“anyword.”For example,(4)has four variables: NP, Det,AP, and N: itsays“AnyDetfollowedbyanyAP followedby
any N can constitute an NP.”Of these variables, Det and N are categories (or types) of word; let us concentrate on
them for a moment. In order for rule (4) to be able to put words together, twothings are necessary. First, lexical items
must bemarked forwhatcategory theybelongto. For instance,starandcatbelong tothecategory Noun;the, a, andthis
belong to thecategory Determiner. Second, we need a“meta-principle”ofvariable instantiation, whichcan be seen from
twoperspectives. Fro mthe“top-down”perspective,itallows instances of a category tobe substituted for a variableof
that category, thus“satisfying”or“saturating”the variable. Fro ma“bottom-up”perspective, it allows an individual
word to be analyzed as having a role in a larger structure; this structure can be identified by substituting a variable for
the individual word.
Next, consider the categories NP and AP. These are not categories of words, but categories ofphrases. Such categories
allow us not only to string words together, but also to build the minto larger units that can then co mbine further. A
phrasal category is more abstract than a lexical category suchas Noun and Determiner,inthat itis notinstantiatedjust
by pulling a single word out of the lexicon. Rather, it is instantiated by a string of one or more words and/or phrases
thatsatisfythevariablesin its formation rule (i.e. that are“clipped ontoit”). Thus, for instance, NP can be instantiated
bystars, the little star, this fat cat, and so forth; AP byfat, very skinny, moderately attractive, and so forth.
The reason for using phrasal variables rather than just strings of lexical types becomes clear when the same phrasal
variableappears inseveral differentformation rules. For example,NPappears as a variablein,among other things, the
following formation rules of English (assuming a generic introductory-course set of phrase structure rules).
In(5a), NP is thesubjectofa sentence; in(5 b)itis theobject ofa verbphrase; in (5c) it is theobjectofa prepositional
phrase. The fact that the same variable, with the same set of instantiations, shows up in multiple places is part of what
convinces us we are dealing with a genuine linguistic unit and not just an analytic artifact.
Inintroducing formationrulesas part ofa grammar, wealready havetofacethreeimportantand interlockedempirical
questions. First, what are the actual formation rules for the language under analysis? Second, and more generally, what
is the available repertoire of types for variables in formation rules? For