The hierarchical relation between anaphoric elements and their antecedents
In GB the relation ‘bound’ is defined in terms of the structural relation ‘c-command’. An NP is bound if it is coindexed with a c-commanding NP, where c-command is defined as in (1).
A node α c-commands a node β if neither node dominates the other and the first branching node which dominates α also dominates β (cf. Reinhart 1976, 1981).
By definition, the two instances of the name John are not bound; hence they are free even though they are coindexed. This definition of ‘free’ as ‘not bound’ also holds with respect to Principle C in the following structures, where c-command domains of the coindexed names are indicated by brackets.
a. [John’si mother] thinks that [Johni is unhappy]
b. [Mary’si brother] admires [Mary’si friend]
c. Bill returned [Sam’si bicycle] to [Sam’si house]
For Principle C, the definition of ‘free’ as ‘not bound’ appears to be sufficient.
For Principle A, the defintion of ‘bound’ based on c-command holds for the basic cases. However there are certain constructions in which an anaphor occurs in a position which is not c-commanded by its antecedent.
(3)

In contrast to (3b), the anaphor in (3a) is not c-commanded by its antecedent.
There are several reasons for not modifying the definition of ‘bound’ (or alternatively ‘c-command’) to accommodate (3a) under Principle A. The definition of ‘bound’ as it stands correctly predicts that if the anaphor in (3a) is replaced by a name, then coindexing is allowed since neither coindexed NP c-commands the other.
(4)

If the definition of ‘bound’ is changed for anaphors, then either (4) should be illformed on a par with (4)—which is false, or we must abandon the common thread between Principles A-C, the structural relation of c-command. Secondly, if object NP can bind NPs in embedded subjects, then there is no way to rule out binding of subjects as in (5) without ad hoc complications of the structural definitions involved.
(5)

While it could be argued that (5) is ruled out by Principle C since the men is not free, an analysis where an object NP may bind a subject NP would predict incorrectly that (6) is also ill formed by Principle C.
(6)

Next, while the so-called ‘picture NP reflexive’ cases (e.g., (3)) are acceptable, an anaphor in the subject position of an NP whose antecedent is the object of the matrix verb seems significantly less acceptable.
(7)

Therefore it is reasonable to consider cases like (3a) as outside the range of core phenomena.
Additional evidence for this conclusion comes from the fact that “picture NP reflexives,” unlike other reflexives, can have split antecedents as in (8a)—in contrast to (8b).
(8)

Note further that this property is limited to reflexives and therefore should not be considered as a general property of lexical bound anaphors, as illustrated in (9).
(9)

(See Bouchard 1982 and Lebeaux to appear for further discussion.)
Another construction in which an anaphor does not occur in a c-command relation with its antecedent is given in (10).
(10)

If the anaphor is replaced with a coindexed copy of the name Mary, the result is illformed (excluding emphatic stress on the second instance of the name).
(11)

According to the simplest version of the binding theory, the object of to should c command the object of about. This is also necessary if Principle B is to account for the illformedness of (12).
(12)

In short, the binding theory makes the correct predictions for all NP-types in this construction if the object of to c-commands the object of about.
This c-command analysis could be realized in at least two ways. If the verb talked and the preposition to are reanalyzed as a V, as in (13), then c-command will hold between the relevant NPs in the appropriate manner.
(13)

Alternatively, to might be analyzed as a case-marker adjoined to NP (cf. of in nominals like the destruction of the city) rather than a prepositional head which projects its own phrasal category distinct from NP and thereby blocks c-command between the two NPs. Clearly some special analysis of (10–12) is required in order to maintain the generalization captured by the binding theory as it applies to these constructions.
For the remainder of the discussion the c-command formulation of ‘bound’ will be assumed as the core notion.