a note on the projection problem

A Note on the Projection ProblemAuthor(s): Fred LandmanSource: Linguistic Inquiry, Vol. 12, No. 3 (Summer, 1981), pp. 467-471Published by: The MIT PressStable URL: http://www.jstor.org/stable/4178234 .

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SQUIBS AND DISCUSSION 467

Carroll, L. (1977) Symbolic Logic, W. W. Bartley III, ed., Clarkson N. Potter, New York.

de Morgan, S. (1882) Memoir of Augustus de Morgan, Long- mans, Green, London.

Hintikka, J. (1974) "Quantifiers vs. Quantification Theory," Linguistic Inqluiry 5, 153-178.

Jevons, W. S. (1874) The Principles of Science, Macmillan, London.

Krynicki, M. and A. H. Lachlan (1979) "On the Semantics of the Henkin Quantifier," Jouirnal of Symbolic Logic 44, 184-200.

Quine, W. V. (1974) The Roots of Reference, Open Court, La Salle, Illinois.

A NOTE ON THE PROJECTION

PROBLEM

Fred Landman, University of Amsterdam

In a recent article, Scott Soames (1979) discusses some theories of presupposition that offer semantic or pragmatic solutions for the projection problem (how to calculate the presuppositions of a complex sentence from the presuppositions of its parts). The hardest problem for these theories concerns the case of conflicting presuppositions:

(1) Janet met the king of Buganda or Janet met the president of Buganda.

(2) Janet met the king of Buganda. (3) Janet met the president of Buganda. (4) Buganda has a king. (5) Buganda has a president.

(1) presupposes neither (4) nor (5), although its constituents (2) and (3) do presuppose (4) and (5), respectively.

Soames argues that the difficulty for both the semantic and the pragmatic theories is not that they cannot account for this example (because, in fact, they can), but that they cannot avoid the conclusion that (1) presupposes (1) itself. So (1) can be true or false only if (1) is true. (In pragmatic theories, it can only be uttered correctly, in contexts in which it is true.) As a consequence, (1) can never be false!

To avoid this problem, Soames proposes to embed the theory of presuppositions in the Gricean framework of conversational implicatures, in such a way that complex sentences have the presuppositions of the parts, unless these are canceled by conversational implicatures, or explicitly; this is his principle (90) (p. 653):

(90) A speaker who utters a truth-functional compound, ques- tion, or epistemic modal indicates that he is presupposing

I thank Jeroen Groenendijk and Gerald Gazdar for their helpful comments.



468 SQUlBS AND DISCUSSION

all of the presuppositions of its constituents, unless he con- versationally implicates (or explicitly states) otherwise.

With this mechanism he can account for almost all the cases previous theories could, and in addition for sentences like (1), without being forced to accept them as their own presuppositions.

Soames then notes a serious problem for his own theory, for which he has no solution:

(6) If Haldeman is guilty, Nixon is guilty too. (7) Someone-not Nixon-is guilty.

(7) is a presupposition of the second part of (6), but there seems to be no conversational mechanism that cancels (7) as a presupposition of (6) itself. The same problem appears in (8) and (9).

(8) If someone at the conference solved the problem, then it was Julius who solved it.

(9) Someone solved the problem.

Now this principle (90) is one of the basic assumptions of Gerald Gazdar's theory (Gazdar (1979a,b)), so Soames suggests that Gazdar's theory and his own make the same predictions. Con- sequently, (1) should not be a problem for Gazdar, nor should any other examples discussed by Soames bother him. On the other hand, (6) and (8) should give wrong results in Gazdar's system too. In what follows I will give a short exposition of Gazdar's theory which will show that this suggestion is not exactly true, and I will propose a solution-in Gazdar's for- malism-for the problems (6) and (8).

Gazdar's system works as follows:

(I) For every sentence, a definition is given of the set of all potential implicatures (im-plicatures) of that sentence, and the set of all potential presuppositions (presuppositions).

I will concentrate on so-called clausal quantity im-plicatures. Leaving aside that part of the definition that is not relevant for our purpose, the set of all clausal im-plicatures of a sentence

f, f(4(), is defined as follows:

(10) fJ(') = {X X {PWCP -}} for all i such that (i) 4 = X-+J- Y, where X and Y

are expressions, possibly null. (ii) [4] c rMi

(iii) [IJ C [-i4uI

P and K are Hintikka's epistemic operators; P means 'it is compatible with what the speaker knows that'; K means 'for all the speaker knows, it is true that' (P *-* -K - ). [4] is



SQUlBS AND DISCUSSION 469

the proposition that 4), the set of all possible worlds in which 4) is true; hence, [4] ? [4] means '4) does not entail 4'. (Ex- ample: f(4) V 4) ={P4, P 4), P4, P - 4}.) Consequently, if one utters a disjunction, one should not know whether the disjuncts or their negations are true. (Note that this is not true for conjunctions because of clauses (ii) and (iii).)

The set of all pre-suppositions of a sentence 4), fp(4)), is always given by simple enumeration of the presuppositions of its parts: fp (the king of France is bald or he does not exist) - {K there is a king of France, . . .}.

(II) Given f ((4) and fp(4)), show what the actual implicatures and presuppositions of 4) are. If 4) is uttered in a certain context, then first all clausal quantity implicatures that are consistent with that context are added to it, and the others are canceled; after that, all presuppositions that are consistent with this new context are added.

Definitions: -A set of propositions X is consistent (con X) iff the

intersection is nonempty. -A context M is a consistent set of propositions. Intui-

tively, M is the set of propositions to which the speaker is committed.

-Given two sets of propositions X and Y, the satisfiable incrementation of X and Y, X U! Y, is defined as follows:

XU! Y = XU {y E Y VZCXU Y(con({y} UZ)*-*conZ)}

X U! Y is X together with all those propositions in Y that can be added to X without the risk of inconsistency.

Let [f (4))] be the set of all propositions corresponding to the elements off (4)), and analogously for [h(4))]; the final context of 4), given starting context M is (M U! [f.(4)]) U! [fp(4)]H. All the propositions in the final context that correspond to elements of j(4) are actual implicatures of 4); the same is true for fp()).

This incrementation function can be seen as a formalization of Soames's principle (90): presuppositions are added to the context, unless we have previously added a conversational implicature with which the presupposition is inconsistent. How- ever, the similarity should not be overestimated. Take as an example sentences (1)-(5):

f(l) = {P2, P - 2. P3, P - 3}

fp(l) = {K4, K5} Let M' = M U {[P2], [P - 2]. [P3], [P - 3]} be the context after adding f (1). Now take a look at M" = M' U {[K4], [K5]}. There is a consistent subset of M" that cannot be consistently ex-



470 SQUIBS AND DISCUSSION

tended with {[K4]}, namely {[K51}; so [K4] is filtered by the definition, and analogously for [K5]. So there is no implicature inf.(l) that cancels K4 and K5: K4 and K5 cancel each other. I will come back to this.

Let us now turn to examples (6) and (8). Let (6') and (7') be the representations of (6) and (7).

(6') G(h) -- G(n) too (7') 3x * n G(.x)

(11) f.(6') = {PG(h), P - G(h), PG(n), P - G(n)} (12) fp(6') = {K3x :' n G(x)}

Now, if we increment fp(6'), no inconsistency arises, because a speaker who knows neither that Haldeman is guilty, nor that he is innocent, can still know that someone (not Nixon) is guilty: we can only reach P3x * n G(.x) and P3x * n -G(x), both compatible with K3x * n G(x). If we take (8') and (9') as representations of (8) and (9), the same story can be told about them:

(8') 3x (x is at the conference A x solved the problem) -* j solved the problem

(9') 3x (x solved the problem)

Now Soames is skeptical about the possibility of an elegant solution for this problem in his system (and as a consequence in Gazdar's system too). I think that this skepticism is pre- mature; in fact, I hope to show that a simple extension of Gazdar's definition off, (+) can do the job.

(13) Revised clausal qiuantity implicature definition

f(0) = {x x X {P4, P - @}} for all 0 such that for some (:

(i) = X-e- Y, where X and Y are expressions, possibly null.

(iv) N'] C VA] (iii) [(M ?z [01 (iV M) ] C [-0]

What this amounts to is taking the logical consequences of the parts, rather than the parts of 4 itself (although of course [k] C [e], so this new definition subsumes Gazdar's). Let's first see whether or not it works.

[G(h)] C [3x * n G(x)] so f,,'(6') = {PG(h), P - G(h), PG(n), P - G(n), P3x n G(x, P-3x :?- n G(x) .... .} fp(6') = {K3x * n G(x)}

[P-3x * n G(x)] = [-K3x * n G(x)], so the pre-supposition is canceled iff, (6') is already incremented in the



SQUlBS AND DISCUSSION 471

context. If we note that the first part of (8') entails (9'), it will be clear that the same argument applies here.

Note by the way that only interesting consequences of g are taken into account: although tautologies are consequences of every sentence, they will never reachf f(4) because of (13ii).

It may seem counterintuitive to hold that someone who utters A(C -) P and-at first sight-does not know whether A(c) or -A(c), is now believed to have no knowledge to choose between 3x A(x) and -3x A(x), either; this seems especially strange for -3x A(x). To this I can only say that, if we do not take into account more than just sentence (6) (in case we have an empty context), then it does not seem strange at all. As soon as we have a nonempty context, then indeed there are cases in which it could be strange, but in those cases P-3x A(x) cannot be consistently added to the context, and will be filtered (so there are cases in which the presupposition does not seem filtered: (6) can be said by a speaker who knows (7)).

Returning to sentence (1), we see that fl() now contains P4, P-4, P5, P-5. These implicatuires are enough to cancel K4 and K5. This renders unmotivated that part of the definition of X U! Y which allows pre-suppositions to cancel each other (it is only used for examples like (1)). If we want to block this possibility, we can do so by changing the definition of U! in the following way:

(14) XU! Y= XU{yC YIVZCX(con(ty}UZ)*- conZ)}

This means that pre-suppositions cannot cancel each other any longer, which in turn makes the satisfiable incrementation a real formalization of Soames's principle (90).

References Gazdar, G. (1979a) Pragmatics, Academic Press, New York. Gazdar, G. (1979b) "A Solution to the Projection Problem,"

in Ch.-K. Oh and D. A. Dinneen, eds., Syntax and Se- mantics, Volume II, Presupposition, Academic Press, New York.

Soames, S. (1979) "A Projection Problem for Speaker Presup- positions," Linguistic Inquiry 10, 623-666.

INTENSIONAL VERBS AND

FUNCTIONAL CONCEPTS:

MORE ON THE "RISING

TEMPERATURE" PROBLEM

Sebastian Lobner, University of Tokyo

Jackendoff (1979) deals with what one might call the "rising temperature problem" raised by Barbara Partee, namely, the invalidity of the inference from (1) and (2) to (3).

(1) The temperature is ninety. (2) The temperature is rising. (3) Ninety is rising.



a note on the projection problem

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