Single Idea 13708

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

Full Idea

S5 is the strongest system, since it has the most valid formulas. That's because it has the fewest models; it's easy to be S5-valid since there are so few potentially falsifying models. K is the weakest system, for opposite reasons.

Gist of Idea

S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid

Source

Theodore Sider (Logic for Philosophy [2010], 6.3.2)

Book Reference

Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.145


A Reaction

Interestingly, the orthodox view is that S5 is the correct logic for metaphysics, but it sounds a bit lax. Compare Idea 13707.

Related Idea

Idea 13707 Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible [Sider]