Monday, June 16, 2008

A semantic trichotomy

MacFarlane presents a trichotomy within the discipline of semantics: presemantics, semantics proper, and postsemantics. MacFarlane understands presemantics as Belnap presented it in his article "Under Carnap's Lamp." Presemantics is a theory of the available semantic values and their relations. Linguistic expressions do not enter into presemantics, unless they are themselves some of the objects under consideration as possible values. In a phrase, the point of presemantics is to make it clear upon what truth depends. Semantics proper, in MacFarlane's words, "brings together grammatical and presemantic concepts to give an account of how the semantic values of expressions depend on the semantic values of their parts." (p. 187) Semantics proper is the more or less familiar enterprise of computing semantic values of large expressions or sentences from the values of their atomic parts. Read more

There seems to be a question as to whether semantics proper is supposed to be restricted to just compositional semantics.
If the parts of a sentence are all that one can use to compute the value of a sentence, then it would be restricted to compositional semantics. The phrasing given leaves open the possibility that the semantic value could depend on things in addition to the values of the constituent parts. On this broader reading would it still have to be recursive? I think so although I can't supply a good argument at present. It seems that the incompatibility semantics from Brandom's fifth Locke lecture, which is noncompositional yet recursive, fits into this picture. That would be an example.

Semantics proper imposes a constraint on presemantics by requiring that there be appropriate presemantic types to assign to the linguistic expressions. As MacFarlane puts it, the more expressive the language, the more fine-grained semantic values will need to be to preserve compositionality. (The phrasing here and a later discussion of postsemantics hints that semantics proper is supposed to be compositional.) This point interests me but it is unclear what the relation is exactly between expressive power and the grain of the semantic values. An example: to preserve compositionality in a language with the modal operators 'possibility' and 'necessity' we move from using just truth values using propositions as sets of worlds. However, if we switch to a tense logic, adding the binary operator 'until' increases expressive power but does not require more finely grained semantic values. As another example, the addition of an infinitary conjunction to a first-order language increases expressive power but doesn't require new semantic values. There seems to be some dependence there but it isn't straightforward. (As an aside, the notion of expressive power interests me a lot but I haven't found any extended discussion of it. There is some in Anil Gupta's Revision Theory of Truth and I've come across smatterings in different logical sources, e.g. Blackburn's Modal Logic. I hear there are some discussions in the paradox literature. I don't think I know of anything beyond those though.)

Postsemantics is the mediator between "the semantic values required for the purposes of compositional semantics and the fundamental semantic notions in terms of which the use of language (e.g., proprieties of assertion and inference) is to be explained." (p. 227) (This is the other place at which it seems like semantics proper is intended to be compositional.) There are two examples given that illustrate this nicely. In classical logic, postsemantics is what specifies implication. The compositional truth-values of sentences are not enough. A further stipulation, which is a part of postsemantics, that implication is truth-preservation from premises to conclusion in all interpretations is needed. The other example, due to Dummett I think, is that of multi-valued logic. Suppose one has a set of multivalues with a proper subset of designated values. The semantics provides for each sentence a multivalue that depends on the multivalues of its component parts. The validity of inferences from those sentences, however, depends not on the multivalues determined by semantics but on the designatedness of those sentences. This depends on the multivalues, but there are no operations directly on designatedness. Consequence is defined on designatedness, which is something that semantics seems not to be interested in. Postsemantics then gets to impose further restrictions on presemantics, e.g. by requiring presemantics to provide distinctions of designation. The other important role that postsemantics fills on this picture is that it is what is supposed to interface with pragmatics. This tantalizing suggestion is undeveloped. It would be probably be instructive to go through some of the philosophy of language literature to see to what extent this distinction is in play or could be drawn. I wonder how much of MacFarlane's postsemantics is incorporated into pragmatics elsewhere in the philosophical literature. Although, I'm not entirely sure how much pragmatics on this picture coincides with pragmatics as used, say, in Grice.

On MacFarlane's picture, presemantics and syntax feed into semantics proper which outputs some values. Postsemantics takes these values, possibly doing something to them, before passing them off to pragmatics. The interface between postsemantics and pragmatics isn't developed, so the rest of the paragraph is pretty speculative and rough. Is the directedness presented here required? Suppose one is a wild-eyed Wittgensteinian or someone with inferentialist sympathies. Then one would try to start on the pragmatics end of things. The natural interface would be postsemantics, which, while imposing some restrictions on presemantics, doesn't seem to say much about semantics proper. The discussion of Dummett following the introduction of postsemantics makes this clear. Starting with pragmatics or the use of a language would provide one with some material for developing a postsemantics. To some extent this might feed into a presemantics. It seems like it would only provide some points to check the semantics against: however the semantics is developed it can't contradict this stuff. That isn't much constraint. Although, if one wants to start at the pragmatics end of the picture (the literal picture is on page 188) one might be using a different sense of pragmatics. While there do seem to be some points of interaction, semantics and postsemantics seem like they can be developed independently although ideally there would be a nice story linking them. The values taken by postsemantics are already present in the presemantics, None of presemantics, semantics proper, or postsemantics determines either of the others. Although this paragraph started by describing the relationships between them with a definite order of dependence, this doesn't seem to be mandated. MacFarlane's ideas are then compatible with those of our Wittgensteinian friend. [Edit: This paragraph is admittedly a bit lame. I think my desire to use the phrase "wild-eyed Wittgensteinian" overwhelmed my sense for when a paragraph is sufficiently developed to show others.]

At the outset I said that MacFarlane presents a semantic trichotomy. I don't think MacFarlane anywhere claimed this was an exhaustive distinction, although things proceed as if it were. Prima facie it seems to be exhaustive. There are probably further distinctions to draw within postsemantics. The interface between it and pragmatics seems a little hazy. Even if it isn't quite exhaustive, the modularity of these distinctions is quite appealing and is put to some good work by MacFarlane.

No comments: