more from this thinker     |     more from this text

Single Idea 7794

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

Full Idea

In S4 there are fourteen modalities: no-operator; necessarily; possibly; necessarily-possibly; possibly-necessarily; necessarily-possibly-necessarily; and possibly-necessarily-possibly (each with its negation).

Clarification

S4 is one of the five main systems of modal logic

Gist of Idea

There are seven modalities in S4, each with its negation

Source

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

Book Ref

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

A Reaction

This is said to be 'more complex' than S5, but also 'weaker'.

The 7 ideas with the same theme [version imposing two conditions on accessibility]:

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]