Further to this consideration of the necessity that the semantics in terms of
which analyticity is judged be complete there is the question of the domain of
the truth conditions and the supposed metaphysical character of logical necessity.

Logical necessity appears both to be semantic and to be metaphysical.
It appears to be (and is generally held to be) a metaphysical concept possibly
because in its most common definition "true in all possible worlds" the notion
of "possible world" features crucially and is generally held to be a
metaphysical concept.

However, logical necessity is a property of propositions, and propositions are
the meanings of sentences.
Since it is a property of semantic entities it must surely be semantic in
character.
Only one aspect of the proposition is relevant to the judgement of necessity,
and that is the truth conditions.
The truth conditions represent the truth values of the proposition under each
possible circumstance, in every possible world.
The possible worlds are therefore the domain of the truth conditions,
considered as a function.

Thus we have it that in a definition of the semantics of a language there must
be assigned to each judgement a proposition.
What is a proposition?
We don't need to know.
For our present purposes we need only an abstract semantics, and for an
abstract semantics we can chose convenient abstract representation for
propositions which incorporate the information we need to have in a proposition.
In particular we can chose some suitable representation for the truth
conditions which form an essential part of the meanings of judgements.
In doing so we must determine from our understanding of the subject matter of
the language the domain of discourse which will be the domain of the truth
conditions considered as a function.

In the case that the language is for talking about the world (rather than some
mathematical domain or some fictional subject matter) then the determination of
the domain of the truth conditions reflects the presumptions which are embedded
into the language about the nature of the world.
For some purposes it would be ideal if this were simply choice of a
representatives for the possibilities which did not exclude any possible state
of affairs, but in practice languages evolve for use in the real world and some
of its features are assumed by our languages.

Thus, in the design of a language or in the activity of modelling the semantics
of a natural language an activity is required which is similar to metaphysics.
In the design case it amounts to deciding upon a metaphysic on the basis of
which the language is offered, in the other case it is the discovery from the
target language of that metaphysic which is essentially presupposed in the use
of the language.

Thus, at the margin, some things become necessary as a result of language
choices.
If these are not *really* necessary, then we have a language which is only
properly applicable in some possible worlds, those which satisfy the
metaphysical presumptions.
When applied in possible worlds which comply with the metaphysic those features
will appear to be necessary when we might want to say that they are not really so.

Another aspect of the design of a language or of its semantic analysis is the
assignment of meanings to names in the language.
If a name is a rigid designator, then it is probable that the designation will
be at least part of the meaning of the name (much more discussion in the area later).
If some referring expression is not a rigid designator and its sense does not
uniquely determine its reference in every possible world, then the reference
will be contingent and will have to be fixed by the possible world.
i.e. a possible world, just like an interpretation of a first order language in
model theory, must stipulate the reference of names which are not rigid
designators.
(indefinite descriptions require some thought)