Pragmatic Grammar

This article is part of a series entitled Language Games. See also:
1. Wild Grammar; 2. Combinatorial Grammar; 3. Pragmatic Grammar

In a famous 1966 paper, Keith S. Donnellan claimed to have identified a linguistic phenomenon unexplained by the traditional accounts of Russell, and, more contemporarily, Strawson.

Definite descriptions – phrases like the king of France, or John’s brother – were held, classically, to single out the one and only object, if it exists, which meets the criteria of the description. The truth-value of a sentence containing a definite description was assessed via the properties of this description’s unique referent. (Sentences for which no unique referent exists – like The present king of France is bald – were taken by Russell to be false and by Strawson to have no truth value.)

In a hypothetical situation suggested by Donnellan [1] and modified by Kripke, two patrons at a bar discuss a man in the corner with a champagne glass. “The man over there drinking champagne is happy tonight,” [2] one says. Though the man they point to is indeed happy, he happens to be drinking sparkling water, while another man “over there”, who is drinking champagne, and whom neither patron sees, “has been driven to drink precisely by his misery” [2]. Traditional analysis would take the sentence to be false in virtue of the properties of the sentence’s unique referent, whom neither party intended to talk about and neither party even knew about. This analysis falls short.

Donnellan’s phenomena weren’t picked up by Russell’s treatment for good reason – his analysis resides at the level of pragmatics.

An Overview

Donnellan identified two possible uses of a definite description – the attributive and the referential use. The attributive use singles out whoever happens to meet the description’s criteria. The referential use, by contrast, is used pragmatically to direct the audience to an intended referent. The sentence “The man over there drinking champagne is happy tonight” is true under the referential use and false under the attributive one.

Which use is intended is not detectable through analysis of the meanings of the definite description’s words alone – through syntax or semantics, that is. The distinction is a pragmatic one – it depends additionally on the intentions of the speaker and the situation in which the speaker finds himself.

Saul Kripke, in an article regarding the distinction [2], collects additional examples from various authors. In one example, originally due to Linsky, one onlooker observing a happy couple remarks to another, “Her husband is kind to her.” “Yes, he seems to be,” the other replies. Although the man is not, let’s say, her husband, but in fact her lover, “to whom she has been driven precisely by her husband’s cruelty” [2], traditional analysis would deem both the onlookers’ statements false in virtue of the cruelty of a man they’ve never met. In another example, a historian evaluates a religious narrative – which refers persistently to The Messiah – for historical accuracy. If the narrative were true of its intended protagonist, and yet this protagonist were not in fact the Messiah – and even if someone else were – it would be improper for this historian to deem the manuscript historically false [2]. These all seem to fly in the face of Russellian analysis.

Kripke elucidates the attributive-referential distinction by defining a spoken sentence’s semantic referent and speaker’s referent. The semantic referent is that picked out by the meaning of the words. The speaker’s referent is that to which the speaker intends to refer. In the attributive use of a definite description, the speaker’s referent is by fiat nothing more than the semantic referent. In the referential use, the speaker’s referent is simply an object that the speaker believes coincides as a matter of fact with his sentence’s semantic referent. Whether it actually coincides is up in the air. [2]

A further explication of this distinction will be of use, especially later. Barwise and Perry (see Moulin [3]) take the attributive-referential distinction to be one between so-called value-loaded and value-free descriptions. Moulin, describing their work, paraphrases (bracketed words mine):

The value-free [attributive] interpretation of a definite description is a relation, a partial function from situations to individuals; the value-loaded [referential] interpretation is the value of that function when applied to some particular context. The value-free interpretation hence gives a description, and the value-loaded an individual… [3]

Rephrasing this explanation in terms that make its similarity to Kripke’s transparent, we might say that the value-free (attributive) interpretation returns whichever object happens, in the real world, to satisfy the description’s criteria, while the value-loaded (referential) interpretation gives the value the speaker takes, in light of his intentions and presuppositions, to satisfy the definite description.

The attributive-referential distinction is independent of the de dicto-de re distinction, which concerns the scope relation between a definite description and a modal or intensional operator. Nonetheless, or perhaps consequently, these two distinctions can interact in non-trivial ways. Different authors have put forth differing views regarding which of the four conceivable combinations are realizable. Kripke argues that de dicto descriptions can be neither attributive nor referential, while Moulin [3] purports to provide examples of both; Moulin claims that de re descriptions must be referential, while Kripke offers (bizarre) examples of the de re attributive. My command of the literature is not sufficient to root out and analyze the exchanges regarding these matters, if they exist.

The relationship between the two distinctions can be summarized, it seems, in the following way. The attributive-referential distinction can arise whenever a mere definite description is present; this definite description need not be syntactically embedded within an intensional operator. If it is, though, then it might alternate in scope with this operator. If it does, finally, both the attributive or referential uses remain available.

The philosophers’ apparent disagreements might be eased somewhat, it seems, if we introduce a certain subtle distinction. Recall Kripke’s claims regarding the de dicto:

[T]he de dicto use of the definite description cannot be identified with either the referential or the attributive use… If a description is embedded in a (de dicto) intensional context, we cannot be said to be talking about the thing described, either qua its satisfaction of the description or qua anything else.

Kripke seems to insist that a definite description can only be taken to be used attributively or referentially in virtue of the intentions of the sentence’s speaker. If we accept this definition, then Kripke is surely right about the de dicto. There’s another sense, though – and a more flexible one – in which we might understand the attributive-referential distinction. When a description is embedded within, say, a propositional attitude verb, and taken de dicto, we might ask whether the holder of the attitude uses the description in the attitude ascribed to him attributively or referentially. In this way, we can extend the purview of the attributive-referential notion to areas in which, originally, Kripke would have declined to define it altogether. This seems to be what Moulin does below. (It seems unlikely that this approach could be further extended to the case of modal operators; in any case, we’ve done enough already to construct examples.)

Let’s enjoy some examples of these interactions.

De dicto – referential (Moulin). “Charlie Brown believes that the little red-haired girl is beautiful.” [3] That this description is de dicto is clear – the little red-haired girl resides within Charlie Brown’s belief. Furthermore, Charlie Brown (but not the speaker!) uses the description referentially. (Indeed, note, à la Kripke, that the speaker has no intended referent.) Charlie Brown uses the description little red-haired girl only because of a supposed incidental correspondence between its semantic referent and his intended referent (who happens to be named Heather).

De dicto – attributive (Moulin). “John believes that the person who stole his bicycle (whoever it is) is red-haired.” [3] A de re reading here, even taken referentially, would yield an implausible proposition whereby John believes that some person — whom the speaker, though not necessarily John, takes to have stolen John’s bicycle — has red hair. In fact, in the definite description – which scopes underneath the propositional attitude verb believes – John identifies his belief with the semantic referent, whoever it may be, of the person who stole his bicycle. John (but not the speaker!) takes the description attributively.

De re – referential (Quine). “The number of planets is necessarily greater than 7.” [4] Here we understand the definite description the number of planets as residing (syntactically) underneath the modal operator necessarily. On a de dicto reading, this sentence seems false – if things had gone another way, apparently, we could have had fewer planets. If we take the number of planets de re with regard to necessarily, then the sentence asserts nothing more than that 9 is necessarily greater than 7, which is true. Of course, in this case, the speaker uses the number of planets to point referentially to 9 — if someone challenged him on the actual number of planets, he would brush such considerations aside and reaffirm his statement in an amended form.

De re – attributive (Kripke). “The number of planets (whatever it may be) is necessarily odd.” [2] This bizarre sentence needs to be explained. Here, Kripke supposes for the sake of argument that “I have no idea how many planets there are, but (for some reason) astronomical theory dictates that that number must be odd.” In this case, in the simple sentence “The number of planets (whatever it may be) is odd”, the number of planets is used attributively; the same remains true if we add necessarily and take the de re reading in the final sentence “The number of planets (whatever it may be) is necessarily odd.” The number of planets is de re with respect to necessarily, and it’s used attributively. Taken de dicto, again, this sentence would be false.

Nested Definite Descriptions

Let’s examine a few of the subtleties that can arise in sentences with nested definite descriptions. Consider the sentence:

The wife of the student’s professor is lucky.

This sentence contains two definite descriptions, one nested within the other: the student’s professor is nested within the larger the wife of the student’s professor.

This could be a sensible thing to say in various situations. Imagine first that this sentence is spoken privately between two members of the audience at a public lecture given by some student. When both definite descriptions are taken attributively, the sentence could mean something like “This student’s professor, whoever he may be, is surely such that his wife, whoever she may be, is lucky.” In particular, the audience members might know neither the student’s professor nor his wife.

Imagine, now, that the student is accompanied onstage by, among others, a man in a chair behind him who appears particularly dignified. The sentence’s previous use, described above, might still occur. Meanwhile, now the sentence has an additional possible use, something more like “The man behind the student, whom I take to be his professor, appears such that his wife, whoever she may be, is lucky.” In this case, the inner description is used referentially and the outer description is used attributively. Note that the man might not actually be the student’s professor.

Imagine still further, now, that the man on stage is sitting next to a woman on stage who seems to enjoy the man’s attention. In this case, both previous uses could occur, and yet now this sentence could also be taken to mean something further still, namely that “The woman on stage, whom I take to be the wife of the man on stage, whom I in turn take to be the student’s professor, appears lucky.” In this case, both descriptions are used referentially. It might be the case that neither is the man the student’s professor nor is the woman his wife.

The final combination – in which the inner description is used attributively, and the outer one referentially – presents us with the most difficulty. In short, it’s hard to see how a complex definite description could be used referentially when certain of its components are used attributively.

Following Moulin, we might view a complex definite description as a (possibly nested) family of functions from situations to individuals. If any particular one of these functions is taken attributively – or value-free – then its value depends on the as-of-yet-unsettled state of the real world. If further functions invoke a function interpreted in such a way, then these further functions too must inherit its uncertainty. In other words, if any description is used attributively, then outer-more descriptions must used attributively too. To be concrete: if one of the audience members uses The wife of the student’s professor to point to a particular woman, it doesn’t make sense to understand the student’s professor as being used attributively.

Imagine a situation in which the dignified man is absent, and in which only the woman, perhaps along with others, resides onstage. One onlooker, referring to the woman, might utter our sentence, taking it to mean something like “That woman, whom I take to be the wife of the student’s professor, whoever he may be, appears lucky.” What to make of this? This meaning seems no more attributive than the last. In this case, the speaker seems to take the entire The wife of the student’s professor referentially, prix fixe, without bothering to resolve the inner description first. If it were found that the woman was the wife rather of an administrator – and that the student’s professor’s wife was actually unhappy – the onlooker would not retract his statement, but amend it.

The referring capacity of a definite description, in short, depends on the absence of value-free elements within it.

There might be another way we could get around this. We could concede that the value of a definite description containing an attributive definite description is indeterminate for the time being, and yet insist that once this inner description has been resolved attributively, the outer one may still be resolved referentially. This possibility is particularly plausible in the case of, say, contracts, which are often “frozen” documents, insisting that they be interpreted only later, after, perhaps, the values of certain descriptions have been resolved attributively. Once these are resolved, further descriptions can be resolved referentially.

To collapse this process to the present, we might choose to resolve a definite description containing an attributive definite description to a set of conditional referents, each determined referentially from one of the inner description’s possible ultimate referents. In this way, a definite description containing an attributive definite description can convey meaning referentially.

In the famous law case Estate Ira Collins Soper v. Gertrude [5], two co-proprietors of a company took out a life insurance policy that dictated that when the first-to-die of the two proprietors was to die, funds would be granted “to the wife of the deceased Depositor.” [5] The first to die, Ira Collins Soper, was married, but had earlier faked his own suicide, moved, and then illegitimately married for a second time; when he died, the funds went to his second “wife”. (The first wife eventually found out and objected; the court found against her.) Though the inner definite description, the deceased depositor, clearly can only be, and was, taken attributively, it seems that the outer description, the wife of the deceased depositor, was taken referentially – in advance and contingent on a resolution of the inner definite description. (Many legal scholars, incidentally, hold that this was an inappropriate opinion.)

Thus we see that, especially in situations (like those furnished by contracts) in which resolution of a description’s value can be delayed, we may plausibly take inner descriptions attributively and outer descriptions referentially.

Games

In this section, I’ll try to overload sentences with attributive-referential ambiguities. We’ll see what we can come up with.

Game 1: Construct a family of sentences 1, …, n, …, such that the nth sentence contains a linear nested chain of n definite descriptions, each of which can be taken either attributively or referentially.

Solution: Consider an infinite collection of people, consisting of a single person P and an infinite supply of others, among which unidirectional relationships exist in precisely such a way that these relationships can be modeled by a directed binary tree in which people correspond to nodes, P is the root, and each given node points to exactly two other nodes, the left arrow pointing to someone who for all purposes appears to be this node’s friend and the right arrow pointing to someone who secretly actually is this node’s friend. Now consider the sentences:

  1. P is smart.
  2. P’s friend is smart.
  3. P’s friend’s friend is smart.
  1. P’s friend’s friend’s … friend is smart.

If we accept the peculiarity, discussed above, of using attributive expressions within referential definite descriptions, we find that the various interpretations of any such sentence n correspond precisely to the 2n paths from the root node to a node in the nth level of depth (where the root has depth 0). If instead we reject this possibility, then there are only two interpretations – given by taking every description to be referential except, possibly, the last.

These interpretations are indeed pragmatically distinct. Fixing an n and any particular interpretation of sentence n (that is, a choice of attributive or referential for each of its constituent definite descriptions), we may suppose that among the residents of the tree’s nth level of depth, the node singled out by (the path corresponding to) the interpretation we’ve chosen is smart, while all of the others are not. In this situation, the sentence would be true under the interpretation we’ve selected and none of the others.

Note that a roughly analogous effect can be obtained somewhat more trivially using a family of the following form:

Alternate: Consider an infinite collection of people, P1, P2, … , Pn, … such that each person has (a set disjoint from those of the others consisting of) a public friend and a secret friend. Now consider the sentences:

  1. The empty group is (vacuously) cooperative.
  2. The group consisting of P1‘s friend is cooperative.
  3. The group consisting of P1‘s friend and P2‘s friend is cooperative.
  1. The group consisting of P1‘s friend, P2‘s friend, …, and Pn’s friend is cooperative.

Here, we may independently take each description Pi’s friend to be either attributive or referential.

Game 2: Construct a family of sentences 1, …, n, …, such that the nth sentence contains a hierarchical binary tree arrangement of 2n – 2 definite descriptions, each of which can be taken either attributively or referentially.

Solution: Consider an infinite collection of people, consisting of an infinite subset P1, P2, …, Pn, … and infinitely many others, among which unidirectional relationships exist in such a way that to each distinct pair of people – for example, P1 and P2 – we associate four distinct others, determined respectively by the properties of, in this case, being P1‘s public or secret friend and being P2‘s public or secret friend. Now consider the sentences:

  1. P1 is smart.
  2. [The friend of P1 and of P2] is smart.
  3. [The friend of [the friend of P1 and of P2] and of [the friend of P3 and of P4]] is smart.
  1. [The friend of [the friend of [ … [the friend of P1 and of P2] … ] and of [ … [the friend of P(2n-1) and of P(2n)]]] is smart.

In this solution, we understand a description of the form The friend of P1 and of P2 as a sort of “binary” or “two-to-one” description, which designates that unique individual, if he exists, who is both the friend of P1 and the friend of P2. The absurd idea, of course, is that each of these two friendships, independently, can be taken either attributionally or referentially. This yields four possible referents for this single definite description.

The interpretation structure of this family is very strange. Each sentence n (implicitly) contains, to be precise, as many definite descriptions as there are edges in a complete binary tree of height n (where the root has height 0), or, 2n – 2. The number of possible interpretations, though, is not 2^(2n – 2), but rather 4^(2n – 1). This is because the ultimate referent is not determined independently on an edge-by-edge basis; rather, the referent is determined bottom-up, and each passage from a pair of two children to their common parent produces 4 independent possibilities. There are 2n – 1 parent nodes in a tree of height n.

For example, in sentence 2 above, there are 4interpretations; resolving the referent of each of the three bracketed descriptions independently introduces an additional factor of 4.

Game 3: Carry on this procedure for even more subtle sorts of ambiguities.

Of those there are many. Thanks for reading.

References:

  1. Donnellan: Reference and Definite Descriptions
  2. Kripke: Speaker’s Reference and Semantic Reference
  3. See Bernard Moulin’s A pragmatic representational approach of context and reference in discourses, part of the book Conceptual Structures: Applications, Implementation and Theory, edited by Ellis, Levinson, Rich, and Sowa.
  4. W. V. O. Quine: Reference and Modality, from From A Logical Point of View.
  5. Supreme Court of Minnesota. Estate Ira Collins Soper v. Gertrude.
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