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Single Idea 15131

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

Full Idea

In S5, necessity and possibility are not themselves contingent matters. This is plausible for metaphysical modality, since metaphysical possibility, unlike practical possibility, does not depend on the contingencies of one's situation.

Gist of Idea

If metaphysical possibility is not a contingent matter, then S5 seems to suit it best

Source

Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §1)

Book Ref

-: 'Dialectica' [-], p.255

A Reaction

This is the clearest statement I have found of why S5 might be preferable for metaphysics. See Nathan Salmon for the rival view. Williamson's point sounds pretty persuasive to me.

The 18 ideas with the same theme [strongest system, with three accessibility conditions]:

7791 The simplest of the logics based on possible worlds is Lewis's S5 [Lewis,CI, by Girle]
14973 In S5 all the long complex modalities reduce to just three, and their negations [Cresswell]
13604 Real possibility and necessity has the logic of S5, which links equivalence classes of worlds of the same kind [Ellis]
14686 S5 modal logic ignores accessibility altogether [Salmon,N]
14691 S5 believers say that-things-might-have-been-that-way is essential to ways things might have been [Salmon,N]
14693 The unsatisfactory counterpart-theory allows the retention of S5 [Salmon,N]
14627 S4, and therefore S5, are invalid for metaphysical modality [Salmon,N, by Williamson]
9560 S5 provides the correct logic for necessity in the broadly logical sense [Fine,K]
9065 S5 collapses iterated modalities (◊□P→□P, and ◊◊P→◊P) [Keefe/Smith]
9748 System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn]
14626 In S5 matters of possibility and necessity are non-contingent [Williamson]
15131 If metaphysical possibility is not a contingent matter, then S5 seems to suit it best [Williamson]
13708 S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid [Sider]
7793 ◊p → □◊p is the hallmark of S5 [Girle]
7795 S5 has just six modalities, and all strings can be reduced to those [Girle]
18814 'Absolute necessity' would have to rest on S5 [Rumfitt]
12204 The logic of metaphysical necessity is S5 [Rumfitt]
19032 S5 is undesirable, as it prevents necessities from having contingent grounds [Vetter]