Tuesday, September 26, 2006

Two-dimensional semantics

Frege had sense and reference. Kaplan has character and content. Jackson has a-in/extensions and c-in/extensions. All of these are supposed to account for the difference in cognitive significance of sentences or terms when the sentences and terms are intensionally different but extensionally the same. Frege's notions don't line up with Kaplan's. For sentences (similarly for terms) senses are propositions that denote truth or falsity as reference. For Kaplan, contents are true or false and propositional. The characters are functions from worlds to extensions. Kaplan's distinctions don't quite line up with Jackson's. The character/content distinction maps pretty well to the c-in/extension distinction, but the character is supposed to account for the cognitive significance of differing sentences/terms with the same content. The a-intension and extension are supposed to do this for Jackson.

It seems like it would be possible to extend Kaplan's theory to Jackson's, but it might mean changing how "actually" works in Kaplan's semantics. (It would also mean accounting for the bit about character just mentioned.) Why "actually"? I don't remember if "actually" denotes whichever world w is in the context or if it denotes the actual world @ regardless of the context. Both views on "actually" are out there, e.g. Jackson likes the former and Perry likes the latter. So, why "actually"? Jackson wants the a-extension of a term to be the extension of the term in a world w, under the assumption that w is the actual world. If Kaplan's view is that "actually" denotes w, then it should work just fine. If his view is that "actually" denotes @, then the a- and c-in/extensions collapse. (The library's only copy of Themes from Kaplan is out.)

The next question is how motivated this is. For Kaplan, the character is roughly the linguistic meaning (roughly). I guess the c-intension is supposed to correspond to that. But, if we move the cognitive significance to the a-intension, how well does the c-intension capture the linguistic meaning? Kaplan's point is that the linguistic meaning of a term is what gives it its cognitive significance outside of its content. I guess the a-intension includes the linguistic meaning for the languages we speak, as well as the linguistic meaning for the languages of all those other people in the possibluum (possibility+continuum=possibluum. That term is from John Perry. He used it to tease David Lewis at UCLA. )

(I debated naming this post "Love 'actually' " but I stopped myself, for better or worse.)

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