Intermediate Syntax Propositional Structure of Noun Phrases
Linguistics 322
Intermediate Syntax
In the English as in most but not all languages (i.e. Chinese)
number can be extracted from the noun leaving a lexical-propositional form
of the noun. From book and books we get object predicate:
BOOK is a predicate in its own right. It takes no arguments. It is an argument of the grammatical category [NUMBER]:
Number takes but one argument: a predicate object which is always a noun phrase in English. Although one could assign a theta role name to the argument, it does not appear to be necessary to do so, since only one kind of argument can be assigned by number. [NUMBER] has two features in English: [±Plural]:
It is possible to represent propositional structures in tree-structure form. Example 4 has the following structure:
5.
Number is required for all English count nouns. Mass nouns cannot be modified for number:
Number is a grammatical category (GC) of English, restricted to count nouns. Before we attempt to formalize this, let account for the derivation of the surface form.
Both features of number are marked with the inherent features [+Bound,
±Count]:
8.
feature inherent features [+Plural] [+Bound, ±Count, N+____ ] [-Plural] [+Bound, ±Count, N+____ ]
The first pass to the lexicon adds the features indicated in (9). We include the nominal features for count and mass nouns discussed below, gender necessary for agreement (agreement), and human needed to determine the appropriate Wh-word who or what or which. The feature is intended to include all humans and animals who the pronoun who would be used for such as pets and domestic farm animals with names:
9.
Since [+Plural] is bound and it is weak, is must lower to a the first nominal host which it always c-commands as determined by the host feature "[N+____ ]":
10.
No more processing occurs. In the second pass to the lexicon, the lexical entry for book contains the default information that spells [+Pl] out as the right adjoined suffix '-(e)s'. The category Nu in the original position has no host and cannot receive phonetic information:
11.
Definiteness
Definiteness is an operator that referring to discourse and pragmatic situations. In a nutshell definiteness is old information within a discourse. This 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).
Let us name the operator [DEFINITE]. It has two features: [+Def] and [-Def]. The books would have the following logical structure:
12.
We will discuss the feature [+Count] shortly. [+Def] is contains the feature set [±Dem] for demonstratives. [+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. There is no lowering. In (12) [-Plural] lowers to BOOK; BOOK,[-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 12 as NP. There is another school that label it as DP:
13.
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. Bite also that same principle of node labelling would force us to use NuP, which somehow does not seem intuitive.
The problem of number 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.' 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 when it serves a purpose:
14.
The indefinite article present 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:
15 . one book ([-Def, +One, +Emph])
16. the one book ([+Def, +One., +Emph])
17. a book ([-Def, +One, -Emph])
18 . *the a book. (cannot be [+Def] and [-Def] at the same time.
If 'a' carries the features indicated in (17), then the feature set [D, -Def] is lowered to the quantifier of the noun. Adjoined to 1, it is spelled as as 'a'. There is no phonetic residue in the remaining features outside a emphasis marking. The derivation of a book is the following assuming [QUAN [+One]] is the logical form for one:
19 .
Lexical items, inserted in the second lexical pass, are shown in colour.
Count Nouns
Nouns fall into two basic lexical classes: count nouns and mass (noncount) nouns. As the name implies count nouns are nouns which can be counted. Mass nouns cannot be counted:
20. one book, two peaches, five men, eight women, 28 trees, 58 mosquitoes.
21. *one sand, *two waters, *five snows, *eight *airs, *28 oats, *58 veals.
Count nouns must be marked with the feature [+Count]:
22.
book orthographic form +N, -V category +count countable -Bound bounding ____ subcategorization Case
Conceptually, we can count books. However, water is something we cannot count at first glance. Mass nouns are marked with the feature [-Count]:
23.
water orthographic form +N, -V category -count countable -Bound bounding ____ subcategorization Case
If it is true that conceptually we cannot count water, then when we select a quantifier, we must select a noun that is countable. Otherwise we get strings like 21 above which are semantically ill-formed.
When an indefinite mass noun is used, there is no quantifier onto which [-Def] can lower:
24. Corn grows in Iowa.
25. *A corn grows in Iowa.
In this case we would say that [-Def] is [-Bound] when it does not subcategorize a quantifier. As long as we insist that 'a' is [-Def], then we have no choice. The choice of phonemic representations is tied to syntactic form. There is no doubt about it. So there seems to be nothing wrong with doing it here.
One other fact about mass nouns. They have no plural form:
26. *Corns grow in Iowa.
[-Count] presupposes [-Pl]. The problem is how to formalize this. one way to do this may be through feature percolation. In the singular a count noun must occur in the scope of a quantifier:
27 *John bought book.
28. *Deer was eating Mrs. Cornborough's roses.
Many mass nouns appear to have a plural form:
27. The rains of Vancouver return faithfully every year.
28. The clear cool waters found around BC attract moose.
Here, the plural has the meaning of types of, kinds of, species of. The plural form,. therefore, has a different meaning and constitutes a different lexical noun. These have a singular form recognizable in specific contexts:
29. Of the rains of Vancouver, the mid winter rain is the most drenching.
Distinct lexical entries are different lexical items, but they are linked to a common morpheme.
Quantifiers.
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:
30. [QUANT] --> [±Count].
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:
31. one book
32. *one books
33. two books
34. *two book
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. What is the propositional structure of (7)? At first glance it appears to be:
Let us first look at the feature [-Plural]. Note that the feature [+Plural] cannot be selected:
You most likely have noticed that [ONE] is singular, or [-Plural]. This is a logical contradiction of [+Plural], which means more than one. Rather than selected a feature such as [+Plural] in (9), suppose we adopt the underspecified '±' for the feature:
An agreement rule specifies that [±Plural] must be [-Plural] in the immediate scope of [ONE]. This rule is rather intuitive; but let us put the formal way of expressing it aside for the moment.
Now let us look at [ONE]. Although [ONE} is predicate in its own right, it is not the proposition we are interested in. [ONE] is a feature of [QUANTITY]--[+One]:
38. [QUANT [ +Count [+One]]] < [NUMBER [-Plural]] <BOOK >.
Next there is the problem of count and mass nouns. As you probably know English nouns (and nouns in many other languages) are divided into two classes: count nouns and mass nouns. The former you can count, the latter you cannot. The task is to represent this conceptually, which logical form is dependent on. Count nouns are count nouns because we can count them. If you see three books on the table, you can count three books. The fact that we can count the books indicates that we can conceive the fact that there are three of them. It is part of the conceptual meaning of books and hence part of the propositional meaning. If we can see that books are countable, then the feature [+Count] is part of the conceptual meaning of BOOK. In other words, [+Count] is one of the features that make up BOOK. So let us add [+Count] to BOOK. This will be important as we shall soon see.
39. [QUANT [ +Count [+One]]] < [NUMBER [-Plural]] <[BOOK [+Count]]>>.
Next is the problem of the so-called indefinite quantifiers: some, few, many, much, more, less, a few, little, fewer, and so forth. This lies is opposed to the so-called definite numerals: one, two, five, one half, two thirds, 11/35ths, -8, -1.5, -234.82815, pi (the circumference of a circle divided by its radius), the square root of minus one, irreal numbers, and so forth. We cannot use the features definite or specific since these are already conscripted for other uses. Let us use the feature "fixed value" (±FV) to differentiate the definite set from the indefinite set.
Finally we need to differentiate between the indefinite ([-FV]) numerals mentioned above and the lack of a marker:
40. Monkeys like bananas for dinner.
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 quantifiers can be broken down according to the following feature tree:
41.
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]:
Mary has no freckles.
Since negation gets really hairy, we won't push it here. (see negation).
The tree structure representation of 15 is the following:
41.
Number lowers and adjoins to the noun in its scope. [+One] is [-Bound] and spelled out as one. [-Def] is phonetically null:
42.
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 :
43. *a sand.
'A' is [+Count], but sand is [-Count]. Another example is
44. *John saw dog.
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:
45. an apteryx, a tonic melody by Schönberg.
If the feature [+One] is marked with the feature [+Emph], then it is spelled out as one:
46. one overweight pterodactyl, one pre-Cambrian unicorn.
If [+One] follows [+Def] and is marked [-Emph], it is phonetically null; otherwise it is one:
47. the poem by Schiller, the orangutan's tail
48. the one poem by Schiller, the one orangutan in the forest.
Here, one tends to mean the only one. The lexical entry for
a , an, and, one is a common entry. We will start with the conceptual form rather than the orthographic form:
49.
context [+One] conceptual feature [EMPTY] [+Def] [____-Emph] orthographic form a [____-Def, -Emph] [-Vocalic] orthographic form an [____-Def, -Emph] [+Vocalic] orthographic form one [____+Emph] orthographic form Quan category +Count inherent feature +FV inherent feature
In the plural it is possible to generate the plural with no overt quantifier:
50. Dogs chase cars.
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.
Agreement.
The demonstrative determiners show agreement with the head noun:
51. these books, this book
52. that leprechaun, those leprechauns
The agreement holds between the determiner and the head no matter how far away the head is.
53. those three leprechauns.
The feature of number is inherent in numerals. Numerals too must agree:
54. *those one leprechauns
53. *that three leprechauns
55. *that two leprechaun.
The features of the head percolate onto all the operators modifying the head:
56.
'j' is [+Pl], 'k' is [+Count], and 'l' is [+Def]. It is uncertain whether the feature [+Def] actually percolates unto NP and down to N, though we indicated it here. Perhaps and most likely the feature percolates only if required. If this is so, we have not worked into the theory the concept of a required feature. It seems to be overkill to have all features percolates onto all relevant nodes. We will leave this issue for now. Let us agree that it is not necessary to percolate the feature of definiteness onto the noun. Then we can simply the above structure somewhat:
57.
Note, however, we are able to account for checking. The feature [+Count] is inherent in both the quantifier and in the noun; these two features must match. 'l' represents this feature and it matches. However, the above system of representing features shows this very awkwardly. The system of features and their representation clearly needs an overhaul.
The feature of number is important for determining quantifiers,
as we show below. 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:
49. DEFINE <2> <ADD < [QUANT [+One]]> < [QUANT [+One]]>>.
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):
50. 2 is defined as the addition of 1 plus 1.
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]:
51. one and a half pounds
52. one and one hundredth degrees on the scale.
[+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:
53. zero books (no books)
54. *zero water (no water).
Note that 'no' is [±Count].
Every numeral greater than 1 contains the grammatical feature [+Pl].
Go to Agreement and Percolation
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and Structure
