### Single Idea 8480

#### [catalogued under 4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic]

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.