Limits Of X-Bar Theory

Over Generation

X-bar theory can produce sentences that are NOT well formed; It over-generates (generates ungrammatical sentences).

Because X-Bar theory says complements are optional we end up with verbs not having the correct number of arguments. e.g:
*The philosopher loves
*The philosopher smiled the breadbox.

Fixes: Selectional Restrictions

Selectional Restrictions limit the semantic properties of arguments
e.g.
#My toothbrush loves raisins.
#The bolt of lightening killed the rock

Fixes: Theta Roles and Thematic Relations

Theta Roles and Thematic Relations limit the sentences that are valid in the Grammar - they prune off the overgenerated X-Bar sentences.

Ordering of Grammar Generation

X-bar → Theta Criterion → Expl. Insertion → EPP & Binding conditions → Judgments.

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Undergeneration

Word orders that X-Bar Theory can't derive (VSO, VadvO, V Neg O) are generated by head to head movement.