[This is the first in what I hope will be a series of occasional entries in which I will exhibit a famous example sentence and explain why it is famous. Kind of like a history of semantics in 42 examples. Mostly, I will pick examples as they crop up in my teaching or writing. That is the case with today’s example, which was relevant in the seminar I’m currently teaching with Sabine. What follows is an elaboration on my class notes.]

When one looks at a sentence like Grijpstra is playing the drums again, it makes a lot of sense to think that the sentence conveys two propositions: that Grijpstra is playing the drums and that Grijpstra has played the drums before. The first proposition is asserted as the new information, while the second proposition somehow has the status of old news, as being taken for granted, as presupposed. And so, it makes a lot of sense to think that it is a good idea to build a system of semantic interpretation that assigns to a sentence two separate propositions, its assertion and its presupposition. Perhaps the best known such system was developed by Lauri Karttunen and Stanley Peters in their seminal 1979 article “Conventional Implicature” (why they used that term rather than “presupposition” is an obscure story of its own).

After 52 pages of carefully devising a two-dimensional architecture for presuppositions and after giving an appendix with painstaking logical rules for their system, Karttunen & Peters drop a bombshell in the form of a one-page “note”. They note that their system cannot deal with the sentence Someone managed to succeed George V on the throne of England, which they observe is an odd thing to say. Their system correctly predicts that the sentence asserts that someone succeeded George V to the throne, but it incorrectly predicts that the presupposition is that it was difficult for someone to do that. If their predictions were correct, there should be nothing wrong with the example, since someone did succeed George V and since doing so was difficult (in fact, impossible) for anyone else.

Karttunen & Peters conclude that their two-dimensional system needed fixing by finding a “way of linking the choice of a person who is implicated to have difficulty to the choice of a person who is asserted to have succeeded”. They expected that this deficiency would be “remedied through further research” but that the task would not be “a trivial one”. In fact, they point out that “the problem arises directly from the decision to separate what is communicated in uttering a sentence into two propositions”. So, their note and their example spelled doom for two-dimensional approaches to presupposition.

One possible defect in their example is that it uses the presupposition trigger manage and it turns out to be quite hard to figure out what manage presupposes. Karttunen & Peters cite an article by Linda Coleman (“The case of the vanishing presupposition”) in the proceedings of the first annual meeting of the Berkeley Linguistic Society, which shows that the presupposition of manage is rather elusive. It turns out that Coleman’s proposal is perhaps the first place something like the Strongest Meaning Hypothesis was proposed. She argues (roughly) that manage has a set of progressively weaker meanings and that in any given occurrence the strongest sensible meaning is perceived. (Coleman’s paper is quite properly cited – although with the wrong title – in the seminal paper on the Strongest Meaning Hypothesis by Mary Dalrymple, Makoto Kanazawa, Yookyung Kim, Sam Mchombo, and Stanley Peters, the same Peters as in Karttunen & Peters.)

There is a perhaps not unreasonable reaction to the particular example using manage that would explain its oddness without dooming the two-dimensional set-up. Perhaps, manage simply presupposes that its complement is something that is difficult to do, that is, it simply presupposes something about the verb phrase without connecting to the subject at all. Perhaps, what is odd about their example is that succeed George V on the throne of England is simply not difficult (for the relevant people) or the question of difficulty just doesn’t arise for that property.

In any case, the problem can be illustrated with other examples. In fact, there is another famous example in this story. When Irene Heim in her 1983 WCCFL paper “On the Projection Problem for Presuppositions” turns to the problem, she uses a different example sentence (without any comment as to why): “Karttunen & Peters (1979) point out a difficulty with sentences like A fat man was pushing his bicycle. Their rules assign to [this sentence] a presupposition that they admit is too weak: that some fat man had a bicycle. On the other hand, a universal presupposition that every fat man had a bicycle would be too strong. What one would like to predict is, vaguely speaking, a presupposition to the effect that the same fat man that verifies the content of [the sentence] had a bicycle. But it is neither clear what exactly that means nor how it could be worked into K&P’s theory.”

In the same year 1983, in his book Quantification and syntactic theory, Robin Cooper says that a one-dimensional representation like there is an x: x succeeded George V & PRESUPPOSED (it was difficult for x to succeed George V) would be better than the two-dimensional Karttunen & Peters analysis. Ever since, similar proposals continue to be made (for example, quite recently Paul Dekker’s article “A Multi-Dimensional Treatment of Quantification in Extraordinary English” in L&P – Dekker uses a representation very much like Cooper’s but then proceeds to give a two-dimensional semantics, which suggests that the main problem with K&P’s system was that it had two unconnected representations of their sentence rather than that there are two meanings associated with the sentence).

But wait a minute. What would it even mean to say about the sentence that it claims that someone succeeded George V, about whom it is presupposed that he found it difficult to do so? How can it be that something is supposedly already being taken for granted about someone who is not even introduced into the discourse until the very sentence is uttered? Heim recognizes this problem and suggests that one way this could be is if it was already presupposed that everyone had this property (since then whoever is introduced indefinitely by the sentence would be entailed to verify that presupposition). But this is clearly not so in her fat man example. It is not reasonable to think that it would be presupposed that every fat man has a bicycle and so it is unreasonable to think that about some indefinite fat man we already have the presupposition that he has a bicycle. Heim’s conclusion is that in effect there is no presupposition here, even though there is a presupposition trigger; she gets rid of the presupposition by the process she dubbed “local accommodation”. In the end, it is as if the sentence asserts of some fat man that he has a bicycle and that he pushed it. The Case of the Vanishing Presupposition, indeed. These are clearly very tricky issues, so it’s no surprise that the George V example and the Fat Man example continue to be debated.

One recent development: Karttunen & Peters’ problem of binding across dimensions was adduced by Chris Potts in his work on conventional implicatures (this time, the term was more appropriately used). He argued that while K&P’s problem was indeed a problem for them since they wanted to use a two-dimensional system to treat something that is better treated in a single dimension, there are indeed ingredients of meaning (conventional implicatures) that are located in a separate dimension. And lo and behold, Potts says, there what K&P predict, that there can’t be binding across dimensions, is actually correct. For example, he observes, a quantifier cannot bind into an appositive relative clause: No reporter believes that Ames, who is often the subject of his columns, is a spy. The sentence doesn’t have a reading where the quantifier no reporter binds the pronoun his in the appositive. So, Potts says, it makes sense to treat appositives as operating in a second dimension, and K&P’s binding problem becomes a virtue of the analysis.

A wrinkle: as observed by Danny Fox in our seminar a couple of weeks ago, sentences like Every candidate thinks that his wife, who is of course his biggest supporter, will vote for him or No candidate suspects that his wife, who is after all his biggest supporter, will vote against him actually seem to have readings where binding into the appositive occurs. It seems that once the anchor of the appositive (his wife) contains a bound variable, then the appositive can as well. If these observations hold up, appositives would also appear to have to be treated in one dimension, perhaps the way that Philippe Schlenker will sketch at NELS 40 in a month.