Kamp’s actual example

In class today I presented the following example:

(1) Once everyone now alive hadn’t been born yet.

I attributed the example to Hans Kamp’s paper “Formal Properties of Now“. This attribution is incorrect. The example Kamp uses to make the point that we need a second time parameter to fix the reference of now is the following:

(2) A child was born who will become ruler of the world.

The idea here is that there is an existential quantifier with two restrictions (child and will become ruler of the world). Because of the time reference of the predicate child we want the existential quantifier to have scope under the PAST tense. But then the predicate will be ruler of the world would be counting forwards from that past time rather than from the utterance time, as it intuitively does. So, Kamp’s formal solution posits the two time indices that we talked about today and then he says that there is a covert now operator on the embedded expression x become ruler of the world.

The example (1) I gave I reproduced partly from memory and from Bob Stalnaker’s brief mention of it in his seminar yesterday. It turns out that something like (1) occurs in the literature but is attributed to Frank Vlach’s dissertation (1973, also UCLA). I currently have no access to Vlach’s dissertation but Johan van Benthem cites him for the following example:

(3) One day, all persons alive now will be dead.

This one might treat as having the following semantic structure:

(4) FUT all (\lambda x. now (x alive)) (\lambda x. x dead)

Again, it seems obvious that the sentence has a reading where we are talking about one future time t’ at which everyone who is alive at the time of utterance is dead. This would give the same argument for double-indexing as the example (1) we used.

Tim Sundell just pointed out to me that there is a problem with (1), which also applies to Vlach’s (4) but not to Kamp’s (2). Tim’s point is this:

We all hear (1) as potentially ambiguous, depending on the relative scope of the existential quantifier over past times — contributed by once (together with all the funky morphology) — and the universal quantifier over individuals now alive. We saw that for the argument for double-indexing to go through, we had to focus on the “surface scope” reading where the claim would be that there is one past time at which everyone now alive hadn’t been born yet. It seems clear that the sentence has such a reading. But, Tim correctly points out, the two scopings actually have the same truth-conditions! If for everyone now alive there is a time at which they weren’t yet alive, then one just takes the relevant time before the birth of the oldest individual in the bunch and voilà! one has the one time at which all of them weren’t born yet. Put another way: try to come up with a situation where one of the scopings makes the sentence true and the other doesn’t — you will find that this task is impossible.

So, does that make (1) unsuitable to make the argument for double-indexing? It is certainly less suitable than Kamp’s actual example (2). In the end, (1) may still work but one would have to show that the scope PAST > everyone now alive is actually available and receives a sensible interpretation. That won’t be easy. Danny Fox has in his book (pp. 70ff.) an example that has the same feature that the two scopings converge in their truth-conditions, but he then provides indirect evidence that both scopings exist:

(5) In our class that consist of 40 students, at least one girl is taller than every boy.

So, one could rescue (1) from irrelevance by using Fox’s kind of evidence to fix the scope of the universal quantifier to below PAST tense and then observe that now still picks up the speech time. But that’s probably too much bother. In any case, as Tim mentioned to me, it is very interesting that we can have strong intuitions of scope ambiguity even with sentences where the two scopings are equivalent.

It is not very hard to fix (1) to make examples that do make the point for double-indexing:

(6) Once everyone now in this room was wearing a hat. (7) Once nobody now alive had been born yet.

(6) clearly has a reading where it claims simultaneous hat-wearing at some point in the past, which is truth-conditionally distinct from the weaker claim that for everyone there is a (potentially different) time in the past at which they wore a hat.

(7) has a sensible reading where it makes the same claim as (1), but here the wide-scope reading for nobody now alive would make the absurd claim that for none of us who are now alive is there a time in the past at which we had already been born.

So, (6) and (7) can be used for the argument without the worries that (1) and (3) raise.

Note finally that the example we used to argue for double world-indexing is also immune from this worry:

(8) It might very well have been that everyone actually here was somewhere else instead.

Here, the truth-conditions of the two scopings clearly diverge, depending on whether there is one possible world where everyone is somewhere else.

I made (8) up this morning. Examples like this were discussed by Crossley & Humberstone (1977) but I don’t have a copy of that here. Max Cresswell (1990) uses:

(9) It might have been that everyone actually rich was poor.

which works just as well as my (8).

REFERENCES

  • M.J. Cresswell: 1990. Entities and Indices. Kluwer.
  • J.N. Crossley and L. Humberstone: 1977. “The Logic of Actually“. Reports on Mathematical Logic, 8, 11–29.
  • J.F.A.K. van Benthem: 1977. “Tense Logic and Standard Logic”. Logique et Analyse, 80, 395-437.
  • Danny Fox: 2000. Economy and Semantic Interpretation. MIT Press.
  • Hans Kamp: “Formal Properties of Now“. Theoria, 37, 227-273.
  • Frank Vlach: 1973. Now and Then: A Formal Study in the Logic of Tense Anaphora. PhD Dissertation. UCLA.

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