I've been away for a while and didn't get the opportunity to read Jason's posts until last night. Since I have a great deal of respect for his work in philosophy of language and linguistics, I feel that I should at least make an attempt to clarify my position in light of his comments.
First, I want to reiterate that I am here taking it as a background presuppostion that construction-level effects are unavoidable in a general theory of language. Although the way I have cast this claim (in the jargon of constructions) makes it appear controversial, I don't think it is. All I want to claim is that lexical semantics is insufficient for determining the semantics of complex strings and that whatever else is needed is itself part of semantics. So, for instance, knowing the semantic interpretation of 'a', 'R', and 'b' in the string 'aRb' is insufficient for determing the proposition expressed by 'aRb'. In addition, we need to know (minimally) whether sentences of the for of 'aRb' are to be interpreted as 'a stands in R to b' or as 'b stands in R to a'.
Now what I want to claim is that if you want to be a construction grammarian of a more robust sort, this little bit of (largely) uncontroversial semantics gives you a pretty solid platform on which to stand. The reason is that the need to take into account the form of the string 'aRb' in interpreting it implies right at the start (as it were) that languages have resources which satisfy the Construction Grammarians definition of a construction. To my mind, this shows that languages have [must have? --not quite!] the sorts of construction-level resources that Construction Grammarians claim they have.
Of course, Construction Grammarians want more than this from a construction-based grammar. And, in my opinion, it is in their attempt to push such resources past the uncontroversial point that they have (potentially) made a significant contribution to philosophical semantics. As I see it, that contribution is the insight that there is no principled distinction between minimal and robust constructions. A construction is minimal only if its semantic contribution is minimal; it is robust only if its semantic contribution is robust. I have no general take on what a minimal (robust) semantic contribution is; in fact, I doubt a principled disintction can be drawn here either. But we might start (as perhaps Montague did) with an extreme minimalism according to which constructions never contribute anything beyond function-application (or, predication) relations. A still minimal, but less minimal, view might (following Geach) allow constructions to introduce function-composition as well as function-application. At the opposite extreme, robust constructions might contribute such semantically nontrivial relations as causation or intentionality.
Now if Construction Grammarians are right that there is no principled distinction between minimal and robust constructions (so that we can retain the former while throwing out the latter), then constructions themselves become a possible source of semantic richness. And it is here that an interest in linguistic constructions begins to lock horns with linguistic theories that posit rich underlying logical forms, especially when those logical forms are being posited primarily in order to account for semantic richness rather than, say, grammaticality judgments. At this point, then, I have simply tried to sketch a view according to which constructions themselves might provide an alternative explanation of semantic richness.
In my last post, I was wondering why philosophers of language (and, to a large extent, linguistic semanticists) had opted for the LF account rather than the construction-based account. [Last time I said "suckered". It was a poor choice of words, but I didn't intend anything derogatory. I was trying to convey the idea that the LF approach was tempting to the point of making philosophers blind to alternatives.] I suppose that there are lots of reasons. One, as Jason notes, is that most philosophers have been exposed to and convinced by the arguments for a fairly robust level of LF. But I wonder if the temptation of the LF approach isn't at least greatly enhanced by its resonance with the Fregean view that our grasp of propositions is necessarily mediated by sentences.
In retrospect, I think that part of my interest in the question was this. If Frege's thesis locates an appealing picture about the structural relations between forms and meanings in language, might not that picture actually provide a presumption in favor of the LF approach (i.e., in favor of only minimal constructions)? I don't mean to insinuate that there are currently a lot philosophers out there today who accept Frege's thesis, most I would guess reject it. But I, at any rate, do find that Frege's thesis has some intuitive pull. And so, even if we reject the thesis, might it not still have a tacit indirect influence on which alternative we favor?
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