Definition
Possibility is the status of what could be true — what is true in at least one way things could have gone. That a tossed coin lands heads is possible; that a square has three sides is not. Possibility does not require actuality: many things are possible that never happen.
In modal logic, possibility is written ◇P, read 'it is possible that P'. It is the weak modal status. It demands only one successful alternative, whereas necessity demands that every alternative succeed.
Why it matters
How it works
On the possible-worlds account, ◇P is true exactly when P holds in some world accessible from the world of evaluation. Where necessity is universal quantification over worlds, possibility is existential quantification: one witnessing world is enough.
This makes possibility and necessity formal mirror images. ◇P is equivalent to 'not necessary that not-P', and □P is equivalent to 'not possible that not-P'. The pair behaves like the quantifiers 'some' and 'all': what 'some' is to 'all', possibility is to necessity. Reasoning about possibility therefore reasons about whether any alternative scenario can be coherently described — which is why genuine impossibility marks the limit of consistent thought.