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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.
15544 | If what is actual might have been impossible, we need S4 modal logic [Armstrong, by Lewis] |
14972 | S4 has 14 modalities, and always reduces to a maximum of three modal operators [Cresswell] |
16958 | In S4 the actual world has a special place [Dummett] |
14671 | What is necessary is not always necessarily necessary, so S4 is fallacious [Salmon,N] |
9747 | The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
7794 | There are seven modalities in S4, each with its negation [Girle] |
15102 | S4 says there must be some necessary truths (the actual ones, of which there is at least one) [Cameron] |