither mental nor physical”, elements of platonic realm that prepositions and transitive verbs pick out.

Russell's argument thus proceeds by elimination: either predicates are referring expressions or they reflect the activity of the mind; if predicates reflect the activity of the mind then the objectivity of statements about a mind independent reality is undermined; therefore predicates must be referring expressions. This argument fails if there is some alternative account of how predicates function that Russell has neglected to eliminate. But Russell saw no such alternative. He saw none because the dominant model of how expressions might function other than by referring was provided by the method of eliminative paraphrase embodied in the theory of descriptions. This method cannot be applied to eliminate predicates. For what are the equivalent contexts “ … a ” in favour of which predications of the form “Fa” are to be eliminated? There are no such contexts; predication is so fundamental a combination that no language that names or quantifies over objects could fail to incorporate a predicative device in order to say something about them.

19.1.1 A Disquotational Theory of Predication

But is there a third way that Russell neglected to consider? Is there a way of construing predicates that does not attribute a referential function to them but still respects the fact that predicates make an essential contribution to the statements they are used to make without undermining the objectivity of these statements? Quine saw it, or at least thought he did.

(p. 428)

Like Russell, Quine was impressed by the theory of descriptions. However for Quine the theory revealed not only how expressions of a particular form (“the ϕ”) contribute to the contexts in which they occur but without referring. For Quine the theory of descriptions also revealed that there is a great gulf between meaning and reference in general. But if an expression's being meaningful and an expression's bearing a referential function are different things then this opens up the possibility that a predicate may function “merely as a contextually meaningful word … a syncategorematic expression which names nothing, abstract or concrete” (Quine, 1939: 704).

However, in order for Quine to generalize legitimately in this way from the theory of descriptions it was also necessary for Quine to see the theory of descriptions as a limiting case. This is because the theory of descriptions shows how a certain form of expression makes a contextually significant contribution by eliminating them from the contexts in which they occur; consequently the significance of the contribution made by these expressions may be articulated without using them. But, as we have seen, predicates cannot be eliminated in this way. In order then to generalize from the example that the theory of descriptions provides it was therefore necessary for Quine to allow for the possibility that an expression may be contextually meaningful even if it cannot be eliminated from the contexts in which it occurs; in other words, an expression may be meaningful and make an objective contribution to the sentential contexts in which it occurs even if the only way to specify its contribution is by using the expression in question to say what it means.

This insight, if it is one, emerges in the course of a famous, or infamous, passage in which Quine dismisses the view of an imaginary realist (McX) who maintains that the adjective “red” picks out a universal held in common by different red things:

One may admit that there are red houses, roses and sunsets, but deny, except as a popular and misleading manner of speaking that they have anything in common … the word ‘red’ or ‘red object’ is true of each of sundry individual entities which are red house, red roses, red sunsets … That the houses and roses and sunsets are all of them red may be taken as ultimate and irreducible, and it may be held that McX is no better off, in point of real explanatory power, for all the occult entities which he posits under such names as ‘redness’. (Quine 1948: 10)

In order to appreciate the significance of what Quine says here, two related confusions must be cleared away. First, even if, as Quine maintains, McX is wrong to think that there are universals (“occult entities”) which appear under the name “redness” it does not follow that the adjective “red” is not a referring expression. After all, grammatically at least, adjectives are not names. Second, Quine characterizes himself as having argued “that we can use general terms, for example, predicates without conceding them to be names of abstract entities” (1948:12). But even if McX is mistaken in thinking that predicates are a special kind of name—names of abstract entities—this still leaves open the possibility that predicates are referring expressions which are not names.

Once these confusions are set aside, Quine's account comes (at a first approximation) to this. The contribution that “(is) red” makes to the contexts in which it (p. 429) occurs is fully captured by the use of the expression (outside quotation marks) to say what function “red” performs; there is no more to be said about “red” than that it is true of red things. The attempt to say any more about the contribution made by this adjective—that, for example, it refers to a universal—is to add nothing but metaphysical excess and mystery to what has already been said. More generally, there is no more to the contribution of predicates than is captured by the instances of the following ‘disquotational’ schema.5

(P)F” is true of x iff x is (an) F

The disquotational theory of predication that Quine so presents appears to reduce the phenomenon of predication to a collection of trivialities.6 For no one—not even the opponents of Quine who hold there is something more to be said about predication than the instances of (P) assemble—will wish to deny that the instances of (P) are true. Nevertheless the disquotational theory appears to offer something non‐trivial, a third way of thinking about predication that allows predicates to make an objective contribution to the contexts in which they occur but without bestowing a referential function upon them.

Predicates are used to frame apt descriptions of how things are. “Red” is used to describe things that are red rather than some other colour, “square” is used to describe things that are square rather than some other shape, and so on. Predicates are used in this way to map the objective contours of reality. What is it that enables predicates to do so? The answer provided by the disquotational theory could not be more straightforward: “red” is true of every red thing and nothing else, “square” is true of every square thing and nothing else, and so on. But doesn't this just mean the adjectives “red” and “square” are used to apply to whatever things we may happen to call “red” or “square” rather than map objective contours? Doesn't this just undermine whatever confidence we may have had in the objectivity of the statements that “red” or “square” are used to make?

Not on the face of it. Each instance of the disquotational schema (P) mentions a predicate “F” and employing a bi‐conditional specifies necessary and sufficient conditions for “F” to apply to an object x. A predicate “F” that appears on the left‐hand side of an instance of (P) is thus paired with a description on the right‐hand side of the circumstances in which it may truly be applied. Whether a predicate mentioned on the left‐hand side of an instance of (P) makes an objective contribution to the contexts in which it occurs will therefore depend upon whether the circumstances described on the corresponding right‐hand side are themselves objective. Now note that the right‐hand side of instances of (P) describe circumstances that appear perfectly objective, an object's being red, an object's being square; there is no mention (p. 430) on the right‐hand side of the subjective interventions of speakers who call this or that “red” or “square”. If appearances do not deceive us it follows that the objective contribution of the predicate mentioned on the corresponding left‐hand side is thereby secured.

Of course, it is true that the disquotational theory uses the predicate that is mentioned on the left‐hand side of an instance of (P) to specify on the right‐hand side the circumstances in which the predicate applies. But it does not follow that the circumstances described on the right‐hand side fail to be objective. Moreover, the practice of using a predicate that is also mentioned to describe the circumstances in which it applies appears to be all but inevitable. This is because, for at least the primitive predicates of our language, there may be no other way of describing what these circumstances are. Our capacity to provide a discursive description of the application of predicates must come to an end somewhere; we cannot always be expected to describe F‐things without using the predicate “F”. So in the end it may simply be “ultimate and irreducible” that some things are F and hence that “F” is true of them.

In response it may be suggested that so far from being inevitable the circularity the instances of (P) exhibit is avoided by a realist account of predication that construes predicates as referring devices. In place of (P) such an account will appeal to the instances of the following rule for predication.

(P*)F” is true of x iff x instantiates the referent of “F”.

This rule appears to avoid the circularity inherent in (P) because its instances do not involve the use of a predicate to explain its own application conditions; the predicates whose application conditions are to be explained appear inside quotation marks on both right‐ and left‐hand sides of (P*)'s instances. But this is only possible because the instances of (P*) incorporate auxiliary predicative machinery of their own—‘instantiates the referent of “F” ’—predicative machinery that is used to say how an object must stand to the referent of a predicate “F” in order for “F” to be true of it. In order to provide a fully general account of predicative expressions it follows that the realist must also provide an account of the conditions under which this auxiliary machinery is to be applied. But this brings the realist face to face with an uncomfortable dilemma. Either the application conditions of this auxiliary machinery will be accounted for by the instances of (P*) or they will not. If the former is the case then there is a subset of (P*)'s instances that exhibit the special form:

(P*‐) ‘instantiates the referent of “F” ’ is true of x iff x instantiates the referent of ‘instantiates the referent of “F” ’.

If so, then the same predicative machinery that is mentioned on the left‐hand side of some instances of (P*)—i.e. those that exhibit the form (P*‐)—is used to describe its own application conditions on the right. But then at least some instances of (P*) exhibit the same kind of circularity that is inherent to instances of (P). Alternatively, the application conditions of this predicative machinery is to be explained by appealing to an additional principle of the following kind: (p. 431)

(P**) ‘instantiates the referent of “F” ’ is true of x iff x instantiates* the referent of ‘instantiates the referent of “F” ’.

Like instances of (P*), instances of (P**) make use of their own distinctive auxiliary predicative machinery (“instantiates* the referent of”). But then the realist is set upon the course of infinite regress. In order to achieve generality the realist must provide an account of the application conditions of this novel machinery. But to avoid circularity the realist must introduce further auxiliary machinery to do so (“instantiates** the referent of”) and so on.

The difficulties the realist confronts here are a symptom of a point already noted: predication is a fundamental linguistic combination that cannot be eliminated; there is no getting away from the use of predicates. It is important not to overreact to this situation. From the fact that the realist cannot provide a reductive account of predication that treats predicates as referring devices it does not follow that predicative expressions do not refer. It only follows that the realist cannot fault (P) on grounds of circularity and that consequently the realist must provide some other grounds for preferring a referential account.

However even if (P) is not to be faulted for circularity there is a related charge of question begging that is worth considering. Quine denies that predicates are referring expressions and endeavours to account for their application conditions by using them. This provokes the suspicion that the issue of whether predicates refer is somehow being ignored. Here is one way of articulating the suspicion. It can be agreed upon all hands that the instances of (P) are true; no one will wish to deny that a predicate “F” is aptly used to describe F‐things (if there are any). The instances of (P) may thus be taken to record a semantic achievement—that of being in a position to use predicates to aptly describe worldly things. But how is this achievement to be secured? The realist offers, in outline at least, a discursive account of how this can be done: a predicate “F” refers to a universal Φ, and so applies to the particulars that instantiate Φ (application is secured as the composition of reference and instantiation). By contrast, Quine offers no account of how we can succeed in co‐ordinating predicates with the contours of an extra‐linguistic reality. Instead Quine just affirms (P)'s instances. It consequently appears that Quine takes for granted what he seeks to establish—that predicates can be used without discharging a referential function.7 For in the absence of such an account a mere appeal to instances of (P) can hardly be claimed to obviate the necessity to conceive predicates as referring expressions; we are simply left in the dark concerning whether the necessity for so‐conceiving predicates indeed arises in the course of securing the semantic achievement recorded by (P)'s instances, or not.

It is critical to a proper appreciation of the disquotational theory Quine advocates that it be recognized not to beg the question in quite this way. For it is not so much the affirmation of (P)'s instances that provides the substance of this theory as the denial that there is anything else significant or general to be said about predication. (p. 432) According to Quine, there is no theoretical necessity to say anything other than (P); rather than being left in the dark by the disquotational theory we are led into darkness if we succumb to the temptation to say anymore. Whether the disquotational theory merits our acceptance turns upon whether this is truly so.

19.1.2 The Limits of Disquotationalism

Is there really nothing to be said but (P)? That depends (in part) upon what kinds of concern an account of predication is obliged to address. If our concern is that of the early analytic philosophers—that of securing the objectivity of scientific discourse—then it appears (P) cannot say enough. If there is a worry about whether a predicate “F” makes an objective contribution to the statements in which it occurs then there will likewise be a worry about the objectivity of what “F” is used to say; one cannot impugn a vehicle of expression without thereby impugning the content that the vehicle expresses. So if there is a concern about the objectivity of “F” as it appears on the left‐hand side of a relevant instance of (P)—i.e. where “F” is mentioned—there will be no less of a concern about the objectivity of the circumstances of its own application that “F” is used to describe on the corresponding right‐hand side. It appears therefore that (P) cannot say enough to assure us of the objective contribution of “F”.

This concern about objectivity is related to another. Before stating the objection it is necessary—in order to avoid a distracting detail—to introduce a qualification to what has already been said. Reflect that the same string of sounds or letters in one language could mean something different in another language. It follows that merely disquoting a string and using it in one language may fail to describe its application conditions in another. Quine draws the conclusion that a string is never simply true of an object, but true in a language L, for appropriate L, of an object (see his 1953c: 134–5). He therefore recommends that (P) appear in the relative form:

(P L )F” is‐true‐in‐L of a iff Fa

But this does not mean that what a predicate (relative to a given language) is used to state fails in some sense to be objective; it just means that the same string may mean different things in different languages. So even a realist account must recognize this form of benign linguistic relativity and allow what, from their point of view, constitutes the same predicate having different meanings in different languages, viz. the same predicative string referring to different universals in different languages. To accommodate this fact, reference must—like being true of—be framed relative to a language.8 So, more fully, a realist account of this kind must state: (p. 433)

(R) For any predicate “F” and language L, “F” is true‐in‐L of an object a iff a falls under the referent‐in‐L of “F”.

We are now in a position to state the aforementioned objection. (P L) is distinctively beset by difficulties familiar from discussion of Tarski's theory of truth.9 This is because (P L) is a schema, shorthand for a list of its instances. Because (P L) merely provides an enumeration of its instances it fails to state what is common—by way of purpose or function—to its different instances. It no more states what predicates have in common than merely providing a list of friends states what friends have in common. Moreover because (P L) does not state what its instances have in common, (P L) provides no idea of how to apply the concept predicate to novel strings that are added to a language, or how to apply the concept to a new language. (P L) provides no more guidance upon this matter than a mere list of existing friends guides one in applying the concept friend to someone new. It is therefore difficult to avoid the suspicion that the disquotational theory fails to provide the kind of insight that one might otherwise have expected of an account of predicates and predication.

By contrast, a referential account of predicates underpinned by (R) appears to avoid these difficulties. The instances of (P L) collectively state what it takes for any given predicate to be true (in any given language in which it occurs) of an object: what it takes for “green” to be true‐in‐English of an object is that it be green, what it takes for “round” to be true‐in‐English of an object is that it be round, and so on. But the instances of (P L) fail to state what it takes for predicates in general to be true of objects. This is why (P L) fails to capture what is common among its different instances. A referential account of predicates appears to steal a march here upon its rival because it is able to attain a far higher level of generality. It is able to do so because it assigns a univocal purpose to predicates—to refer to universals. It is important to note how (R) achieves this higher‐level of generality. Each instance of (P L) both mentions and uses a predicate to specify its application conditions. Consequently, (P L) is obliged to remain schematic rather than axiomatic; we cannot intelligibly replace a predicate both when it is mentioned and when it is used with the same bound variable. By contrast, (R) only mentions predicates. This is because it seeks to account for the application conditions of predicates not by using them but in a different way to (P L)—by appealing to the referents of (mentioned) predicates and the capacity of objects to fall under these referents. Because predicates are only mentioned it follows that they may be uniformly replaced with a bound variable and (R) is correspondingly more general than (P L).

Does (R) thereby steal a march upon its rival? Well for one thing it is questionable whether (R) achieves so much. We have already reflected that the application conditions of some predicates (“instantiates”, “falls under”) cannot—on pain of infinite regress—be specified without using the predicates in question. So it appears that (R) cannot succeed in full generality. For another thing, while generality is a theoretical virtue to be prized in the abstract it is unclear whether such generality as (R) (p. 434) achieves is especially to be desired in the case at hand. For while (R) states what is uniform to a range of different predicates it says nothing about the application of a single one. We will not be able fill this gap—to specify the application conditions of a given predicate—until an account is forthcoming of how individual predicates pick out their referents. And, so far, the realist has supplied no more than a promissory note that a satisfactory account of this kind will be forthcoming. By contrast, (P L) avoids the need to tackle such vexed issues: instead it supplies directly the application conditions for each given predicate of a given language. And while (P L) offers no uniform account of predication, (P L) provides a template for supplying application conditions for predicates, a template that—when impressed upon a particular language—is grasped as clearly by us as the expressions of the language to which it is applied.

Evidently the arguments that we have so far considered fail to be entirely satisfactory. Is the realist simply pursuing a craven desire for generality, seeking a form of objectivity so naive that only a primitive would otherwise be drawn to it? Or is the nominalist (Quine) failing to supply an explanation where reason demands one, making illicit appeal to the very phenomenon (our use of predicates) that vexes our understanding, trapping us off from reality by encircling us with our own words? That depends upon what is required of an account of how language is responsive and responsible to the world and its states. Since there is no such agreed account to fall back upon there appears little prospect—so far—of relief from the interminable dialectic of charge and counter‐charge that prevails between realist and nominalist.

19.1.3 A Challenge for Disquotationalism

There is, however, an objection that arises concerning the use of (P L), an objection that does not rely upon disputed background assumptions. The nominalist assumes that names are referring expressions. (P L) is then used to show that there is no need to construe predicates as likewise referring; predicates need only be construed as strings that are true or false of the objects names pick out. If this method of argument is a good one then it appears that the same method may be deployed to show that there is no need to construe names as referring expressions. The nominalist must therefore either (i) abandon the use of (P L) to show that predicates do not refer, or else (ii) demonstrate that there is a relevant difference between the different ways in which the method is deployed.

This case against the nominalist may be developed in the following stages. Let us begin by focusing our attention upon the collection of name‐predicate sentences in English that exhibit the monadic form “Fa”. Take “Socrates swims” as our target sentence. By nominalist lights, whether this sentence is true (or false) depends on whether “swims” is true (or false) of Socrates. In other words,

  1. (1) “swims” is true of Socrates iff Socrates swims

If this construal of “Socrates swims” is accepted then “Socrates” occurs as a referring expression while it is merely the string “swims”—its referent being nowhere in (p. 435) sight—that is true (or false) of Socrates. But what stands in the way of turning this analysis on its head and offering the alternative construal?

  1. (2) “Socrates” is true of swimming iff Socrates swims

If (2) is accepted then it is “swims” that occurs as a referring expression while “Socrates” is consigned to the role of a string true (or false) of swimming. Unless the nominalist supplies a principled reason for preferring (1) to (2), (1) can hardly be used to show that “swims” is not a referring expression.10

There are a number of responses available to the nominalist worth disentangling. The nominalist may begin by countering that (1) is to be preferred to (2) because we are already committed to names having reference. But if ordinary practice does already enjoin such a commitment then it should be possible to explain to us wherein this commitment consists—what it is about our use of names that constrains them to be counted referring expressions. The nominalist now encounters a dilemma. If it is not possible to give such an explanation then it remains an open possibility that it is not principle but prejudice that speaks in favour of (1). But if such an explanation can be given then we should be able to inspect directly whether the use of predicates is similarly, or at least analogously, constrained to names and decide upon that basis whether predicates are referring expressions. Either way analyses like (1) become redundant, unable to establish unaided that predicates are not referring expressions.

A second nominalist response seeks to bypass this concern by arguing that analyses like (2) founder when the realist applies them to more complex constructions. Take “Socrates is older than Plato” as our target. Because “is older than” is asymmetric this sentence says something different from, and incompatible with, “Plato is older than Socrates”. When the disquotational strategy is applied to this sentence the analysis results

  1. (3) “Socrates” and “Plato” are true of being older than iff Socrates is older than Plato

Obviously (3) is inadequate. It simply says that “Socrates” and “Plato” are true of being older than but provides no inkling of whether or how “Socrates” and “Plato” are true of this relation in such a way as to guarantee that it is Socrates that is older than Plato rather than the reverse. Hence (3) leaves us without the means for distinguishing between what is said by “Socrates is older than Plato” and “Plato is older than Socrates.”

This objection is not insuperable. The realist can augment (3) with additional resources to get around this problem. He may add primitive operators (“in that order”) to his ideology and use the order in which “Socrates” and “Plato” are written down to show the way in which they are true of being older than: (p. 436)

  1. (5) “Socrates” and “Plato” are true of being older than (in that order) iff Socrates is older than Plato

Of course appeal to additional ideological (primitive operators) or ontological resources (for example, ordered pairs) would do little to aid the realist if the nominalist had no corresponding need of these additions. But the nominalist does need them, and implicitly presupposes them. Applying the disquotational strategy of (1) to “Socrates is older than Plato” yields

  1. (6) “is older than” is true of Socrates and Plato iff Socrates is older than Plato.

But this analysis provides no basis either for distinguishing between the case in which “is older than” is true of Socrates and Plato in such a way that Socrates is older than Plato, and the case in which it is true of them in such a way that Plato is older than Socrates. If we do not immediately notice this fact it is simply because we are habituated in English to using the order in which “Socrates” and “Plato” are written down to mark this difference (you may have relied upon this convention when scanning the left‐hand side of (6)). But even if we are habituated in English to doing so this does not excuse the nominalist from recognizing that he or she already relies upon additional ideological resources—in this case relying upon an implicit convention about the use of word order in English—to make sense of relational constructions.11

The nominalist may make a far more basic objection: that (2) is grammatically precarious in a way that (1) is not; that ‘ “Socrates” is true of swimming’ just isn't tolerable English. But whether one feels inclined to report a sense of queasiness (or not) can hardly be taken to settle this or any other philosophical issue; one needs a stronger stomach for doing philosophy. It remains an open possibility that our sense of grammatical unease arises from what is accidental—laid down by the contingencies of biological and historical development—rather than essential about the forms we speak. So once again the nominalist must provide an argument to show that (1) is to be preferred to (2).

This third response faces a further difficulty, a case of the pot calling the kettle black. Insofar as (2) is grammatically precarious, (1) appears no less questionable. Whoever says: ‘ “swims” is true of Socrates’? Nobody, I conjecture, outside a philosophy or a linguistics department. Following Strawson, one may endeavour to find a paraphrase of this latter construction that is more tolerable in ordinary language.12 The availability of such a paraphrase is suggested by the familiar equivalence of the oratio recta construction ‘ “Socrates swims” is true’ with the oratio obliqua ‘It is true that Socrates swims’. This suggests that the oratio recta ‘ “swims” is true of Socrates’ is equivalent to the oratio obliqua form, (p. 437)

  1. (7) It is true of Socrates that he swims.

But once this paraphrase is allowed there seems no reason to disallow the corresponding oratio obliqua form,

  1. (8) It is true of swimming that Socrates does it

and so the intelligibility of the oratio recta construction ‘ “Socrates” is true of swimming’. Strawson concludes, “No distinction between subject and predicate is therefore marked by the availability of paraphrase in the ‘true of’ construction.”

Nevertheless these paraphrases do highlight the fact that there is a grammatical asymmetry between (a) (1) and (7) and (b) (2) and (8). Whereas (1) and (7) employ the same expression (“swims”) in the same grammatical category as it appeared in the original target sentence (“Socrates swims”), (2) and (8) convert the predicative “swims” into the noun phrase “swimming”. The realist who employs (2) and (8) is obliged to do so because the relational expressions “x is true of y” and “it is true of x that” only accept names or noun phrases in their open positions. The nominalist who uses (1) and (7) does not demand that “swims” undergo this kind of transformation because he makes no attempt to place an expression picking out the referent of “swims” in the open positions of these relational predicates. By contrast, the realist cannot avoid doing so.13

This asymmetry suggests that the appearance is no more than superficial that (2) and its ilk—constructions in which it is predicates that pick out elements of reality—may be used to obviate the necessity of assigning reference to names. This is because the meta‐language (the extended fragment of English) in which (2) is framed uses a name (“swimming”) rather than a predicate to assign a referent to the predicate “swims”. It follows that the realist cannot avoid assigning some names reference—names in the meta‐language for the referents of object language predicates. But once it is allowed that some names have reference it is difficult to see what principled motive there can be for preferring (2) as an analysis to (1), that is, for denying outright that names in the object language (“Socrates”) are referring expressions. The nominalist's use of (1) avoids this kind of awkwardness; (1) does not use predicates in the meta‐language to assign referents to object‐language names.

It is far from evident that this objection to (2) is critical. The objection plays upon what appears to be a meta‐linguistic prejudice in favour of the nominal. However this appearance itself appears superficial, nothing more than the consequence of a grammatical fact already noted, that “is true of” requires names to be completed into a whole sentence; a fact that makes it grammatically inevitable that the referents of predicates—of which object‐language names are true—are picked out by names in the meta‐language. Of course if we grammatically blinker ourselves in this way then we won't be able to see logically right or left. But why would we want to blinker (p. 438) ourselves in the first place? Why should we accept in advance that the use of the “is true of” idiom provides the touchstone for determining whether a word, of whatever kind, is a referring expression? Do we not thereby beg the question in favour of the view that it is only names that are referring expressions?

No doubt the nominalist will reply: there is no need to accept this in advance; whether the ‘is true of’ idiom turns out to perform the touchstone role will depend upon whether by its employment we succeed in saying everything that needs to be said about the relationship between predicative expressions and the world.14 Does the nominalist thereby succeed in saying everything that needs to be said about this relationship? That depends upon whether there are features of the use of predicates that cannot be captured or understood if predicates are conceived as mere strings true (or false) of objects. Are there such features of use?

19.2 Quantification and Reference

Names are paradigmatic devices of reference. By looking to see what features of use compel us to construe names as referring devices, we may hope to establish whether the same or analogous features compel us to construe predicates likewise. What makes names appear paradigmatic devices of reference?

In part it is the stereotypical interaction of names with the universal and existential quantifiers “every object is such that” and “some object is such that”, what Quine has dubbed the “unequivocally referential idioms of ordinary language” (1960: 242). Why does Quine say so? Why are quantification and reference to be linked in this way? Because these quantifier phrases may be used to make explicit statements about what objects exists. It is because of the interaction between (i) singular sentences that involve only names and (i) quantified statements that may be parlayed as explicit statements about the existence of objects that (iii) there is reason to think that names pick out objects—the objects that are said to exist by quantified statements (1960: 240; 1969b: 94).

Focus upon the role of the existential quantifier. It is the operation of existential generalization that controls the interaction between singular statements in which names occur and general statements that feature the existential quantifier. When applied to “Socrates is wise” this operation licenses us to infer “someone is wise”, or more formally, “(∃ x)(x is wise)”. The name “Socrates” is thus extracted from the position in the original sentence in which it occurred and a quantifier phrase (p. 439) or bound variable inserted into the position left vacant by the name. The resulting sentence is equivalent to the existence claim “There is an object which is wise.” This transition makes sense if “Socrates” is a referring device that picks out a thing of the kind (a wise thing) that is then said to exist. In applying the operation of existential generalization to “Socrates is wise” we thereby quantify over what the name picks out; the object to which “Socrates” refers is assigned as a value to the variables of quantification. It follows—insofar as the validity of this operation is accepted—that there is no escaping the obligation to construe names as referring devices. So if a corresponding rule can be found, or indeed licensed, that applies to predicates—an operation that leads us to quantify over what these expressions stand for—then there can be no less of an obligation to construe predicates as referring devices.

Are there corresponding predicative operations of an appropriate form? Let us begin by considering where there is an operation that enables us to infer “(∃ X)(Socrates X)” from “Socrates is wise” by extracting “ … is wise” from the latter sentence and inserting a bound variable “X” into the predicate position left vacant to yield the former quantified locution. Sometimes it has been claimed to be built into the very distinction between names and predicates that the former but not the latter are susceptible to quantification: “When we schematize a sentence in the predicative way “Fa”, or “a is an F”, our recognition of an “a” part and an “F” part turn strictly on our use of variables of quantification; the “a” represents a part of the sentence that stands where a quantifiable variable could stand, and the “F” represents the rest” (Quine, 1969b: 95). It follows that the very idea of quantification into predicate position is a contradiction in terms—predicates, by definition, are inaccessible to quantification. Quine has even gone so far as to claim that in a finite universe, where existential and universal quantification are eliminable in favour of finite disjunctions and conjunctions of atomic sentences, “the very distinction between names and other signs lapses in turn, since the mark of a name is its admissibility in positions of variables” (see his 1969a: 62).

These claims rest upon the questionable assumption that names and predicates cannot be distinguished by other means. In fact, if we simply rely upon the familiar formal and informal clues that we use to distinguish names from other sentence parts—to distinguish names from verbs, adjectives and other particles—it appears that English actually permits quantification into a variety of non‐name positions. Suppose that whereas Socrates and Plato are both men, Socrates is also wise. It follows that while there is something that Socrates and Plato both are (men) there is also something that Socrates is but Plato isn't (i.e. wise). Suppose too that Plato does whatever Socrates does. It follows that if Socrates scowls then Plato scowls too. In the former case we have an inference that depends upon quantification into both noun and adjective positions. In the latter case we have an inference that depends upon quantification into verb position. Since English permits inferences of this form it is difficult to see how their intelligibility can be denied.15

(p. 440)

But is quantification into noun or adjective position genuine predicate quanti‐ fication? If a predicate is simply the rest of a sentence that remains once the name (or names) has been subtracted, then the predicate of “Socrates is wise” is not merely the adjective “wise” but the concatenation of the copula plus “wise”. Predicate quantification proper must therefore involve the replacement of not just an adjective or noun but the entire predicate—copula included—with a bound variable or quantifier phrase. But quantification of this form does not appear to be allowable in English.16 The position occupied by a predicate grammatically requires to be replaced by a predicate, otherwise the sentence in which it occurs is reduced to a list. So the bound variables or quantifier phrases that replace predicates must (if there are any) have the grammatical character of predicates too. But English contains no expressions of this form; it contains only pronouns and quantifier phrases that are noun‐like. When these expressions are used to replace the predicate in “Socrates is wise” a sensible sentence is reduced to a nonsense list (“Socrates it”, “Socrates something”).

It is unclear what weight to place upon these considerations. On the one hand, noting the mere absence of a form of expression in English hardly establishes that such expressions—if they were to be introduced—would be unintelligible. On the other hand, a philosopher cannot simply stipulate that expressions—even if artificially introduced—bear the significance with which he or she would wish them to be invested; a philosopher may well be the victim of their own wishful thinking. However, there is evidence of a limited form of predicate quantification in English, namely in cases where the predicate is a verb that can be replaced with a quantificational pro‐verb “do” or “does” (recall “Plato does whatever Socrates does”). What stands in the way of generalizing from such cases, treating pro‐verbs as a species of a more generic form of variable and introducing pro‐predicates as a further instance capable of standing in the place of predicates that are not verbs? It may only be the neglect—rather than the wisdom—of our ancestors that has prevented us from so doing until now.

There is another possibility. Rather than being neglectful perhaps the construc‐ tions our forebears envisaged already obviate the need to introduce a category of pro‐predicates. It is the copula that supposedly separates an adjective or a noun from a predicate proper. Following Frege, however, the copula is often conceived as merely an auxiliary device without content of its own, a device for converting an adjective or noun into a verb phrase where grammar demands one (Dummett, 1973: 214). Alternatively, the copula may be conceived as the limiting and trivial case—akin to multiplying by 1 or adding 0—of a class of adjective and noun operators that include “—was … ”, “—looks … ” and “—became … ” (Geach, 1980: 182). But if the copula is empty, or redundant, then there is nothing of substance to separate quantification proper from quantification into noun or adjective position. It is unclear what purpose the former might achieve that the latter does not already accomplish. More generally, it is unclear just what significance the distinction between predicates (p. 441) and other predicative particles should bear. As Ramsey once remarked and Strawson has repeatedly emphasized, it is important to bear in mind when considering such matters “that the task on which we are engaged is not merely one of English grammar; we are not school children analysing sentences into subject, extension of the subject, complement and so on” (1925: 13).

Is the copula a mere grammatical device empty of content? Even though Frege suggested the idea, it is often thought that Frege himself supplied the deep reasons to the contrary (Dudman 1974: 80–1; Wright 1998: 81). Frege was concerned to mark the difference between a sentence and a mere list; the fact that the former but not the latter may be used to convey a judgeable content. He did so by reflecting that whereas a name is a complete expression, a predicate is essentially incomplete, an expression with a gap (or gaps) that results from the extraction of a name (or names) from an entire sentence. It is because a predicate is incomplete in this way that the insertion of a name (or names) into this gap (or gaps) yields a sentence that is capable of expressing a thought. Since it is a predicate with a copula (or a verb) that results from the extraction of a name (or names) from a sentence, rather than an adjective or noun (without a copula), it follows that Frege cannot elide the difference between a predicate and a noun or an adjective without undermining his own account of what distinguishes a sentence from a mere list.

Dudman and Wright's criticism rests upon a failure to appreciate what distinguishes—by Frege's lights—an incomplete from a complete expression. It is the fact that the former (predicates) but not the latter (names) have argument positions, positions that are shown to us by their successive occupation by different names—an appreciation of the incompleteness of the predicate “ξ scowls” thus arises from recognizing what is common to “Socrates scowls” and “Plato scowls”, an appreciation of the incompleteness of “ξ admires ζ” arises from recognizing what is common to “Plato admires Socrates” and “Aristotle admires Plato”, and so on. It is in this sense that Frege likened predicates to arithmetical functors, expressions of an incomplete kind that are recognized as the patterns common to (e.g.) “2.03 + 0”, “2.13 + 1”, and “2.33 + 3” (Frege 1891: 133). Because the notion of an expression with an argument position does not essentially rely upon the presence of the copula, Frege is correspondingly free to maintain the incompleteness of predicates while dismissing the semantic relevance of the copula. Even from the perspective of natural language this should have been apparent all along. For many sentences lack the “is” of copulation, featuring occurrences of intransitive and transitive verbs instead.

We have been discussing whether quantification into the position of adjective or noun is to be assimilated to or distinguished from predicate quantification. But, according to Quine's influential views, the only intelligible quantification is quantification into name position. So for many this is likely to appear an idle boundary dispute: if it is permissible in English to quantify into what appears to be adjective, noun or verb positions then appearances must deceive us; they must deceive us no less than if English permitted what appears to be quantification into predicate position. So if what appears to be an adjective or noun yields to a quantifier phrase—for (p. 442) example, in the operation that takes us from “Socrates is wise” to “Socrates is something”—this can only be because the adjective or noun is really a name and the copula a two place predicate that relates a name of one kind (“Socrates”) to another (“wise”) (1970: 67). If Quine is right about this then there is no possibility of quantifying into predicate position and consequently the possibility of so quantifying provides no basis for supposing that predicates refer.

19.2.1 Quine's Animadversions on Predicate Quantification

Is Quine right to insist that only quantification into name position is intelligible? He offers a battery of related reasons for doing so.17 For present purposes it is important to bring into focus one key argument that Quine employs. It appeals to a link between quantification and naming:

Consider first some ordinary quantifications: ‘(∃ x)(x walks)’, ‘(x)(x walks)’, ‘(∃ x)(x is a prime number)’. The open sentence after the quantifier shows ‘x’ in a position where a name could stand; a name of a walker, for instance, or of a prime number. The quantifications do not mean that names walk or are prime; what are said to walk or be prime are things that could be named by names in those positions. To put the predicate letter ‘F’ in a quantifier, then, is to treat predicate positions suddenly as name positions, and hence to treat predicates as names of entities of some sort. (Quine, 1970: 66–7)

Predicates have attributes as their ‘intensions’ or meanings (or would if there were attributes), and they have sets as their extensions; but they are names of neither. Variables eligible for quantification therefore do not belong in predicate position. They belong in name positions. (1970: 67)

The argument of these passages may be schematized in the form,

  1. (A) Variables eligible for quantification occur only in name position.

  2. (B) Predicates are neither names of their intensions (meanings) nor their extensions (sets).

  3. (C) Variables eligible for quantification do not belong in predicate position.

This argument evidently begs the question. Take premise (B). Even if predicates are neither names of their intensions nor their extensions it does not follow that predicates cannot stand in a semantically significant relation—call it reference if you like—to other items. It remains open that (e.g.) predicates pick out—without being names—referents that are neither intensions nor extensions, worldly items that are available to fall within the range of a corresponding quantifier. Quine simply fails to engage with the Fregean thought that the referents of predicates are neither senses nor objects but concepts.18

(p. 443)

Switch to (A). Since predicates occupy different positions in sentences to names this premise presupposes what the argument is intended to show. Quine supports this premise by asking us to consider “some ordinary quantifications: ‘(∃ x)(x walks)’, ‘(x)(x walks)’, ‘(∃ x)(x is prime)’ ” where the bound variable “x” figures in name position. He then generalizes from these examples: “The quantifications do not mean that names walk or are prime; what are said to walk or to be prime are things that could be named by names in those positions. To put the predicate letter “F” in a quantifier, then, is to treat predicates as names of entities of some sort.” But this argument does not appear convincing either. Just because some quantifications—the “ordinary” ones in which the bound variable figures in name position—quantify over items that could be named by names in those positions it does not follow that all quantification quantify over items in just this way. Consequently it does not follow either that quantifying into predicate position is tantamount to treating predicates as names. Quine's argument against predicate quantification consequently fails.

If there is any substance to what Quine says, there must be another argument operating in the background of his thought that forges a more intimate connection between naming and quantification than a brute induction from ordinary cases provides. The following remark from “Reference and Modality” is suggestive of what this connection might be:

The connection between naming and quantification is implicit in the operation, whereby, from ‘Socrates is mortal’, we infer ‘(∃ x)(x is mortal)’, that is, ‘Something is mortal’ …. The idea behind such inference is that whatever is true of the object named by a given singular term is true of something; and clearly the inference loses its justification when the singular term in question does not happen to name. (Quine, 1953d: 145; see also 1939: 705–6)

The important phrase here is “whatever is true of the object named by a given singular term is true of something”. How do we advance from the idea of a predicate being true of an object named to the idea of a predicate being true of something—an object for which we may lack a name altogether? Consider the sentence “Socrates is mortal.” The role of the name “Socrates” is to pick out an object o. Once o is picked out the name “Socrates” drops away, its task completed (“the singular term is used purely to specify its object, for the rest of the sentence to say something about” (Quine, 1960: 142–3, 177)). The role of the predicate “is mortal” is then to be true (or false) of o regardless of how it is named—regardless of whatever else Socrates may be called. Because the predicate assumes a role that is independent of the accompanying name we are thus able to form the conception of a predicate true (or false) of an arbitrary object. It is then a short step to an appreciation of quantification itself, as what results from applying the predicate to each object in the domain.

But so far from sub‐serving Quine's rejection of predication question, this account of how naming and quantification are connected leaves open the possibility that predicate positions are accessible to quantifiers. This is because nothing has been done to rule out the possibility that there are predicates and quantifiers similarly related. To make out this possibility, it need merely be established that (i) there is a basic class (p. 444) of predicates that refer to worldly items of which (ii) a further class of predicates are true (or false) independently of how these items are picked out. Once again, it is a short step from the idea of a predicate that is true (or false) of an arbitrary item of this kind to the idea of a quantifier that includes these items in its range.

It is important to appreciate what is unquestionably right about this line of thought: (i) if there is reason to conceive of predicates as referring expressions then there is a corresponding motivation to conceive of quantifier expressions that stand in predicate position as ranging over the items that predicates pick out. But it does not follow (ii) that if quantifiers are eligible to be placed in predicate position then predicates are referring expressions.19

Why? Because the idea that quantifiers of a given kind range over an associated domain of entities was arrived at via the assumption that expressions of the kind whose positions they occupy are independently conceived to be referential expressions, expressions that drop away once an object is picked out. So one may grant the connection between naming and quantification that Quine points to while doubting that quantification into the position of predicates involves quantification over items that predicates pick out, or, for that matter, anything else. The doubt can intelligibly be raised so long as it remains questionable whether predicates are referring expressions. Contra Quine, it appears that the accessibility of a position X to quantification cannot be used as a test for whether constant expressions that occupy X are referential.

19.2.2 Prior on Quantification

This criticism of Quine takes advantage of a gap in his argument—the gap that opens up because his conception of quantification runs the risk of being parochial, arising from reflection upon what may turn out to be the limited and special case of names. But one may also arrive at the same objection from a more principled standpoint. The most forceful and influential articulation of such a standpoint is owed to Prior (1971: 33–47). I distinguish two components of the view that I will call (a) neutralism and (b) anti‐formalism.

According to neutralism, the mere use of a quantifier phrase does not of itself oblige us to construe the sentence in which the phrase occurs as making a statement about a domain of entities over which the quantifier ranges. Whether the quantifier is so committing will depend upon whether the constant expressions—names or predicates—that occupy the position bound by the quantifier are already committing. Neutralism thus rejects Quine's claim that a quantified statement is eo ipso a statement of existence. A quantified statement need only be construed as a statement of existence if the singular forms that gave rise to the quantified statement were (p. 445) (implicitly) existence affirming in the first place. Prior goes far as to say: “I doubt whether any dogma, even of empiricism, has ever been quite so muddling as the dogma that to be is to be the value of a variable” (1963: 118).

Prior provides support for neutralism by appealing to examples from natural language. He asks us to consider, for example, the sentence “I hurt him by treading on his toe” and its existential generalization “I hurt him somehow.” Since there is no need to construe the adverbial phrase “by treading on his toe” as a referring expression, there is no need to construe the quantifier phrase “somehow” that replaces it as ontologically committing either. The adverbial quantifier “somehow” simply does generally what the adverbial phrase “by treading on his toes” does singularly: “no grammarian would count ‘somehow’ as anything but an adverb, functioning in ‘I hurt him somehow’ exactly as the adverbial phrase ‘by treading on his toe’ does in ‘I hurt him by treading on his toe’ ” (Prior, 1971: 37). Appeal is thus made to the idea that the role of a quantifier that binds a position X is to generalize upon the semantic function of the category of constant expressions that occupy X; how a quantifier generalizes depends upon what semantic function the corresponding category of constant expressions perform.

This conception is neutral because it does not presuppose that quantifiers generalize in a uniform way upon the categories of expressions whose positions they bind. This opens up the possibility that different categories of constant expressions perform different semantic functions and hence that different styles of quantifier generalize in different sui generis ways. Whether this possibility is realized will depend upon whether the similarities and differences that obtain among the different categories of constant expressions signal underlying differences of semantic function. So it cannot be assumed—by Quine or anyone else—that just because name quantifiers range over a domain of entities to which names refer, predicate quantifiers must range likewise over a domain. Whether predicate quantifiers carry with them an associated ontology, as name quantifiers do, will depend upon whether names and predicates function in relevantly similar ways, picking out elements of a domain.

The neutral component of Prior's view is open to a substitutional development.20 Developed in such a way, a variable that occurs in a position X in a given sentence is thought of as a place marker for constant expressions of the grammatical class Ξ that are eligible to be inserted into X. The sentence that results from binding this (p. 446) variable with a universal quantifier is true if and only if every sentence that results from inserting a Ξ constant into X is true. The sentence that results from binding the variable with an existential quantifier is true if and only if at least one sentence that results from inserting a Ξ constant into X is true. This account of the quantifiers is neutral in the following sense. Whether a quantifier is ontologically committing will depend upon whether the class of constants that provide substitution instances for the variables it binds are referential expressions.

There is, however, no obligation to develop the neutral conception in this way, and Prior resists it. The substitutional treatment of quantifiers encounters a familiar difficulty. The sentence “I hurt him somehow” may be true even though there is no adverb in our language that specifies how it was done—how it was done may be literally unspeakable. So this sentence may be true even though there fails to be at least one sentence that results from inserting a constant into the position occupied by “somehow”; it is not a necessary condition of “I hurt him somehow” being true that such a sentence exists.

To avoid this difficulty Prior appeals to the anti‐formalist component of his view. His view is anti‐formalist in the sense that “I do not think that any formal definition of ‘something’ is either necessary or possible, but certain observations can usefully be made about the truth‐conditions of statements of this sort” (1971: 35). Prior observes that it is a sufficient condition of “something is red‐haired” being true that there is a true sentence in which “something” is replaced by a specific name. But it cannot be a necessary condition because “its truth may be due to the red‐hairedness of some object for which our language has no name”. The only way to supply a necessary condition is to use the quantifier “something” to rehearse the truth‐conditions of the very contexts in which it occurs:

If we want to bring an ‘only if’ into it the best we can do, ultimately, is to say that ‘For some x, x is red‐haired’ is true if and only if there is some red‐haired object or person, but this is only to say that it is true if and only if, for some x, x is red‐haired. (1971: 36)

The same point is then carried over to apply mutatis mutandis to quantifiers that bind variables of other categories. “I hurt him somehow” is true if there is a true sentence in which “somehow” is replaced with a specific adverb. But it is true if and only if I hurt him somehow—a necessary condition is expressed by using the adverbial quantifier itself. There is no avoiding the use of even the name quantifiers to explicate the truth‐conditions of the sentences in which they occur—there is no prospect of intelligibly reducing generality to something else. So there can be no objection to the use of predicative quantifiers to explicate the truth‐conditions of the sentences in which they occur. And because there is no avoiding their use there is no necessity to explicate their truth‐conditions by assigning a domain of entities for them to range over or, alternatively, a class of constants to provide substitution instances. By deploying this insight Prior endeavours to develop the neutral component of his view so as to avoid the pitfalls of a substitutional approach to the predicative quantifiers, but without thereby being obliged to treat predicative quantifiers as ranging over the elements of a domain.

(p. 447)

Has Prior given a convincing account of the quantifiers? Prior provides precious little argument for his view. At one point he attempts to show that there is an absurdity in the opposing view he attributes to Quine, that quantified forms commit us to the existence of kinds of entities to which we are not committed by the singular forms that entail them: “The alleged emergence of these new ontological commitments has an almost magical air about it” (1971: 43). But this argument cannot be made to carry much weight. For Quine has no need to deny that singular forms are ontologically committing. Rather quantified forms are conceived by Quine as “explicitly presupposing entities of one or another given kind” that are “not explicitly presupposed” by their corresponding singular forms. This does not mean Quine must deny that these singular forms implicitly presuppose such entities or that he must be convicted of incoherence when he refuses to quantify over predicative expressions because—by his lights—they are not ontologically committing (cf. Quine, 1939: 706–7, 1953b: 102, 113). At other points Prior seems to write as if Quine were espousing a form of reductionism about generality to which Prior's own anti‐formalism is an anti‐reductionist antidote. But it hardly follows from the fact that, by Quine's lights, values must be assigned to variables in a semantic treatment of object language quantifiers that Quine is committed to the absurd view that devices of generality are thereby obviated in the meta‐language in which these assignments are made.

The fact of the matter is that Prior does no more than issue an invitation to think about quantification in a manner to which we are ill accustomed. But this is not really an objection to his view. It is a struggle to provide even the contrary position that quantifiers inevitably harbour ontological commitment—that existential generalizations are inevitably equivalent to existence claims—with an argument in its favour. Reflecting upon the use of “I hurt him somehow” Prior remarks, “we might also say ‘I hurt him in some way’, and argue that by so speaking we are ‘ontologically committed’ to the real existence of ‘ways’; but once again there is no need to do it this way, or to accept this suggestion” (1971: 37). When dealing with an issue of as great a generality as generality it should hardly come as a surprise that arguments that are discursive and convincing are difficult to come by. But this is a source of cold comfort if our concern is to establish whether by quantifying into predicative positions we thereby presuppose that predicative expressions are referring.21

19.2.3 Where are We?

Let us retrace the route that led to this sombre reflection. The disquotationalist about predication says that there is no more to be said about predication than is said by (p. 448) the instances of the schema (P) “F” applies to x iff x is F. Whether a predicate can be used in this way to provide an exhaustive account of its own application conditions depends upon whether there is some aspect of the use of predicates for which (P) cannot account. Quantification became an issue for us because of the connection that obtains between quantification and reference in the case of names; a quantifier that binds name position quantifies over the referents of names that are eligible to be inserted into this position. If a similar connection obtains in the case of predicates then (P) fails to capture everything there is to be said about predicates; it fails to capture the fact that predicates are referring expressions. However, even if it is admitted that devices of generality may bind positions in which predicative expressions occur, it does not follow that predicative expressions have reference. This is because it remains to be established that if predicative quantification is admitted such quantification is relevantly akin to the more familiar name kind that inevitably brings reference in its wake. Recognizing this reveals a gap in Quine's arguments against quantification into predicative position. For these arguments rely upon the assumption that predicate quantification—if it were admitted—would be just like quantification into name position. The strategies Quine employs suggest no means of plugging this gap that do not rely upon the prior acceptance of the thesis that predicates are referring expressions.

The neutralism and anti‐formalism of Prior provide an alternative framework for thinking about quantification that denies a structural link between quantification and reference. By the lights of neutralism, a predicative quantifier is ontologically committing only if predicative expressions refer. Echoing the disquotational treatment of predication, his anti‐formalism denies the necessity of assigning quantifiers a range of entities in order to account for the truth conditions of the sentences in which they occur; ultimately the role of quantifiers can only be explicated by using them.

If we find ourselves able to accept Prior's view—or at least the neutral component of it—then we must investigate whether predicates are referring expressions before settling whether predicative quantifiers range over a domain of entities. It remains unclear whether Prior's conception of quantification is acceptable. Nevertheless, the gap identified in Quine's arguments against predicate quantification indicates that there is a necessity anyway in establishing whether there are other reasons—that have nothing to do with quantification—for conceiving of predicates as referring expressions. It is therefore to an examination of the behaviour of predicates themselves, independently of their liaisons with quantifiers, to which we must turn.

19.3 Identity and Identification

Identity is expressed in English by those uses of “is” that are telescoped versions of “x is the same object as y”. It is the occurrence of names in statements of identity that marks out names as paradigmatic cases of referring expressions. An appreciation of (p. 449) the significance of these constructions is owed to Frege. He laid down the requirement that if we are to understand an expression as referring to an object then we must be able to recognize the object as the same again: “If the symbol a is to designate an object for us, then we must have a criterion that decides in all cases whether b is the same as a, even if it is not always in our power to apply the criterion” (1884: §62). For if we lacked such a criterion of identity we would have no conception of which object the symbol “a” picked out. Indeed if we lacked altogether a conception of which object “a” picked out it would be questionable whether “a” was even being used by us as a name of an object. Our understanding of the fact that “a” is a referring expression is correspondingly bound up with our grasp of the conditions under which identity statements—that may also be called recognition statements—of the form “a is the same object as b” are true.

A grasp of the conditions under which “a is the same object as b” is true cannot, however, be arrived at independently of an appreciation of other contexts in which the proper names “a” and “b” occur. In the most basic cases these are typically constructions of the form “x is an N”, where “N” marks the place for a common noun. These constructions are important because there is no asking after the identity of an object in abstraction from a specification of the general kind to which it belongs; what it takes for a to be the same object as b depends upon what kinds of object a and b are. So we cannot begin to set about answering the question “is a the same object as b?” unless we can already answer the question “same what?” We do so by using a common noun to say what a and b are.

Suppose that standing on the Embankment our companion points towards the Thames and says upon consecutive days “That is a” and “That is b”. Whether a is the same object as b depends, for example, upon whether our companion is using “a” and “b” to pick out a flowing river or, alternatively, the droplets of water that happen to fill the river bed when the pointing gesture is made. Whether our companion is using “a” or “b” in one or other of these ways will thus depend upon his or her willingness to endorse such common noun constructions as “a is a river” and “b is a river”. This is because a grasp of the noun “river” carries along with it a basis for identifying and distinguishing between objects of the river kind.

This is also why common nouns such as “river” or “person” that take the plural are often called count nouns. We may intelligibly be asked to count the number of rivers or persons there are. How many rivers? How many persons are there? Because correct counting requires that the same object not be counted twice these questions could not intelligibly be asked unless our grasp of “river” and “person” already provided a basis for identifying and distinguishing between the same and different rivers and persons. This contrasts with the case of adjectives. Like count nouns, adjectives carry with them a criterion of application; to grasp the significance of the adjective “red”—no less than to grasp the significance of the noun “river”—requires having a conception of the distinction between the things to which expression applies and those to which it does not. But, unlike count nouns, adjectives do not carry a criterion of identity with them. If asked “how many red things are there?” we do not (p. 450) even know where to start counting because a grasp of “red” does not settle where one red thing finishes off and another begins.22

The status of names as referring devices then is bound up with their occurrence in identity statements and interaction with common nouns. Are their corresponding grounds for attributing reference to predicative expressions? Obviously predicative expressions cannot themselves occur in the identity construction “x is the same object as y” or the common noun construction “x is an N”; predicative expressions are just the wrong grammatical shape to fit in the “x” and “y” positions that proper names occupy in these constructions. But are there analogous statements into which predicative expressions do grammatically fit that provide grounds for attributing a referential status to them?

Frege proposed that statements of co‐extension among predicates be viewed as analogous to identity statements (see his 1892–5: 120–2). The relation of co‐extension is expressed by constructions of the form “For every x, x is a Φ if and only if x is a Ψ”, where “Φ” and “Ψ” mark positions that predicative expressions are grammatically eligible to fill. Statements of co‐extension are analogous to identity statement in respect of the inference patterns they sustain. Where “a” and “b” are proper names and “F” a predicate, then from the identity statement “a = b” and “Fa” the sentence “Fb” may be inferred. Likewise, where “F” and “G” are predicates and “M(Φ)” a second level predicate with an argument position for a first‐level one, then from the co‐extension “∀x (FxGx)” and “M(F)” the sentence “M(G)” may be inferred.

Of course, this inference pattern breaks down where, for example, modal words, intentional verbs or quotation intervene. For example, it cannot be inferred from “a thing has a heart if and only if it has a kidney” and “John thought he had a heart” that “John thought he had a kidney.” But the same vocabulary disrupts the former inference pattern too. For example, it cannot be inferred from “Hesperus is the same object as Phosphorus” and “John thought he saw Hesperus rise in the evening” that “John thought he saw Phosphorus rise in the evening.” Nevertheless, insofar as some definite and principled circumscription can be made of the contexts that are extensional—i.e. contexts from which the disruptive vocabulary is excluded—the following analogy remains. Co‐extensive predicates and co‐referential names are intersubstitutable salva veritate in extensional contexts. It is because of this analogy between predicates and names that (in part) Frege felt compelled to construe predicates, like names, as referring expressions.

If the analogy is accepted—with the significance Frege read into it—further corroborative evidence for the claim that predicates are referring expressions may be found. Frege introduced the notion of reference in contradistinction to that of sense: whereas the referent of an expression is the item for which it stands, the sense of an expression is a particular way of thinking (a mode of presentation) of the referent. Frege introduced the notion of sense in order to account for the fact that identity statements in which different names occur are often not only true but also (p. 451) informative (“Hesperus is the same as Phosphorus”). Such statements are informative because in picking out the same object with different names we draw upon different modes of presentation—different bodies of information—to amplify our identification. In the same way a true but informative co‐extension statement (“a thing has a heart iff it has a kidney”) may be viewed as a case in which different modes of presentations associated with different predicates (“heart”, “kidney”) are used to pick out the same underlying referent (Frege, 1891; Dummett, 1973: 209).

It may be objected that co‐extension is too coarse‐grained a relation to provide a proper analogue of identity; that, in fact, we should be unwilling to identify the referents of predicates unless the predicates in question are necessarily co‐extensive. Natural kind statements may be taken as a source of examples of predicates so related. From this point of view “a thing is a horse iff it is a member of the species Equus caballus” is necessarily true, a statement in which different modes of presentations associated with “horse” and “Equus caballus” are used to pick out the same underlying referent (Wiggins, 1984: 127–8). But even in the case of necessarily co‐extensive predicates it may be questioned whether the concepts thereby picked out are really the same, albeit under different modes of presentation. The difficulty we encounter here is not so much that of finding an analogue of identity for predicates; it is rather that there appear too many analogous relations, more or less fine‐grained (co‐extensive, necessarily co‐extensive, structurally isomorphic …).

Yet whatever relation, however fine‐grained, we light upon the same basic problem remains. Let it be granted that there is the similarity that Frege makes out between names and predicates—that predicates, like names, sustain in an extensional fragment of our language comparable principles of inference. But why think that this formal analogy suffices to show that predicates are referring expressions? To say that the predicates “F” and “G” are co‐extensive is just to say that “F” and “G” are true of the same things. There appears no necessity to construe “F” and “G” as referring expressions in order to establish that they have the same extension; it appears only necessary to determine that they are true of just the same range of objects. Why not, indeed, turn Frege's way of thinking on its head and exploit the co‐extensive occurrence of predicates to explain away what might otherwise have superficially appeared to be instances of co‐referring predicates? To say that two predicates have the same reference is—from this point of view—to say nothing more than that they are co‐extensive (true of just the same individuals).

Let it be granted too that the uses of (e.g.) the predicative expressions “horse” and “Equus caballus” draw upon different bodies of information. But what reason is there to suppose that in drawing upon these different bodies of information we are exploiting different modes of presentation of the same referent? Why not say instead that the predicates simply have different application conditions: that even though they apply to the same individuals our understanding of what it takes for “horse” to apply to an object is different from our understanding of what it takes for “Equus caballus” to apply? A related difficulty afflicts Strawson's proposal that the criterion of application associated with the use of a predicate “F” serves as a criterion of identity for the referent—the property or universal—that “F” picks out (see his 1976: 23). Say (p. 452) this if you like. But why think of a predicate as any kind of referring expression in the first place? Indeed, why not take the equation of the criterion of application for a predicate with a criterion of identity for the universal it picks out as showing that the predicate is not a referring expression at all (a predicate only really has a criterion of application)? To this Strawson may respond that there is no need to treat his proposal in so reductionist a spirit (Strawson, 1979: 54). But equally, it may be stressed, there appears no need (so far) to treat his proposal in an inflationary spirit either.

The formal analogy that Frege makes between names and predicates therefore fails—at least in isolation—to establish that the latter, like the former, are referring expressions. Once again we are obliged to go looking for other reasons to construe predicates as referring expressions. By so construing predicates it may appear that an explanation is provided of the fact that different predicates apply to the same things. This appears especially plausible when different predicates are necessarily co‐extensive; their extensions coincide in all possible worlds because they rigidly refer to the same property and therefore invariably apply to the same objects (whatever objects happen to instance the property in question). But while this explanation is plausible enough it is unclear what it really achieves for us. If the fact that two different predicates necessarily apply to the same objects cries out for explanation, the fact that two different modes of presentation necessarily present the same referent demands no less of an explanation.

What is it about our linguistic practice that makes it so overwhelmingly natural to construe names as referring devices? Doubtless it is (in part) the interaction of names with demonstratives (“this”, “that”). We often learn to use a name “a” to refer to an ostensible object because someone points to the object in question and says, “This is a”. By learning to judge whether “This is a”—what is sometimes called a ‘recognition statement’—is true or false we learn to identify what “a” picks out. We do so because it is only by acquiring a grasp of the criterion of identity associated with the use of the name “a” that we are able to isolate what the demonstrative “this” is being used to pick out; if we do not, in the end, come upon this criterion we will be left at a loss as to what object “this” is being used to refer to.

Do predicates interact with demonstratives in comparable fashion so as to suggest that predicates are also referring expressions? It is certainly true that predicates and demonstratives do interact in a superficially similar way. We often come to learn to use a predicate “F” because someone points and says, “This is F”. But Dummett sees an important contrast between the role of demonstrative in statements of this form—crude predications—and their role in recognition statements (1973: 232–3, 241, 406–8). Whereas in “This is a” the demonstrative is used to pick out the object to which “a” refers, the demonstrative in “This is F” is used only to pick out an object to which “F” applies. So learning how to use a predicate does not involve learning to identify something as the referent of the predicate. It just involves learning when to apply the predicate to an ostensible object, an object that is F. When the semantic contribution of names and predicates are so understood in relation to these “quite primitive linguistic performances” and “fundamental practices” the conclusion becomes inescapable, Dummett maintains, that there is nothing in the (p. 453) understanding of a predicate that corresponds to the identification of an object as the referent of a name (1973: 406).

The interpretation that Dummett imposes upon crude predications is, however, far from inescapable. One way in which the contrast Dummett has in mind between recognition statements and crude predications shows up is when repeated use is made of them to enable a hearer to catch onto their significance. When “This is a” is repeatedly and successfully used the demonstrative picks out the same object—what “a” refers to—again and again. By contrast, the repeated and successful use of “This is F” does not rely upon the demonstrative picking out of the same object again and again. The crude predication will succeed even if different objects are picked out each time a use of it is made. It is only required for the successful employment of the predication that the objects picked out are F. This difference arises because whereas Dummett interprets the copula in “this is a” as the “is” of identity—so that the recognition statement embodies the form “x = a”—the “is” in “this is F” is construed as the “is” of predication—so that the crude predication embodies the form “Fx”. But this way of construing the difference between recognition statements and crude predications fails to take into account the possibility of ascribing an alternative form to “this is F”.

Evidently a crude predication cannot be assigned the form “x = a” because, as we have already reflected the predicate letter “F” cannot grammatically figure in an identity statement. Nevertheless, as we have also reflected, predicate letters can figure in statements of co‐extension. This suggests the form “∀ x (this: x ↔ Fx)” for “This is F” where “this” occurs in predicate position and the copula expresses the “is” of co‐extension. If such a predictival use of demonstratives could be made out this would provide the basis for an alternative interpretation of crude predications, an interpretation in which the referent of a predicate is picked out by a demonstrative just as the referent of a name is picked out by a demonstrative in a recognition statement.

Is it possible to use demonstratives in predicate position? It certainly is possible to place demonstratives in the position of adjectives and adverbs. Consider, for example, the predication “The rose is this colour” accompanied with a pointing gesture at a red book (Searle, 1970: 116). Or take the injunction “Don't talk like that.” Is it not straightforward and natural to construe these demonstratives as devices of reference?

Dummett does not consider such varieties of demonstrative construction. However, he does argue independently of the grammatical propriety of these constructions that no predicate or predicative expression could perform the role of demonstrative. In order to press the analogy with recognition statements Dummett considers the possibility of a sentence of the form “For all x, K(x) if and only if P(x)”, a sentence where ‘K(ξ) ’is intended to perform a role analogous to a demonstrative in a recognition statement. But what, asks Dummett, might the predicate “K(ξ) ” be? He replies, “The only suggestion that comes to mind is that ‘K(ξ) ’ be a disjunction of predicates of the form ‘ξ = a’ ” (1973: 242). Such an analysis will fail if there are objects that lack names in the language. For then “P(ξ) ” may be true of some object α unnamed in the language even though there fails to be a corresponding disjunct of “K(ξ) ” of the form “ξ = α”. Dummett suggests that “we might just (p. 454) escape this objection by replacing the constituents “ξ = a” by predicates of the form “that is ξ”, accompanied by a pointing gesture derived from recognition statements” (1973: 242–3). But, as Dummett next points out, this revised analysis will not help in the case of an infinite domain. Moreover, it has the absurd consequence anyway that a universal quantification involves reference to all the objects in the domain, a consequence that is absurd because “when I say that all men are mortal … I do not have in mind some African chief of whom I have never heard” (1973: 243).

The difficulties that Dummett places in the path of accepting a predicative device akin to a demonstrative relies upon the assumption that “K(ξ)” be analysable in terms of identity constructions manufactured from either names or demonstratives drawn from recognition statements (in terms of “ξ = a” or “that is ξ”). This is just to assume that it is ultimately through the channel of recognition statements that reference must flow. But what we have been entertaining is the possibility that crude predications and other forms of demonstrative construction provide an independent channel of reference to the world. In that case “K(ξ)” need not be analysable. It may demonstratively pick out its reference in the characteristic and sui generis way of predicative expressions. By learning to judge whether “For all x, K(x) if and only if P(x)” is true or false we may thereby learn to identify what “P(ξ)” picks out by demarcating what “K(ξ)” refers to. Because Dummett assumes that “K(ξ)” must consist of ingredient expressions that refer in the manner characteristic of singular expressions his arguments fail to rule out the possibility of demonstrative identification of the referents of predicates.

While Dummett fails to rule out this possibility it nevertheless remains to be established that a referential construal of demonstratives in predicative position is imposed upon us. While it may be intelligible to interpret the crude predication “This is F” as making reference to what “F” picks out, it is no less natural to read this predication as Dummett does—as a predication of an ostensible object to which “F” applies. Of course there is no reason to suppose that crude predications must admit of only one analysis, that there is need to treat these different analyses as competing. Still the question remains: why take the referential construal of a crude predication seriously?

Yet even if it cannot be established that such a construal is imposed upon us, we should have been wary anyway of a proposal that links reference too closely to the possibility of demonstrative identification. There are just too many things inside and out of space and time to which names purport to refer to which we lack demonstrative access—objects and events in the distant past or future, numbers and other abstract objects, and so on. It can hardly be demanded that the referents of predicates be available for demonstrative identification when so many referents of names cannot be accessed in this way. But unfortunately this reflection still leaves us in the dark about whether or not predicates are referring expressions. And, sadly this is a state of affairs that is by now all too familiar.

But our troubles would be swept away if sense could be made of the idea that predicates might undergo grammatical transformation and thereby become eligible to fit into name position. Once transformed predicates would be able to figure directly in identity statements and be the subjects of common noun constructions and have (p. 455) their status as referring expressions confirmed that way. Because the transforms of predicates would thereby be shown to occur in explicitly referential position this would provide a basis for affirming that the predicates from which they are transformed occur in “implicitly referential position” (Strawson, 1960: 51).

It is the prevalence of nominalization in natural language—the transformation in which a verb or an adjective is turned into a noun—that makes this doctrine a plausible one. Nominalization allows us to transform (e.g.) the adjective “courageous” in “Wallace is courageous” into the noun “courage”, a noun that is capable of figuring as the subject of the predication “courage is a virtue” or the object of “Wallace has courage.” It is also the prevalence of nominalization in natural language that makes the traditional theory of universals so natural to adopt. According to this theory, universals are those things that can be referred by either a predicate (“resembles”) or a name (“resemblance”). By contrast, particulars are things that can only be referred to by names (“Socrates”). It was a theory of just this kind that Strawson advanced in Individuals (see his 1959: 137–213). But the very coherence of this way of thinking—and the associated prospect of securing reference for predicates by transforming them into names—is cast into doubt by what Frege took to be an insight into the essential nature of reference itself.

19.4 Frege on Reference

Frege arrived at this (purported) insight into reference by generalizing from the case of names. Proper names refer, or purport to refer to objects; “Russell” refers to a philosopher, “16” to a number and so on. But, in addition to proper names, Frege recognized a class of complex names that also pick out objects, for example, “the teacher of Wittgenstein” and“42”. What is noteworthy is that complex names pick out objects because they have a structure; they refer by virtue of containing proper parts that also refer. For example, “the teacher of Wittgenstein” picks out Russell because “Wittgenstein” refers to one of his pupils. Frege identified a fundamental principle of substitution governing the contribution of the naming parts of a complex name to the reference of the whole: if a constituent name of a complex name is substituted for another with the same reference then the reference of the whole remains unchanged. Thus the substitution of “2+2” for the co‐referential numeral “4” in “42” results in a complex name “(2+2)2” that also refers to 16. From this principle of substitution Frege generalized. Noting that names occur in sentences too, Frege famously, or infamously, proposed that sentences be taken as complex names of truth‐values. In this way he arrived at a principle of substitution governing the contribution of the naming parts of a sentence to the reference of the whole: “If our supposition that the reference of a sentence is its truth‐value is correct, the latter must remain unchanged when a part of the sentence is replaced by another word with the same reference” (1892a: 64).

(p. 456)

What Frege then took to be an insight was this: that substitution exerts an essential control on reference; if two expressions have the same reference then they must be intersubstitutable salva veritate (without change of truth‐value). Call the substitution principle controlling reference that Frege endorses the “Reference Principle”.23 At first sight the Reference Principle may appear obvious or trivial. But it is far from toothless. It led Frege to deny that an occurrence of an expression inside the scope of modal operators, intentional verbs or quotation marks—what are often called intensional contexts—has the same reference as an occurrence of the same expression outside their scope—in extensional contexts (1892a: 58–9). Even though “Hesperus” and “Phosphorus” are intersubstitutable in extensional contexts (“ … is a planet”, “ … is brightly visible”) these expressions fail to be intersubstitutable salva veritate in intensional contexts (“John thought he saw …. rise in the morning”). Because sameness of reference presupposes intersubstitutability salva veritate Frege concluded that “Hesperus” and “Phosphorus” cannot have the same reference in extensional and intensional contexts. In order to render intelligible the failure of substitutability salva veritate inside the scope of an intentional verb Frege argued instead that occurrences of “Hesperus” and “Phosphorus” must, in contexts of this kind, refer to their different senses or modes of presentation

The Reference Principle also led Frege to deny that names and predicates are capable of co‐referring. If the name “wisdom” and the predicate “is wise” co‐refer then “wisdom” and “is wise” must—at least in the absence of modal operators, intentional verbs of quotation marks that generate non‐extensional contexts—be intersubstitutable salva veritate. But they are not. The attempt to substitute “wisdom” for “is wise” in “Socrates is wise” so far from leaving the truth‐value of the sentence unchanged results in a mere list of names (“Socrates wisdom”); names and predicates are not even intersubstitutable salva congruitate, never mind salva veritate. Frege concluded that names like “wisdom” and predicates like “is wise” have “an essentially different behaviour, as regards possible substitutions … i.e. the references of the two phrases are essentially different” (1891: 50).

If Frege is right to deploy the Reference Principle the way he does then it follows that the traditional theory of universals rests upon a mistake, the mistake of supposing that the universal picked out by a predicate (“resembles”) may also be picked out by a name (“resemblance”). It also follows that the prevalence of nominalization in natural language can do nothing to lend support to the doctrine that predicates are referring expressions. Since they fail to be intersubstitutable the Reference Principle dictates that the grammatically singular transform of a predicate cannot co‐refer with a predicate. As a consequence the grammatical outputs of the process of nominalization must be interpreted differently. Either (i) the transformation of a predicate into a grammatically singular expression is merely grammatical. In other words, a logically (p. 457) perspicuous representation of the sentences in which the nominalization occurs must show that they are merely idiomatic variations on sentences in which the predicate appears untransformed. Or (ii) the transformation is genuinely logical in which case a perspicuous representation must show that the nominalization performs a quite different role in the sentences it occurs in from the predicate from which it is derived. In that case the fact that the nominalization of a predicative expression refers (if it does) provides no support for the view that the predicative expression from which it is derived refers too.

19.4.1 The Concept Horse Paradox

Is Frege right to deploy the Reference Principle the way he does? Is the Principle even true? Before answering these questions it is important to trace another connection between the Reference Principle and the issue of predicate reference, a connection that casts in doubt the very idea that predicative expressions are referring.

Frege's thinking about predication was beset by the notorious Paradox of the Concept Horse (see his 1891). Frege maintained that predicates are referring expressions; he called the worldly items to which predicates referred ‘concepts’ and contrasted them with the worldly items picked out by names that he dubbed ‘objects’. Because the Reference Principle prevents predicates from ever co‐referring with names—they fail to be intersubstitutable—Frege was obliged to deny that concepts are ever to be picked out by names or objects by predicates. Frege therefore concluded that the worldly division between concepts and objects is an exclusive one: concepts can no more be objects than objects concepts because the referent of a predicate can no more be picked out by a name than the referent of a name by a predicate. But this conclusion has some puzzling consequences. According to Frege, the referent of the predicate “ξ is a horse” is a concept. But what concept is it? One might expect to answer, as Frege sometimes does, “the concept horse”. But since “the concept horse” is a singular phrase—that fails to be intersubstitutable with “ξ is a horse”—it must pick out an object. Since no object is a concept it follows, paradoxically, that the concept horse is not a concept. Worse still the predicate “ξ is a concept” cannot even be satisfied by the referent of a predicate. Grammatical propriety requires of “ξ is a concept”—like “ξ is a horse”—that its argument position “ξ” be filled with a name, not a predicate. Since names only pick out objects it also follows, paradoxically, that the only grammatical completions of “ξ is a concept” are false sentences.

What is responsible for the Paradox of the Concept horse arising? According to one plausible treatment of the paradox, Frege was led astray by the misleading nomenclature of ‘concepts’. This makes it appear as if concepts are objects because “concept” may be used to construct definite descriptions (“the concept horse”)to pick concepts out, and first level predicates (“ξ is a concept”) to say what the referents of predicates are like. However, it may be argued, a proper appreciation of the logical—rather than grammatical—role of “the concept horse” and “ξ is a concept” reveals otherwise: it is really first‐level predicates that are being used to (p. 458) refer to concepts, second‐level predicates to characterize them; there is consequently nothing in this way of talking to belie the predicative nature of the underlying concepts. Frege did not avail himself of this way out. Because of the presence of the definite article, Frege felt obliged to insist that the phrase “the concept horse” must be construed as a proper name that stands for an object, not a concept (1892: 45–6). But one might allow for different uses of “the” and construe contexts in which “the concept horse” occurs as involving the completion of a second‐order predicate by a first‐order one. Thus in “the concept horse applies to Shergar”, it is the “the concept … applies to Shergar” rather than “the concept horse” that forms a logical unit, the former completed by the first‐level predicate “ξ is a horse” where the resulting whole just means “Shergar is a horse.”24 In a similar spirit “ξ is a concept” may also be construed as a second level predicate that may be completed with grammatical propriety by a first‐level predicate. Since “ξ is a concept” is intended to characterize concepts in general—where a concept is conceived as the referent of (at least) every first‐level predicate—the second‐level predicate to which “ξ is a concept” is deemed equivalent must be such that any first level predicate may be inserted into its argument position so as to yield a true sentence. Assuming the Law of Excluded Middle, “Φ is something which everything either is or is not” is a plausible candidate; the result of completing the argument position “Φ” by a predicate is a sentence that says the law holds for the corresponding concept. Thus “the concept horse is a concept” may be construed as the completion of “Φ is something which everything either is or is not” by “ξ is a horse” where the resulting sentence is “a horse is something which everything either is or is not”. Since neither the construal of contexts that embed “the concept horse” nor those that involve “ξ is a concept” belie the nature of what “ξ is a horse” picks out—by using a name to pick it out or a first‐level predicate to say what it is like—paradox appears thereby to be avoided (Geach, 1951: 133; Dummett, 1973: 216–17).

Unfortunately this response does not go deep enough. For even when the terminology of concepts is abandoned altogether it remains questionable whether the very idea of assigning reference to predicates is even intelligible. I will call this residual difficulty that survives the abandonment of Frege's terminology the Reference Problem to distinguish it from the version of the Concept Horse Paradox lately considered. The Reference Problem arises in the following way.25 If there is to be any intelligibility to the claim that a given category of expressions have reference then it must be possible to say of an expression in that category that (1) it has some referent or other—i.e. to make clear that the expression is not, in fact, empty—and (2) to specify what, in particular, the expression refers to. It is easy to see how these procedures may be undertaken with respect to the category of proper names. We can say (e.g.) of the name “Myomar” that it is not empty because, in fact, there is something (p. 459) “Myomar” refers to. Moreover, we can specify what “Myomar” refers to, namely Burma.

  1. (1*) (∃ x) (“Myomar” refers to x)

  2. (2*) “Myomar” refers to Burma

But when it comes to the category of predicative expressions the Reference Principle prevents our undertaking these procedures in any straightforward way. The Reference Principle dictates that it is only possible to refer to what an expression “X” picks out by employing another “Y”, where the latter is intersubstitutable salve veritate with the former. It follows that “X” and “Y” must, at least, belong to the same syntactic category otherwise they would fail to be intersubstitutable altogether. But the predicative machinery we use to say that an expression has reference all appear to be two place predicates (“x refers to y”, “x stands for y”, “x picks out y”, “x denotes y”) that grammatical propriety requires to be completed by names or variables fit for binding name positions—the name of an expression in one position, and a first‐order variable that includes what the expression stands for among its values or a name that refers to it directly. It follows that we can neither use this vocabulary to say that a predicate has reference nor to specify what the predicate picks out. Consider the following attempt to do so.

  1. (3) (∃ X) (“ξ is a horse” refers to …)

  2. (4) “ξ is a horse” refers to …

The attempt to ascribe reference to or specify the referent of “ξ is a horse” using the familiar vocabulary of reference misfires because grammar prohibits our inserting a predicate constant or variable intersubstitutable with “ξ is a horse” into the blanks marked by “ … ”. So whatever expressions are used to fill the blanks they cannot—by the Reference Principle—co‐refer with “ξ is a horse”. And since the only other forms of vocabulary apparently available for ascribing reference to predicates (vocabulary such as “x stands for y”) are subject to the same grammatical prohibitions it appears that reference cannot be intelligibly assigned to predicates.

19.4.2 Three Ways Out

How are we to respond to the Reference Problem? Prima facie this successor to the Concept horse paradox presents a stark dilemma. Either it must be denied that predicates are referring expressions, or, the Reference Principle must be given up. Embracing the latter horn of this dilemma hardly seems advisable. If we give up the Reference Principle altogether then it becomes doubtful whether we can hold on to what was a significant insight on Frege's part—that there are very many ordinary contexts in which we succeed in picking out an individual and where what we say about it is true or false irrespective of whatever name we may happen to use to pick that individual out (“If words are used in the ordinary way, what one intends to speak of is what they mean [Bedeutung]” Frege 1892a: 58). If, for example, it is (p. 460) true to say of Venus that it is a planet with a shorter period of revolution than the Earth, then it is true no matter whether we harness one or other of the co‐referring devices “Hesperus” or “Phosphorus” that pick Venus out to the task of saying that this is so. In such contexts it is legitimate to infer from the truth of the statement “Hesperus is a planet with a shorter period of revolution than the Earth” that the statement “Phosphorus is a planet with a shorter period of revolution than the Earth” is also true. Evidently in some circumstances the Reference Principle does receive straightforward application and a philosophically convincing account of the matter should render intelligible why in some, but not other, circumstances this should be so. To simply deny the Reference Principle is to precipitately deny the prospects of providing a philosophical account of this kind.

Must we therefore take the former course and deny predicates reference altogether?26 To think so would appear to be a premature overreaction to the Reference Problem. For a number of intriguing proposals have been made about the semantics of predicates that suggest a variety of different ways of respecting the Reference Principle while construing predicates (in some sense) as referring expressions. They include the claims that: (i) the notion of reference is ambiguous as between semantic levels; (ii) it is only a proper part of a predicate that refers; (iii) whereas names figure in the reference relation to objects, predicates figure in a different sui generis word–world relation to concepts.

Proposal (i): Dummett

Proposal (i) arises from reflection upon the Fregean doctrine of levels. According to that doctrine, it is senseless to attempt to say the very same thing about expressions of different levels. Consequently, it is senseless to attempt to say that first‐level predicates, like 0 level names, are referring expressions. It follows that if there is a relation of reference between, say, first‐level predicates and the worldly items they pick out, then this relation can be no more than—as Dummett puts it—“analogous” to the reference relation that obtains between names and the objects they pick out.27 It is also a corollary of this position that there is no such thing as the Reference Principle. Instead there are many such principles, for each level a different principle governing the interchange of ‘referring’ expressions of that level (a different Reference Principle for names, for first‐level predicates, and so on).

What evidence is there that the notion of reference is ambiguous in this way? Dummett finds relevant evidence in the double use of the pronouns “what” and (p. 461) “which” to construct relative clauses (1973: 213–14). Contrast, for example, “what you gave me yesterday” and “what I used to be and Peter has just become”. According to Dummett, the former construction is first order, picking out an object, whereas the latter construction is higher‐order. It is because relative clauses of the former kind are first‐order that they may be used to pick out the referent of names. Thus, for example, the relative clause “what ‘Mount Everest’ stands for” may be used to pick out the referent of the name “Mount Everest”. Why? Because “what ‘Mount Everest’ stands for” and “Mount Everest” are completely interchangeable expressions (witness the sample substitution “Mount Everest is a dangerous mountain”, “What ‘Mount Everest’ stands for is a dangerous mountain”). So their referent, if they have one, must be the same. Analogously, relative clauses of the latter kind may be used to pick out the referents of predicates. Thus, for example, “what ‘ξ is a horse’ stands for” may be used to pick out the referent of the predicate “ξ is a horse” because, again, the expressions “what ‘ξ is a horse’ stands for” and “ξ is a horse” are completely interchangeable (consider “Shergar is a horse” and “Shergar is what ‘ξ is a horse’ stands for”).28 However, by contrast to “what ‘Mount Everest’ stands for”, “what ‘ξ is a horse’ stands for” fails to be interchangeable, completely or otherwise, with any name whatsoever. So relative clauses of the form “what ‘ξ is a horse’ stands for” cannot refer in the same sense as relative clauses of the form “what ‘Mount Everest’ stands for”. Consequently, Dummett maintains, we are able to see that there is a legitimate use of “—stands for … ” (and its cognates) in connection with predicates that “displays its analogy with (and type‐difference from) its use in connection with proper names” (1973: 254).

How then does Dummett propose to use “—stands for … ” to say that a predicate has reference and specify its referent? To say that the name “Mount Everest” has reference Dummett offers the construction “There is something which “Mount Everest” stands for.” Here the relative clause ‘which “Mount Everest” stands for’ is naturally read as a definite description of an object, the “something” that precedes it correspondingly interpreted as a device signifying first‐order generality. Accordingly, “There is something which ‘Mount Everest’ stands for” is just a roundabout way of saying “There is such a thing as being Mount Everest”, a statement that may be rendered symbolically, “For some x, x is Mount Everest” (where “is” signifies identity).

To say that the predicate “ξ is a horse” has a reference Dummett offers the analogous construction:

  1. (5) There is something which “ξ is a horse” stands for

How is this statement to be understood? Since the relative clause ‘which “ξ is a horse” stands for’ is predictival the ‘something’ that precedes it must be interpreted (p. 462) as a device expressing second‐order generality. Accordingly, Dummett maintains, (5) is just a roundabout way of saying “There is such a thing as being a horse” that may be rendered symbolically, “For some Φ, for every x, Φ x if and only if x is a horse.” Since it is “impossible” to deny that there is such a thing as being a horse Dummett concludes that “the appearance of tendentiousness in the thesis that reference can be ascribed to predicates thus apparently wholly dissolves away” (1973: 218).

To specify the referents of predicates Dummett introduces a class of predicative expressions derived from predicates in the following way. If the main verb of a predicate is the copula then the corresponding predicative expression results from dropping the copula. For example, “a horse” is the predicative expression that corresponds to “ξ is a horse”. If the main verb of a predicate is other than the copula then the predicative expression results from converting the main verb into the participial form of the same tense. For example, “running” is the predicative expression that corresponds to “ξ runs”. According to Dummett, predicative expressions may be used to pick out the referents of their corresponding predicates. They do so when they are conjoined with relative clauses where “what” performs the role of a higher‐order pronoun. Thus “a poet” picks out the referent of “ξ is poet” when the former expression is conjoined with the relative clause “what Blake was but Hayley was not” prefixed by the copula (“A poet is what Blake was but Hayley was not”). Similarly “a horse” may be used to specify the referent of “ξ is a horse” when the former expression is conjoined with the relative clause ‘what “ξ is a horse” stands for’ prefixed by the copula:

  1. (6) A horse is what “ξ is a horse” stands for

The Reference Problem arose because—it appeared—that the only machinery available (“—stands for … ”) for saying that a predicate has reference or specifying its referents are all two place predicates that grammatical propriety requires to be completed by names or variables fit for binding name positions (recall (3) and (4)). So long as the Reference Principle is respected we appear, therefore, to be left in an impossible predicament, the predicament of being unable to say that a predicate has reference or to specify what the predicate picks out. Dummett's ingenious proposal promises to extricate us from this predicament. For, according to Dummett, there is a use of “stands for” that when harnessed to the machinery of higher‐order quantification, pronouns and predicative expressions enables us to say that a predicate has reference and to specify its referents without employing names and lower‐order variables to do so and thereby belying its predicative nature.

It is questionable, however, whether Dummett's proposal fulfils its brief. The worry is that the higher‐order variables, relative clauses, and predicative expressions Dummett employs are no more interchangeable with predicates than names or name variables are.29 Surface grammar prohibits not only the relative clause “what ‘ξ is a (p. 463) horse’ stands for” but also the predicative expression “a horse” being interchanged with the predicate “ξ is a horse” (“Shergar is a horse”, “Shergar what ‘ξ is a horse’ stands for”, “Shergar a horse”). They fail to be interchangeable because the relative clause and predicative expression, by contrast to the predicate, lack a copula. Predicative expressions that are participial conversions of a verb other than the copula are no more interchangeable with the predicates from which they are derived (“Shergar runs”, “Shergar running”). Another failure of substitution casts doubt upon the use of higher‐order quantifiers to say that a predicate has reference. If it is correct to say that there is something which “ξ is a horse” stands for then it ought to be possible to specify what “ξ is a horse” stands for. We ought to be able to construct a sentence of the form: “There is something (namely … ) which ‘ξ is a horse’ stands for.” But the natural fillings for the “namely … ” clause are gerundive expressions like “being a horse”—expressions to which Dummett makes appeal—that are no more interchangeable with predicates than predicative expressions (“Shergar being a horse”).

Proposal (ii): Wiggins

Proposal (ii) arises from an appreciation of what are perceived to be the shortcomings of Dummett's account. First consider the class of cases where a predicative expression is derived from a predicate whose main verb is the copula. In such cases the failure of interchange between the predicative expression (“a horse”) and its corresponding predicate (“is a horse”) appears to establish that—contra Dummett—these expressions do not co‐refer. Nevertheless, it also appears that the predicative expressions of the relevant class are referring expressions. For—as Wiggins points out—the positions of these predicative expressions are accessible to a species of quantification we understand fairly well in ordinary English. We understand that if the statement “Shergar is a horse” is true then the statement “there is something Shergar is” is also true. In this latter statement the quantifier “there is something” binds not the entire predicate position occupied by “is a horse” but rather the position of the predicative expression “a horse” inside the predicate. Consequently the copula—that, while adjacent to, nevertheless lies outside the position occupied by “a horse”—is left unbound at the end of the latter statement when the position of the predicative expression in the former statement is bound. Moreover, it also appears that we are able to specify what is quantified over by the binding of the position of predicative expression in “Shergar is a horse.” We do so by attaching a “namely … ” clause to the corresponding quantified statement; witness, “There is something Shergar is, namely a horse.”

According to Wiggins the same quantificational procedures may be seen at work when attention is switched from predicates whose main verb is the copula to other predicates. In such cases it is not the predicative expression—conceived à la Dummett—that results from converting the verb into its participial form that is subjected to the rigours of quantification. It is rather the expression that results from shedding the inflections that convert the verb into its finite form; witness the transition from “John walks” to “there is something John does, namely walk”. Wiggins (p. 464) concludes that while predicates do not refer, parts of them do—the parts that result from, where relevant, the subtraction of the copula or the finite form of the verb (“(a) man”, “(a) horse”, “(an) admirer of Hegel”, “wise”, “run”, “walk”, “sit”, “work”, “sleep”)(1984: 132–4). So while, for Wiggins, “ξ is a horse” does not refer, it is nevertheless possible to say that a part of this predicate has reference and to specify its referent:

  1. (7) There is something “a horse” stands for

  2. (8) A horse is what “a horse” stands for

It is important to emphasize two questionable aspects of Wiggins' proposal. First, it assumes that expressions that occur in positions open to quantification are inevitably referring. But we have already seen this to be a questionable assumption (Section 19.2 above). For what our earlier discussion of quantification and reference showed was that it is necessary to establish whether a category of expressions are referring before settling whether these expressions range over an associated domain of entities. But Wiggins' proposal does nothing to establish whether “a horse” or “walk” are referring expressions independently of their occurring in positions accessible to quantification; he assumes rather that “a horse” and “walk” are referring expressions because they may be subjected to the rigours of quantification. Consequently Wiggins' proposal fails to establish that parts of predicates are referring expressions even if predicates are not.

Second, it is essential to Wiggins’ proposal that predicates and their grammatical parts (“a horse”, “run”, and so on) belong to different semantic categories. It is because Wiggins conceives them to do so that he is able to deny that predicates have reference—thereby distancing Dummett's proposal from his own—while affirming that parts of predicates are referring expressions. But if the distinction between a predicate and its parts is merely grammatical then not only do Wiggins’ reasons for doubting the reference of predicates become questionable but also the reasons that have been given for rejecting Dummett's proposal that predicative expressions may be employed to pick out the referents of predicates.

We have already had occasion to consider the Fregean suggestion that the copula is a mere auxiliary device without content of its own that does no more than convert a phrase into a verbal phrase where grammar demands one (Section 9.2.1 above). From this point of view, as Dummett remarks, the copula is akin to the pronoun ‘it’ when used to supply a grammatical subject even though the sense of the sentence in which it occurs requires none (consider, for example, the role of “it” in “it is raining”) (1973: 214). If the copula (or the finite form of a main verb other than a copula) has no more significance than that of a grammatical tick then the failures of substitution that obtain between a predicate and a predicative expression are entirely superficial; such failures of substitution hardly establish that predicates and predicative expressions cannot co‐refer. Similarly, if these grammatical features are entirely superficial then the failures of substitution between predicates and their grammatical parts hardly establish the predicates and their proper parts cannot co‐refer either.

(p. 465)

In that case: (a) the criticisms that have been made of Dummett's proposal lapse; (b) the differences that separate proposal (ii) (Wiggins) from proposal (i) (Dummett) transpire to be merely grammatical. Of course, it requires an argument to show that this is so—that the copula, or the finite form a main verb, are without logical significance. But it cannot be assumed that they bear logical significance either. Moreover, the arguments presented in favour of this assumption have already been seen to be weak—for what appears to be logically significant about the structure of predicates is not the copula, nor the finite form of the main verb other than the copula, but the presence of argument positions (see Section 19.2.1 above). It consequently remains unclear whether, or how, it is to be established that proposal (ii) is distinct from proposal (i), or that proposal (i) is undermined by substitution failures.

Proposal (iii): Wright

Proposal (iii) promises to lift us free of entanglement with the issues that bedevil the assessment of proposals (i) and (ii). According to Wright, predicates do not refer; nevertheless, he declares, predicates figure in an alternative word–world relation to the worldly items they pick out.30 Predicates do not refer because, Wright holds, the Reference Principle rules out the possibility of a singular expression picking out the referent of a predicate; for if such cross‐reference were possible then the Reference Principle would demand the inter‐substitution of these expressions, thereby reducing a sentence to a list. Consequently the Reference Principle rules out the possibility of an intelligible thought of the form ‘ “is a horse’ refers__” being framed; for Wright holds, contra Dummett, that “—refers to___” is a verb that is required by grammatical propriety to be completed by singular expressions to form a (singular) sentence. Wright takes this as a reductio of the assumption that the relation between predicates and the worldly items they pick out is reference, i.e. the relation expressed by the verb “—refers to___” that obtains between names and the objects they pick out. It follows that predicates and the worldly items—call them properties—that predicates pick out must figure in a different word–world relation. Wright dubs this relation ‘ascription’. So whereas it is the role of a name in a (singular) sentence to refer to an object, it is, Wright claims, the role of a predicate to ‘ascribe’ a property. Correspondingly, whereas the inter‐substitution of names is governed by the Reference Principle, the inter‐substitution of predicates is governed, Wright claims, by the Ascription Principle. This principle says, “co‐ascriptive expressions will be cross‐substitutable salva veritate in extensional contexts, and salva congruitate in general” (Wright, 1998: 87).

What are the advantages of proposal (iii) purported to be? That, as we have seen, (αa) it enables us to maintain a conception of predicates as standing in a semantically significant word–world relation, a conception that is not liable to reductio (p. 466) via the Reference Principle. That (β) it is a conception of predicates that allows us to explicitly state the semantics of individual predicates. Of course, proposal (iii) denies that predicates are referring expressions. So, by the lights of this proposal, it is neither possible to state that predicates have reference nor to specify their referents. Nevertheless, it is possible to state that predicates have ascription and to specify their ascripta. For even though predicates cannot intelligibly refer to but only ascribe properties, this puts “no obstacle in the way of reference to the relevant ascripta by the use of relevant singular terms” (1998: 87). In other words, even though names and predicates cannot co‐refer (or co‐ascribe), the worldly items that predicates ascribe may also be referred to by singular terms. So even though ascription is expressed by a verb “x ascribes y” that grammatical propriety requires to be completed by singular expressions to form a sentence, this does not prevent us from using this verb to state that predicates have ascription and specify their ascripta. For first‐order bound variables and singular terms may be employed to quantify over, and refer to, the very properties that predicates ascribe:

  1. (9)x (“is a horse” ascribes x)

  2. (10) “is a horse” ascribes the property of being a horse

What are the disadvantages of proposal (iii)? The most significant, perhaps, is that it is open to the complaint that ascription is reference in all but name, and that proposal (iii) does not resolve but merely masks by re‐labelling the difficulties that the Reference Principle poses for the intelligible assignment of reference to predicates. Wright responds to this concern by making appeal to what he takes to be common sense intuitions about names, predicates and their contrasting roles. What does it mean for a predicate to stand in the relation of ascription? Wright answers: “for its sense so to relate it to that property … that it may be used in concatenation with an appropriate singular term to say of the bearer of that term that it has the property … in question” (1998: 88). That relation, Wright declares, is “pre‐theoretically, every bit as clear as the ordinary notion of reference as applied to singular terms”; moreover “It is also pre‐theoretically utterly intuitive” that so‐conceived ascription is not the relation that obtains between singular terms like “the property of being a horse” and the properties to which they refer. But, contra Wright, a more sober assessment of the deliverances of common sense suggests otherwise.

What does seem to be “mere common sense to one innocent of Frege's thought about the matter” is that whereas names are used to pick out objects, predicates are used to describe the objects thereby picked out. But from the fact that predicates are used to describe the objects picked out by names it does not follow—at least not without further ado—that when a predicate “F” is used to describe some object x, there is inevitably some other thing y to which F is also related (viz. the ascriptum of “F”). Of course, it does not follow either that there is no such y—that F does not also lie in a relevant relation to a property or concept that semantically underpins the capacity of “F” to describe x (see Section 19.1 above). But common sense does not itself settle whether this is so. Common sense underdetermines whether predicates require a semantics that relates them only to the objects they are used to describe, (p. 467) or whether predicates must also stand in a further distinctive relation (reference or ascription) to properties or concepts in order to fulfil their descriptive function.

It remains the case, however, that ascription, as Wright conceives of it, is distinct from reference, at least if reference is the relation that obtains between a name and its bearer. For, according to Wright, ascription is the relation expressed by the open sentence (S): “ξ is fitted to be used, in concatenation with an appropriate singular term, to say of the bearer of that term that it falls under the concept Φ” (1998: 89). Evidently (S) cannot be satisfied by a name and the object it picks out—for a name cannot be used, in concatenation with a singular term, to say anything whatsoever. It follows that the intelligible avenue for the expression of the thought that ascription is no more than reference in disguise is that ascription is a composite relation—roughly speaking, a composite of the reference relation between predicates and properties, and the functional relation between predicates and singular terms that enables predicates to be used to describe the objects picked out by singular terms. However, Wright dismisses the suggestion that ascription is a composite relation, demanding “an argument that this is so—that it is a definite mistake to treat ascription as a sui generis form of relation between an expression and a concept” (1998: 89). He goes on to express scepticism that such an argument will be forthcoming, an argument that isolates a common ingredient in the way predicates and singular terms relate to their associated properties/concepts and objects without rubbing out the all too obvious differences that obtain between predicates and singular terms. But it is entirely unclear what warrants Wright's scepticism here. For Wright's own description of ascription is composite: (S) not only incorporates reference to the concept Φ ascribed by the predicate ξ (for some Φ and ξ) but also points up the functional difference between predicates and singular terms with respect to describing the bearers of singular terms. Wright therefore owes an argument on behalf of proposal (iii) that ascription is, despite appearances, a sui generis form of relation and that it is a definite mistake to treat ascription otherwise.

We began this section with a dilemma: either predicates fail to have reference or the Reference Principle must be given up. Three proposals that attempt in different ways to evade this dilemma have been considered. Enough has now been said to indicate that each of these proposals faces significant difficulties of its own, although it remains to be established that any can be ruled out of court. Nevertheless each of these proposals assumes that there is a theoretical necessity to uphold the Reference Principle in full generality. However in the next section I will argue there is no such necessity. The Reference Problem results from a misconception about the Reference Principle. Once we see that the Reference Problem results from such a misconception, it will become evident that Frege did nothing to establish that predicates and their corresponding nominalizations cannot co‐refer.

19.4.3 Suspending the Reference Principle

The Reference Principle was introduced in the following terms: co‐referential expressions are intersubstitutable salva veritate. So stated the principle is open to familiar (p. 468) counter‐examples. For example, as we have seen, “Hesperus” and “Phosphorus” are co‐referential but still fail to be intersubstitutable salva veritate inside the scope of an intentional verb like “believes” or “knows”. Modal operators and contexts of direct quotation generate other familiar counter‐examples. To preserve the Reference Principle it is therefore necessary to restrict the principle so as to exclude the troublesome contexts that generate counter‐examples to it—to exclude so‐called ‘intensional’ contexts in which there is no guarantee that the substitution of co‐referential expressions will preserve truth‐value. In order for this restriction to be justified—rather than an ad hoc manoeuvre to preserve an otherwise appealing principle—it is also necessary to offer an account of what the features of these contexts are that result in the intelligible suspension of the Reference Principle.

What these features are will vary from case to case. In the case of a statement involving an intentional verb it is plausible, as Frege proposed, that the truth‐value of the whole is a function not of the usual referent of a singular term but of the sense or mode of presentation of its usual referent. In other cases different accounts will be fitting. This is nicely illustrated by an example of Quine's (1953d: 139–40). Even though the statement “Giorgione was so‐called because of his size” is true, and “Giorgione” and “Barbarelli” are co‐referring, it still does not follow that “Barbarelli was so‐called because of his size” is also true. In this case the failure of substitution is accounted for by the fact that the context “x was so‐called because of his size” is not only a function of the reference of “Giorgione”/“Barbarelli”. As Quine puts the point, “Failure of substitutivity reveals merely that the occurrence to be supplanted is not purely referential, that is, that the statement depends not only on the object but on the form of the name” (1953d: 140).

Even though the details may vary of what accounts for the suspension of the Reference Principle in a given intensional context, it has nevertheless become orthodoxy to assume that intentional verbs, modal operators, devices of quotation and the like are between them responsible for what failures of substitutivity salva veritate among co‐referring expressions there are. So it has become orthodoxy to assume that absent the presence of the familiar forms of intensional vocabulary that routinely disrupt substitution between co‐referring expressions, the Reference Principle will hold sway. But it appears that the successes that have been made in explaining away some (important) counter‐examples to the Reference Principle have blinded us to the possibility of others. For there are other failures of substitution among co‐referential expressions even in what are routinely taken to be extensional contexts—i.e. even in the absence of what are usually taken to be intensional devices. Once these counter‐examples are understood aright it becomes questionable whether Frege was ever justified in deploying the Reference Principle to show that names and predicates are incapable of cross‐reference.

One significant source of counter‐examples to the Reference Principle is furnished by the failures of substitution that occur between relational predicates and their converses. If we consider the fact in virtue of which it is true that some A is before B then, as Russell once remarked “it seems plain that this fact consists of A and B in succession, and that whether we describe it by saying “A is before B” or by saying “B is after (p. 469) A” is merely a matter of language” (Russell, 1913: 85). There are, in other words, not two independent chunks of reality, one responsible for the truth of “A is before B”, another responsible for the truth of “B is after A”. It is for this reason that the facts of temporal succession may be fully stated employing just one of these expressions. Russell thus arrived at the conclusion that the predicate “x is before y” and its converse “x is after y” must pick out the same relation.31 But even though these predicates are co‐referential they cannot, as Russell recognized, be substituted for one another salva veritate. Substituting the former predicate for the latter in,

  1. (1) A is before B

generates the statement,

  1. (2) A is after B

a substitution that is hardly guaranteed to preserve truth‐value. This is a failure of substitutivity salva veritate that occurs in the absence of intentional verbs, modal operators, devices of quotation etc. But it does not follow that “x is before y” and “x is after y” are not referring expressions. For the more modest conclusion to draw is simply that these predicates do not merely refer to the relation they pick out; the positions in which they occur are not purely referential.

Following Russell let us employ “succession” as a “neutral” expression for this relation (1913: 88). It is essential to an understanding of the contribution the expressions “x is before y” and “x is after y” make to the contexts in which they occur that they not only pick out the succession relation but do so in different ways to which these contexts are sensitive.32 How so? In general there is a rule associated with the use of each n‐place predicate R n that determines how the n objects referred to by the singular terms flanking the position of a predicate in a sentence are to be correlated with the argument positions of the n‐place relation R n picks out. Thus, in particular, there is a rule associated with “x is before y” that determines that the object picked out by a left‐flanking singular term in a given sentence is to be correlated with one argument position (p 1) of the succession relation while the object picked out by the corresponding right‐flanking name is to be correlated with the other (p 2). But, by contrast, “x is after y” is associated with the converse rule according to which the object picked out by the right‐flanking singular term in a given sentence is to be correlated with p 1 and the object picked out by the corresponding left‐flanking singular term is to be correlated with p 2. It is because “x is before y” and “x is after y” not only pick out the relation of succession but also come associated with converse rules about how the objects referred to by their flanking singular terms are to be correlated to the argument positions of the succession relation that they fail to be intersubstitutable salva veritate.

(p. 470)

Such failures of substitution are not restricted to relational predicates and their converses. Consider, for example, “x is between y and z” and “x and y are end points of a line on which z lies”. Since the latter predicate simply spells out what the former means it follows—by Russell's reasoning—that the latter refers to the relation that the former picks out. Nevertheless, it is because these predicates are associated with different rules for correlating objects with argument positions that these predicates fail to be intersubstitutable.

We are presented then with a significant class of cases where it appears entirely intelligible that the Reference Principle should have been suspended, suspended because the expressions in question are not merely referential; in such cases there is no reason to suppose that because relational predicates fail to be intersubstitutable salva veritate that they also fail to co‐refer. What's more, a consideration of these cases also casts doubt upon Frege's employment of the Reference Principle to show that names and predicates do not co‐refer. 33

Relational predicates impose a structure upon the contexts in which they occur; they do so because they are associated with rules for correlating the referents of flanking singular terms with the argument positions of relations. By contrast, expressions that occur in name position impose no such structure; they are associated with no rules of this kind. For this reason names and relational predicates cannot be inter‐substituted. Does it follow that names and relational predicates cannot co‐refer? No. For what has already been said about relational predicates allows for the intelligible suspension of the Reference Principle in such cases. Relational predicates, we have suggested, perform two distinct semantic roles: (i) they refer to a relation; (ii) they correlate objects with argument positions. It has been argued that failures of intersubstitution (p. 471) between co‐referring predicates are rendered intelligible by noting that relational predicates that agree with regard to (i) may nevertheless differ with respect to (ii). Recognizing that relational predicates are multifunctional in this way provides insight into the failures of substitution that obtain between names and relational predicates. It is because, for example, “succession” embodies the first, but not the second, of these functions that “succession” cannot intelligibly be substituted into contexts where the predicate “x is before y” occurs.

This account of substitution failures among names and relational predicates does not, however, extend straightaway to substitution failures among names and non‐relational predicates. Monadic predicates such as “x is wise”, no less than names, do not have rules for correlating different objects picked out by flanking singular terms with different argument positions of a relation. It is therefore an entirely conventional matter—one without semantic significance—whether a name is written to the right or left of a monadic predicate sign. For this reason what appears in English as “Socrates is wise” may be accurately represented in the formal language of predicate calculus as “Fa”. Nevertheless, there is a rule associated with the use of a monadic predicate (e.g.) “x is wise”, a rule according to which the object picked out by the singular term—whether right or left‐flanking—is correlated with the argument position of the property or concept “x is wise” picks out. By contrast there is no such rule associated with a corresponding singular expression (e.g.) “being wise” that—intuitively at least—picks this property out. So even a monadic predicate imposes a structure in this limiting sense. This is signalled by the fact that when predicates undergo the process of nominalization, transforming “x is wise” into “being wise”, “x is between y and z” into “between” and so on, the argument positions of the corresponding predicate expressions disappear (or, at least, are syntactically bound). Consequently there is no route back from the isolated inspection of a nominalized predicate that occurs in name position to an appreciation of the structure imposed by the corresponding predicate (whether the structure of “x is between y and z” or “x is wise”) upon the sentences in which it occurs. This just highlights the fact that expressions that occur in name position do not carry the same semantically relevant structural information as expressions that occur in predicate position; this structural information is lost once a predicate is nominalized. But rather than showing that names and predicates do not co‐refer, this fact provides the basis of a general explanation of why names and predicates may fail to be intersubstitutable salva veritate even though they co‐refer. It is because the contexts in which predicates occur are sensitive to the structural information predicates carry—information that co‐referring nominalizations have given up—that the latter expressions fail to be intersubstitutable with the former.

The failures of substitution that occur between names and predicates need not then betoken the absence of co‐reference between these expressions. It need merely be the consequence of the intelligible and legitimate suspension of the Reference Principle in certain cases. Allowing for co‐reference between names and predicates may, however, appear to carry with it an unacceptable cost—namely a commitment (p. 472) to a property‐theoretic version of Russell's paradox.34 For if the property expressed by the predicate “x is not predicable of itself” may be picked out by a corresponding singular term (viz. “being not‐predicable of oneself”) then it appears that either this property must be predicable of itself, or not. But to suppose either that this property is, or that it is not, predicable of itself leads to contradiction. But it does not follow from this contradiction that names and predicates do not co‐refer. It need only follow, as Russell immediately acknowledged, that the gerundive expression “being not‐predicable of oneself” and the corresponding predicate “x is not predicable of itself” fail to pick out a property. This may lead one to question whether it is the role of predicates to refer at all. But the fact that some predicates are determined by logic to be incapable of referring hardly settles that no predicates refer. After all, we do not take the fact that some names do not refer to establish that no names refer. Indeed the possibility that a predicate might fail to pick out a property—that some predicates should be empty—is just what should be expected if it is the ordinary function of predicates, at least in more favourable conditions, to refer.

19.4 Conclusion

What has been established by the foregoing discussion? We have a negative result. When the Reference Principle is understood aright—when it is understood what range of intelligible exceptions the principle properly admits—then it becomes apparent that the Reference Principle cannot be employed to show that names and predicates are incapable of co‐reference. In particular the principle cannot be employed to show that predicates and their derived nominalizations are incapable of co‐reference. But, alas, this still leaves us without a positive result. We are still without reason for affirming that predicates and nominalizations co‐refer and are therefore hardly in a position to affirm that predicates are referring expressions because their nominalizations pick out (say) properties.

Preceding sections argued that we have no more reason to affirm that predicates are referring expressions because of their interaction with quantifiers, demonstratives and other particles. The fact of the matter is that we are neither in a position to rule in, nor to rule out, a referential construal of predicates and related predicative expressions. This state of affairs is to be lamented. It is true that twentieth century philosophy of language gave rise to an extraordinary variety of sophisticated proposals that have greatly illuminated our understanding of a number of otherwise perplexing constructions—treatments of definite descriptions, demonstratives and adverbs stand out. One might even go so far as to say that these proposals mark the high water mark of analytic philosophy. But until an understanding is achieved (p. 473) of predication—that most basic and pervasive of linguistic constructions—what is essential to language will remain obscured from us.


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                                                                                                                                                                    Thanks to audiences at the Universities of Leeds and York. For further discussion I am grateful to Kit Fine, Jane Heal, Jennifer Hornsby, Keith Hossack, April Jones, Mark Kalderon, Guy Longworth, Mike Martin, Joseph Melia, Alex Oliver, Gabriel Segal, Mark Sainsbury, Peter Simons, Mark Textor, and especially Barry C. Smith. I am also grateful to the Arts and Humanities Research Council who funded the period of leave during which this chapter was written.

                                                                                                                                                                    (1) This interpretation of Frege—that identifies two distinct ingredients in his notion of reference—is owed to Dummett (1973, 1981).

                                                                                                                                                                    (2) Of course we should also be prepared to countenance the possibility that, upon reflection, the notion of reference may become detached from the class of prototypical expressions relative to which it is often introduced. See Sainsbury “The Essence of Reference” (this volume) for a sustained discussion of reference per se.

                                                                                                                                                                    (3) This separation of issues gives rise to the dictum with which Kreisel is credited: “the problem in the philosophy of mathematics is the objectivity of mathematical statements, not the existence of mathematical objects”.

                                                                                                                                                                    (5) As it stands (P) applies only to adjectives and nouns. For present purposes I leave aside complications that arise from adapting (P) to cover the case of transitive and intransitive verbs and other predicative expressions.

                                                                                                                                                                    (6) This theory is analogous to—but also to be distinguished from—Tarski's theory of truth that relies in similar fashion upon the schema (T) “p” is true iff p. Quine remarks on the parallel in his 1953c: 136–8.

                                                                                                                                                                    (7) See Armstrong, 1978: 16–7 and Hochberg, 1978: 139–40 for different versions of this complaint. See also the exchange between Devitt (1980) and Armstrong (1980).

                                                                                                                                                                    (8) This is not the only way to accommodate the relativity in question. For rather than qualifying the relations of reference and being true of, making them hold only relative to a language, predicative strings may be individuated more finely and indexed to a language. Then (P) may be written: “F L” is true of a iff F La. And (R) becomes: “F L” is true of a iff a falls under the referent of “F L”.

                                                                                                                                                                    (9) See the criticisms of Tarski's theory of truth in (e.g.) Field, 1972 and Dummett, 1978: xx–xxi.

                                                                                                                                                                    (10) Quine, who first raised an objection of this form, suggested a somewhat different reductio: “On what grounds, indeed, can we take issue with someone who even outdoes the nominalist and repudiates everything, the concrete as well as the abstract, by construing all words indiscriminately as syncategorematic expressions designating nothing?” (1939: 704; see also 1980: 165). Quine answers by arguing that expressions that occur in positions that are open to quantification cannot be construed as syncategorematic. Whether reference, or lack of it, can be linked in this way to the accessibility, or inaccessibility, of a position to quantification will be discussed in the next section.

                                                                                                                                                                    (11) Davidson recognizes this requirement in his description of predicate satisfaction: “Thus ‘Dolores loves Dagmar’ would be satisfied by Dolores and Dagmar (in that order) provided Dolores loves Dagmar” (Davidson, 1969: 48). The problems faced by the nominalist and realist who employ the ‘is true of’ idiom do not end with the recognition of order. They must also introduce some device (ontological or ideological) to distinguish a collective from a distributive reading of “is true of”.

                                                                                                                                                                    (13) We catch our first glimpse here of the so‐called paradox of the concept horse, a conundrum that arises from the fact that grammar often obliges us to use a name (“swimming”) to talk about the referent of a predicate (“swims”), thereby (apparently) belying the predicative nature of what the predicate picks out. See Section 19.4.1 below.

                                                                                                                                                                    (14) This is, effectively, the strategy Davidson employs when he argues that there is no need to assign predicates reference in order to generate an adequate truth theory for a first‐order language; for this purpose, it is merely required that objects, or sequences of objects, satisfy (‘satisfies’ being the converse of ‘is true of’) predicates. He writes, “Here, the call for entities to correspond to predicates disappears when the theory is made to produce T‐sentences without excess semantic baggage” (Davidson, 1977: 210). Davidson assumes here that predicates in natural language occur in positions that are not open to quantification. This assumption will be placed under scrutiny in the next section.

                                                                                                                                                                    (17) See Quine, 1947, 1953b and 1970: 66–8. Boolos, 1975 and Shapiro, 1991 develop the countervailing case for second‐order logic. See MacBride, 2003: 135–42 for an overview and assessment of this debate.

                                                                                                                                                                    (18) Frege's thinking about predicate reference will be explored in Section 19.4. See Heck and May “Frege and Semantics” (this volume) for further discussion of Frege's views.

                                                                                                                                                                    (19) Strangely Dummett recognizes (i) when he remarks “To construe the reference of predicates after the model of the name‐bearer relation entails admitting second‐level quantification as legitimate” (1973: 227) but evidently fails to appreciate (ii) when he later adds “there can be no reservation whatever about the existence of concepts, relations and functions provided that we are prepared to admit second‐level quantification (1973: 245).

                                                                                                                                                                    (20) Witness Marcus and Sellars' treatment of quantifiers and ontological commitment. Like Prior, Marcus advocates a neutral conception: “where we are already ontologically committed in some sense, then, all right: to be is to be the value of a variable” (see her 1971: 78). Marcus later adds the clarification: “There are even in ordinary use, quantifier phrases that seem to be ontologically more neutral, as in ‘It is sometimes the case that species and kinds are, in the course of evolution, extinguished.’ It does not seem to me that the presence there of a quantifier forces an ontology of kinds or species. If the case is to be made for reference of kind terms, it would have to be made, as for proper names, independently” (Marcus, 1978: 121–2). Sellars comes close to entertaining the same view when he remarks, “there is no general correspondence between existentially quantified formulae and existence statements. Only in those cases where the variable which is quantified is a variable of which the values are singular terms will a quantified formula be the counterpart of an existence statement” (Sellars, 1960: 255). Unlike Prior, Sellars and Marcus develop the neutral insight in a substitutional way.

                                                                                                                                                                    (21) One difficulty that confronts Prior's conception of quantification is whether it blocks or hinders the provision of a systematic semantics of the kind that Tarski and Davidson have made familiar. Different advocates of the Prior view have taken contrary views concerning whether (i) anti‐formalism blocks a recursive definition of truth for a language and (ii) it is necessary to provide such a semantics. See Williams (1981: 189–217) and Hugly and Sayward (1997: 241–316) for further discussion of this and related issues.

                                                                                                                                                                    (23) To denote the substitution principle that Frege endorses Wright employs the expression “Reference Principle” (see his 1998: 73). But this principle has also been dubbed, variously: “Principle of Interchangeability”, “Frege's test for identity of reference”, and “Principle of Interchange”. See Carnap, 1947: 51, 98, 122, Geach, 1955: 227 and Furth, 1968: 12.

                                                                                                                                                                    (24) See Dummett, 1951: 102 and Geach, 1955: 228. The suggestion that Frege is misled by the definite article into thinking that “the concept horse” denotes an object is developed more systematically in Parsons, 1986: 455–63.

                                                                                                                                                                    (25) Different versions of this argument are to be found in Dummett, 1951: 101; Furth, 1968: 17–21; Searle, 1970: 102–3; Dudman, 1976: 78; Long, 1978: 79; and Wright, 1997: 74–5.

                                                                                                                                                                    (26) This first horn of this dilemma is arguably embraced in Furth, 1968: 23–45. According to Furth, what is intelligibly to be grasped about the notion of reference is what may be formulated in terms of the contexts “has the same reference as” and “has a reference”. From the point of view that Furth develops, what it means for two predicates to have the same reference is just that they are co‐extensive; what it means to say that a predicate has reference is just that every completion of the predicate by a singular term that has a reference results in a sentence with a truth‐value. Of course, this does not imply, nor does Furth take it to imply, that predicates have reference in the same sense that names do.

                                                                                                                                                                    (28) Dummett develops here a suggestion of Frege's: ‘we should really outlaw the expression “the meaning of the concept‐word A”, because the definite article before “meaning” points to an object and belies the predicative nature of a concept. It would be better to confine ourselves to saying “what the concept word A means”, for this at any rate is to be used predicatively: “Jesus is, what the concepts word ‘man’ means' in the sense of ‘Jesus is a man’ ” (Frege, 1892‐5: 122).

                                                                                                                                                                    (30) See Wright, 1998: 84–90. Related versions of this proposal may be found in Searle, 1970: 97–102 and Sen, 1982: 104. By contrast to both Sen and Wright, Searle goes on to develop proposal (iii) in a nominalistic spirit, conceiving of the properties ascribed by predicates as “parasitic on predicate expressions” (1970: 119–21).

                                                                                                                                                                    (31) It is arguable that the early Frege was also wedded to this conception of relational predicates and their converses (1879: §3). See Williamson, 1985 and Fine, 2000 for related arguments in favour of Russell's conclusion.

                                                                                                                                                                    (33) Fitzpatrick (1960) suggests that the following example (due to Geach, 1969: 91–2) provides a counter‐instance to the Reference Principle: suppose (1) The first man who ever stole a book from Sneads made a lot of money by selling it and (2) Robinson is the first man whoever stole a book from Sneads. Yet despite the fact that “Robinson” and “the first man who ever stole a book from Sneads” are co‐referring (on the assumption that definite descriptions are referring expressions) the substitution of the former for the latter in (1) generates the nonsense: (3) Robinson made a lot of money by selling it. This is nonsense because “it” no longer has the antecedent “a book” which it had in (1). Geach denied that this example constitutes an exception to the reference principle, dismissing this suggestion on the grounds that the “usually recognized exceptions” to the reference principle arise “when we replace one designation by another in direct or indirect quotations, in modal contexts, or with intentional verbs like wants” (1961: 93–4). But this seems to be an overreaction to the case in hand. The more modest conclusion to draw is that the definite descriptions “the first man … ” is not merely a referential expression. Wolterstorff provides another counter‐example involving definite descriptions, noting that while co‐referential “ ‘John’ ” and ‘the name “John” ’ fail to be intersubstitutable in the context ‘We gave him the name “John” ’ generating, when the latter is substituted for the former, the nonsense construction, ‘We gave him the name the name “John” ’ (see his1970: 70–1). Wolterstorff concludes that, “the following principle should not be accepted. If two expressions designate the same thing, then in substituting the one for the other in some context one never changes sense into nonsense” (1970: 71). Oliver (2005) offers a different range of counter‐examples to the Reference Principle, involving centrally, cases in which definite descriptions fail to be intersubstitutable with proper names that occur in apposition to pre‐modifying adjectives. Thus consider the nonsense that is produced by substituting “the referent of ‘Russell’ ” for ‘Russell’ in “Clever Russell solved Frege's Paradox”: “Clever the referent of ‘Russell’ solved Frege's Paradox.”

                                                                                                                                                                    (34) See Russell, 1903: §101 and Geach, 1955: 228–9. It is noteworthy that versions of this paradox afflict both proposals (ii) and (iii) above. See Wiggins, 1984: 134 and Wright, 1998: 90. Only proposal (i) evades this paradox since it retains the structure of the Fregean hierarchy. See Dummett, 1973: 254.