6.1.8. Examples and problems

We will begin with a couple of extended but straightforward examples.

If Dan is the winner and Portugal is the place he would most like to visit, he will visit there before long

Dan is the winner and Portugal is the place he would most like to visit
Dan will visit Portugal before long

(Dan is the winnerPortugal is the place Dan would most like to visit)
Dan will visit Portugal before long

(Dan is the winnerPortugal is the place Dan would most like to visit)
Dan will visit Portugal before long

(Dan = the winnerPortugal = the place Dan would most like to visit)
→ [ _ will visit _ before long] Dan Portugal

(d = n ∧ p = [the place _ would most like to visit] Dan) → Vdp

(d = n ∧ p = ld) → Vdp
if both d is n and p is l of d then V fits d an’ p

V: [ _ will visit _ before long]; l: [the place _ would most like to visit]; d: Dan; n: the winner; p: Portugal

Al won’t sign the contract Barb’s lawyer made out without speaking to his lawyer

¬ Al will sign the contract Barb’s lawyer made out without speaking to his lawyer

¬ (Al will sign the contract Barb’s lawyer made out ∧ ¬ Al will speak to his lawyer)

¬ (Al will sign the contract Barb’s lawyer made out ∧ ¬ Al will speak to Al’s lawyer)

¬ ([ _ will sign _ ] Al the contract Barb’s lawyer made out ∧ ¬ [ _ will speak to _ ] Al Al’s lawyer)

¬ (S a (the contract Barb’s lawyer made out) ∧ ¬ P a (Al’s lawyer))

¬ (S a ([the contract _ made out] Barb’s lawyer) ∧ ¬ P a ([ _’s lawyer] Al))

¬ (S a (c ([ _’s lawyer] Barb)) ∧ ¬ Pa(la))

¬ (Sa(c(lb)) ∧ ¬ Pa(la))
not both S fits a an’ c of l of b and not P fits a an’ l of a

P: [ _ will speak to _ ]; S: _ will sign _ ; c: [the contract _ made out]; l: [ _’s lawyer]; a: Al; b: Barb

When analyzing either a predication or an individual term, make sure that you remove all the largest individual terms it contains. That is, if you identify a component individual term, make sure that it is not part of a compound term that is itself a component of the sentence or term you are analyzing. To analyze Al will speak to his lawyer as [ _ will speak to _’s lawyer] Al Al would be to ignore an important aspect of its structure. Of course, when applying this maxim, it is important to distinguish individual terms from other noun phrases. For example, although Dan is the winner of the contest can be analyzed initially as Dan = the winner of the contest, the grammatically similar sentence Dan is a winner of the contest should be analyzed as [ _ is a winner of _ ] Dan the contest because a winner of the contest is not an individual term.

Also, when you locate a definite description, make sure that you have identified the whole of it. What you are most likely to miss are modifiers, usually prepositional phrases or relative clauses, that follow the main common noun of the definite description. For example, although the place might be an individual term in its own right in other cases, in the example above is it only part of the term the place Dan would most like to visit. Similarly, the contract is only the beginning of the individual term the contract Barb’s lawyer made out. In both of the these cases, the rest of the definite description is a relative clause with a suppressed relative pronoun; that is, they might have been stated more fully as the place that Dan would most like to visit and the contract that Barb’s lawyer made out, respectively. It might help here to think of prepositional phrases and relative clauses as modifying a common noun before the definite article is attached. That is, the phrases above have the form the (place Dan would most like to visit) and the (contract Barb’s lawyer made out), so any component of these sentences containing the initial the must also contain the whole of the following parenthesized expressions.

There are some cases where a prepositional phrase or relative clause following a common noun should not be counted as part of a definite description. Some prepositional phrases can modify both nouns and verbs, and a prepositional phrase following a noun within a grammatical predicate might be understood to modify either it or the main verb. The sentence The dog chased the cat on the mat is ambiguous in this way since the mat might be understood to be either the location of the chase or the location of the cat, who might have been chased elsewhere. This sort of ambiguity can be clarified by converting the prepositional phrase into a relative clause, which can only modify a noun; if this transformation—e.g.,

The dog chased the cat that was on the mat

—preserves meaning, then the prepositional phrase is part of the definite description. On the other hand, since anaphoric pronouns cannot accept modifiers, replacing a possible noun phrase by a pronoun will show the result of taking a prepositional phrase to modify the verb. This can be done by moving the noun phrase to the front of the sentence, joining it to the remaining sentence-with-a-blank by the phrase is such that, and filling the blank with an appropriate pronoun (he, she, or it). In this example, that would give us

The cat is such that the dog chased it on the mat

So, the prepositional phrase on the mat should be taken to modify cat or chased depending on whether the first or second of the displayed sentences best captures the meaning of the original. Of course, when a potentially ambiguous sentence is taken out of context, it may not be clear which of two alternatives does best capture the original meaning; in such a case, either analysis is legitimate.

Not all relative clauses contribute to determining reference. Those that do are restrictive clauses, and it is these that should be included in definite descriptions. Other relative clauses are non-restrictive. Non-restrictive clauses cannot use the word that and, when punctuated, are marked off by commas. Restrictive clauses are not marked off by commas in standard English punctuation and may use that (but are not limited to this relative pronoun), and they can in some cases be expressed without a relative pronoun. It is easiest to tell what sort of relative clause you are faced with when more than one of these differences is exhibited. For example, the relative clause The cat that the dog had chased was asleep or The cat the dog had chased was asleep is clearly restrictive while the one in The cat, who the dog had chased, was asleep is clearly non-restrictive. This means that the relative clause in the first is part of the definite description the cat that the dog had chased. The relative clause in the second would instead be analyzed as a separate conjunct to give the dog had chased the catthe cat was asleep as the initial step of the analysis.

Another indication of the difference between the two sorts or relative clause is that a non-restrictive clause can modify a proper name—as in Puff, who the dog had chased, was asleep. And, since neither prepositional phrases nor restrictive relative clauses can modify a proper name, putting a proper name in a blank that was left when you removed an apparent individual term can show whether you really removed the whole of the term. For example, Puff on the mat was asleep and Puff that the dog had chased was asleep are both ungrammatical.

Glen Helman 28 Aug 2008