chapter 1: conventionalism in the service of analyzing necessity in terms of analyticity

I'm not sure what will survive from outline 2.2.2, but I've decided that I should probably just go ahead and work as if the outline had been accepted. So with that brief introduction, I jump into hypothetical Chapter the First.

Chapter 1. Conventionalism as presented in Carnap's Meaning and Necessity and explicated and defended in Ludwig, Sidelle and Thomasson.

 So what's Carnap's main thesis? I'll give it in the brief and ready and omit much of the argument he gives for why we should prefer his theories to competitors. For a semantical system (essentially a formal language with formal semantics), we can understand each term of the system as having an extension and an intension. Specifically, the extension of the singular referring term 'Walter Scott' is the individual person Walter Scott; the extension of the predicate 'blue' is all actual and only actual blue things; the extension over which a variable ranges are individuals in the domain of discourse. It's a bit unclear what exactly the intension of such terms are. But it seems that Carnap comes to the answer in round about fashion. By talking about what's true as a matter of how the world has turned out to be and what's true independently of how things just happened to be. If the statement s is 'Pa' where 'P' is a predicate term and 'a' is a singular referring terms is true it may be so as a result of happenstance, on the other hand if s₁ is 'Pa₁' is L-true, then the truth of this statement is independent of how the world happens to be. Carnap claims that the truth of s₁ is a matter of meaning alone or has to do only with the semantical relations of the system under consideration. Perhaps in the modern idiom, we could rephrase Carnap's assessment model theoretically. If s₁ is true "come what may" then we could say that it's true in all models -- another way of saying that it's truth doesn't depend on the particular admissible assignment of properties to the individuals of the world. So, for instance two singular referring terms ('a' and 'b') have the same intension if the statement 'a = b' is L-true. Two predicate terms ('is-human' and 'is-a-rational-animal' is Carnap's well worn example) have the same intension iff the statement '(∀x)(is-human(x) ↔ is-a-rational-animal(x))' is L-true. If we can make sense of this implicit definition of intensions, then the intensional values over which variables are said to range can be contrasted to the extensions over which variables range.
 There are intensional and extensional contexts. Extensional contexts occur in statements in which only the extensions of those terms which occur are relevant to the truth value of the statement. In extensional contexts, coreferring terms may be substituted salve veritate. On the other hand, in intensional contexts substitution salve veritate is guaranteed possible only for L-interchangible terms (that is terms which are interchangibility preserves L-truth). (§ 11-12) On Carnap's view, there are contexts which are neither extensional nor intensional. An example of this is a belief sentence like, 'John believes that D'; we're not necessarily guaranteed that we can substitute salve veritate an L-equivalent term 'D₁' for 'D' in this sentence. (§ 13)
 A crucial chapter looks to be V (p. 173-204). The extremely short version is summarized in 39-1: "For any sentence '. . .', 'N(. . .)' is to be true iff '. . .' is L-true'." This seems to be the crux of the matter. Because the rules for 'N' are simply semantical rules of the system S₂, as an easy consequence, we see that if 'N(A)' is a true sentence of S₂ then so is 'N(N(A))' because since 'N(A)' is true it must be true in virtue of semantical rules alone and so 'N(N(A))' is true also.
 Carnap asserts (180) that since a modal system involves intensional as well as extensional contexts, it might be easier, when dealing with the domains over which variables range, to think of the intensional values of variables. That is, we should think of variable as ranging over the individual concepts that are the intensions of singular terms. But to make progress we must take all individual constants in S₂ to be L-determinate -- this means that they can be paired 1-to-1 with individuals in a well ordered matrix.

 What's happening on pages 180-1? We have a definite description U_i and a state description R_n. (The state description is just a denumerable class of sentences which describe the distribution of properties across individuals.) The question of whether any individual is picked out by U_i is "simply a logical question" given our assignments. "Thus the description U_i assigns to every state description exactly one individual constant; any individual constant may be assigned to several state descriptions." If there is no individual that is so picked out by U_i, then 'a*' will be the individual constant that is picked out. If another definite description, U_j, is L-equivalent to U_i then U_j will assign the same individual concept under the same state description and these two things will express the same individual concept given that there are L-equivalent. So, the crucial conclusion is that, "we might say that an individual concept with respect to S₂ is an assignment of exactly one individual to every state (which is a proposition expressed by a state description)". Because of the stipulation that individual constants are L-determinate (unambiguous), we can claim that there is a function from world states to individual constants (I'm not really sure what form these would take the idea seems to be that we can assign (some disparate) individuals which satisfy a definite description to each state description, so it seems like there will be an individual concept for 'the tallest mountain in the world').
 There is a treatment of variables of higher order, too. Propositions can be reasonably represented by world-states. For example, the proposition expressed by the sentence 'the book is on the table' could be understood to be the set of all world states in which the book is on the table. Since the attribution of a property to an individual is essentially what makes a proposition, and propositions are represented by world-states, we can think of properties as maps from classes of world-states to individual constants. If we clumsily represent a certain proposition as 'Pc' (something like 'c is P'), then the proposition is just a class of world-states, and this class of world states is determined by seeing in which c is P. So it makes sense to say that the properties can be thought of the pairing of classes of world states with individual constants such that the proposition 'Pc' is true. Perhaps we can think of the property 'P' as an map from all classes of world states to individual constants, such that for a class of world-states c, such that the individual constant ic has property P, then P(c) = ic. Two-place relations can be represented by assignments of ranges to ordered pairs of individual constants.

On pages 181-3 it seems that Carnap takes individual concepts to be "paired" with definite descriptions, and so for different world-states, the individual concept is associated with possibly different individual constants. It's easy to see how a conventionalist view could get going in this sort of semantic set up, in which those picked out by rigid designators don't even feature in sentences of a semantic system.

How plausible are rigid designators for natural kind terms? We might hold that they're not even names at all and so there's no purchase for rigid designation.

Where with Chalmers? Chalmers has appropriated Carnap and tried to adapt Kripke to that...

 [more from Carnap here]

 [Sidelle here]

 [Thomasson here]

 [Ludwig here]

We can't even secure reference without some sort of relations holding between those things which we pick out in the act of the refernce. NO differentiation would be possible is there weren't differential relations borne among those things we want to indicate. So the idea of reference without some sort of differential relational properties is misbegotten.

As far as the first desiderata is concerned -- how do we even determine the truth of a statement like 'φ(s)' without (1) having a good idea of differentiated reference, (2) using the differential relational properties had by those things we manage to pick out to determine this truth.

<-- part B here -->

[Fine's desiderata here]

May want to add a bit about why on the sort of semantical system Carnap has in mind both desiderata are satisfied. Semantic uniformity is satisfied because the systems S, S₁ and S₂ have formal syntax and semantics -- they're syntactically and semantically perspicuous in Fine's terms. And the right core content is satisfied because semantic values are assigned to designators in S, S₁ and S₂ by semantical rules which it, seems reasonable to suppose that we have epistemic access to. In other words, it seems that both of Fine's desiderata are satisfied by the system Carnaps has set up for us. So, I guess part of the project can be seen as the effort to make natural language seem more like the semantical systems of Carnap.
 Given Carnap's presentation, why is Fine worried about semantic uniformity for referential quantification and right conceptual content being at odds? It seems that the Quinean idea that it's incoherent for variables to range over intensions.

  Here is chapter one as of 27 April 2006.