IV 228
Vagueness/language/Lewis: not the language is vague, but the use. - E.g. David Kaplan: the sun is not colder than Sirius, when the sun is not cold "in a sense".
Language: is not vague itself! But the use of language by individuals or communities, conventions, etc. is vague. I.e. not a point, but a fuzzy region is marked in space.
1) For example, suppose that the only vagueness concerns "warm" and "cold" as extensional adjectives. Then the indices should have a descriptive coordinate of a positive real number, as the limit temperature between cold and warm things.
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Extension.
I.e. at an index i the extension of "cold" is the set of things with the temperature less than or equal to this value (at the world and time coordinates).
Vagueness: a vague extension "this is cold" is true, among some but not all descriptions (delineations).
But propositions with vague constituents are not necessarily vague. Example "This is cold or warm but not both".
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Disjunction/Lewis.
IV 229
The description coordinate is not contextual. It is similar to the determination coordinate in that we generalize over it rather than fix it.
We could say that a proposition is true over a set s of descriptions at an index i, then and only if for every index i' the equal i is except perhaps at the description coordinate, the proposition is true at i' then and only if the description coordinate i' belongs to s.
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Truth/Lewis, >
Measuring, >
Degrees.
Truth/Grade: given a normalized measure function ...+.
Notice: the degree of truth of a truth-functional construct of propositions is not a function of the degrees of truth of its constituents.
Example "x is cold" and "x is warm" can be both true to degree 5 at an index i, but "x is cold or x is cold" is true to degree 5 at an index while at the same index
"x is cold or x is warm" is true to grade one.
Vagueness: Example "possibly" is related to the world coordinate.
Vagueness: Example "in a sense" form ...+ ...
Vagueness: Example "__er than": Form: ((C/C)/N)/(C/C). Intension: "x is colder than y" is true at an index if the set of descriptions under which "y is cold" is true at i, a true subset is the set of descriptions under which "x is cold" is true at i.
It follows that the Sun is not colder than Sirius unless "in one sense" the Sun is cold.
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Intension/Lewis.