Wacek and Ken, (01)
vQ> This encourages me to ask another question: do propositions
> involve indexicals? (Would there be proposition-indexicals?)
> Does the statement 'he is wise' correspond to a (number of)
> proposition(s) about a particular individual at a particular
> time each, or can it correspond to a proposition which still
> does not have the 'he'-part resolved? (02)
KC> I think it's hard to consider any meaning of a proposition
> like that without considering that it has an intended referent
> for the indexical - that is, that it refers to a particular
> individual. (03)
I agree with Ken. (04)
If we consider a proposition to be the "language-independent meaning"
of a sentence, then it should also be context independent as well. (05)
That point follows from the fact that different languages have
different means for representing anaphoric references and their
referents (e.g., inflexions, gender, different kinds of articles,
demonstratives, etc.). Some artificial languages (predicate
calculus, for example) replace all such mechanisms by variables,
which are, in effect, name-like labels. (06)
If all such languages are able to express the "same" propositions
(in whatever sense of "same" seems reasonable), then the simplest
assumption is to assume that the "language-independent meaning"
is converted to a context-independent form by assigning specific
referents to the indexicals. (07)
KC> I suppose one can consider "open propositions" as having meanings
> in which some indexical or other is like a variable... (08)
In the predicate calculus, expressions with unbound variables are
used only in the intermediate steps of certain rules of inference.
Tarski's version of model theory ignores them. Other versions might
consider them implicitly bound by a universal quantifier -- thereby
giving them a default binding. (09)
In the lambda calculus, an explicit marker (such as the letter lambda)
is used to mark the variables that are not bound by quantifiers.
That technique converts the expression into a function definition. (010)
John (011)
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