Definite Descriptions
Definite NPs denote definite or specific entities. Names, possessive NPs such as John’s jacket, demonstrative NPs such as that boulder, those tablets, and referring pronouns are all examples of definite NPs. We will focus on NPs that begin with the definite article the.
Definite NPs refer to given information in discourse; information that the speaker can assume to be familiar to the hearer (Chafe 1974; Givón 1984). Definite NPs have characteristics of both names and quantifier phrases. They have a structure that is similar to quantifier phrases like some fans of Rosemary Clooney or every yacht in the marina. At the same time, definite NPs pick out a specific entity just as a name does. The dual nature of definite NPs led to a classic philosophical debate about their analysis.
Russell’s Theory of Descriptions
Bertrand Russell assumed that the meaning of names can be represented by singular definite descriptions. Assume that the definite description the greatest Greek philosopher has the same reference as the name Socrates. To the extent that the definite descriptions pick out the same individual as names, the descriptions supply a meaning for names. Frege used definite descriptions to illustrate the sense of names.
Kearns treats names and definite descriptions as very different logical entities. Names are treated as individual constants, whereas definite descriptions can be analyzed as generalized quantifier phrases. It would be very surprising if generalized quantifier phrases provide the meaning of names.
Alternatively, we can entertain John Stuart Mill’s theory of the meaning of names (A System of Logic). Mill claimed that names have denotation (reference), but not connotation (sense). Mill observed that even though the English town Dartmouth was originally settled on the mouth of the river Dart, it’s name cannot be equated with the definite description ‘the town on the mouth of the river Dart’. For example, the sentence ‘Dartmouth is Dartmouth’ is not informative, whereas the sentence ‘Dartmouth is the town on the mouth of the river Dart’ is informative. This would not be the case if the town’s location were part of the meaning of the word Dartmouth.
Russell proposed two requirements for the correct use of a definite description to denote an individual. The first is called existential commitment–there must be an individual denoted by the description. The second is the uniqueness requirement–there must be only one individual. These two requirements are an integral part of Russell’s analysis of the definite article:
3 The King of France is bald.
∃x (KING OF FRANCE(x) & ∀y (KING OF FRANCE(y) —> y = x) & BALD(x))
Existential Commitment Uniqueness Requirement
‘There is a King of France’ ‘There is only one King of France’ ‘He is bald’
Russell’s analysis contains three conjoined propositions. If any of them are false the entire proposition is false. Since there is currently no king of France (existential commitment), the complete proposition has a truth value that is false.
Since Russell’s analysis includes the existential quantifier, it should have semantic characteristics similar to other quantified phrases.
The as a Generalized Quantifier
The uniqueness requirement creates a problem for Russell’s analysis–it isn’t compatible with the use of the in plural descriptions like the books on that shelf. The uniqueness requirement claims that there should only be one book on the shelf. This observation leads to the question of how we can separate the semantic work of the from the expression of number. Ideally, the would have the same analysis for both singular and plural descriptions.
Compare this situation to our analysis of the quantifier some. The following sentences demonstrate a similar difference in number:
5 Some dog ripped open the rubbish.
Some dogs ripped open the rubbish.
The number distinction was analyzed as follows:
6 Some Fs are G |F ∩ G| ≥ 2
Some F is G |F ∩ G| ≥ 1
Both of these analyses interpret some as the cardinality of the intersection of two sets. The difference in the absolute values corresponds to the number of the noun. Applying the same approach to the definite determiner yields:
8 The Fs are G F ⊆ G & |F| ≥ 2
The F is G F ⊆ G & |F| = 1
This analysis accounts for both of Russell’s requirements. The existence commitment is implicit in the cardinality measures, while the uniqueness requirement is only true for singular definite descriptions.
Familiarity Effects
The interpretation in (8) treats the definite determiner as a kind of universal quantifier. We have determined that NPs with the universal quantifier are strong NPs. Actually, the features of strong NPs were first noticed for definite NPs and only later extended to NPs with universal quantifiers.
One feature of strong NPs is the familiarity effect–the speaker must establish a specific subset of individuals earlier in the discourse. The is used with a familiar referent while a introduces a novel referent.
A quantificational analysis of the predicts this familiarity effect for definite NPs. A definite NP expresses a universal quantification over some background set of entities which contains just one member. The identification of the background set induces the familiarity effect. Because the background set only contains one member, the hearer is also able to identify a specific individual. The familiarity of the individual is more salient than the familiarity of the background set for the definite determiner.
Few definite NPs provide a complete description–a fully interpreted proposition that does not rely upon context. Most definite NPs only provide incomplete descriptions. Despite this difference, most analyses of definite NPs focused on complete descriptions like the following:
13a The author of Waverley
b The king of France in 1770
These definite NPs are similar to names in that they refer to a single individual regardless of context. Such complete singular definite descriptions provide the strongest support for Russell’s uniqueness requirement. For incomplete descriptions the uniqueness requirement must work with information supplied by the speech context. This context enables hearers to fix the background so that there is just one set that is salient, and this set only contains one member.
The contextual dependence for the contrasts with that of other strong NPs:
14a All men are mortal.
b Every man is mortal.
c ? The men are mortal.
Ralph is mortal.
The man in the blue suit is mortal.
Scopal Ambiguity
The analysis of definite NPs as a type of quantified phrase also predicts that they would exhibit the scopal ambiguities that we have seen for other quantified NPs. Kearns provides the following example:
16 Rex has been buying vintage cars in a remote country district... Several cars had not left the garage in 30 years.
[Several x: CAR(x)] [The y: GARAGE(y)] ~ LEAVE(x,y)
17 When the rental firm was liquidated, several cars had not left the garage in 30 years.
[The x: GARAGE(x)] [Several y: CAR(y)] ~ LEAVE(y,x)
Compare Kearns’ example to the following sentences which do not exhibit scopal ambiguity:
Every woman loved the man.
Every woman loved the men.
Referential Opacity
Treating definite descriptions as referring expressions on par with names leads to a problem which the philosopher Quine called referential opacity. Kearns introduces a couple of basic logical principles as part of her discussion.
Leibniz’s Law (the Indiscernibility of Identicals)
If A and B are identical, anything which is true of A is also true of B, and vice versa.
Principle of Substitutivity
If
1 ‘a’ refers to a and ‘b’ refers to b, and
2 ‘a = b’ is a true identity statement, and
3 S1 is a statement containing the expression ‘a’, and
4 S2 is a statement identical to S1 except that the expression ‘b’ appears instead of ‘a’,
Then
S1 and S2 have the same truth value.
We can apply the principle to the following case:
19a Mohammed Ali = Cassius Clay true
b Mohammed Ali was a boxer true
c Cassius Clay was a boxer true
These principles should be true of definite descriptions assuming that definite descriptions are referring expressions like names. Consider the following example:
20b Earth is inhabited by humans. true
The third rock from the sun is inhabited by humans. true
Quine identified two kinds of contexts in which the Principle of Substitutivity fails, and named them opaque contexts. Contexts where the Principle of Substitutivity holds are transparent contexts.
One type of opaque context is found in sentences with modal expressions:
23b Yuri Gagarin might not have been the first man in space. true
c Yuri Gagarin might not have been Yuri Gagarin false
24b Necessarily, nine is nine. true
c Necessarily, the number of planets is nine. false
The second type of opaque context occurs with verbs such as know, believe, think and hope. These verbs express an attitude that the subject adopts toward the proposition in the verb’s complement, and are called propositional attitude verbs. The complement phrases describe the mental contents of someone rather than an objective state of affairs.
Quine’s example goes as follows:
There is a certain man in a brown hat whom Ralph has glimpsed several times under questionable circumstances on which we need not enter here; suffice it to say that Ralph suspects he is a spy. Also there is a grey-haired man, vaguely known to Ralph as rather a pillar of the community, whom Ralph is not aware of having seen except once at the beach. Now Ralph does not know it, but the men are one and the same (1976:187).
Quine tells us that Ralph knows the pillar of the community is Bernard J. Ortcutt. Quine then examines the following sentences:
26b Ralph believes that Ortcutt is a spy. false
c Ralph believes that the man in the brown hat is a spy. true
d Ralph believes that the man seen at the beach is a spy. false
Note: the embedded predicates here have the same truth values:
The man in the brown hat is a spy. false
The man seen at the beach is a spy. false
The propositional attitude contexts are non-truth functional since the their ultimate truth value is not a simple function of the truth value of the embedded proposition.
The Principle of Substitutivity seems to fail in opaque contexts. Since it is a logical principle we would like to find a way to preserve it in some way. Kearns suggests rejecting the assumption that definite descriptions are referring expressions. The analysis of descriptions as quantified expressions provides the basis for rejecting this assumption.
You may be wondering why anyone would want to link definite descriptions to referring expressions in the first place. Marga Reimer (2003) provides an introduction to the issues associated with the meaning of names. She outlines three approaches to the meaning of names:
i) Description theories
ii) Causal theories
iii) Hybrid theories
Description Theories
Description theories tackle the meaning of names by connecting them to a definite description. Frege (1892) and Russell (1919a) appealed to description theories in response to a theory of J. S. Mill (1867) who proposed that the meaning of a name is tied to its referent. We have already discussed the limitations of such referential theories of meaning. Frege’s famous sentence
(1) Hesperus is Phosphorus.
exposed one problem with the Millian approach. Since both names have the same referent (Venus), the Millian theory of meaning based on reference does not account for the difference between (1) and (2).
(2) Hesperus is Hesperus.
The description theory have an advantage in that it would translate the names into definite descriptions:
(3) Hesperus = the evening star
(4) Phosphorus = the morning star
The description theory then predicts that (1) is informative because (5) is informative.
(5) The evening star is the morning star.
The central claim of description theory is that a name successfully refers to the extent that its referent satisfies the descriptions associated with the name.
Kripke (1980) raised the problem of unwanted necessity with respect to description theory. He notes that Aristotle might be described as the last great philosopher of antiquity. If such a description helps to fix the reference of the name Aristotle then description theory should predict that (6) is a tautology:
(6) Aristotle was a philosopher.
A second problem that Kripke raised is the problem of rigidity. Names are rigid across possible worlds while definite descriptions are not. Consider again the description of Aristotle as the last great philosopher of antiquity. If this description provides the meaning of the name Aristotle, it should behave in other possible worlds in the same way the name behaves. Kripke offered (7) as a test case.
(7) Aristotle was fond of dogs.
We can imagine a possible world in which the individual identified as Aristotle pursued a different line of work, say a short order cook. In such a world, the name Aristotle picks out the short order cook, while the definite description picks out Plato. Thus, the definite description fails to pick out its intended referent in this modal context.
Reimer states that many contemporary philosophers of language feel there is something ‘magical’ about description theories of reference. Michael Devitt (1990), for example, begins with the assumption that nothing inside an object can fully determine its relation to something outside that object. He then asks (p. 91):
How can something inside the head refer to something outside the head? Searle sees no problem: It just does. That's the real magic.
Causal Theories
Kripke (1980) introduced the causal theory as an alternative to the description theory of nominal reference. The central idea behind his theory is that a name refers to whatever is linked to it in the appropriate way. The linking is not dependent upon a speaker’s ability to associate any identifying descriptive content with the name. The causal theory has two main components: reference fixing, and reference borrowing.
Reference fixing occurs when a name is first associated with a referent. This may be done by a naming event, e.g., “You are Ortcutt,” or by description, as when the astronomer Leverrier fixed the description of Neptune as the cause of perturbations in the orbit of Uranus. After the initial reference-fixing, speakers pass the name on from one to another through communicative exchanges. Speakers form links in a causal chain that stretches back to the original dubbing of the object with that name. Speakers thus ‘borrow’ their reference from other speakers earlier in the chain.
The phenomenon of reference change poses a serious challenge for the causal theory of reference. One example is Gareth Evans’ discussion of the word Madagascar, which was originally used to refer to part of the African mainland, but which now refers to the island off the east coast of Africa. Marco Polo was allegedly responsible for this change in reference. He mistook the name to refer to the island when the inhabitants were using it to refer to the African mainland.
Another problem for causal theories of reference is that they do not provide an account of the semantic content of names, the strength of description theory.
Hybrid Theories
According to hybrid theories the reference of a proper name is the main source of descriptive information associated with it. Evans offers the following motivation for a hybrid theory:
An urn is discovered in which are found fascinating mathematical proofs. Inscribed at the bottom is the name ‘Ibn Khan’ which is quite naturally taken to be the name of the constructor of the proofs. Consequently it passes into common usage amongst mathematicians concerned with that branch of mathematics. ‘Khan conjectured here that…’ and the like. However suppose the name was the name of the scribe who had transcribed the proofs much later; a small ‘id scripsit’ had been obliterated. (2001, p. 306)
The causal chain for the name ‘Ibn Khan’ has a missing link. Kripke’s theory would link the name to the scribe rather than the mathematician since the original naming event concerned the scribe. This attribution differs from the intuition that current speakers are using the name to refer to the ancient mathematician who discovered the proofs rather than the scribe who recorded them. Evans argues that the name refers to the mathematician, since it is the mathematician who constitutes the ‘dominant causal origin’ of the descriptive information associated with the name, i.e. mathematician who proved such-and-such.
Evans argues that his theory has the virtues of the description and causal theories and none of their vices. It allows descriptions to shape reference, while acknowledging the importance of causal links. One problem for the theory is that it could result in phantoms. Assuming a school of ancient mathematicians originally constructed the proofs found in the urn, then the name ‘Ibn Khan’ has become erroneously associated with a single, phantom mathematician.
Modality, Descriptions and Names
Kearns examines the following modal sentence:
27a Mozart might not have died young.
b ◊ ~ DIE YOUNG(m)
We have analyzed such sentences as asserting that on some possible world Mozart lived to a ripe, old age. For this claim to be true, we have to assume that the aged Mozart on that world corresponds to the person on our world who was a child prodigy and musical genius. Names are rigid designators. Nathan Salmon (2003a) defines a rigid designator as:
a term designates an object x rigidly if the term designates x with respect to every possible
world in which x exists and does not designate anything else with respect to worlds in
which x does not exist.
Descriptions, like quantifiers, are not rigid designators. Descriptions pick out individuals in relation to a background set. In modal contexts, descriptions are free to pick out different individuals in different possible worlds. Kearns notes that definite descriptions are rigid when they have wide scope over the modal operator. Compare
◊ [The x: FIRST MAN IN SPACE(x)] ~ g = x
[The x: FIRST MAN IN SPACE(x)] ◊ ~ g = x
Propositional Attitudes and Descriptions
Propositional attitude verbs demonstrate the distinction between de dicto beliefs and de re beliefs. A de dicto belief is based on the words used to describe something. This makes the description a central component of the belief. More technically, the description is in the scope of the belief predicate.
de dicto - the description has narrow scope
34a Ralph believes that the man in the brown hat is a spy.
b BELIEVE(r, [The x: MAN IN THE BROWN HAT(x)] SPY(x)) true
c Ralph believes that the man seen at the beach is a spy.
d BELIEVE(r, [The x: MAN SEEN AT THE BEACH(x)] SPY(x)) false
A de re belief is based directly on the thing itself rather than its description. Speakers acting on a de re belief can use different descriptions of something to make themselves intelligible in different contexts. The description is not part of the content of a de re belief, and so the description has wide scope over the belief predicate.
de re - the description has wide scope
[The x: MAN IN THE BROWN HAT(x)] BELIEVE(r, SPY(x)) true
[The x: MAN SEEN AT THE BEACH(x)] BELIEVE(r, SPY(x)) true
Under the de re reading, the two propositions above have the same truth value. For the de dicto readings in (34b and d), the two propositions have different truth values.
Propositional Attitudes and Names
Names with the same referent such as Mohammed Ali and Cassius Clay can be substituted in modal contexts without affecting the truth value:
28a Mohammed Ali = Cassius Clay true
b Mohammed Ali might never have won the world title true
c Cassius Clay might never have won the world title true
This shows that modal contexts are not opaque for names. Propositional attitude contexts, on the other hand, are opaque for names.
46a Lydia hopes there will be an essay question about Tully. false
b Lydia hopes there will be an essay question about Cicero. true
Propositional attitudes raise complicated issues since they simultaneously involve i) the proposition the thinker holds, and ii) the words used to state the thinker’s proposition. We could try to keep these two factors separate, in which case we could claim that in this sense Lydia is writing about a single man who goes by the names Tully and Cicero. On the other hand, we must acknowledge that Lydia, herself, hopes the essay question will be on Cicero.
Translation across languages introduces yet another wrinkle to this problem. English textbooks don’t report the literal beliefs of people in other countries if they do not speak English. We cannot truthfully state that Galileo believed the earth revolves around the sun since he spoke medieval Italian. Translation forces us to put propositions into other words, and creates an uncomfortable distance between mental content and language.
It may even be more difficult to accurately represent the propositional attitudes of young children. Children lack the vocabulary to express most abstract concepts, and often use words in ways adult speakers regard as over extensions. For example, Bowerman (1978) reported that the child C used the word kick to refer to waving limbs. Is this child’s kicking concept different from an adult’s or is the child extending the word kick to the concept adults express as wave?
As Kearns (116) states:
In summary, propositional attitude reports contain embedded sentences which denote mental contents. Our system of semantic representation, on the other hand, uses symbols which denote things and situations in reality and possible realities, not conceptual representations in a thinker’s mind. Any reality-denoting representational system seems to be the wrong sort of system in principle for representing mental contents.
Fiction
Kearns discusses the meaning of names without a referent (e.g. Brogdasa) and names with a referent (e.g. Bernard J. Ortcutt, Mozart), but she doesn’t tackle names of fictional characters, e.g. Sherlock Holmes, Pegasus, Snoopy. Fictional names lack a real referent, so they would seem to be in the same boat as names that lack a referent. Compare the following sentences:
1. Brogdasa is becoming larger.
2. Sherlock Holmes plays the violin.
Kearns has told us that Russell thought that (1) couldn’t be evaluated since Brogdasa lacks a referent. This situation is similar to a sentence in predicate logic that lacks an argument:
3. Larger ( ).
On the other hand, we can judge the truth of (2) relative to the fictional world Arthur Conan Doyle created. In this world Homes solves mysteries with the aid of his trusty sidekick Dr. Watson, and plays the violin to stimulate his thinking. Applying Russell’s solution to fictional characters would derive an open sentence as in (3), but ordinary speakers, or at least those who have read about Sherlock Holmes, might object. Russell (1919b:169-170) felt otherwise:
[M]any logicians have been driven to the conclusion that there are unreal objects.
...In such theories, it seems to me, there is a failure of that feeling for reality which
ought to be preserved even in the most abstract studies. Logic, I should maintain,
must no more admit a unicorn than zoology can; for logic is concerned with the real
world just as truly as zoology, though with its more abstract and general features. To
say that unicorns have an existence in heraldry, or in literature, or in imagination, is
a most pitiful and paltry evasion. What exists in heraldry is not an animal, made of
flesh and blood, moving and breathing of its own initiative. What exists is a picture,
or a description in words. Similarly, to maintain that Hamlet, for example, exists in
his own world, namely in the world of Shakespeare's imagination, just as truly as
(say) Napoleon existed in the ordinary world, is to say something deliberately confusing,
or else confused to a degree which is scarcely credible. There is only one
world, the “real” world: Shakespeare's imagination is part of it, and the thoughts that
he had in writing Hamlet are real. So are the thoughts that we have in reading the play.
But it is of the very essence of fiction that only the thoughts, feelings, etc., in Shakespeare
and his readers are real, and that there is not, in addition to them, an objective
Hamlet. When you have taken account of all the feelings roused by Napoleon in
writers and readers of history, you have not touched the actual man; but in the case of
Hamlet you have come to the end of him. If no one thought about Hamlet, there would
be nothing left of him; if no one had thought about Napoleon, he would have soon
seen to it that some one did. The sense of reality is vital in logic, and whoever juggles
with it by pretending that Hamlet has another kind of reality is doing a disservice to
thought. A robust sense of reality is very necessary in framing a correct analysis of
propositions about unicorns, golden mountains, round squares, and other such pseudo- objects (Russell 1919b, cited in Salmon 1998).
Saul Kripke (nd) and Peter van Inwagen (1977) take an opposing view, and regard fictional characters as real things. They are not actually physical or mental objects, but abstract entities, man-made fictional artifacts. They exist as robustly as the fictions, novels, stories, etc. in which they occur. However, Holmes is still a man of flesh and blood in fiction, in reality Holmes is merely a fictional character.
They further claim that names for fictional characters come about through a conventional pretense that creates the make-believe world of storytelling. The sentences about Sherlock Holmes in the fiction merely pretend to express propositions. Language also allows us to speak about the fictional characters from a standpoint outside the fiction. This transforms a fictional name for a person into a name of a fictional person. Salmon suggests making a distinction
between ‘Holmes1’, for the fictional name that pretends to refer, and ‘Holmes2’ for reference to the fictional character. Salmon asserts that Russell has ‘Holmes1’ in mind, but that speakers use fictional names in the sense of ‘Holmes2’.
Truth can be stranger than fiction, and the philosophical literature often refers to strange ideas from the past. Kripke discusses the planet Vulcan. Not the home planet of Mr. Spock, but the planet hypothesized by Jacques Babinet in 1846 and thought by Urbain Le Verrier to account for the eccentric orbit of Mercury. There could have been a planet between Mercury and the sun, but astronomers have determined otherwise. Kripke extends his account of fictional characters to hypothetical creations like Vulcan. Thus, ‘Vulcan1’ refers to the nonexistent planet, while ‘Vulcan2’ to Babinet’s hypothetical planet.
Salmon points out that on Kripke's account, it is true that according to the stories Holmes1 plays
the violin, and that On Le Verrier's theory Vulcan1 influences Mercury's orbit. But it then seems odd to claim the proposition that Holmes1 plays the violin and the proposition that Vulcan1 influences Mercury are merely pretense, and have no real propositional content. Salmon asks ‘How can Le Verrier have believed something that is nothing at all?’
Note the propositional attitude verb in Salmon’s question. Fictional contexts also include the use of propositional attitude verbs, as in the following sentence:
Lois Lane doesn’t believe Clark Kent can fly. (after Salmon 2003b)
We are now dealing with the propositional attitude of a fictional character.
Discussion (de Swart 225)
Consider the following sentences:
i) Mary believes that a professor was caught shoplifting.
ii) Chris wants to marry a Spanish linguist.
Although both of these sentences contain indefinite NPs rather than definite NPs, they have an ambiguity due to a propositional attitude verb. Translate each sentence into logical expressions that spell out the ambiguity involved. Explain informally how the interpretation of the indefinite NP in these opaque contexts leads to different interpretations of the sentences.
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