chapter 4: insuring that the right conceptual content is associated with the predicate terms of quantified modal sentences

  The issues of semantic uniformity and right conceptual content canvassed by Fine concern only individual variables and the actual singular referring terms which are substituted for them. But if we're aiming to make sense of a sentence in which a modal operator is in the scope of a quantifer by understanding its substitution instances (in general, and the singular terms that occur in them in particular) as having the right sort of conceptual content, and then by seeing that this conceptual content allows to make sense of the instances and so allows us to understand the quantified sentences themselves, it seems we must also spend some time addressing the conceptual content associated with the 'contexts' of these sentences. For example, if we want to take up Fine's second proposal for understanding a quantified sentence like '(∃x)φ(x)', we'd understand it by understanding an instance 'φ(t)' and we'd do this by recognizing the conceptual content had by the special name 't'. To make things even more explicit, we could make sense of a sentence like '(∃x)(x > 7)' by seeing that there is an instance, say, '(9 > 7)' which is true in virtue of the conceptual content associated with '9'. And that's as far as Fine's presentation of the proposal carries us.
  Of course, if we want to claim that '9 > 7' is true in virtue of conceptual connections alone (and so is '(9 > 7)' and '(∃x)(x > 7)' ), it seems that at a minimum we need to claim there are conceptual contents had by both the singular referring term '9' and the rest of the sentence -- what Fine calls the context -- '( ... > 7)'. In this specific case, the conceptual contents of the context might be spelled out in terms of the constituents '>' and '7' and their mode of combination (well return to this example over and over again later), but in order to consider the issue in more generality, let's consider a case in which the context is a monadic preciate such as 'is F'. In general, for a substitution instance sentence like 'φ(t)', we'll be concerned with the conceptual contents had by both the singular referring term and the context 'φ(_)' which in our most general case is just a predicate like 'is F'. Briefly, we can assess whether the sentence 't is F' is true or false by determining whether the conceptual content had by the term 't' "matches" the conceptual content had by 'is F'. How to understand "matches"? An obvious response is to claim that the predicate term 'is F' expresses a concept F-ness, say, and that the conceptual content had by 't' is such that it allows us to determine, on the basis of conceptual knowledge alone, whether that which is named 't' is such that the concept F-ness rightly applies to it or in linguistic terms whether that which is named 't' falls under the concept expressed by the predicate 'is F'.

So we have to say something more about concept possession works to tell a story about how such things might go. Two options: we don't possess a concept unless we exactly those things (even counterfactual things) to which the concept applies, or the more reasonable view on which we may have a concept without knowing every dimension, so to speak, of those things to which the concept applies.

This invites another complication for conventionalism and requirement for the right core content: it might be that we could analyze necessity in terms of analyticity, such that any sentence that held of necessity was true in virtue of meanings alone, but that a speaker might be competent with the predicates and terms and that a sentence constructed from these predicates and singular terms was true in virtue of meanings alone, but that the speaker didn't know this, not possessing the concepts expressed by the predicate he competently used. In this case it seems that the right conceptual content requirement is given up for a requirement about the meanings of the predicates that express the concepts in question and the meanings of the singular terms involved. Needs more work, but it's a start.