Martin (1992: 124-5):
However, as Havilland and Clark (1974) point out, phoric nominal groups may presume information that is implied rather than directly retrievable (see also Clark and Havilland 1977). Consider [3:56] below:
[3:56] He bumped into a branch;he hadn't noticed the tree at all.
In [3:56] the identity of the tree has to be established with respect to one of its parts — the branch realised in the preceding clause. Haviland and Clark referred to indirect reference of this kind as bridging… . Bridging depends on experiential connections between presuming and presumed which facilitate the recovery of an implied identity. The relevant lexical relations will be taken up in detail in Chapter 5 (Ideation). Implicational relations between parts and wholes or among parts are very common… . Similarly subclasses may be bridged from classes… . Alongside these taxonomy focussed examples, bridging may depend on experiential relationships of various kinds… .
 Here 'bridging' (indirect "reference") conflates two different kinds of cohesion: reference and lexical cohesion (meronymy).
 Here 'bridging' conflates reference with lexical cohesion (hyponymy).
 The examples of 'bridging' provided in the text include relations of synonymy and collocation — types of lexical cohesion, not reference.
 These lexical relations belong solely in Chapter 5 ('the company words keep'); this chapter (3) is concerned with the semantics of reference.
The fundamental inconsistency in this chapter arises from the interpretation of the 'semantics of reference' as 'participant identification'. Reference is concerned with marking the textual status of elements: their identifiability — not with their (ideational) identity.