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This is a two-dimensional intension, since there are two distinct roles that possibilities play here: as a context of use, and as a circumstance of evaluation (a possible situation relative to which we evaluate whether the relevant object exists or the relevant kind or property is instantiated).
But I left the notion of a circumstance of evaluation rather underspecified.
A single proposition may be true with respect to one circumstance of evaluation and false with respect another.
So we know that expressions are associated with characters, which are functions from contexts to contents; and we know that contents are things which, for each circumstance of evaluation, determine a reference.
On the view being discussed, an expression like "according to the Greek myth" is, qua intensional operator, a circumstance-shifting operator, one that shifts the circumstance of evaluation of the sentence following it.
(Note that "old-style contextualism" can also be stated in Kaplan's framework; it involves variation in content with respect to the context of utterance rather than in truth value with respect to the circumstance of evaluation).
Similar(47)
The horizontal axis represents those same possible worlds as circumstances of evaluation, relative to which we evaluate the truth or falsity of the proposition expressed.
The foregoing suggests a pleasingly minimalist answer to this question: perhaps, since contents are things which together with circumstances of evaluation determine a reference, contents just are functions from circumstances of evaluation to a reference.
The main question is whether circumstances of evaluation need contain any indices other than a possible world.
Given this usage, we can think of circumstances of evaluation — the things which play the theoretical role outlined in §2.1.5 — as made up of indices.
The content of a linguistic expression, at a context, determines a corresponding intension, which is a function from possible worlds (circumstances of evaluation, really) to extensions.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com