External necessity concerns relations or incompatibilities among things outside the mind. Mental implication asks how awareness of one meaning brings another into thought. A connection in external reality does not by itself make the intended concomitant intelligible to every audience.
For example, the printed discussion invokes “ʿamā” (blindness) and “baṣar” (sight). Blindness is a deprivation of sight in a subject capable of sight, so explaining absence of sight already requires the notion of sight—even though blindness and actual sight cannot coexist in the same respect.
The point is to distinguish coexistence in the external world from needing a concept in order to understand another concept. These are not the same relation.