July 10, 2004

Trapped on a toastless scope island

Eric Bakovic writes here about  Charles Harrington Elster's the slippery piece of toast that always hits the floor jelly side down. Eric says that:

No matter how many pieces of toast Elster has managed to get his readers to round up in their collective imagination always does not quantify universally over a set of objects, even if it tries to do so indirectly by quantifying universally over a set of events associated (one-to-one) with those objects.

And Eric's right that Elster's slippery NP fails to quantify over pieces of toast in the right way. But why? Is it because in general always cannot quantify over objects, or because there's something amiss with the particular structure Elster used?

The semantics literature contains loads of evidence that always (and this applies also to other quantificational adverbs, such as never, usually, sometimes) does not simply quantify universally over times, but can quantify over events, or even situations. The best known reference is David Lewis (1975, "Adverbs of Quantification", In E. Keenan (ed.) Formal Semantics of Natural Language, CUP, 3-15), but more recently there is Kai von Fintel's 1994 UMass dissertation and work of Schubert & Pelletier, Mats Rooth, Ariel Cohen and many others.

Why should we think always can quantify over objects? The following examples should show you why:

 I always shoot cats (/a cat) on sight.
 [Meaning: for every cat I see, I shoot it. I'm an avid cat photographer you see.]

 Mary always beats me in a game of ping pong.
 [Meaning: for every game of ping pong I play with Mary, she wins.]

 If a farmer owns a donkey, he always beats it.
[Ahh, donkeys. Semanticists at least since Geach love donkeys, and I'm sure the above sentence has come up in a bunch of places. Everybody should read what the inimitable Larry Horn says about donkey sentences here.  Anyway, the example above means something like: for every for every farmer and for every donkey owned by that farmer, the farmer beats the donkey. At ping pong, presumably.]

Lewis famously argued that what always quantified over was what he termed cases, bunches of individuals tied together in some situation. That is, the claim is not that always does not have a temporal quantification reading, as in W.C. Fields I always keep a supply of stimulant handy in case I see a snake--which I also keep handy. The claim is that sometimes always (and sometimes too!) quantifies over cases. There's a lot more to say about how we decide what always quantifies over, since there's some really fun pragmatics involved, but I'll tell you more about that in a separate post. For now, I'll just comment on why always can quantify over cats, games, farmers and donkeys but not easily over toast in Elster's example.

The problem with the slippery piece of toast that always hits the floor jelly side down is that the quantificational element always occurs in a relative clause, and the variable for the piece of toast is introduced in a higher clause. Semantically, the structure of the NP is something like this:

the x [slippery(x) & toast(x) & RC]

Here RC is the meaning of the relative clause, which could be represented as:

for every e ([e is an event of x with jelly hitting the floor] implies [e is an event of x hitting the floor jelly side down])

The problem is simply that relative clauses, as has often been observed, are what we term scope islands: I've put a quick guide to scope islands and scope terminology in the yellow box below. An operator (like always) within a relative clause does not like to take wider scope than operators outside the relative. So it seems Elster's problem is not that he doesn't understand the meaning of always, but that he formed a relative clause a tad sloppily, leaving within it an always that couldn't quite perform the function that he might have expected it to. Then again, we might hypothesize instead that Elster really is the sort of guy that repeatedly drops the same piece of toast over and over again, and supposes that this is the sort of everyday experience with which his readers will empathize. Ceteris paribus, I prefer a theory in which we simply assume Elster said what he meant, but unfortunately we don't have so much as a single sticky crumb of evidence to go on.

By the way, here's my theory of toast. Toast will tend not to fall horizontally since it is aerodynamically unstable in this configuration. As a result, in flight (and this could also be a result of initial angular velocity) it will tend to head towards a vertical orientation while dropping. The momentum built up during this manoeuvre will normally take it slightly beyond the vertical equilibrium position. The toast is just about to compensate for this over-rotation when SPLAT. It hits the floor close to the vertical, but tilted slightly onto the butter/jelly side. After that, bad news is inevitable. So here's my advice to Elster, apart from being more careful with his relative clauses. You have three options:
  1. Eat the toast upside down, with jelly initially underneath
  2. Eat very close to the ground, so that the toast does not have time to make even a quarter rotation. Eating very high up may also help.
  3. Sandwiches, you fool!

A Quick Intro to Scope Islands

Here's a simple illustration of the scope island effect:

(1) A diplomat visited every country

Example (1) can mean either that there was a diplomat, and that diplomat visited every country or that every country was visited by some diplomat or other. In the first case we say that a diplomat has wide scope over every country (and conversely that every country takes narrow scope), and in the second that every country takes wide scope.

(2) A diplomat who visited every country was exhausted.

In example (2), a diplomat must take wide scope over every country, because every country is in a relative clause, and a relative clause is a scope island. So (2) can only mean that there is a diplomat and that diplomat visited every country and was exhausted. it cannot mean that for every country there was some diplomat or other who visited that country and was exhausted.

Posted by David Beaver at July 10, 2004 04:46 PM