Categories and constituents

Categories and constituents

• Two goals: first, to build up slowly the ideas of category and constituent in grammar, so that it does not seem obvious.

• Second, to prepare the way to see the connection between constituents in a phrase-structure grammar and certain “symbolic” approaches to mind.

Two points of view

1: What’s real and central in grammar are notions like Noun and Verb (and Noun Phrase and Verb Phrase). Then we find real nouns, like dog and John and Monday. Many of them are good nouns, but some of them are defective; they don’t “do” all the things that they “should do”.

2nd point of view

What’s real are sentences (or corpora):

John is leaving Wednesday with his dog.

When we look at a language, we find an enormous range of “places” where a given word can appear. (“Places” meaning environments, perhaps meanings). No two words are quite alike, but words do form clusters with regard to their grammatical behavior. For example, ...

The days of the week (Monday…Sunday) share a lot in common. We can simplify our description by generalizing over that set of words.

Likewise, Proper given names (John, Jerry, …).

As we form larger and larger classes, there are fewer things that they have in common.

Categories: we have 4 things in mind when we make them:

1. (Lexical categories): Morphology

2. Meaning (semantics)

3. External distribution

4. (Phrasal categories): internal distribution

...

Morphology

• What suffixes may appear with a given stem: ‘s, NULL, s;

• ed, s, ing, ed

• er, est, ness

Meaning

• Reference to objects in the world

• Reference to n-ary predicates:

• unary: tall, sleep

• binary: eat (human, food), saw (human, object)

• ternary: give (human, human, object)

External distributionRoughly speaking: this means, what this word

(or phrase) can appear next to (before, after).

Nouns appear after articles (=noun determiners, nominal determiners), after adjectives. before Prepositinal Phrase complements.

the dog, my dog, the taste of champagne, the war of the worlds

Internal distribution (phrases)

• A “noun phrase” has three parts: a determiner, followed by an adjective, followed by a noun.

• Some of these are “optional”: that is, we may still call something an noun phrase even if not all 3 are present.

Classical view of categories

Gardner (340f.): By the middle of this century, a certain position had become entrenched as the “right way” to think about categories, concepts, and classification…And yet in the past thirty-five years, during the very period when cognitive science has been in the ascenancy, this view of how we categorize the world has undergone the most severe attack, until today virtually no one holds it in its pure form.

Classical view(Bruner) “…a category was arbitrarily defined (any

set of attributes could have been targeted), and each item unambiguously fitted (or failed to) into that category. The traditional recipe: a category and a set of defining features, just like the featherless biped….Philosophers…Anthropologists…nneuroscience, a search was on for detectors that registered unambiguously to all lines that were oriented in a certain direction but to none otherwise oriented.” 341

• Cf also Lakoff, Women, Fire, and Dangerous Things.

(Gardner): 1. “Categories are arbitrary. Nothing in the world or in our nervous system determines how we must slice up our observations. Cutures and languages do this work. Items can be grouped together in any number of ways to form categories, and people can learn to identify or construct those categories defined by their culture.

2. Categories have defining or critical attributes. All members…share these defining attributes, no nonmembers share them, and there is no overlap between members and nonmembers.

3. The intension (or set of attributes) determines the extension of a category (which items are members). Hence it makes no sense to talk about a category as having an internal structure, with some items standing out as better members than other items. Boundaries are sharp and not fuzzy.”

“When applied to categories, this meant that to know a category was to have an abstracted clear-cut, necessary, and sufficient criteria [sic] for category membership. If other thought processes, such as imagery, ostensive definition, reasoning by analogy to particular instances, or the use of metaphors were considered at all, they were usually relegated to lesser beings such as women, children, primitive people, or even to nonhumans.” (Rosch and Lloyd, cited 342).

• Rosch’ work on prototype categories

• Berlin and Kay on color categories

• Wittgenstein on family relations among categories, evolving into radial categories.

Back to categories for words (etc)

Noun properties (?English):• Takes articles• Takes preceding adjectives• May appear as subject of a sentence• May appear as object of a preposition• Has singular and plural form; plural is realized

as /s/• Refers to an object or set of objects• May take possessive ‘s• May serve as antecedent to a pronoun

Verb

• Has present-tense form (-s in 3rd singular)

• Has past-tense form (-ed)

• Agrees with its subject noun phrase

• Refers to a predicate (1 or more arguments)

• Follows the subject immediately

• Appears at the beginning of a verb-phrase

Where this is heading...We may think of “behaviors” of a word [and

not just words…] as a vast set of attributes, each of them a value along a dimension. Let’s say there are n dimensions (n is a number). Then a given word is a set of specifications for those n attributes.

“Categories” are clusters of such points, or regions in that space.

Hypostatization

• taking the color of the wine bottle for the color of the wine.

• In this case, our goal is to see that we develop categories like lexical category and constituent in order to better understand linguistic facts, like distribution; then we take category and constituent to be real, and forget where they came from.

Is that wrong? bad?Probably. The jury’s still out. It’s not

expected back soon.

A big issue -- one that separates the first and second cognitive revolutions -- is whether there is a role to be played by cognitive representations: in this case, syntactic representations -- our beloved trees.

The first cognitive revolution

• thoroughly endorsed syntactic trees:

S

NP VP

det N

the cat is on the mat

VP det N

PP

• and said that somehow or other, trees like this are in the mind.

• Whatever that might mean.

Connectionist-style models

• do not (appear to?) fare well with representations of this sort.

• So ultimately one must choose between the models and the representations.

• Maybe it’s good enough for the connectionist models to deal with the facts that the representations were invented to deal with.

• We’re a bit in the same state that Einstein and his cohort had to deal with with regard to old-style Newtonian time: do you keep to it, or do you (following Mach) say that time is just one way to organize the facts, and the facts are what we really care about organizing…?

Words, Categories, Languages

• There are many ways to think about sentences in a language.

• Even trying to classify different ways to think about language is hard.

• One great divide separates those focusing on given corpora (singular: corpus), and those on a grammar abstracted away from any given corpus.

What’s real?• Is it the corpus -- the utterances?

• Or is it something more abstract that (perhaps) gave rise to the utterances -- perhaps an ability, a capacity?

• Mach, of course, would choose the first of these.

• Is that choice liberating or repressive?

• It’s liberating if you think it means you can use any description that you want, since no one is more real or less real than any other.

• It’s repressive if you think it means that no theory is worth developing.

Let’s take Mach seriously...

• and ask what linguistic science can do to compress or abbreviate the observed data.

• First of all, there are words...

Words, first

• There are many words in a language (10,000-100,000). How complex or how simple is a description going to be that tells us what combinations will be encountered in English (or another language)?

Categories, first

• We may start with a pretheoretic idea that words fall into a small number of groups, and the “behavior” of words in each group is pretty much the same.

• “Behavior” means the decision whether a word can appear in a given context or not.

Constituents

• Constituents are useful constructs to help us define what “contexts” means in the preceding slide (…in a given context…).

• But how, exactly?

If we think of words as events in time...

• we will be very tempted to think of each word as being the “cause” of the next, since causality generally seems to go from past to the future in this world.

• This leads us to a model like this:

1st word...

EmitterThe

EmitterdogThe

…next word...

dog isThe Emitter

is on EmitterdogThe

Eventually,The dog is on the mat.

• But sentences are not sequences where each word is independent of what precedes it.

• We could try the hypothesis that the emitter is in a particular state after it emits a particular word, and that state is responsible for emitting the next word, and then transitioning to the next state.

Here is a view:

• At any given moment, a speaker has uttered a certain number of words, and that leaves open certain choices for the next word, and closes off other choices.

• Let’s let grammar be the study of that.

• Let’s say that a person (or speaker, or grammar)

Grammatical and lexical words

• Closed class = grammatical, open class = lexical.

• Again, this is an easy intuition to begin with; we’ll challenge it in a moment. But let’s stick to it at first.

Category

• Our first intuition is that some simplicity will emerge out of the fact that some statements will hold for many different words.

• Templates, simple patterns:

mattheonis

box

spot

dog

cat

the

How many words can be substituted there?Many.

Does that tell us that cat, dog, spot, box, …, comprisea single category?