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Single Idea 15102

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

Full Idea

S4 says there must be some necessary truths, because the actual necessary truths must be necessary. (It says if there are some actual necessary truths then that is so - but the S4 axiom is an actual necessary truth, if true).

Gist of Idea

S4 says there must be some necessary truths (the actual ones, of which there is at least one)

Source

Ross P. Cameron (On the Source of Necessity [2010], 2)

Book Ref

'Modality', ed/tr. Hale,B/Hoffman,A [OUP 2010], p.140

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]