Two related desiderata for a conventionalist thesis

If we want to analyze 'it is necessary that S' somehow using 'it is analytic that S', that is, to defend a version of conventionalism about modal claims, we must first understand quantification into modal contexts as intelligible. The reason is that we wish to have a semantic story on the conventionalist view for sentences like '(∃x)φ(x)' where the context 'φ( )' might be "opaque". Kit Fine asserts that there are two proposals for understanding quantification in. The first is that a quantified sentence like '(∃x)φ(x)' can be understood as intelligible if (1) the quantifier is taken to be referential, and (2) there is a proper substitution instance 'φ(t)' of the quantified sentence. A proper substitution instance is one in which semantic uniformity with the quantified sentence is preserved. Since, we've assumed that quantification is purely referential, then a proper instance must be such that 't' plays a semantic role of pure reference. In other words, 't' can play no other semantic role, else we fail to have a proper substitution instance. On this proposal, the original quantified sentence will be true just in case there is a proper substitution instance. For the case of a purely referential quantifier, the sentence will be true just in case, there is a substitution instance in which the the substituend is purely referential. It might be the case that for different types of quantification (and I'm not sure what those would come to be, but there might be)
  On the other hand, we can make sense of '(∃x)φ(x)' if we hold that there are a priviledged class of names all of which have the right (as Fine calls it) "core content" (I take it to mean conceptual content, such that if 'n' is one of this class then if the substitution instance 'φ(n)' is intelligible. Moreover, the quantified sentence is true just in case there is such a special name that 'φ(n)' is true. But the truth of this sentence is determined in a way different from that of 'φ(t)' of the first proposal. The truth of 'φ(n)' is determined by comparison of the relevant conceptual contents of the name 'n' and the context 'φ( )'. I'm guessing that this comes down to "checking" whether that which is named by 'n' is such that by meanings (or conceptual considerations) alone we can tell whether 'n' is 'φ( )'. Fine makes the astute observation that on this "special name" proposal for understanding, it seems unlikely that quantification is purely referential. In purely referential quantification, the truth of 'φ(t)' is determined exclusively by whether that which is named by 't' is in the extension of the predicate created by the context 'φ( )'. There need be no conceptual apparatus and deployment at all to determine the intelligibility or truth of the quantified sentence. On the other hand, it doesn't seem that whether the actual referent that is picked out by the special name 'n' is in the extension of predicate indicated by the context 'φ( )' has anything to do with the assessment of the intelligibility or the truth of 'φ(n)' and so the quantified sentence '(∃x)φ(x)'. (It does seem like the referent of 'n' will be in this extension, but almost incidentally so.)
 I think that to make a conventionalist thesis work, we need both. And to understand what the committments of conventionalism are, it's helpful to see what sort of postion one would take to be "in the intersection". Perhaps working exclusively in the context of an interpretive truth theory would make things easier (or even possible -- I'm not sure how we could do it with a different system of semantics). Since the only kinds of base clauses are for singular terms and predicates, it seems natural to consider what it would take to accomodate both proposals: semantic uniformity and a sort of special name treatment. It seems that dealing with predicates is easier. First off, we're not really quantifying over predicates (unless we've got names for them), so semantic uniformity seems to be guaranteed. In a sentence like '(∃x)φ(x)', if we assume that 'φ( )' expresses a predicate which the quantified sentence claims has a nonempty extension, so for a substitution instance like φ(t) to insure that we have uniformity, the context must also determine a predicate which has that named by 't' in its extension. I can't think of any cases in which semantic uniformity wouldn't be preserved from a quantified sentence to it's instances. Could, for instance, 'is a schnurg' play a different semantic role in 'There is something such that it is a schnurg' and 'Bob is a schnurg'? Doesn't seem so, but it warrants thinking about.
 In terms of the second desiderata, it seems that our view on concepts provides an answer to whether the predicate expressed by the context 'φ()' has the right sort of associated conceptual content. For example, we might hold that to possess a concept is just to know the precise application conditions of that concept, in all the gory detail that's required. For example, to have the concept WATER one must know that if x is water then x is H₂O. This sort of view of concepts guarantees that we have the right conceptual content to know when a sentence like 'φ(s)' is true (provided, of course, that we have the right conceptual content associated with the name 's'). It's interesting to note that we might be able to competently use a predicate that expresses a concept without possessing the concept.
  So we're primarily concerned with singular terms.