1. Davidsonian Metasemantics: Quantification over Meaning Theories
On a broadly Davidsonian metasemantics, one aims to give a theory of meaning (cast as a compositional truth theory) for the idiolect of some particular speaker, let's say Kurt.
The central point I want to emphasize is that what one actually gives is a theory: a set of axioms. (It is not so important what the details of this theory are, or even whether it is a truth theory as opposed to an assignment of intensional meanings---the sort of thing about which Quinians and Davidsonians tend to be sceptical).
So long as everything goes ok, the axioms of this meaning/truth theory then logically imply Tarski-style T-sentences such as:
(i) "Es regnet" is true when uttered by Kurt at time t if and only if it is raining near Kurt at time t.These T-sentences of the truth theory are then tested by comparing them with more observational sentences which express the conditions under which the speaker hold-true the various sentences.
(ii) Kurt holds true "Es regnet" under circumstances that it is raining nearby.I've called these statements of U-facts, for "usage facts". In this context, we can call them HT-sentences. The two kinds of statement here---the T-sentences of the truth theory and the HT-sentences recording the U-facts---are to be logically connected by a Principle of Charity: maximise the degree to which the sentences held true by Kurt are true (on the theory being tested).
On a Davidsonian conception of metasemantics, the two main features I want to focus on are:
(D1) The semantic theorist is quantifying over meaning (truth) theories proposed for a particular speaker.2. Lewisian Metasemantics: Quantification over Interpreted Languages
(D2) The U-facts select the "right" theory via a Principle of Charity.
The Lewisian approach is conceptually quite different. On the one hand, one may describe all sorts of interpreted languages which may or may not be spoken by a speaker. These languages are, to all intents and purposes, abstract entities. The status of semantic theory is then quite different, for the description of an interpreted language consists in definitions and stipulations: a language $L$ may simply be defined to be such that: the alphabet of $L$ is ...., the $L$-strings are ..., the referent of string $\sigma_1$ in $L$ is ..., etc.
For example, one might define a language $L$ such that:
(iii) the proposition that $L$ assigns to "Es regnet" in context C = the proposition that it is raining (in C).Now the problem of relating the language to the speaker is a problem of identifying which language the speaker speaks (or "cognizes", as I prefer to say). So, the U-facts are thought of as pinning down claims of the following kind,
(iv) Kurt cognizes $L$.How one does this is a rather complicated matter that I don't want to get into here. But, roughly, Kurt cognizes $L$ just when the meanings that Kurt assigns to $L$-strings are the meanings that $L$ assigns to those strings. (In fact, Lewis himself (Lewis 1975) gave a quite different analysis, in terms of social conventions, and disavowed the brief explanation just given.)
So, on a Lewisian conception of metasemantics, the two main features I want to focus on, corresponding to the Davidson case, are:
(L1) The semantic theorist is quantifying interpreted languages.3. Comparison
(L2) The U-facts select which language the agent speaks/cognizes.
In discussing this topic on several occasions in talks over the last few years (I've given four or so talks on this material since 2008) and with colleagues, I've mentioned that debates formulated in the Davidsonian approach can often be reformulated within the Lewisian one, and vice versa. But, even so, I think there are definite theoretical advantages to the Lewisian conception. I don't want to go into them here, as they're a bit convoluted, so will write about them at a later point.