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Single Idea 11004

[catalogued under 4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic]

Full Idea

In S4 necessity is said to be informal 'provability', and in S5 it is said to be 'true in every possible world'.

Gist of Idea

Necessity is provability in S4, and true in all worlds in S5


Stephen Read (Thinking About Logic [1995], Ch.4)

Book Reference

Read,Stephen: 'Thinking About Logic' [OUP 1995], p.118

A Reaction

It seems that the S4 version is proof-theoretic, and the S5 version is semantic.