Practice question · Estimate
In S5, any string of modal operators reduces to its final operator. Set the number of operators remaining after reducing a string of five.
Estimate on a scale from None remain (0) to All five remain (5).
Hints
- S5 collapses iterated modalities entirely.
- Whatever the length of the string, only the last operator survives.
Show the answer
1 (answers within ±0.4 count)
Why
Just one, whatever the original length. This collapse is what makes S5 the natural choice for logical necessity, it encodes the thought that whether something is necessary is not itself a contingent matter.
Practise Modal Systems and Possible Worlds
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