more from Theodore Sider

### Single Idea 13704

#### [catalogued under 5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth]

Full Idea

It isn't clear which formulas of modal propositional logic are logical truths, ...especially for sentences that contain iterations of modal operators. Is □P→□□P a logical truth? It's hard to say.

Gist of Idea

It is hard to say which are the logical truths in modal logic, especially for iterated modal operators

Source

Theodore Sider (Logic for Philosophy [2010], 6.3)

Book Reference

Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.137

A Reaction

The result, of course, is that there are numerous 'systems' for modal logic, so that you can choose the one that gives you the logical truths you want. His example is valid in S4 and S5, but not in the others.

Related Idea

Idea 13711
System B introduces iterated modalities **[Sider]**