more from Rod Girle

Single Idea 7795

[catalogued under 4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5]

Full Idea

In S5 there are six modalities: no-operator; necessarily; and possibly (and their negations). In any sequence of operators we may delete all but the last to gain an equivalent formula.

Gist of Idea

S5 has just six modalities, and all strings can be reduced to those


Rod Girle (Modal Logics and Philosophy [2000], 3.5)

Book Reference

Girle,Rod: 'Modal Logics and Philosophy' [Acumen 2000], p.46

A Reaction

Such drastic simplification seems attractive. Is there really no difference, though, between 'necessarily-possibly', 'possibly-possibly' and just 'possibly'? Could p be contingently possible in this world, and necessarily possible in another?