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Full Idea
Lewis was suspicious of boxes and diamonds as regimenting ordinary modal thought, …preferring a first-order extensional theory including possible worlds in its domain and an indexical singular term for the actual world.
Gist of Idea
For modality Lewis rejected boxes and diamonds, preferring worlds, and an index for the actual one
Source
report of David Lewis (Anselm and Actuality [1970]) by Robert C. Stalnaker - Mere Possibilities 3.8
Book Ref
Stalnaker,Robert C.: 'Mere Possibilities' [Princeton 2012], p.83