Full Idea
The five systems of propositional modal logic contain successively stronger conceptions of necessity. In S4 'it is poss that it is poss that p' implies 'it is poss that p'. In S5, 'it is poss that it is nec that p' implies 'it is nec that p'.
Gist of Idea
S4: 'poss that poss that p' implies 'poss that p'; S5: 'poss that nec that p' implies 'nec that p'
Source
Alex Orenstein (W.V. Quine [2002], Ch.7)
Book Reference
Orenstein,Alex: 'W.V. Quine' [Princeton 2002], p.151
A Reaction
C.I. Lewis originated this stuff. Any serious student of modality is probably going to have to pick a system. E.g. Nathan Salmon says that the correct modal logic is even weaker than S4.