1 Two-Dimensional Semantics – the Basics

‘Two-dimensional semantics ’ denotes a family of semantic theories rooted in intensional semantics, held together by shared general ideas, yet divided by deep divergences in semantic aims and philosophical aspiration. 2d-theorists agree that our sentences ’ truth-values vary with what the facts are, as well as with what the sentences mean. To model this twofold dependence of truth on fact and meaning, 2d-semantics assign our expressions inten-sions of more than one kind. The resulting formal framework, common to all 2d-sematics, distinguishes one dimension of actual worlds and primary intensions from a second dimension of counterfactual worlds and secondary intensions. (Hence two-dimensionalism.) These formal similarities often ob-scure the deep conceptual rifts between different interpretations of the 2d-framework. Kaplan interprets it to capture context-dependence, Stalnaker understands it to model meta-semantic facts, and Chalmers construes it to display the epistemic roots of meaning. 1. Intensional Semantics Intensional semantics is anchored in five ideas. First idea: meaning is rep-resentation. The (literal) meaning of a sentence can be equated with how the sentence represents things as being. Second idea: representational content equals truth-conditions. How a sentence represents things as being is encap-sulated in its truth-conditions. How ‘Pavarotti is famous ’ represents things as being can be gauged from the situations the sentence is true in, i.e. that accord with how the sentence represents things as being. Third idea: truth-conditions are truth-value-distributions over possible worlds. Truth-conditi-ons can be understood as assignments of truth-values across possible worlds. We can model the truth-conditions of ‘Pavarotti is famous ’ by as-signing the sentence the truth-value true in all possible worlds that accord with it, and the truth-value false in all that don’t. Here a possible world is taken to be a comprehensive counterfactual alternative to the way our actual world is. A possible world hence encapsulates a complete specification of all facts, and the space of possible worlds comprises a world for each possi-ble counterfactual variation of our own. Some possible worlds, like those similar to ours save for the fact that Pavarotti isn’t famous (and whateve