Is Reference a Pseudo Relation?
Talk of reference is part of ordinary language, but to talk of a reference relation is to go beyond ordinary language. Is it to go too far? Does it embody a misconception about the nature of reference or the meaning of “refers”? Let us consider some relations in good standing. Spatial and temporal relations have a claim to be paradigms: objects and events clearly stand in spatial and temporal relations. These are real objective relations, not projections of language, observable and measurable. If one object is to the left of another, it is a certain distance to the left. Distance relations can be more or less and they are composed of sub-relations (a mile, say, is composed of shorter distances). One object can be much further away than another. Similarly with temporal relations: before and after, a century ago, in the distant future. These relations have extents and degrees. Thus we have locutions like “very far away”, “close by”, “long ago”, “just now”—as well as precise measurements using scales with units. Is the reference relation (if we are to talk that way) anything like these relations, logically speaking?
Reference is not a magnitude, so we cannot speak of amounts or degrees of it. Words do not differ in the quantity of reference they carry, so we cannot say that one word is more referential than another. Objects can be more or less distant from each other, but words cannot differ in how referential they are. We cannot say that one word is “very referential” or another “slightly referential”, as we can speak of objects as very distant or somewhat distant. There are no units of reference, with each relation of reference made up of more or less of these units. Is reference perhaps more like physical relations such as impact or gravity? But again we can speak of almost touching but not “almost referring”, of the degree of impact but not the “degree of referring”, of gravity as more or less intense but not of “intense reference”. Psychological relations are no different: sensations can be more or less intense and they can be measured–but not so for reference relations. Love comes in different strengths, but not reference. When we examine the relations that exist between objects we find that they admit of the kinds of characterizations mentioned, but reference doesn’t—it has no magnitude, direction, or intensity. Words refer or they don’t; there is no more or less. There is no metric of reference in the way there is a metric of space, time, and physical force.
It is notable that reference has been compared to other relations that do admit of the kind of characterization just mentioned. Thus reference has been compared to perception, acquaintance, grasping, and reaching. But we can speak of these relations as having degrees and gradations: I can see one thing better than another, I can be more intimately acquainted with one person than another, I can grasp things more or less firmly, I can reach further than you can. These are relations that admit of such qualifications. But the idea of more or less successful or intensive reference sounds peculiar: I either do it or I don’t. Words don’t denote with degrees of success or intensity, partially or completely, as if they aim at an ideal that they can fail to meet. I can see an object clearly or obscurely, or grasp an object securely or insecurely, but I can’t refer to an object with these qualifications. I refer to Plato as well or as strongly as I refer to any person closer to me in space and time. Referring is not an act that can vary along a dimension of adequacy. I can see the Empire State building partially or in poor light, but I cannot refer to the Empire State building partially or in poor light: I just refer to it tout court. I can grasp a knife tightly or loosely, but I cannot refer to a knife tightly or loosely. So referring is not analogous to relations that can vary in these ways. Reference is more like identity, which also has no degrees and cannot be measured. It is not like the relation of being older than: one object can be much older than another, but no object is much more identical to an object than other objects are—and no word is much more referential than another. Thus we are inclined to say that reference is a non-natural relation, while those other relations are natural relations. Reference seems not to belong to the empirical world alongside spatial and temporal relations and physical and psychological relations. It seems curiously thin, insubstantial, featureless, a mere shadow or skeleton. We never see reference. It seems like a relation in name only. It cannot be observed, detected, or measured. It has no empirical depth. It lacks a nature.
So far I have considered reference for singular terms, but there is also satisfaction—the (putative) relation between a predicate and its extension. Each object in a predicate’s extension satisfies it, so there are many relations contained in a single predicate—relations to all the objects of which it is true. The predicate radiates out to every object in its extension, scooping them up, gathering them together—the metaphors come easily. The predicate “planet”, say, encompasses all the celestial bodies that are planets—not just those in our solar system but also unknown planets in deep space. That word I just typed in quotation marks has a semantic relation to all those far-flung objects—they all satisfy it. But it is a funny kind of relation, appearing to span great distances instantaneously and undetectably. Compare the Sun: it stands in various relations to the planets—spatial, gravitational, electromagnetic. The planets vary in their distance from the Sun, moving around it in different ellipses; different degrees of gravitational force reach the different planets; light emanates from the Sun and strikes the different planets with varying intensity. These are real substantial relations—tangible and measurable. But the satisfaction relation is nothing like these: it does not vary in its amount; it cannot be detected by instruments; it does not act across space. There is no semantic force or semantic radiation or semantic separation. Reference seems like a film laid over reality, not part of reality. The Sun has genuine relations to the planets, with a depth and nature, but the word “planet” has nothing like this—it is just blankly “true of” each and every planet. It isn’t even like the members of its extension—a “picture” of them; it merely applies to them, equally and blandly. It has the mere form of a relation with none of the substance. We might call it a “quasi relation” or a “formal relation” or (more brutally) a “pseudo relation”. If it is a relation at all, it is not a relation in the full-blooded way that other relations are relations. Identity has been declared a pseudo relation because of its dissimilarity to other relations, and reference and satisfaction seem to cry out for the same appellation. They count as relations only by courtesy not by right.
Is there anything we can say positively to capture what is special about reference and satisfaction? Here is one thing we can say: for a predicate to be satisfied by an object is for a certain sentence to be true. For example, for the predicate “planet” to be satisfied by the object Mars is for the sentence “Mars is a planet” to be true: that is, if you substitute the name “Mars” into the open sentence “x is a planet” you get a true closed sentence. This suggests a theory: what it means to say that Mars satisfies “planet” is that “Mars is a planet” is true. Call this the “substitutional theory of satisfaction”. It is modeled on the substitutional theory of quantification: what it means to make a true quantified statement is for substitutions of names into a suitable open sentence to yield a true closed sentence. The putative relation of “quantifying over” is explained in terms of the truth of closed sentences obtained by substitution. There is nothing more to that relation than the truth of such sentences. Similarly, there is nothing more to satisfaction than the truth of certain closed sentences obtained by substitution. The substitution instances are basic, logically and metaphysically. In effect, we do away with satisfaction as a real relation and replace it with the truth of substitution instances. There is no reaching out or radiating; there is just sentential truth, taken as primitive. In the case of “refers” the theory looks like this: for a name to refer to an object is for a certain identity sentence to be true. For example, for “Hesperus” to refer to Phosphorus is for the sentence “Hesperus is identical to Phosphorus” to be true. We don’t explain the truth conditions of the latter sentence by invoking reference; we explain reference by invoking the identity sentence. There is no more to reference and satisfaction than the truth of certain sentences—there are no independent notions of reference and satisfaction. These notions are intra-sentential—defined by reference to the truth of sentences (which is not defined in terms of reference and satisfaction). The substitutional theory is a deflationary theory—an anti-realist theory. Just as truth is declared a pseudo property by the deflationary theory of truth, so reference and satisfaction are declared pseudo relations by the substitutional theory of reference and satisfaction. If this kind of theory is on the right track, we have an explanation for why so-called semantic relations differ from natural relations—they are grounded in quite different kinds of fact. Natural relations are extra-sentential, but semantic relations are intra-sentential. We have a tendency to reify semantic relations, which leads us to strange metaphysical pictures and suspect metaphors, but in fact they amount to nothing more than substitution and truth. As people used to say, semantic relations are “logical constructions” out of sentences and truth; they are not primitive features of the universe.
The spirit of the substitutional theory can be captured as follows. We have locutions that appear to state relations between whole sentences and worldly entities such as facts or states of affairs or situations. Thus we say that a sentence can “correspond” to such entities or “denote” them or “picture” them. We then wonder what the nature of these alleged relations might be, comparing them to other relations we find in nature; but this leads us to perplexity because they seem non-natural, thin, elusive. We find ourselves contemplating a metaphysics that can tolerate such peculiar relations, or we decide to reject them outright. But there is an alternative: we can explain the meaning of these locutions by reference to the truth of certain sentences. All that it means to say that a sentence corresponds to a fact or denotes an existing state of affairs is that the sentence is true: there is nothing more to the sentence “snow is white” corresponding to the fact that snow is white than that sentence being true. The putative correspondence relation vanishes on analysis into a statement asserting the truth of a sentence. We don’t analyze truth by means of correspondence; we analyze correspondence by means of truth. Thus “corresponds” expresses a pseudo relation: it appears to denote a real relation, but on closer examination it does not. The term is logically misleading, inviting mistaken reification. The fog clears when we recognize that correspondence is nothing more than the truth of a sentence: the relational term disappears under analysis. We can talk in the relational style if we like, but all we mean is captured by the non-relational paraphrase. It sounds agreeably pompous to speak of the sentence “snow is white” designating an existing state of affairs—as if we have got to the metaphysical foundations—but really this is just a misleading way of stating the banal fact that “snow is white” is true. So, at any rate, says the deflationist, and he appears to gain support from the evident oddity of semantic relations in general. Given the deflationary theory, that is just what we should expect—a deep difference between real relations and relations that are mere shadows or projections of language.
It is not necessarily an error to bring natural relations into the general theory of reference. Reference may well be intertwined with, even dependent upon, such relations as perception, causal chains, and mental imagery. There may be supervenience between such natural relations and semantic relations. The trouble comes when we try to analyze reference in such terms: for then we find ourselves saying strange things about reference derived from truths about the underlying natural relations. If reference is perception, then we will be able to say that reference can be clear or obscure, from this angle and not that, enhanced by a microscope or telescope, etc. If reference is having a mental image of an object, then we will be able to speak of distorted reference, vivid reference, faded reference, etc. If reference is a causal chain of reference-transmitting links, then we will be able to speak of segments of the reference relation, the history of the reference relation, the amount of energy that went into it, etc. Suppose we divide the chain into links and treat each link as a unit of measurement—call it the “Kripke”. Then we will be able to say that one chain consists of 532 Kripkes while another consists of 1567 Kripkes: we will be able to compare causal chains on a scale, and even speak of the rate of a causal chain—how many Kripkes per hour it can boast. We have a natural empirical relation here, laid out in space and time, capable of deeper characterization. But we surely don’t want to say that the naming relation itself has these kinds of properties. Does my referring to Plato with his name consist of semantic segments or divide into a certain number of Kripke units? Is someone who says “’Plato’ denotes the author of the Republic” really saying that there is a long causal chain of communicative links going all the way back in time to a certain Greek author? If so, some reference relations are longer than others, some slower than others, some more efficient than others. Such facts may be relevant to the existence of reference, but it is surely a category mistake to define reference in these terms. Do we want to say that denotation is composed of carbon atoms just because people are and people make up chains of communication? Such chains involve making noises, but does reference consist of those noises? Causation involves energy transfer, but does reference?
Compare the relation of quantifying over, in which variables take values instead of names having denotations. This too is a semantic relation–a relation between words and things. In virtue of what does it hold? It may hold in virtue of causal connections between utterances of bound variables and objects in a domain, or maybe mental images of objects occurring simultaneously with such utterances. But do we want to say that quantifying over objects can be analyzed in these terms? If so, we will have to say that quantifying over things can be causally complex, can vary in causal complexity from case to case, can be indistinct or fleeting or fragmentary. These characterizations indeed apply to the alleged basis of the semantic relation of quantifying over, but it looks like a category mistake to apply them to the relation itself. It isn’t a relation of perception or communication or imaging.  These relations have all sorts of properties that quantifying over simply doesn’t have; it abstracts away from all of that. Similarly for singular reference and satisfaction: they stand apart from any psychological or physical properties that might serve as a supervenience base. Seeing an object, say, is a complex psychological and physical relation, which admits of multiple kinds of qualification and evaluation; but referring to something you are seeing does not inherit all of that baggage. We can therefore never identify referring with seeing: seeing is just the wrong kind of relation for referring to be.
A final point: it has been a longstanding puzzle how words can refer to non-existent objects—for how can a non-existent object stand in a (real) relation to a word? How can “Sherlock Holmes” refer to a certain brilliant but non-existent detective? He isn’t there to be referred to! But if all that it means to say that “Sherlock Holmes” refers to a brilliant detective is that the sentence “Sherlock Holmes is a brilliant detective” is true, then we have reference on the cheap, since that sentence is true. If reference is a pseudo relation, explicable in terms of substitution and truth, then we will be able to tolerate reference to such objects as Sherlock Holmes. Reference just isn’t very demanding of nature, unlike space, time, force, causation, etc. If talk of reference is just projection from talk of sentences and truth, then all that reference requires is that certain sentences be true—not that words somehow reach out with special semantic tentacles into the world outside of them. Real relations like distance and gravity require existent objects related by objective facts of nature, but reference doesn’t require anything so strong—you can happily refer to what does not exist, so long as certain sentences are true. When God created sentences and truth he had already done all he needed to do to create semantic relations; no further creative act was necessary.
 Memory belongs in this list, since it is a genuine relation that admits of the qualifications I have cited—memories can be faded, partial, distorted, and more or less vivid than other memories. The relation thinking of also belongs here. So reference differs from all of these. We can reasonably say that reference isn’t psychological.