In possible worlds semantics, which condition correctly defines a necessarily true proposition?
AIt is true in the actual world and at least one other accessible world
BIt is true in more than half of all possible worlds
CIt is true in every possible world accessible from the actual world
DIt is true in the actual world, regardless of other worlds
Necessity is truth across all accessible worlds. 'Accessible' is key: different modal systems (K, S4, S5) define accessibility differently, which changes what counts as necessary. A proposition true only in the actual world is contingently true, not necessarily true.
Question 2 True / False
Possible worlds semantics makes a metaphysical claim that other universes physically exist alongside our own.
TTrue
FFalse
Answer: False
This is the most important misconception about the framework. Possible worlds are mathematical constructs used to assign truth conditions to modal and counterfactual statements — they are no more 'real' than the numbers in a formal proof. The framework is compatible with any metaphysical view about what actually exists; it is a tool for logical analysis, not an ontological commitment.
Question 3 Short Answer
How does possible worlds semantics assign a truth value to the counterfactual 'If it had rained yesterday, the match would have been cancelled'?
Think about your answer, then reveal below.
Model answer: The sentence is evaluated by looking at the closest possible worlds in which it rained yesterday (worlds minimally different from the actual world except for the rain) and checking whether the match was cancelled in those worlds. If it was cancelled in all such closest worlds, the counterfactual is true.
This Lewisian analysis resolves the key challenge of counterfactuals: their antecedent is false in the actual world, so a simple truth-functional account would make them vacuously true. By shifting evaluation to nearest accessible worlds, possible worlds semantics gives non-trivial, context-sensitive truth conditions.