1

In modal logic, if one knows a proposition p, then p is true (though the converse does not necessarily hold).

Suppose now that p is impossible. Does that mean that p is false (though a false proposition is not necessarily impossible)?

4

If you agree with the principle :

□p→p,

replacing p with ¬p gives :

□¬p→¬p

that is :

¬◊p→¬p.

We can red it as :

if p is impossible, then p is false.

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