Logical Structure of Noun Phrases
Definiteness is an operator that referring to discourse and pragmatic situations. In a nutshell definiteness is a referent whose existence is commonly understood to both the speaker and the addressee. Definiteness falls into two types: a common referent introduced in a discourse:
(1) Look, there's a unicorn eating apples in our orchard! I wonder how many apples the unicorn is going to eat.
In the first sentence the unicorn is mentioned for the first time, this is establishing the existence of the unicorn for the first time. The indefinite article or an indefinite quantifier must be used in such a situation. In the second sentence, the unicorn refers back to the unicorn introduced in the first sentence. Here, the existence of the unicorn has been established. This must be the case if the two sentences are in the same discourse.
The same holds true for apples. apples is mentioned for the first time in the first sentence. Our orchard is definite here. It belongs to the type definite forms discussed in the following paragraph.
The lexical item unicorn (see ) refers to any of a set of conceptual creatures that have one horn but that never have more than one horn. 1 The NP a unicorn in the first sentence in See Look, there's a unicorn eating apples in our orchard! I wonder how many apples the unicorn is going to eat. has reference, but its identity is not established. In the second sentence the referent of the unicorn can only be the same unicorn that is eating the apples. If another indefinite determiner is used, note the strangeness of the example:
(2) ?Look, there's a unicorn eating apples in our orchard! I wonder how many apples a unicorn is going to eat.
The indefinite determiner in the second sentence cannot refer to a known unicorn. That is, it cannot refer to the unicorn that is eating apples in our yard. It can only refer to another unicorn whose existence is being asserted.
The second type includes items which are commonly understood to exist such as the moon, the sun, the family pet, appliances and furniture in the family home (the stove, the fridge, the couch, the recliner, and so forth):
The first sentence is intended to signal a new discourse (the speaker is addressing his wife who was at home when he entered the house). The dog here can only refer to the family pet whose existence is understood to both of them. The definite determiner in the first sentence in See Look, there's a unicorn eating apples in our orchard! I wonder how many apples the unicorn is going to eat. denotes reference to the orchard on the property or in a specific location close to where the utterance occurs. That is, if I uttered See Look, there's a unicorn eating apples in our orchard! I wonder how many apples the unicorn is going to eat. , the orchard could only be the one on my property or the only one that is visible.
A more interesting sentence is the following:
This sentence is ambiguous. The first reading is similar to that of See Hi, honey, I'm home. I just ran over the dog. . The event of running over the dog took place in the driveway. In the driveway is a modifier of the event adjoined to VP.
In the second reading, in the driveway is a modifier of the dog. The information here is that the speaker ran over the dog that was in the driveway as opposed to some other dog. Note that the driveway here implies the driveway leading up to the garage or carport located in the same lot as the house. The problem here is the dog. The speaker cannot say use the here if this the first time there was a dog in the driveway. He could say it if there was some dog that always laid in his driveway at the time when the speaker would drive home and the speaker's wife was aware of this situation.
Let us name the operator [DEFINITE]. It has two features: [+Def] and [-Def]. [DEF] and its argument form an object. The NP the dog would have the following logical structure:
The features [+Def, -Dem] are inherent to [DEF]. The feature [+Ct, -Pl, +FV, +QF] are inherent in ONE. The first pass to the lexicon adds the features [+Ct, [ Pl] to DOG (see ). The features [+FV, +QF] are discussed in Logic Form of Noun Agreement:
[+Def] is contains the feature set [Dem] for demonstratives. Demonstratives refer to the proximity of an object with respect to the addressee. There are other uses of the demonstrative pronouns, but we won't cover them here. [+Dem] contains the feature set [Close]. The demonstratives this and that are [+Dem, +Close], the demonstratives that and those are [+Dem, -Close]. The is [-Dem]. The definite determiners are not bound in English. In See the feature [+Plural] in ONE is copied to the blank Plural feature in DOG. `DOG, [-Pl]' is spelled out as book.
The next issue deals with labelling. On the one hand, Many linguists including me have labelled the object in See as NP. There is another school that label it as DP:
Which is correct? In some sense or another both are correct and incorrect. The difference depends on one's point of view. The DP label reflects the argument structure of the logical form. The NP labels fails to capture this. Yet it directs marks the object (the entire structure--see 12) as NP. This seems intuitively correct. Note also that same principle of node labelling would force us to use NuP, which somehow does not seem intuitive. We will adopt the NP label which corresponds to object. It perhaps would be better to use the label object.
The problem of empty number category disappears if we choose to delete empty nodes at surface structure (the structure after lexical insertion) and the phrasal node Nu. 25 to 30 ago such rules did exist--they were called `tree pruning rules.' If a node dominates a form no phonetic content, it is pruned including the phrasal node dominating it. However, the case of NP vs. DP does not disappear. The theory of percolation determines that the node contains both features, and in this sense both NP and DP are correct to this extent. We could call the node `D/NP' which captures this claim and amalgamates both approaches. Even so, there are those who would be horrified by such an approach. The problem lies in the arbitrary nature labelling. Not having a firm conviction, we will allow any of these three approaches. We will use the NP approach (traditional), and may use the D/NP approach above when it serves a purpose (if it ever does):
Note that number is adjoined to NP rather than to N. This is because of the logical structure of the object. Consider the following transitive noun:
Example See a cup of tea. forms a conceptual unit. There is one such unit, and the unit is singular in view of the fact that there is only one of them. Cup of tea is a NP (or a N-bar) in the syntax. Number must take scope over the unit. Think of it this way:
(10 16. John drank something (singular).
) a.
b. 17. What (singular) did he drink?
c. 18. He drank a cup of tea.
This conceptual unit is an object. The object is modified by the indefinite quantifier `a', and by the container cup. The preposition of is a dummy preposition. We defer until the use and nature of this dummy and other prepositions. Thus tea is the object that is drunk. Let us adopt Figure See a) and modify it with the addition of the term object:
The indefinite article presents another problem. Most linguists assume that `a' is an indefinite article and others a reduced form of the numeral one. In fact, it has the features of both. The word one does not mark definiteness as it can follow the. `a' cannot follow the. The feature for oneness is [+One]. In prenominal position one is emphatic, `a' is not:
(12 one book ([-Def, +One, +Emph])
) a.
b. the one book ([+Def, +One., +Emph])
c. a book ([-Def, +One, -Emph])
d. *the a book. (clash: cannot be [+Def] and [-Def] at the same time.
If `a' carries the features indicated in (17), then the feature set [D, -Def] is copied to the quantifier of the noun. Adjoined to 1, it is spelled out as `a''. There is no phonetic residue in the remaining features outside of emphasis marking. The derivation of a book is the following assuming [QUAN [+One]] is the logical form for one:
Lexical items, inserted in the second lexical pass, are shown in colour.
Quantifiers are operators that modify nouns. In common language there are two kinds of quantifiers: counting quantifiers and non-counting quantifiers. Let us assign the feature [+Count] to counting quantifiers and [-Count] to non-counting quantifiers:
The counting quantifiers include all digits and fractions or decimals. They forms have a definite value based on the logical basic mathematics. The non-counting quantifiers are those words which refer to an indefinite value: some, many, several, few, a few.
Quantifiers are distinct from but related to the Grammatical category of number:
The grammar must account for the ungrammatical sentences. Many linguistics books breeze over this. Rarely is this relationship formally accounted for. One way to account for this formally is to refer to the propositional structure of the noun phrase. In English numerals never occur as affixes adjoined to nouns. Numerals are separate words; thus numeral plus noun forms in part a noun phrase.
All numerals are marked with the feature [+Count]. This includes negative integers: -2, fractions and decimals: 1/3, three fifths; irrational numerals: pi (p); and imaginary numerals: 2i (two times the square root of minus one). These numerals are also marked with the feature [+FV] (Fixed Value). Quantifiers marked with the feature [-FV]. They split into those that modify count nouns and those that modify mass nouns. The former include:
(16 some books
) a.
b. several books
c. most books
d. many books
e. few books
f. a few books
g. more books
h. fewer books
i. a lot of books
j. lots of books
(17 some rice
) a.
b. most rice
c. a lot of rice
d. much rice (how much rice?)
e. a little rice
f. little rice (he ate little rice for dinner)
g. less rice
(18 *several rice
) a.
b. *most rice
c. *many rice
(19 *much books
) a.
b. *a little books
c. *less books.
The quantifiers can be broken down according to the following feature tree:
Much is an unusual quantifier. It can be used only in the presence of certain verbal operators:
It can't be used in declarative sentences:
The quantifiers a lot of or lots of must be used instead.
Note that zero is a strange number and has baffled the best mathematicians for centuries. We won't consider it here, except to note that if 1 and 0 are the prime numerals and if 1 is [+One], then 0 is [-One]. No is a negative quantifier; like `a', it is [-Def]:
Since negation gets really hairy, we won't push it here. (see negation).
As we mentioned above the feature [Count] is inherent in nouns. Here, features are not copied. The quantifier and the noun must both be generated, and they must match. If they do not match they clash and the phrase (or sentence containing the phrase) is rendered ungrammatical. There is feature clash in See *several rice ) and See *much books ). In See some books ) and See some rice ) there is no clash as the features agree.
Let's go through the derivation of:
Example See the two books. has the following logical structure:
On the first pas to the lexicon, the features of the noun book are selected which include the inherent feature [+Ct]. Links are established between each head and the head it governs:
The features connected by links must match. [+Ct] matches. Plural is not specified. The positive value of the feature is copied to BOOK. In the second pass to the lexicon D is spelled out as the, TWO as two. BOOK+{+Pl] undergoes the default rule creating the nounstem book plus its inflectional ending `-s':
The green arrows show linking; the red arrows show the splitting of the noun into a noun stem and an inflectional affix.
Now let us look at [ONE]. [ONE] is a conceptual predicate. it contains the features [+Ct] and [+One], or to be more precise, [+One] is a feature embedded in the feature of [+Count]:
There is a close connection between [+One] and [-Pl]. The former is a conceptual feature referring to oneness, and the latter is a grammatical feature required in all nouns and in subject-verb agreement. In order for quantifier-noun agreement to work, the quantifier must contain the feature of plurality. Thus, See [QUANT [+Count [+One]]] <BOOK >. is replaced with:
It may appear redundant to include both features. We could derive See [QUANT [+Count [+One, -Pl]]] <BOOK >. from See [QUANT [+Count [+One]]] <BOOK >. be a redundancy rule:
[-One] is the feature that underlies all numerals greater than one. The feature [+Pl] is derived by another redundancy rule:
Russian shows the difference between [+One] and [-Pl]. The word for clock is a plural form. 2 But it is a count noun:
The numeral odni is a plural adjective that agrees with the noun which is plural only. Thus, conceptually, asy can refer to one or more than one clock, but it is grammatically plural.
Finally we need to differentiate between the indefinite ([-FV]) numerals mentioned above and the lack of a marker:
The only information we have is that there is more than one monkey that likes more than one banana for dinner. We have an indefinite but unspecified quantity. Let us name the feature separating these as "quantified": [QF}. [-QF] is lexically empty in English. The [-FV] quantifiers mentioned above are [+QF].The tree structure representation of See one book ([-Def, +One, +Emph]) ) is the following:
Number lowers and adjoins to the noun in its scope. [+One] is [-Emph] and spelled out as phonetically null. [+Def, -Dem] is spelled out as the:
One of the requirements for interpretation is that the features [+Count] in QUANT and the head of the object be the same. If they are not the same, the sentences crashes in the interpretive component (determining the meaning of the sentence). This process is what Chomsky calls checking. If a given feature occurs more than one in an object, the features must be checked. In 40 above, the feature Count is plus in places; the phrase can be interpreted. An example where the features do not match is:
'A' is [+Count], but sand is [-Count]. Another example is
The lack of an overt determiner is interpreted as [-Count, -Def], but dog is [+Count].
The feature [+One] has some special lexical spell out rules. When it is unemphatic, it is spelled out as `a' or `an' depending on the first phoneme of the following word:
If the feature [+One] is marked with the feature [+Emph], then it is spelled out as one:
If [+One] follows [+Def] and is marked [-Emph], it is phonetically null; otherwise it is one:
(40 the poem by Schiller, the orangutan's tail
) a.
b. the one poem by Schiller, the one orangutan in the forest
c. one poem by Schiller, one orangutan in the forest.
When the quantifier one occurs in the scope of the definite determiner, one tends to mean the only one. It does not have this meaning when it is not in the scope of a definite determiner as in See the poem by Schiller, the orangutan's tail c). The lexical entry for a, an, and one is a common entry. We will start with the conceptual form rather than the orthographic form:
Quantifiers are all [-Bound]. I know of no quantifier that occurs as an affix in English. Just remember that quantifiers and number are related but distinct forms: the former is conceptual, the latter grammatical.
In the plural it is possible to generate the plural with no overt quantifier:
Dogs and cars are quantified, but the amount is unspecified. Non-overt quantifiers are assigned the feature [-QF] (quantified). Non-quantified quantifiers are phonetically empty.
The demonstrative determiners show agreement with the head noun:
The agreement holds between the determiner and the head no matter how far away the head is.
The feature of number is inherent in numerals. Numerals too must agree:
The demonstrative determiners are marked for the feature of plurality which is not marked. The feature is copied from the quantifier where it is derived from the appropriate feature of oneness:
There are two ways we can view the quantity feature. The first way is mathematical and deeply intuitive. However, it is probably a turn-off to those who hate mathematics. 2 can be defined as the addition of 1+1:
DEFINE is a predicate, perhaps primary feature which means that it cannot be defined, and it takes two arguments. (50) is the sentence derived from the complete proposition containing (49):
Numerals can be defined in set theory of mathematics. From our perspective here, NULL is considered a prime. The set {NULL} () is defined as zero. Set theory is too complex to consider here. Let us adopt the simpler form above which is sufficient for our purposes here.
The second way we can view quantity is to go an infinite set of lexical features: one, two, three, four, minus one, minus two, and so forth. Every lexical feature that is greater than one or less than minus one has the grammatical feature [+Pl]:
[+One] has the feature [-Pl]. Zero is a special problem. For one thing, it seems to take the plural of count nouns, but since it is [+Count], it can take a mass noun in the scope of its argument:
Every numeral greater than 1 contains the grammatical feature [+Pl].
Indefinite determiners are somewhat problematic. The forms a, one, some, several and so forth are usually called indefinite determiners. In section See Quantifiers. we analyzed these forms as quantifiers. Suppose we go one step further and analyze them as indefinite quantifiers--that is, the are quantifiers and bear the feature [-Def]. If we do this then a new problem arises: where does the feature [-Def] come from? They are not part of the conceptual form.
There already exists the conceptual form of definiteness. If [+Def] is generated here, then it stands to reason that [-Def] does too. If so, then it is copied to the quantifiers marked [-FV]. The quantifiers can never be definite:
Since [-Def] cannot be in the conceptual form, let us suppose that the [-QF] quantifiers are marked as [-Def] in the lexical entry of each quantifier. In this case the phrases in See *the some books ) crash because the feature of definiteness clashes: the is [+Def] and some is [-Def] and the two forms are linked.
The quantifiers that have a fixed value can occur either with a definite determiner or they are marked indefinite:
These quantifiers are not marked for definiteness.
In the lexicon the feature bundle [D -Def] is not assigned a phonetic form. Phrases such as See the two books b) are interpreted as indefinite because of the absence of a definite determiner.
In the first pass to the lexicon the feature [-Def] is added to ONE, links are established between the adjacent heads, and the repeated features are checked for matching or clashing. The features all match:
In the second pass to the lexicon the phonological form is assigned to each form:
There is noun operator that denotes no specific reference: the universal quantifier any. Consider the following sentence:
The NP any morsel of food does not refer a specific morsel of food, but to any morsel of food that happens to come along. Sometimes this use of any is called the free choice any. This implies that our dog has free choice to any morsel of food, which is true, but this is not it means logically. Note that if a specific event is denoted, the universal quantifier cannot be used:
If our dog has eaten a morsel of food, there is no free choice here. The morsel o f food is specific. In See Our dig will eat any morsel of food that is given to him. will eat does not denote a specific event, any of an indefinite number of events. In See *Our dog ate any morsel of food last night. ) ate and is buying each refer to a specific event.
The word any is considered to be a universal quantifier by most linguists. Other universal quantifiers include all, both, every, and each. If this is true, then any, like the other universal quantifiers must occur first in the noun phrase:
Since the definite determiner implies a specific object, any cannot modify a definite noun:
Any, therefore, is marked as [-Def]. In See Any car is likely to be a lemon. ) any appears to be singular:
But this is not the case as shown in See Any, therefore, is not marked for number. Any is not a normal quantifier as seen in the following example:
Any, therefore, is not marked for number.
There is another function of the word any: the negative polarity any:
Note that any is plural here. We won't cover this function of any here.
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