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Notes
Cf the sketch of these ideas by the character Louis in my dialogue on impossibilities, WWBB, pp. 63ff. He puts the point more clearly than I could.
I would actually prefer to think of the “worlds”, not as points but as partition cells of some suitably fine-grained partition of logical space, where “suitably fine-grained” means that makes all the distinctions between the possibilities that are relevant to the purposes at hand.
In Stalnaker (1968), I put an absurd world, where everything is true, into the model in order to interpret conditionals with impossible antecedents, but I didn’t mean it to be taken seriously; a more sober but equivalent formulation of the semantics would do without it.
Equivalent in the sense that the two formulations make the same sentences true in the same models.
I have ignored names in this sketch; if the language has names, they need to be treated, within the scope of a box, like free variables.
But in the conservative theory, identity statements with rigid designators are always necessary if true. Doesn’t the Goliath/Lumpl statement involve rigid designators? The concept of a rigid designator is more complicated in the counterpart semantics.
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Stalnaker, R. Responses. Philos Stud 133, 481–491 (2007). https://doi.org/10.1007/s11098-006-9062-z
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DOI: https://doi.org/10.1007/s11098-006-9062-z