Full Idea
Is there any sense in which, despite an ascription of necessity to p, it is held that not-p is possible? If there is, then the original claim then it was necessary is not a claim of 'logical' necessity (which is the strongest necessity).
Gist of Idea
It is only logical necessity if there is absolutely no sense in which it could be false
Source
Ian McFetridge (Logical Necessity: Some Issues [1986], §1)
Book Reference
-: 'Aristotelian Society' [], p.137
A Reaction
See Idea 12181, which leads up to this proposed "test" for logical necessity. McFetridge has already put epistemic ('for all I know') possibility to one side. □p→¬◊¬p is the standard reading of necessity. His word 'sense' bears the burden.
Related Idea
Idea 12181 Traditionally, logical necessity is the strongest, and entails any other necessities [McFetridge]