Insensitive Semantics, Chp. 6

Welcome back! Time to report on our most recent meeting of our reading group, this one concerned with chapter 6. I presented, and my handout is available here.

Chapter 6 is concerned with arguments that have become known as binding arguments. The purpose of a binding argument is to show that a sentence (the “target sentence”) contains more material in its LF than one hears in spoken language or sees written down on the page. For example, a binding argument might be mounted to show that there is more to the LF of the target sentence many students failed than meets the eye (ear), by pointing to an example like.

1. In every class, many students failed.

That sentence has at least one reading on which it says that in every class, many students in that class failed. The fact that (1) has that reading is supposed to show that in (1), there is an extra constituent in the LF of the clause many students failed. Roughly, the LF of (1) might look like [In every class x] [many students in x failed]. Binding arguments then draw the further inference that a similar constituent is present in the target sentence, so that the LF of the target sentence is roughly many students in x failed, where x somehow needs to be assigned a value.

C&L point out that this argument, by itself doesn’t establish that the target sentence is context-sensitive, since it at most shows that there’s an extra element to the LF of the sentence. It does not show that the interpretation of that extra element varies with context.

As C&L say themselves, that’s not a particularly deep observation, nor is it very controversial. The proponents of binding arguments, such as Stanley or Szabo don’t ever think that, by themselves, these binding arguments establish context-sensitivity. Rather, they’re one part of the argument for semantic context-sensitivity.

So the much more interesting aspect of C&L’s discussion is about whether a binding argument succeeds in its stated goal, and that issue has wider ramifications. The binding argument crucially wants to draw an inference about the LF of a sentence from the way quantification works in that sentence. And historically, the ability to handle quantification in language (natural or formal, for that matter) has been a huge point in favor of logical systems that could do it, and a huge point against logical systems that could not (see Frege vs. Aristotle). And the data C&L cite run counter to some very basic assumptions about how quantification and natural language are related.

The main argument C&L present is that the binding argument overgenerates: it seems to show that there are hidden indexicals where we should not expect any. Consider, for example, the sentence (2)

2. Everywhere I go, 2+2=4

C&L argue that by the lights of the binding argument, (2) shows that the sentence 2+2=4 contains an extra element in its LF, just as (1) shows that many students failed does. Thus, by the lights of that argument, the LF of 2+2=4 is something like 2+2=4 at x. And that seems kind of crazy.

When I first read that argument, I thought it was kind of silly. After all, there’s an important difference between (1) and (2). In (1), the interpretation of the subordinate clause many students failed varies as we consider different classes. If we interpret the quantifier using Tarski-style variants on variable assignments, then depending on what is assigned to x in the interpretation of For every class x, many students in x failed, the truth-conditions of many students in x changes. By contrast, in (2) we seem to say no more with the quantified sentence than we already do with the unembedded 2+2=4. That sentence, by itself, is true iff everywhere and everywhen, 2+2=4. Hence, for all that our intuitions about truth-conditions require, the LF of (2) might be (3).

3. For all places x, if Sally goes to x, then 2+2=4.

And in that case, we can accommodate the reading of (2) without positing a place-variable in the target sentence 2+2=4.

However, if we look closely at the text of C&L at page 74, we notice their remark that the reason we have to posit a place variable in 2+2=4 that is bound by everywhere I go is not in order to account for the truth-conditions, but in order to satisfy a syntactic constraint. As they say, if we did not posit such a variable, the quantifier would have nothing to bind. And that in turn would violate a pretty widely adopted constraint on the licensing of binders such as quantifiers, wh-phrases, etc. Generally, binders are unacceptable if they do not bind anything (for references and examples, see the
handout on page 2).

So what the examples that C&L mention really show is not so much a problem in one subsidiary argument about context-sensitivity. Rather, they show that widely accepted constraints on syntactic well-formedness, together with assumptions about the syntactic realization of quantification in natural language, lead to deeply weird consequences.