Scope Lab: Quantifiers & Possible Worlds
“Every x has some y” and “some y works for every x” use the same words in a different order. So do “necessarily, if P then Q” and “if P, then necessarily Q.” Build situations and watch the statements come apart.
Choose a scenario
Draw the relation
Click a dot on the left, then a dot on the right, to add or remove an arrow.
The two statements
Challenges
“Necessarily” means “true in every possible world,” and “possibly” means “true in at least one.” □(P → Q) only rules out worlds where P is true and Q is false. It doesn't make Q true everywhere.