outline 2.1

1. One consequence of conventionalism (about modality) is the view that necessity can be understood or analyzed in terms of analyticity. The view is advocated by Carnap and the empiricists and more recently by Alan Sidelle, Annie Thomasson and Kirk Ludwig. Challenges to the view come from the Kripke-Putnam assertions of necessary aposteriorities and contingent a priorities. I'd like to get clearer on how a species of the conventionalist view might be spelled out, and what kind of committments one would have to make in order to hold a conventionalist view. So the specific example is how can 'it is necessary that S' be analyzed in terms of 'it is analytic that S'. Kit Fine gives us a good place to get started in his "The Problem of De Re Modality" with his assertion that there are two separate proposals for making sense of quantified sentences in which quantfication is "into" a modal context. First is the semantic uniformity thesis -- a quantified sentence can be understood (is coherent) if it has a proper instance, that is an instance in which the singular referring substituend plays the same semantic role as was to be played by the referential variable (if quantification was to be purely referential). Second is the "right core content" or "special names" requirement -- a quantified sentence can be understood (is coherent) if a substituend is named in a special way such that the name has the right conceptual content so that the resultant is comprehensible. Gorey details aside, it seems that these two proposals for when such quantified sentences make sense serve as two desiderata.


2. Explain how this is so: we need the first to make sure that our statements are about something, the second to make sure we have the right sort of conceptual link to that which we speak about. But more importantly, it seems that straightening out the semantic uniformity thesis might go some way toward saying what problems we migh face in the attempt to defend conventionalism. In other words, we need a semantical system in which to establish uniformity. First we need to consider how the semantic uniformity might go. We should settle on a compositional theory of meaning (like a worked out version of Davidson's).


3. Then we must consider the conceptual side of things. How is it we know something modally relevant to a claim if we know certain special names of things? There are two issues here one concerning predicates the other concerning singular terms. It seems that the predicate issue deals in a question of concepts. On a certain theory, we can say that to possess a concept is to know every counterfactual situation in which it's appropriate to deploy that concept. And so knowing the modally relevant features of predicates (which express these concepts) comes along for free on this view. This sort of view allows one to say when a sentence of the form 'φ(t)' is true given that one has the correct conceptual content associated with the singular term 't'. Of course, that leads us to the question of having the right sort of conceptual content associated with the singular terms. And here we have some options. Gareth Evans' description names, Kaplan's standard names and Ludwig's description names. There are problems with each of these of course, and using each we don't name as many things as we'd like and so there are problems. But on each sort of view, we see why problem with a conventionalist thesis has trouble and it turns out that these trouble spots are exactly the places where our intuitions about modal claims in general seem to break down, so there's some evidence for the conventionalist thesis.


4. If one agrees to Fine's semantic uniformity requirement for quantified sentences, then it seems that other systems of semantics (i.e. 2d semantics) may needlessly conflate conceptual and metaphysical requirements. An interpretative truth theory can make sense of semantics without positing anything like truth makers. Once we've separated the analytic (or meaning) requirements for making sense of a quantified sentence from the conceptual requirements, we can see how a quantified sentence might be intelligible yet so without being known to be so (or at least without being known to be true). On the 2D picture, we become confused because we think that the unintelligibility (or untruth) of a certain sentence has some bearing on a certain metaphysical status (what some possible world is actually like). This seems to be a confusion that we can make sense of with the Fine / Ludwig view of semantic uniformity and conventionalism.

Maybe we could approach this in another way.

1. Claim that we must be able to make sense of quantified sentences which contain modal contexts if we're to be able to start forming a conventionalist thesis. Of course, we need to understand quantification into opaque contexts for other reasons, but we need to be able to make sense of '(∃x)φ(x)' to even begin an explanation of modality in conventionalist terms.
   


2. Claim that both of Fine's desiderata must be satisfied if we're to get the conventionalist thesis off the ground. The first was that in order for us to claim that a quantified sentence is intelligible, there must be a proper instance of such a sentence. If quantification is referential, then a proper instance must be such that the singular referring term which is the substituend is purely referential. The second was that there be a special class of names such that one can tell by meanings (or play of concepts) alone that an instance of the quantified sentence is true.
   


3. Argument for the first desideratum: there must be semantic uniformity between a quantified sentence and its stances if we're to make sense of the quantified sentence. Why? Assuming quantification is referential the variable serves only as a pointer to its values, so then for the quantified sentence to be true there must be a value which is in the extension of the predicate that is picked out by the context in the sentence. But it seems like this will be the case only if there's an instance of the sentence in which the singular referring term in the same context is purely referential. We need semantic uniformity to make certain we're actually talking about the things we assume we're speaking about. If one makes the claim '(∃x)φ(x)' we want to be guaranteed that there is in fact something that is referred to by some 't' such that 'φ(t)' is true. Without semantic uniformity, it doesn't seem like we'd be sure that we'd be expressing what we wanted to express in the quantified sentence.
    There must a semantic theory in which we make these assessments. We have options. I have in mind either an interpretive truth theory style of meaning or some sort of possible world semantics. Perhaps we can a bit about how to insure semantic uniformity on each of these views. It seems like this would come down to giving the appropriate reference and predicate clauses on an interpretive truth theory style of meaning theory, and finding the thing actually referred to on a possible world semantics picture.
   


4.  Argument for the second desideratum: conceptual content. First off, we need to meet a challenge that is posed in Fine. Fine asserts that it's likely that an interpretation of quantified sentences in which their truth is determined by whether there exists a class of special names one of which could be used to create a substitution instance the truth of which is determined by the conceptual content associated with the special name and the remaining context of the instance will be such that quantification is referential. The reason is that the truth of substitution instances are determined by the conceptual content of the substituend rather than that which is pointed to by the referent. Recall that semantic uniformity and referential quantification was possible only if the singular terms of the resultant were purely referential. The substituends of the quantified sentence made sense of in terms of special names are guaranteed to have associated conceptual content, and so it seems that they can't be purely referential. If we want to hold on to both desiderata, we need to argue that the two requirements can be reconciled. It looks like one way to do this is in the context of the reference axioms of an interpretive truth theory. Reference is direct in light of the reference axioms, yet the names of the referents bear certain relations to each other based on how the referents are related by these axioms (I'm thinking here of ref('0') = 0 and ref('1') = successor(0), etc.). This could be spelled out in more detail. The important thing to note is that direct reference can be maintianed and there is some conceptual content to be had in virtue of the relations borne to each other by those which are referred to systematically by reference axioms.
    Can we make sense of the conceptual "special names" requirement (I'll call it the "conceptual requirement" for now on) in terms of a possible world semantics? I'm not sure -- I'll have to think about this one.
    We can (and need to) say more about the conceptual requirement on the interpretive truth theory choice. I have in mind saying more about the conceptual content associated with both singular referring terms and predicate terms. We've had the example of the numerals as singular referring terms which have associated with them the conceptual content needed to determine the truth of relevant modal claims involving them. Kirk Ludwig proposes "description names" as those which are directly referring with the appropriate conceptual content. There are other theories about how this might go with regards to names: Kaplan, Evans, Follesdahl, Kripke, etc.
    There is also a story to be told about the conceptual content associated with "contexts". Predicate terms are given their own sort of application axioms in the interpretive truth theory. We might also hold the view that to possess a concept is to know all the modally relevant situations in which to deploy that concept. This sort of view would provide the right sort of conceptual contents to be associated with the predicates that create the contexts of the sentences we're interested in.
    Finally, we might offer a refinement: we need only a theory of meaning based on a theory of truth with definitive reference axioms. The conceptual content is really just an add-on, we could do all the work we needed with only singular term axioms and predicate axioms. We could take a different view of concepts and still be left with this picture.. What's the possible world semantics analogue?
   


5. Adjudication between my proposal for conventionalism and 2D semantics. It seems that 2D semantics muddies the waters a bit and makes more committments than we need.