Thursday, June 05, 2008

Kaplan-contexts = Lewis-contexts?

According to Lewis (1980), a context is a concrete situation where a sentence could be said, to be identified with a spatio-temporally centered possible world. Lewis seems to interpret Kaplan-context as being things such as his, as opposed to tuples of features of locations (see p. 42 of the reprint).

And indeed Kaplan says the following in ‘Afterthoughts:’

“... we should say that context provides whatever parameters are needed. [Footnote: This, rather than saying that context is the needed parameter, which seems more natural for the pretheoretical notion of a context of use, in which each parameter has an interpretation as a natural feature of a certain region of the world.]” (p. 591, emphases in the original).

In so far as I remember, this interpretation seems to be, in any case, at least consistent with the formal system in “Demonstratives” (p. 543). Or am I wrong here?

5 comments:

Andreas said...

Hi Dan,

I guess I'm not seeing exactly what you mean by being consistent with the formal system.

In the formal semantics of Demonstratives a context is just defined as a tuple of elements of the sets of individuals, worlds, times and positions.

One might read 'provides' in the passage you quote in the following, lax way. When you want to model an utterance in the semantics, choose the parameters of the tuple which is used to represent the context of utterance in a way which corresponds to the facts about the (real-world) context of utterance. That just seems like obvious advice. If you want to model an utterance made by Kripke in NYC on 1/10 1980 in the actual world, then you should choose the parameters of the tuple as Kripke, NYC, 1/10 1980 and @. Right?

I guess what one might want to think about is the infamous requirement that we get in point 10 under the definition of a structure (p. 544), which restricts the set of contexts to those that are proper in the technical sense. Point 10 states that a formal context, i.e. a tuple, must be such that the agent is located at the time of the context at the world of the context. Of course, many have contested that this is a desirable requirement. I can see how one could read into the passage you quote (including the footnote) something to the effect that since, as seems obvious, any real-world utterance situation will be such that the utterer is located at the time and world of her utterance, there just couldn't be any formal contexts (tuples in the model) which failed to satisfy the propriety constraint. But then again, given the debate over this constraint, it doesn't look like it's as trivial as Kaplan might have thought it was.

On the other hand, it really seems as if the point Kaplan is making in your passage is just the small one that we should distinguish between model and modelled, i.e. between contexts qua tuples in the formalism and contexts qua real situations in which we use language.

Hope that makes sense.

Dan López de Sa said...

Hi Andreas!

In the formal semantics of Demonstratives a context is just defined as a tuple of elements of the sets of individuals, worlds, times and positions.

That’s what I don’t see, sorry if I’m being a bit slow. Here are the relevant clauses (p. 543):

2. C is a noneempty set (the set of contexts, see 10 below)

3. If c in C, then

(i) c_A in U (the agent of c)
(ii) c_T in T (the time of c)
(iii) c_P in P (the position of c)
(iv) c_W in W (the world of c)

So contexts are here required to provide the relevant four features: the very tuple of features would trivially do, but so would also do Lewisian contexts (this is what I meant by “consistent” in my original post).

Andreas said...

I don't see exactly what you mean. How exactly do you get your conclusion "contexts are here required to provide the relevant four features: the very tuple of features would trivially do, but so would also do Lewisian contexts" from clause 3?

As I read clause 3, it's just telling us what things are in C. If something c is in C, then it's got an agent which is in U, it's got a time which is in T, it's got a position which is in P, and it's got a world which is in W.

Or, in other words, anything not having one, or more, of these features isn't a context.

So far, there's nothing about the metaphysics of contexts, as far as I can see. What am I missing?

Dan López de Sa said...

As I read clause 3, it's just telling us what things are in C. If something c is in C, then it's got an agent which is in U, it's got a time which is in T, it's got a position which is in P, and it's got a world which is in W.

Or, in other words, anything not having one, or more, of these features isn't a context.


I agree. But Lewisian contexts do "have" all these four features (among plenty of others). That’s why, it seems to me, Lewisan contexts satisfy clause 3 and why Lewis’ interpretation of Kaplan-contexts as Lewis-contexts is at least consistent with the formal system in “Demonstratives.”

Andreas said...

Ok, now I think I'm starting to get it.

I still think, thought, that it's important to remember what Kaplan is trying to do, which is to give a formal semantics, i.e. a model, of how languages with indexicals work. (Cf. his aim to capture entailments and his notion of sentence-in-context.) When he gives definitions of truth-in-a-context, for example, the stuff which he's using is just formalism, abstract entities, i.e. sets, tuples, functions etc. Of course, you're right that ultimately what he wants to model are concrete real-life things, i.e. the situations in which we talk.

It's not clear, in general, though, that we should really think of what people call 'context' when they want to describe how words like 'I', 'that', 'here', 'now', 'she' etc. get to refer as concrete things. Are they collections of molecules? Can a collection of molecules determine reference? But I guess that's really a challenge for both Kaplan and Lewis.