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Full Idea
In S4 there are exactly 14 distinct modalities, and any modality may be reduced to one containing no more than three modal operators in sequence.
Gist of Idea
S4 has 14 modalities, and always reduces to a maximum of three modal operators
Source
Max J. Cresswell (Modal Logic [2001], 7.1.2)
Book Ref
'Blackwell Guide to Philosophical Logic', ed/tr. Goble,Lou [Blackwell 2001], p.141
A Reaction
The significance of this may be unclear, but it illustrates one of the rewards of using formal systems to think about modal problems. There is at least an appearance of precision, even if it is only conditional precision.
| 14970 | Normal system K has five axioms and rules [Cresswell] |
| 14971 | D is valid on every serial frame, but not where there are dead ends [Cresswell] |
| 14972 | S4 has 14 modalities, and always reduces to a maximum of three modal operators [Cresswell] |
| 14973 | In S5 all the long complex modalities reduce to just three, and their negations [Cresswell] |
| 14974 | A relation is 'Euclidean' if aRb and aRc imply bRc [Cresswell] |
| 14975 | A de dicto necessity is true in all worlds, but not necessarily of the same thing in each world [Cresswell] |
| 14976 | Reject the Barcan if quantifiers are confined to worlds, and different things exist in other worlds [Cresswell] |