Contexts and their Centers

According to David Lewis (1980), in order to capture how the truth of a sentence depends on features of contexts and its contribution to the value of longer sentences in which it is embedded, we need a semantically basic two-dimensional relation of a sentence s being true at a context c at an index i. A context is a location—time, place, and possible world, or centered world for short—where a sentence might be said. It has countless features, determined by the character of the location. An index is an n-tuple of features of context, but not necessarily features that go together in any possible context. Thus an index might consist of a speaker, a time before his birth, a world where he never lived at all, and so on. The coordinates of an index are features that can be shifted independently, unlike those of a context, and are used to systematize the contribution of sentences embedded under sentence operators, such as ‘possibly’ or, more controversially, ‘somewhen,’ ‘strictly speaking,’ and so on. Given a context c, however, there is the index of the context, i_c: that index having coordinates that match the appropriate features of c. Hence the basic two-dimensional relation can be abbreviated in this special case: sentence s is true at context c iff s is true at context c at index i_c.

According to David Chalmers (2006), there is a contextual understanding and an epistemic understanding of two-dimensional semantics. Although I am not familiar with the details of “this monster paper” (so described by his author ;-{)}), it seems to me clear that the Lewisian should be counted among the “contextual understanding” approaches, if any does: “the first dimension represents possible contexts of utterance, and the intension involved in the first dependence represents the context-dependence of an expression’s extension” (Chalmers 2006, p. 65) (This is not to say that it cannot be count as also being among the “epistemic understanding” approaches, but never mind this now.)

Notice, however, that Lewis’s contexts are worlds centered at spatiotemporal points, which may or may not be occupied by linguistic tokens, utterances thereof, thoughts, or whathaveyou. Thus, for Lewis, contexts are locations where a sentence might be uttered, but not necessarily locations which contain any utterance of any sentence. (Thus the models for contexts offered in (Chalmers 2006, p. 66) are not appropriate in general.)

One of the two general problems David Chalmers identifies against the contextual understanding of two-dimensional semantics concerns precisely the need to evaluate sentences such as ‘Language exists’ as false with respect to language-free contexts. Thus it seems to me to be directed only against particular versions of the contextual understanding which, unlike Lewis’s, restrict themselves to contexts with specific linguistic/mental centers.

Am I wrong? And anyway is there any reason why, on the contextual understanding, one should so restrict the contexts, against Lewis?

(I think Oscar will be arguing for such a restriction at the LOGOS Seminar. Maybe he’ll also share his reasons here…)