Full Idea
If we see a proposition as a function from possible worlds to truth-values, then the two sets of truth-conditions yield two propositions associated with any statement. A 'primary' for those which express a truth, and 'secondary' for counterfactual truth.
Gist of Idea
Two-dimensional semantics gives a 'primary' and 'secondary' proposition for each statement
Source
David J.Chalmers (The Conscious Mind [1996], 1.2.4)
Book Reference
Chalmers,David J.: 'The Conscious Mind' [OUP 1997], p.63
A Reaction
This is where 2-D semantics becomes increasingly 'Byzantine'. Intuition and introspection don't seem to offer me two different propositions for every sentence I utter. I can't see this theory catching on, even if it is technically beautiful.
Related Ideas
Idea 13958 The 'primary intension' is non-empirical, and fixes extensions based on the actual-world reference [Chalmers]
Idea 13959 The 'secondary intension' is determined by rigidifying (as H2O) the 'water' picked out in the actual world [Chalmers]
Idea 14716 2D semantics can't respond to contingent apriori claims, since there is no single proposition involved [Schroeter]