chapter 3: how to account for Fine's semantic uniformity between a quantified sentence and an instance

  Fine's first proposal for taking as intelligible quantification into opaque contexts is semantic uniformity between a quantified sentence and its instances. I've discussed this before, but just to review and to try to get things ever clearer in my own head, let's say what it comes to again.
  Semantic uniformity is maintained from a quantified sentence (which we can represent as '(∃x)φ(x)' where 'φ' is a metalinguistic variable) to a substitution instance of such a sentence 'φ(t)' where 't' is the substituend for the variable 'x' in the original if each constituent of the '(∃x)φ(x)' that occurs in the instance 'φ(t)' plays the same semantic rôle in each. For example, if quantification in the original is to be purely referential, that is, the context 'φ(_)' merely serves to make a claim of some individual or other regardless of how that individual is picked out, then we say that the role of the variable in '(∃x)φ(x)' is only to pick out a value (an object) for the sentence to say something about. Since, under this interpretation of quantification, 'x' serves only to pick out an object about which a claim (determined from the context 'φ(_)') is made and the value that 'x' picks out does not in any way depend upon any feature of the variable 'x', in order to maintain semantic uniformity in an instance 'φ(t)', it must be that the 't' of the instance is also purely referential. That is, that which is picked out by 't' in no way depends upon any feature of 't' and that which is picked out by 't' is all that matters for the truth of 'φ(t)'.
  This situation seems intuitively right. When we say, "There is something that is F" what we want to claim is that there is some thing or other such that that thing is F; it doesn't seem that we want to claim that there is something such that if we managed to refer to it in some way or another then it will be such that it is F. So, naïvely, we have a way to understand quantification that is purely referential. And, I think Fine's assertion that to understand quantified sentences like '(∃x)φ(x)' as intelligible, if quantification is referential, we must have a proper instance (that is an instance in which semantic uniformity is maintained). His assertion is intuitively right also. The sentence, "There is something that is F" can be understood as making an intelligible claim only if there is some thing which is F independent of how that thing is picked out. We need this much to guarantee that our utterances are really about the world in a meaningful way.

[One question might be whether this is really the right response. If we claim, "There is something that is F" does it really matter whether that thing is F independent of how we refer to it? If one were really concerned over whether there was something that was F and not concerned with other side issues, such as how the langauge worked or other semantic issues, then it seems that he wouldn't care about the other dependencies such as whether our reference to the thing affected whether it was F or not.]

  How can or should we develop the requirement of semantic uniformity? One makes an immediate observation from Fine's presentation of the situation and the example sentence scheme ('(∃x)φ(x)') he uses during his discussion: if we're concerned with proper instances and uniformity in general, we should be concerned, at least, with not only the semantic role of the variable '(∃x) ... x' in relation to an instance ' ... t ...', but also with the semantic role of the context 'φ(_)' of each. It seems reasonable to hold that if the semantic role of that which ranged over singular term values (that is, the variable of the quantified sentence) is different from the singular term which occupies its place in the substitution instance, the respective context of the quantified sentence and the corresponding instance might play different semantic roles.

[Need an example of how this might happen. Maybe "The Smith Family Leap Frogs." How about 'is rigid' also? Compare, 'that name is rigid' and 'that plant is rigid'. It might be that contexts are just ambiguous between different uses. Also, if the semantic role of the context changes it seems that some tennent of compositionality might be violated -- or perhaps this would generate what is termed a linguistic "monster". Perhaps, if we're dealing with an imperfect natural language it may be that semantic shifts are possible, unlike the case in which a regimented language is under consideration. It does seem like a failure of intelligibility of a quantified sentence is possible given Fine's extensive examples in "The Problem"]

Of course, it might also be the case that if a failure of semantic uniformity occured between a quantified sentence and its instances, then the context 'φ(_)' is such that it would be flexible enough to "withstand" such a shift. All the concerns over the shift in semantic role of a context have implicitly been about shifts in semantics of simple predicates like 'is F'. Somewhat less pressing, along the same vein, is the problem of whether contexts involving logical connectives are subject to the same sorts of worries. For example, could the semantic role of '... φ(_)∧ψ(_)...' change from a quantified sentence '(∃x)φ(x)∧ψ(x)' to its instance 'φ(t)∧ψ(t)' because of something the '∧' did? It certainly doesn't seem so, but we should, in the spirit of investigation, try to determine if such a thing is possible.
  And it seems like the only way we can really engage in a systematic investigation of semantic uniformity is if we have a systematic approach to semantics in the form of a theory of meaning. I don't see too many options out there besides a compositional meaning theory a la Davidson's interpretive truth theory.

[perhaps compositionality is much more complicated than we thought -- perhaps not just something like mode of combination, but mode of combination + semantical "jist" and context + further combination]

It seems that we should address only the very simplist cases first given that our concern is over
semantic uniformity rather than the recursive machinery needed to understand meanings generally. In terms of Ludwig's "What is the role of truth theory in a meaning theory?", we should be concerned (at first) only with 'reference axioms' and 'predicate axioms'. After all we're concerned with the semantic roles of the variables, singular terms which take their places and (in the simplist, beginning case) the predicates that form contexts in which the former occur.

  It looks like there must be some sort of direct reference theory at work for semantic uniformity to get of the ground, otherwise it doesn't seem that both variables and proper names could serve only to pick out a referent. According to a mediated reference theory, it's difficult to see how a name could serve only to pick out a referent rather than providing some mode of presentation or cluster of descriptions by which the referent could be determined. Even if we could hold, in two-step fashion, that a singular referring term picked out a referent by way of an associated description, then the denotatum could be "fed" directly to a context to form a sentence, it seems that uniformity will not be preserved, given that quantification is referential. Only the value taken on by variables are supposed to matter in the determination of the truth of the sentence '(∃x)φ(x)', but on a mediated reference theory it seems that the truth of 'φ(t)' must depend somehow on the cluster of descriptions associated with 't'. But it seems that we should at least allow that quantified sentences can be understood as intelligible on both a direct and a mediated theory of reference, so some work must be done to see how a mediated theory of reference could satisfy the first desiderata.

  On the predicate front, it's hard to see how they could be understood in any other way than set theoretically. Given that that's really the only way to determine whether the object which is the value taken on by the variable satisfies the predicate that creates the context. After all, we'd have to check the extension of the predicate to see if that individual was in it, given that we couldn't make use of any conceptual (intensional?) material to perform this check.