Full Idea
The idea of possible worlds has delivered insights on logical possibility (de dicto and de re), propositions, properties and sets, counterfactuals, time and temporal relations, causal determinism, the ontological argument, and the problem of evil.
Gist of Idea
Possible worlds clarify possibility, propositions, properties, sets, counterfacts, time, determinism etc.
Source
Alvin Plantinga (Actualism and Possible Worlds [1976], Intro)
Book Reference
Plantinga,Alvin: 'Essays in the Metaphysics of Modality' [OUP 2003], p.103
A Reaction
This date (1976) seems to be the high-water mark for enthusiasm about possible worlds. I suppose if we just stick to 'insights' rather than 'answers' then the big claim might still be acceptable. Which problems are created by possible worlds?