more from Max J. Cresswell

Single Idea 14972

[catalogued under 4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4]

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


Max J. Cresswell (Modal Logic [2001], 7.1.2)

Book Reference

'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.