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Single Idea 13710

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

Full Idea

In D we add to K a new axiom saying that 'what's necessary is possible' (□φ→◊φ), ..and it can then be proved that tautologies are possible and contradictions are not necessary.

Gist of Idea

In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary

Source

Theodore Sider (Logic for Philosophy [2010], 6.4.2)

Book Ref

Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.166

The 6 ideas with the same theme [version with guaranteed access to some world]:

14971 D is valid on every serial frame, but not where there are dead ends [Cresswell]
13114 □P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed [Fitting/Mendelsohn]
9743 The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn]
13706 Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider]
13710 In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider]
19033 Deontic modalities are 'ought-to-be', for sentences, and 'ought-to-do' for predicates [Vetter]