□ (thing)

In modal logic, □ is the necessity operator.¹

□P
It is necessary that P.

For P to be necessary is for P to be true in all possible worlds. Compare □P with the modal sentence ◊P, which means P is true only in some possible world (possibly P).

□ can be formally defined using ◊, which is the modal possibility operator, and the negation operator ¬ from classical logic.

□P = ¬◊¬P
Necessarily P = Not possibly not P

• modal logic
• necessity
• logical operators
• possible world
• negation

• ◊