Lewisian Semantics for Restricted Type-Identities II
(This is a follow-up to the previous post.) I think I've found a better way to provide for things like population-dependence in a Lewisian semantic framework. The trick is to regard it as a kind of index-dependence without explicitly introducing population-coordinates into the indices.
Recall, we want "pain*" to denote whatever state occupies the pain-role in the relevant population. Unfortunately, the relevant population isn't just the most salient population in the context of utterance, for we want to say things like
2) For all x, x is in pain* iff x is in a state that plays the pain-role in normal members of the population to which x belongs.
(For no good reason I've replaced "kind" in my previous entry by "population".) To make this true the relevant population must systematically correspond to the values assigned to "x": for penguin-values of x, the relevant population is a population of penguins, but for Martian-values it contains Martians. But there's only a single context of utterance of "pain*" in (2) because there's only one occurrence of "pain*". So the variation can't be mere context-dependence.
How can the semantic value of "pain*" depend on the value assigned to the variable x? Most simply because "pain*" somehow contains a hidden instance of that variable: it means something like "pain*-with-respect-to(the-population-for(x))". If, as in "General Semantics", variable assignments are themselves treated as index coordinates, this variable-dependence is just index-dependence. But it's not dependence upon a primitive population-index.
It seems that the value of the hidden pain*-index is almost always the value of whatever "pain*" is predicated of. That is, we probably can't mean "Fred has pain*-with-respect-to(the-population-of(Jones the penguin))" by saying "Fred has pain*". But we can use "pain*" without predicating it of anything, and in this case the index must be determined in some other, presumably contextual, way.
So on this view, "pain*" resembles "relevant", as Lewis says: Both are very indeterminate unless context or index determines a subject. Put in schmentencite fashion, "relevant" means something like "relevant for x", where the value of "x" can be determined by context or by quantificational embedding, as in "People who wish to reproduce any of these images need to contact the relevant authorities".
If "pain*" is in this way systematically ambiguous between various realizers, it makes sense to say that it denotes a realizer, not a role property.