Full Idea
Prior had a strong and a weak reading of necessity, where strong necessity is truth in all possible worlds, while weak necessity is falsity in no possible world.
Gist of Idea
Strong necessity is always true; weak necessity is cannot be false
Source
Robert C. Stalnaker (Mere Possibilities [2012], 4.3)
Book Reference
Stalnaker,Robert C.: 'Mere Possibilities' [Princeton 2012], p.103
A Reaction
[K.Fine 2005:Ch.9 is also cited] The point of the weak one is that in some worlds there might not exist the proposition which is the candidate for truth or falsehood.
Related Idea
Idea 13721 'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist [Sider]