JOURNAL OF
SEMANTICS
AN INTERNATIONAL JOURNAL FOR THE INTERDISCIPUNARY STIJDY OF THE SEMANTICS OF NATIJRAL LANGUAGE
MANAGING EDITOR:
Pieter AM. Seuren
EDITORIAL BOARD:
Peter Bosch Leo G.M. Noordman
REVIEW' EDITOR:
Rob A. van der Sandt
ASSISTANT EDITORS:
G. Hoppenbrouwers A. Weijters
CONSULTING EDilDRS:
). Allwood (Univ. Goteborg),
]. Lyons (Sussex Univ.),
Th. T Ballmer (Ruhr Univ. Bochum),
). McCawley (Univ. Chicago),
R. Bartsch (Amsterdam Univ.),
B. Richards (Edingburgh Univ. )
M. Arbib (Univ. Mass. Amherst),
).
van
W. Marslen-Wilson (Cambridge Univ.), ,
Benthem (Groningen Univ.),
H. Rieser (Univ. Bielefeld),
H.H. Clark (Stanford Univ.),
R. Rommetveit (Oslo Univ.),
G. Fauconnier (Univ. de Vincennes),
H. Schnelle (Ruhr Univ. Bochum),
P. Gochet (Univ. de Uege),
). Searle (Univ. Cal. Berkeley),
F. Heny
R. Stalnaker (Cornell Univ.),
). Hintikka (Florida State Univ.),
A. von Stechow (Univ. Konstanz),
St Isard (Sussex Univ.),
G. Sundholm (Nijmegen Univ.),
Ph. johnson-Laird (Sussex Univ.),
Ch. Travis (Til burg Univ. ),
A. Kasher (Tel Aviv Univ.),
B. van Fraasn se (Princeton Univ.), Z. Vendler (UCSD),
E. Keenan (UClA), S. Kuno (Harvard Univ.), W. Levett (Max Planck Inst. Nijmegen), EDITORIAL ADDRESS:
Y. Wilks (Essex Univ.), D. Wilson (UCL).
journal of Semantics, Nijmegen Institute of Semantics, P.O. Box 1454, NL-6501 BL Nijmegen, Holland
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Volume 3, Number I /2
June 1984
JOURNAL OF SEMANTICS
Special issue on the Comparative Construction Edited by Pieter A.M. Seuren CONTENTS ARNIM VON STECHOW, Comparing Semantics Theories of Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
M J. CRESSWELL, Comments on Von Stechow . . . . . . . . . . . . . .
79
LARS HELLAN, Note on some Issues raised by Von Stechow. . . . .
83
J. HOEKSEMA, To be continued: The Story of the Comparative. . .
93
. . . . . . . . . .
109
LE ON STASSEN, The Comparative Compared. . . . . . . . . . . . . . .
143
PIETER AM. SEUREN, The Comparative revisited. .
ARNIM
VON STECHOW, My Reaction to Cresswell's Hellan's
Hoeksema 's and Seuren's Comments.
.
. . . . . . . . . . . . . . . . . .
183
EDITOR'S PREFACE
The idea of collecting a few studies on the comparative construction in
natural language arose when Arnim von Stechow sent us his bulky paper
with which this issue opens. It seemed an interesting thought to invite those whose work on the comparative is subjected to a critical appraisal
in Von Stechow's article to formulate their reactions, and then to ask Von
Stechow again to give his reply. As it turned out, not all of those invited were able or willing to take part in this teleconference on the comparative, and a few others whose work is not discussed by Von Stechow were. The result is that Hoeksema's article is a reaction to Von Stechow's though the l atter does not, in his main article, discuss Hoeksema (1983),- which had
appeared too l ate anyway for Von Stechow to be able to take it into account. Stassen's contribution represents a rather different angle from
wh ich to look at the comparative, the angle of universalist linguistics. The intrinsic interest of such an approach, combined with the fact that the universalist perspective is clearly underexploited in semantic and gram matical studies, and, moreover, the merits of Stassen's"treatment of this construction made it imperative to add his paper to this collection. Un fortunately, there was not enough time to enable Von Stechow to write down his reactions to this approach and to Stassen's position. The Journal's editors have had word that more is in the offing on the comparative. It m ay thus well be that in one of the next issues this topic
will again be discussed in one or more articles. Reactions to this issue are, of course, most welcome.
Pieter AM. Seuren
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be
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LANGUAGE& COMMUNICATION An Interdisciplinary Journal Editor: R HARRIS . Unwerstty of Oxford, Worcester College. Oxford OX 1 2HB, UK
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A selection of papers Language and communic"tion efficiency: the case of Tok Pis1n, P MUHLHAUSLER. Intonation and meaning in conversation, G McGREGOR. Kinetic patterns of individuality in acoustic and graphic productions. G G HAYOU & S FELDMAN. EJ11psis and coordination: norms and preferences, S GREENBAUM &C F MEYER. The garden path that historical linguistics went astray on.CH-J N BAILEY Realism and language change, TPATEMAN. Co-existent declensional patterns in Hmdi, O S DWIVEOI. Against affability, M L SCHNITZER. The Shark Bay language and its implications for linguistic theory, J B M GUY. The demarcation of metaphor. P PETTIT. Evaluat1on of noncontent speech accommodat10n. R L STREET Jr. The message, the context and the med1um. AFURNHAM. The future machine: a study of the span of speakers' anric1pat1ons in conversation, 0 DCLARKE. Language acqu1stuon, data compreSSIOn and generalization, J G WOLFF. What we might learn from acquired disorders of reading, R 8 FRIEDMAN. On language and communication. J GAGNEPAIN. The social context of language acquisition. J BRUNER.
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FORIS BOOKS PARAMETRIC SYNTAX Case Studies In Semitic and Romance Languages (SGG13)
TRUTH, INTERPRETATION (GRASS2) AND INFORMATION
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cal features is redefined, while obeying the Pro jection Principle.
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major result of these studies Ia what is now
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central role In the development of syntact1c
ilnguiS11cally significant relations are mediated by paths defined on tree representations, which are subject to a non-ambiguity requirement. The
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usually thought. The heart of Path Theory IS Kayne's semmal Connectedness Condition, a government-based sub-tree condition .
theory. In the Government and Blndmg frame work, the Projection principle entails that empty categories are present In structures that exhibit gaps.
On the Content of Empty Categories
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SCOPE OF THIS JOURNAL The JOURNALOF SEMANTICS publishes articles, notes, discussions, and book reviews in the area of natural language semantics. It is explicitly interdisciplin:uy, in that it aims at an integration of philosophical, psychological, and linguistic semantics as well as semantic work done in artificial intelligence. Contributions must be of goodquality (to be judged by members of the board of consulting editors) and should relate toques· tions of comprehension and interpretation of sentences or texts in natural language. The editors welcome not only papers that cross traditional discipline boundaries, but also more specialized contributions, provided they are accessible to and interesting for a wider readership. Empirical relevance and formal correctness are paramount among the criteria of acceptance for publication. INFORMATION FOR AUTHORS Typescripts for publication should be sent in 3 copies to the managing editor. They should be typed on A4 (or similar format), one·sided, double spaced, and with a wide margin and should be accompanied by an approx. 200 words summary. Footnotes and bibliographical references should appear at the end of the typescript. Diagraffis must: be submined camera-ready. All papers submined are subject to anonymous refereeing. Authors receive 20 offprints of their published articles and 10 offprints of their publish· ed reviews, free of charge. Larger numbers can be supplied at cost price by advance ar rangement. PRICES AND CONDITIONS OF SUBSCRIPTION The jOURNALOF SEMANTICS appears in four issues per year of approx. lOOpages each. Subscriptions for private use are available at the reduced rate of Dfl. SO,- per year; the institution rate is Oft. 120,-. The price for single issues is Dfl. 35,- (reduced rate: Dfl. 15,-). All prices include packing and surface postage. Airmail delivery and SAL delivery outside Europe are subject to a surcharge. We regret that no delivery can take place before payment has been received. Subcriptions not cancelled before October 1st auto matically extend to the following year. Placement of orders implies the consent of the subscriber to these conditions. All orders and checks should be sent to Faris Publica tions, P.O. Box 509, 3300 AM Dordrecht, The Netherlands. The JOURNAL OF SEMANTICS is publised for the Foundation Nijmegen Institute of Semantics (NIS), P.O. Box 1454, NL-6501 BLNijmegen, Holland The NIS Foundation is a non-profit organization, set up with the sole aim of furthering the study of the seman tics of natural language.
Journal of Semantics 3: 1
-
77
COMPARING SEMANTIC THEORIES OF COMPARISON ARNIM VON STECHOW
1. INTRODUCTION It is a wholesome plan, in thinking about semantics,
since these serve much the same purpose as is served by experiments in physical science.
B. Russell, "On Denoting" (with "logic" for "semantics").
0. PRELIMINARIES This is a critical and constructive review of recent semantic theories of the comparative. It is critical because
I
want to show that none of the existing theories
gives an adequate account of what I consider relevant data. The article is constructive in so far as
I
try to show how deficiencies
of existing theories can be overcome. At the end a picture emerges of what I believe to be a best theory of the comparative, given the actual state of research and the data discussed. I will discuss proposals by B. Russell, P. Postal, E. Williams, P. Seuren,
E. Klein, D. Lewis, M. Cresswell, and L Hellan. Some other approaches are briefly mentioned (Bartsch-Vennemann, S. Wheeler).
I
try to evaluate
the different accounts with respect to the question how certain linguistic phenomena are treated by them.
I
am indebted to the following people for comments on an earlier
version: Manfred Bierwisch, Max Cresswell, Cornelia Hamann, Irene Heim, David Lewis, Pieter Seuren, Wolfgang Sternefeld and Ede Zimmermann. None of these persons is responsible for my flaws (a necessary truth, I guess). In particular, I have to thank Max Cresswell and the editors of t he Journal of Semantics for improving the quality of my English.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
to stock the mind with as many puzzles as possible,
2 1. THE DATA In particular, I will focus on the following data.
Russell's ambiguity (RA).
How is the ambiguity of (i) explained?
I thought your yacht was larger than it was
(i)
I am considering ambiguous counterfactuals (AC) of the kind (ii):
(ii)
If Ede had smoked less (than he did), he would be healthier (than he is)
be treated adequately within a Russellian account. I will investigate the question in what way the existing theories will have to be revised in order to account for the nontrivial meaning of
(ii).
This will lead to the method
of dauble indexing and it will have consequences for the analysis of (i). A further phenomenon to be explained is the possible presence of
negative polarity items (NPI) in the (iii)
Ede is cleverer than
The same holds good for (iv)
I
Max
than-phrase:
anyone of us
as phr ases : -
is as well as ever
will investigate what the different theories have to say about that. It
will follow that Hellan's account can't explain this phenomenon. The accounts of Russell and Postal (and Williams) are not correct either in view of such data. On the other hand, Cresswell's, Seuren's, Lewis' and Klein's approaches give a nice explanation. Closely connected with the previous phenomenon is the behaviour of
quantifiers and connectives (Q &
C) in comparative complements. There is
a sense in which the following arguments are valid. (v)
Konstanz is nicer than Dusseldorf or Stuttgart
(vi)
Ede is fatter than anyone of us [= someone of us]
:. Konstanz is nicer than Dusseldorf and Stuttgart
:. Ede is fatter than everyone of us In a lot of cases we can replace the than-complement by something more
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
None of the existing theories treats this case adequately, though it could
3 informative. But we have to block unwarranted inferences (UI) like (vii)
(vii):
Ede is fatter than Max .jEde is fatter than everyone
In its actual form, the theories of Russell and Postal can't account for these phenomena. The approaches of Seuren, Lewis and Klein can explain arguments like (v) and (vi), but can't block (vii). Cresswell's theory is adequate, whereas Hellan has nothing to offer in view of such data. If we embed
negative quantifiers (NQ)
into comparative complements
we get statements that seem to be nonsensical in one reading: *Ede is
(ix)
*Ede is
more �
ls
as
� intelligent
�:ore(
intelligent
ls
than l as
S
���(
no one of us
Bill is not
It is fairly obvious that the oddness of these is not due to syntactic factors. Hence an adequate semantic theory should explain it. It seems to me that only Russell's theory can explain this in a straightforward way, though Cresswell has something to say about this phenomenon, too. The
possibility operator (0)
in comparative statements offers a nice
touchstone for the adequacy of theories, as the following examples shows. A polar bear could be bigger than a grizzly bear could be
(x)
Only Seuren and Lewis can treat this example adequately. Russell's and Cresswell's approaches can be improved in order to cover this datum. Hellan 's analysis is unimprovable in this respect.
An
example which does not discriminate so much between different
approaches but which is interesting for its own sake is the following. (xi)
More silly lectures have been given by more silly professors- than I expected. (Chomsky)
This is a case of a
multihead comparative.
There are people who believe
that sentences like this don't have clear truth-cor.ditions at all. I will say what the truth conditions of (xi) are and how we get them as a natural outcome of an adequate comparative semantics (and syntax!). I will briefly go into the question whether degrees can be eliminated from an analysis of simple comparative statements like (xii): (xii)
John is taller than Mary
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(viii)
4 Klein assumes this. He thinks that taller is just a relation between John and Mary. Examples like the following make this claim doubtful: (xiii)
Ede is taller than he is broad
Furthermore such a theory can't express differential readings (DR) of comparative or equative statements, like the following ones. (xiv)
John is six inches taller than Mary
(xv)
Ede is twice as fat as Angelika
(xvi)
I thought Plato could have been more boring
I
think that the only theory which can express all readings of this sentence is an improved version of Russell's account.
2. EVALU ATION OF THEORIES
If we try to evaluate the different theories according to the data considered, we obtain the following score: (xvii) Descriptive adequacy Russell Postal Williams RA AC NPI Q&C UI NQ
0
DR IM
S co re
+ ( +)
-·
-·
+ +
-·
-·
Seuren Lewis K lein +
+
-·
-·
+ +/-
+ + + +
(-) +
(+)
((5 ))
Cresswell
3�
Hellan
+
-· .
+
-·
-·
+
5
3
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
The only theory that treats such cases adequately is Hellan's. Iterated nvdality (IM) helps to decide the question whether we should prefer a scope solution from a double indexing solution. Take the follow ing sentence.
5
The seals for the phenomena have been introduced before. The minuses with a star mark those gaps in a theory which can in principle be filled in. It is surprising to see that the oldest approach viz. Russell's is the one which can to my mind be accommodated to the facts in the best way. It should be added that this table is not necessarily fair because it doesn't weight the different features. For instance, I didn't take into account syntactic merits of the different approaches. Klein's and Hellan's approach are syntactically much better motivated than the others.
3. PER SPECfiVE
D. RUSSEL'S AMBIGUITY AND SCOPE SOLUTIONS
Bertrand Russell was perhaps the ftrst person who had a semantical theory which could explain certain ambiguities found in comparative constructions. In his paper 'On Denoting' he writes: 1 "I have heard of a touchy owner of a yacht to whom a guest, on ftrst seeing it remarked, 'I thought your yacht was larger than it is'; and the owner replied, 'No, my yacht is not
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In the last section I propose an analysis of the comparative, equative and positive which tries to overcome the weaknesses of the existing theories. In a way, this approach will combine the nice features of the existing theories. I don't claim much originality for my proposal: I hope it is just the right combination of long existing ideas. Therefore the last section is called "Synthesis". I have tried to discuss the different theories in a maximally theory neutral way. The only thing I presuppose is the ability to read expressions that look like formulas of predicate logic. Furthermore, some basic know ledge of possible world semantics is assumed. The discussion is informal throughout because I didn't want to bother you with unnecessary tech nicalities. But the paper is hopefully precise enough to enable the reader to translate the analyses into his favourite syntactic-semantic frame-work. Though this article is basically a semantic one, I took care that my own approach is compatible with contemporary syntactic theories, especially with the so-called Governing-and-Binding theory of Chomsky. Section IX is even a purely syntactic one. The implications for the syntax are mostly obvious. I will say quite a number of things as to the structure of adjective phrases. Furthermore, I allude to the thesis that all sentential comple ments behave semantically as nominals and therefore have to be 'raised' in 'logical form'. I11 have, however, to work out the consequences of this claim on another occasion.
6
larger than it is.' What the guest meant was, 'The size that I thought your yacht was is greater than the size your yacht is'; the meaning attributed to his is, 'I thought the size of your yacht was greater than the size of your yacht.' "
I.
RUSSELL
So Russell obviously assumes that the sentence under discussion (I) has the analyses (2) and (3).
I thought that your yacht was larger than it is
(2)
The size x [I thought your yacht is x] is greater than the size x [your yacht is x]
(3)
I thought the size x [your yacht is x] is greater than the size x [your yacht is x]
Thus, the ambiguity of (I) is explained by a scope difference of the nominal "the size x". In (2), it has wide scope, representing a consistent thought of mine. In (3), "the size x" has narrow scope, making my thought contradictory. 2 This explanation is straight-forward and most modern theories pro ceed along these lines. Is Russell's solution the right one? Not entirely, I believe. But before giving reasons for my view let me review some of the modern semantic theories dealing with Russell's ambiguity . The standard method for explaining a non-lexical ambiguity is to assume a scope difference of quantifiers or operators. Every semantic approach to Russell's ambiguity I am aware of proceeds according to this idea (or allows us at least to proceed so). The only account which goes into a different direction is Horn [ 198I]. This is a pragmatic theory. In this section, I want to discuss semantic theories only. Therefore I will ignore Horn's approach in what follows. 3
2. POSTAL
At frrst sight, the several approaches to Russell's ambiguity look very different. But, as I have said, they have a common link: They all work with scope- difference of operators. Let us show this. Postal [ 1973] explains the ambiguity of ( 1) exactly as Russell did
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(I)
7 (4)
[= Postal's (37)) Jim believes that Mary is older than she is
(5)
a . MO RE (x [Jim believes (Mary is old to x)], y [Mary is old to y]) b . Jim believes [MO RE (x [Mary is old to x], y [Mary is old to y])J
In footnote 30, Postal gives an informal account of the intended readings of ills 'formulas'. Thus (38a) [= our (Sa)] can be very crudely and un naturally realized as: Sis more thanl The extent to which Jim believes Mary is old S j exceeds the extent to which she (Mary) is old.'
This is Russell's paraphrase.
3 . WILLIAMS
somewhat peculiar variant of tills analysis is found in Williams [1977). He analyses the two interesting readings of
A
(6)
[= Williams' (111)] John thinks Bill has more hor ses than he has
as (7Xa) and (b) [his (112Xa) and (b)] :4 (7a)
a. John thinks [MO REi (Bill has � hor ses) than MO REi (he has �hor ses)] b. MO REi (John thinks Bill has xi hor ses) than MO REi (he has� hor ses)
On page 133, Williams gives a hint how (7Xa) and (b) have to be read. (7Xb), e.g. means the same as
(8)
The amount � such that John thinks Bill has � horses is greater than the amount� such that Bill has xi horses
Obviously, tills is a Russellian solution. Let me briefly say why I think that Williams analysis is peculiar. He assumes that the 'S-structure' underlying (7Xa) is
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(i)
8 (9)
John thinks [(Bill has MORE horses)] than (He has MORE horses)]
(7Xa) is obtained from (9) by a twofold application of the rule of 'quanti fier interpretation', which adjoins the 'quantifier' MORE to the sentence leaving a bound variable at the original place. MORE means something like ''the amount x". The relation "greater" found in (6) is expressed by than. My objection against this treatment is this. I think it is pretty obvious that the relation 'greater than' is expressed by MORE or the comparative morpheme and not by than. This is seen from the contrast of the following two German sentences (not my Ger man, but my grandmother's): (i) Wagner ist so bedeutend wie Mozart (ii) Wagner ist bedeutender wie Mozart
The contrast in meaning between the equative (10Xi) and the comparative (ii) can't be explained by means of a contrasting 'complementizer': we have wie in both cases. So it must have its source somewhere else.
4. B A RTSCH & VENNEMANN
If worked out properly, then presumably also the analysis of Bartsch & Vennemann [1972] is a Russellian one. Bartsch & Vennemann analyse simple comparative statements like
(II)
Ede is more intelligent than Sue
as (12)
rM (Ede, Intelligence)
>
rhl(Sue, Intelligence)
rM is a measure function that maps individuals plus dimensions into num bers. At frrst sight, it looks as if (I 2) were a Russellian paraphrase of (I2) viz. something like (13)
Ede's intelligence exceeds Sue's intelligence
Consider now a case of Russell's ambiguity, viz. Bartsch & Vennemann's (107a), here represented as (1 4)
John is less intelligent than he believes
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(10)
9 Bartsch & Vennemann analyze this as {15)
rM(John,
intelligence)(i0 )
>
#(John,
intelligence)(iJohn b) '
5. CRESSWELL
The analysis of Russell's ambiguity given in Cresswell [1976] is similar in spirit to the preceeding ones. The details are somewhat different, how ever. Cresswell would analyse Russell's (I) in the following two ways: (16)
a. Ax.[I thought your yacht is x-long]er than Ax [it is x-long] b. I thought (Ax. [your yacht is x-long] er than Ax [it is x-long])
(16) (a) means something like (17): (17)
Every degree x such that I thought your yacht is x-long than any degree x such that your yacht is x-long. 5
is
greater
Here, again the ambiguity of (1) is explained by a SCC?pe- difference of some operator, the A.- operator in this case. In the previous examples, we had a scope- difference of the definite article, ie. Russell's t-operator. So Cresswell's {16Xa) corresponds to Russell's (2), whereas (I6Xb) corres ponds to (3). Notice, incidentally, that despite its superficial similarity to the previous analyses, Cresswell's analysis is essentially weaker in 'ex pressive power': it can't treat certain constructions which Russell's analysis can treat. I shall come back to this point. Variants of Cresswell's approach are Kaiser [1979] and Hamann, Nerbonne & Pietsch [ 1980]. Since these papers don't offer any new aspects for the problems discussed in this paper, they won't be mentioned anymore.
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This is to be read as ''The degree of intelligence John has in the real world i0 is greater than the degree of intelligence John has in the world he believes to be (=iJoh b)." Tllis analysis is not complete, because there n. is more than just one world compatible with John's beliefs. It is exactly the task of the modal operator "John believes that" to create the evaluation worlds iJohn b· Since this is not worked out in Bartsch & Vennemann's book, I will neglect their theory in what follows, despite the merits it has in other respects. As I have said, I believe that Bartsch & Vennernann's account would be equivalent (in the important respects) with Russell's, when worked out properly. Therefore, everything I am going to say about Russell's solution presumably carries over to their theory. More or less the same could be said about Wunderlich [1973].
10 6 . SEUREN
Seuren [1973] doesn't discuss Russell's ambiguity, but his system can account for it. The ambiguity of (I7Xa) would roughly be described by (17Xb) and (c). (I 7)
a. I thought you worked harder than you did b. ( 3e) [I thought you worked hard to e & -(you worked hard to e)] c. I thought ( 3e) [you worked hard to e & -(you worked hard to e)]
(18)
There is an extent e such that I thought you worked to (at least) e but you didn't work to (at least) e (i. e., you worked less).
This is an interesting alternative to Russell: We have only one operator binding the variables in the main and the subordinate clause. Furthermore, there is some syntactic evidence that comparatives contain a negative ele ment (in the than- clause).6 It can be shown, however, that Seuren's analysis is weaker in expressive power than Russell's, a feature it shares with Cresswell's account. Notice again, that the ambiguity is explained via scope-difference of some operator. (I 7Xa) is the consistent, (17Xb) the inconsistent thought.
7.
LEWIS
Lewis [ 1972] assumes that a sentence like (19)
The water is warm
denotes a set of (temperature) delineations, 7 where a delineation is the boundary temperature between warm and cool things. (The idea is, of course, that the actual boundary may change from occasion to occasion.) Let us denote this and similar sets in the following way: (20)
IThe water is warm I
A sentence like (21)
The tomato soup is warmer than the mineral water
would then have to following truth conditions:
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( 1 7Xb) means something like (I 8):
11 (22)
IThe tomato soup is warml
;;:> IThe mineralwater
is warm I)
If we express this by means of 'extent variables', which we used when we discussed Seuren's theory, it comes to something like the following: (23)
(Ve) (The mineral water is warm to e �The tomato soup is warm to e) & ( 3e) [The tomato soup is warm to e & (The mineral water is warm to e)] "'
(24)
a. I hoped the soup be warmer than it is b . II hoped the soup would be warml ¥ IThe soup is warm I c. I hoped (IThe soup is warml f> IThe soup is warm I)
My contradictory hope in (c) is here represented as the proposition that a particular set is a proper subset of itself. Using quantifiers and extent variables, (c) would be represented as (c'): (24)
c'. I hoped [(Ve) (The soup is warm to e �The soup is warm to e) & ( 3e) (The soup is warm to e & (The soup is warm to e))] "'
A similar 'translation' can be given for (24Xb ). This shows that Lewis' approach, too, can explain Russell's ambiguity by means of scope differ ence.
8. KLEIN
As to the aspects relevant to this discussion Klein's analysis of the com parative is virtually the same as Lewis' or Seuren's (cf. Klein [1980]) . Klein's approach has, however, other interesti ng features, to which we will return in section XI.
9.
HELLAN
Hellan treats Russell's ambiguity explicitly (cf. Hellan [1981, p. 20Sff]) . He analyses, among others, the sentence
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This paraphrase shows that Seuren's theory is virtually identical with Lewis'.8 It is clear, then, that Russell's ambiguity can be analysed in the same way in both theories. So (24Xa) can be analyzed as (24Xb) and (c):
12 {25)
John thinks Mary is more intelligent than she is
The consistent thought of John's is represented as {25Xa), whereas {25Xb) is the inconsistent thought {25)
a. {3d1,d2,d3) (John thinks Mary is drintelligent & Mary is dT intelligent & d1=d2+d3&d3 > 0) b. John thinks {3d1,d2,d3) (Mary is drintelligent & Mary is d2intelligent & d1=d2+d3&d3 > 0)
In section III, I will discuss how Hellan obtains these analyses from the surface.
The criticism developed in this section can be summarized in this way: No one lowers or raise s the right thing. The right solution would be to lower or raise the entire comparative complement, i. e. the than-clause. My own approach will do this. But no author realizes that S-complements behave semantically exactly like nominals and hence have scope. Every one seeks the scope somewhere else. But let us come back to our theories. Is there a way to choose among the different proposals? One criterion would be, of course, the adequacy of the analyses in terms of truth-conditions. If one theory gives a correct account of the intuitive truth-conditions of our sentences whereas the other does not, then the former is better than the latter. At the present stage, however, this criterion doesn' t tell us much. As far as the truth-conditions, are concerned, any of the above analyses looks reasonable- at least, as a first approximation. What we have to do is to look more closely at the 'theory of interpre tation', which tells us how the 'logical forms' discussed so far are ob· tained from the 'surface'. I will try to show that the following sentence represents a serious difficulty for theories that try to explain Russell's ambiguity by means of scope-difference, i.e. that work with 'raising' in a sense to be explained. {26)
If Mary had smoked less (than she did), she would be healthier {than she is)
This sentence is ambiguous. 9 There is a reading where both the antecedent and the consequent of the counterfactual are consistent and there are readings where this is not so. Hence we would expect an explanation of
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III. AMBIGUOUS COUNTERFACfUALS AND "RAISING"
13 this ambiguity along the lines of the preceding section,
i. e..
via difference
of scope. It is surprising to see that this is not always possible. The theor ies of Seuren, Klein, Lewis and C resswell can't represent the informative reading at all. The theories of Postal and Williams can't represent the ambiguity in the way we would expect. Hellan's proposal is the only one which can deal with (26). Yet, as we will see later, his theory is semantically inadequate.
In order to represent counterfactuals, I will use the counterfactual operator (SL)
o-+
with the Stalnaker - Lewis - semantics:
�
An S-world is a world
in which S is true.
Let us now have a look at the theory of Seuren (Lewis and Klein).
It is easy to see that this approach can't account for the informative
reading of (26) at all. The reason is that a comparative construction con
tains only one existential quantifier binding both the variable in the main and in the subordinate clause: (27)
& "'(Mary smoked & "'(Mary is healthy to e)]
(3e) [ Mary smoked e-little [ Mary is healthy to e
e-little)]
o-+
(3e)
This is the trivial reading of (26). The only thing we can do is to give wide scope over the counterfactual operator to one or both quantifiers. In each
case we get an absurd reading: (2 8)
a. (3e1)(3e2)[(Mary smoked erlittle & -{Mary smoked e 1little)) o-+ (Mary is healthy to e 2 & "'(Mary is healty to e2 ))]
& "'(Mary smoked e 1-little )) (3e )(Mary is healthy to e 2 & "'(Mary is healthy to e2))] 2 c. Uke (b) with (3e 1) having narrow and ( 3e2) having wide b. (3e 1)[(Mary smoked e 1-little o-+
scope
The reason for the stranding of our attempts is that, in this theory, either
both the main- clause and the subordinate of a comparative are trans parent or both clauses are opaque,
i. e.
under the counterfactual operator.
What we want is that the main- clause of the comparatives be opaque whereas the subordinates be transparent. But we can't express this. So
these theories are too weak in expressive power.
An
objection of the same kind must be raised against Cresswell. He can
have only one reading, namely the 'fully-opaque' one, which corresponds to Seuren's (2 7).
i.e.,
the reading
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is true at a world w iff either (I) there are no possible s1 o-+ Srworlds or (2). Some Srworld where s2 holds is closer to w 10 than is any s rworld where s2 does not hold.
14 (29)
(Ax.[Mary smoked x-little]er than Ax.[Mary smoked x-little]) o-+ (Ax [Mary is x-healthy] er than Ax.[Mary is x-healthy])
have said that Postal's and Williams' theories can't represent the am biguity of (26) in the way we would expect. What would we expect? Well, the trivial reading of (26) should be something like (30) in Postal's and something like (31) in Williams' approach. MORE (x[Mary smoked x-little], y[she smoked y-little]) o-+ MORE (x[she is healthy to x], y[she is healthy to y])
(31)
[MOREi (Mary smoked xrlittle) than MOREi (she smoked xr little)] o-+ [MORE i (she is healthy to xi) than MOREi (she is healthy to xi )]
(30) and (31) are structurally very similar to Creswell's (29). And for the same reason Cresswell can't have the informative reading of (26), Postal and Williams can't have it either - provided we take (30) and (31) as possible logical forms of (26). We can't 'raise' the MORE in (30) and (31) anymore. Raising would give us no well-formed expressions. On the other hand, there is a way to represent the nontrivial reading of (26) in a notation of the style used by Postal and Williams. In order to see this, let us reparaphrase (30) and (31) in a notation which uses Russell's t-operator. We thus get: (32)
LX(Mary smoked to x) LX(she is healthy to x)
< ty(she moked to y)
>
o-+
ty(she is healthy to y)
Now the t-terms are nominals and nominals have scope. We can use this fact in order to represent the informative reading of (26). It is (33).
(33)
t(she smoked to y) A.y[t(she is healthy to y) A.z[LX(Mary smoked to x) y) o-+ (LX(she z)]]
<
is
healty to x)
>
In the system of Montague's PTQ, the t-terms would be of the NP-type whereas the A.-abstraction would be over individual variables. (33) is, indeed, the correct representation of the informative reading of (26). But (33) presupposes a very different system from Postal's or Williams': We would have to 'lower' (or to 'raise') the whole than-phrase of the comparative construction and not only the more-bit, a possibility (and even necessity) never considered by either Postal or Williams. This new system would also suggest a different analysis of Russell's ambiguity in
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(30)
15 epistemic contexts. Remember that Postal and Williams represent the consistent thought o f John which is reported by {34)(a) as {34){b). Now, our discussion suggests that (34){c) would be a safer analysis. {34)
a. John thinks Bill has more horses than he has b . LX (John thinks Bill has x-many horses)> LX{Bill has x-many horses) c. LX(Bill has x-many horses) A.y [LX(John thinks Bill has x-many horses)> y]
{35 )
If Mary had smoked less {than she did), she would be healthier {than she is)
Raising the main- clauses in 'logical form' would yield (36): (36)
<
LX [Mary smoked x-much] 'Az [ty [ Mary is healthy to y] A.w [{z LX [ Mary smoked x-much] ) � (w > ty [Mary is healthy to y ] )] ]
But this means something very different from {35), namely {37) : {37)
If Mary had smoked mo re than she did , she would be less healthy than she is
If we allow 'non-parallel' raising of the clause, e.g. raising of the main clause of t he antecedent and raising of the subordinate o f the consequent , we can even increase the number of absurd interpretations. Let me conclude this discussion by saying that {26) presents a serious difficulty for Postal's and Williams' theory. Now, Postal actually doesn't treat {26) in t he way sketched here. He does something different, which is - to my mind - self-defeating for his whole approach. I will come to this in the next section. It is interesting to see that Postal's (and Williams') method o f 'lowering' or 'raising' the comparative morpheme, i e. MORE, gives the right result for an analysis of Russell's ambiguity but fails in view of our ambiguous counterfactual. This shows to my mind that these authors lower o r raise the wrong thing.
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{34){c), however, is so different from {34){b) that almost all the syn tactic considerations - which I did not discuss - leading Postal and Williams to their analysis would be inconclusive, if this theory were correct . And notice something else. If we allow clauses to have scope, we must forbid that the main-clause of the comparative construction ever gets wide scope in counterfactual contexts. Consider again {26), here repeated as {35).
16
More o r less t he same point can be made with respect t o Hellan's t heory. He raises the comparative mo rpheme plus t he than-complement. Again t his yields the right result for Russell's ambiguity but is not entirely correct for our (26). Thus, Hellan too , seems to raise t he wrong t hing. Let me show thi s in some detail. Hellan doesn't discuss ambiguous counterfactuals, but it is clear from his treatment o f Russell's ambiguity, how he has to analyse t hem. So, let us return to his (25 ), here repeated as (38). (38)
John t hinks Mary is more intelligent than she is
s
(39)
�
John thinks S
� Mary is AP
�
Q
�
A
I
more thanj she is intelligent tj intelligent In order to obtain a 'logical form', we have to 'rais�' t he quantifier Q, i. e. (in Bresnan's terms) we Chomsky-adjoin it to an S leaving a coindexed trace. Thus 'raising' will give us two logical forms namely (40)(a) and (b).
(40)
a.
s
�S � Q· s � � John thinks
mo re t hanj she tj intelligent
is
Mary is t r intelligent
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Hellan's analysis is influenced by Bresnan [ 1 975 ] , who assumes t hat the comparative morpheme er forms a quantifier phrase together with t he than- clause. The underlying structure of (38) is something like
I7 (40)
s
b.
s
Q.
� John t hinks S � Mary is t intelligent
� more t han she i s j tj intelligent
r
Obviously, (40)(a) will serve as 'logical form' for t he representation o f John's inconsistent belief, whereas (40)(b) represents hi s consistent belief, i e. (25)(b) and (a) respectively, here represented as (4 I )(a) and (b). a . ( 3d i ,d 2 ,d 3 ) (John t hinks Mary is d r intelligent & Mary is d T intelligent & d I d 2 +d 3 & d 3 > 0) b . John t hinks ( 3 d i ,d 2 .d 3 )(Mary is d r int elligent & Mary is d T intelligent & d 1 d 2 +d 3 & d 3 > 0) =
=
We get t hese readings from (40)(a) and (b) by means of t he following assumptions. I . The than- clause expresses a propert y of degrees. Thus thanj she is lj intelligen t is that property P which is true o f any degree d iff she is in telligent to degree d . 2 . 'Q uantifier raising' makes a A.-abstract out o f t he sentence t o which the raised quantifier phrase is Chomsky-adjoined . Thus we can read t he highest embedded S in (40)(b) as A.d i [Jo hn thinks Mary is di intelligent] . This is, o f course , the property true of any degree d whatsoever iff John thinks t hat Mary is intelligent to degree d . 3 . We assume t he following meaning rule for er. (4 2 )
Meaning rule for the comparative lerl takes a property of degrees and gives us a nominal (in t he sense
of Montague) t hat applies to properties of degrees again. Let P, Q be any properties of degrees. Then lmorei(P)(Q) is t rue iff ( 3 d I ,d 2 ,d 3 ) [ P(d 2 ) & Q (d I ) &d I d 2 +d3&d 3 > 0] =
It follows from t hese assumpt ions t hat (40)(a) and (b) can be read as (43 )(a) and (b) respectively. (43 )
a . more (Adj [she is df intelligent ] ) (Ad i [John t hinks Mary is dr intelligent]) b. John thinks �mre {Adj [ she is dj -intelligent ] ) (A.d i [Mary is d r intelligent ] )
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(4I )
18
(44)
a. If [ Q i more thanj she has smoked tj little] {8 Mary has smoked t i little) then [ Q n mo re than m she is t m hea lt hy] {S she is t n healthy) b. [Qi mo re thanj she has smoked tj little] (s [ Q n mo re thanm she is t m healthy] (S If Mary has smoked t i little, then she is t n healt hy))
These representations neglect thesubjunctive. It is easily checked that {44)(a) gives us, indeed , t he trivial reading, i.e. t he counterfactual with inconsistent antecedent and con sequent. I f we evaluate it according to Hellan's assumptions, we obtain t he following reading : (45)
( 3 d 1 ,d 2 ,d 3 , d 1 = d 2 +d 3 , d 3 > 0, she smoked d 2 "litt le) ( 3d '! ,d i ,d j , d 'l = d i + d j , d ) > 0, she is d 2 -healthy) [ Mary smoked d r little o-+ Mary is d'rhealthy]
Let me say now , why I think that this reading is not entirely the intended one. Suppose we have four worlds we re the following facts obtain . (Worlds wit h larger numbers are m ea nt t o b e further away from t he real world w0 ).
(46)
Cigarettes smoked by Mary wo : w2 : w3 : w4 :
20 15 10 5
Mary's degree of health
1 2
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I f we evaluate these two readings according to our meani ng rule (42), we obt ain (4 I )(a) and {b). I have grossly trivialized Hellan's o riginal approach in order to bring o ut what I consider to be its essential features. Notice that Hellan's ap p roach is, in a way , perfectly standard . It is entirely reasonable to assume t hat than- clauses express properties. Furthermore , the more is of t he same logical type as determiners, which also take a property and give you a no minal, i. e. a quantifier phrase. And , within a Chomskyan frame-wo rk , q uantifier phrases always have to be 'raised' in o rder to obtain a logical form. Nevertheless, even t his approach is not correct , as we can see from t he fact that it makes t he wrong pre diction s for our {26). At least, it seems to me that this is so . Hellan can have four logical forms for {26), o f which I will represent only the reasonable candidate�, namely t he reading which represents t he trivial conditional and the one which represents t he in formative con d itiona l :
19 It seems to me, that the co u nterfactual (26) should be intuitively wrong in w 0 . Smoking less doesn't always make healthier. Only smoking consider ably less would help . Hellan, however, predicts, that (26) is true in w0, be cause if we take 5 cigarettes for d 1 and the health degree 2 for d ] , then (47) is true in w0 : ·
(47)
Mary smoked 5- cigarettes o-+ Mary is healthy to degree 2
IV. PO STA L AND DOUBLE INDEXING
affirmative answer to t his question is suggested , if we analyse Postal's actual treatment of our critical sentence (26). As I have said , Postal would not analyse the trivial reading of (26) as (30) - though this would be in the spirit o f his theory. He chooses a different formalization . Let us consider his own example : I I An
(48)
If Bob had been taller than he was, he would have made t he team
The two readings of this sentence are represented as follows. (49)
a . I F(MO RE x [WOU LD(Bob was tall to x)w] y [ Bob was tall to y ] ) (WOULD(Bob made t he team)w) b . I F (WOULD(MORE x [Bob was tall to x ] y [ Bob was tall to y ] )w) (WC ULD(Bob made the tea!T' )w)
It requires some good will to interpret Postal's somewhat helpless att empts to build a semant ics for co unterfactuals in view of the fact that the serious proposals existed quite a while before Postal's article was writ ten. 1 2 Postal explains his notation in t he following way . WOULD is a two place predicate , requiring a sentence and a world-variable as arguments. "WOULD(S a) w" means 'Sa holds in w', where w is a hypot hetical world
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Therefore, (45) is true in w0 as well. On the other hand , t he analysis (33) would predict that (26) would be wrong in w0. To my min d , the latter prediction is t he correct one. This shows that Hellan's truth conditions are too weak . Therefo re, his account isn't correct either. So perhaps an accommodation of t he Russellian analysis along the lines discussed in connection with (33) is t he right way out of our dilemma. But it will be shown , that this analysis is defective on other grounds. Before showing t his, let me investigate the question, whether t here is a way to repair the other theories discussed so far.
20 distinct from the real world (cf. p . 392). In footnot e
48 ,
Postal explains
that the w's in (49) had better be bound by a universal quantifie r . Further more, it is clear that the embedded term y [Bob was tall to y]
is
not
evaluated with respect to the hypothetical worlds. It rather has to be evaluated with respect to the real world, as Postal's comment on (49)(a) and (b ) (his (77a) and (b)) shows :
"(77a) [=(49a)] thus represents a reading on which what is compared is Bob's actual height and a hypothetical height reached only in w. (77a) [ =(49a)] then says that, had that hypothetical height in w ex ceeded his actual height, Bob would have made the team in w." (p. 392)
Let us use t he variable w
in order to represent the actual world . What 0 Postal has in m ind with (49) (a) can then be restated in the fo llowing way :
(50)
It
is
is hypothetical & w :f: w0 & tX [ Bob was tall to x in w ] > ty [ Bob was tall to y in w ] � Bob made the team i n w ) 0
(Vw)(w
rather obvious how we have t o restate (49)(b ) .
Details aside ,
(50)
strikes us a s a reasonable account o f t he consistent
reading of ( 48). The essential point of this analysis is that the sentences not in the scope of a WOU LD-predicate are evaluated with respect to the actual world . Their inherent world-variable escapes the quantifying fo rce o f I F. I will make this remark clearer below . But , t hen, Postal's notation misses something . It
is
not always the case that a sentence not in the scope
of a WOULD-operator is to be evaluated with respect to the actual world . To see this, reconsider Postal's treatment o f Russell's ambiguity in belief contexts. Rememb er that Postal analyses the consistent belief of Bob's reported by
(5 1 ) (a) as (5 1 )(b).
(5 1 )
a. Bob believes that Mary is older than she is b . MORE x [Bob be lieves (Mary is old to x)] y [she is old to y]
Now, if we assume that sentences not in the scope o f the WOULD-pre
dicate are evaluated with respect to the actual world then t he embedded sentence "Mary is old to x " escapes the belief- operator and
(5 1 ) (b)
ex
p resses a plain contradiction.
In o rder to make t his argument more perspicuous, let us represent t he
idea that a sentence has to be evaluated with respect to the real world b y means of an 'actuality-operator' :
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Postal goes on and argues that the antecedent of (49a) is consistent where a s the antecedent of ( 49b) is not .
21 (A) ACTUALLY (S) is true in a world w iff S is true in w 0 , where w 0 is the real world Now , if it were correct that sentences outside t he scope of a WOULD predicate always have to be evaluated with respect to t he real wo rld, we could represent (5 1 )(b) equivalent ly as (52): (52 )
MORE ( x [ACTUALLY (Bob believes (ACTUALLY (Mary is old to x)))] , y [ACTUALLY (she is old to y)])
(H) "x believes S" is t rue in w0 iff (Vw )(If w is compatible with everything x believes in w0 , t hen S is true in w) The reader has to bear in mind that t he whole discussion is very sloppy. In particular, I am not distinguishing properly between meta-language and object language . But this is common practice and , hopefully, no confusion will arise from t hat . According to (H), (52) is true in t he actual world w0 iff (i) The x : (Vw)(If w is compatible with Bob's beliefs in w 0 , t hen ACTUALLY (Mary is old to x) is t rue in w) is greater in w0 t han y (ACTUALLY (she is old to y)) This is equivalent to (ii): (ii) The x: (Vw)(I f w is compatible wit h Bob 's beliefs in w, t hen Mary is old to x in w0 ) > the y (she is old to y in w0 ) In view o f t he fact t hat t he universal quantifier doesn't bind t he relevant variable w0 , this is equivalent to (iii) The x (Mary is old to x in w0 ) > the y (she is old to y in w0 ) Q.E.D. This consideration shows t hat in belief- contexts, sentences not in the scope of t he WOULD-operator don't escape t he quantifying force of t he belief-operator: (5 1 ) (b) - not (5 2) - is t he correct formalization of Bob's consistent belief. On t he o t her hand, in Postal's ( 49)(a), the se nt ence not in t he scope o f
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Given Hintikka's semantics for believing , (52) is t rue iff Mary is o lder t ha n herself. Hintikka 's semantics for believing is so mething like this :
22 a WOU LD- operator is supposed to escape the quantifying force of Postal's
I F. But then we have to apply t he ACTUALLY- operator to it , because it
makes this escape possib le . To see this, Jet us t ry to reconstruct Postal's ideas underlying the notation (49). Using the usual procedure of possible wo rld semantics, we want to d rop t he world-variable in t he WOULD. se ntences of (49).
(An
alternative would be to have a wo rld variab le in
each sentence, i.e. also in se nt ences not in t he scope o f a WOULD-pre dicate.) Let us represent , t herefore, Postal's (49 ) (a) rather as (5 3 ) : (5 3)
IF (MO RE x [WOULD (Bob was tall to x)] y [ Bob was tall to y ] ) (WOULD (Bob made t he team))
Post al's comment s on (49), (5 4)
a. ''WOU LD w0
& S is
(S)"
I
believe :
is t rue in a world w iff w is hypot hetical
true in w
&
wf
' ' b . " I F s 1 , s2 •· is t rue in a world w iff (Vw )(If s 1 is true in w , ' t hen s 2 is true in w ' ' In view of these rules, (5 3) is t rue in the real world w iff (Vw ( [(w is 0 ' ' ' hypothetical & w =!= w & (Bob's tallness in w > Bob's tallness in w )) => p ' ' (w is hypothetical & w =!= w & Bob made the team in w )] . 0 This shows that the world-variable of the than-phrase doesn't escape the quantifying force of the IF. Thus, (5 3) can't represent what Postal has in mind with (49) (a). We get the right reading , if we apply t he ACTUALLY-operator to the than phrase : (5 5 )
I F (MORE x [WO U L D (Bob was tall to x)] y [ ACTUALLY (Bob was tall to y)] ) (WOULD (Bob made the team))
I leave it to the reader to check that (5 5 ) is t rue in the real world w iff 0 (50) is the case, and (50) was the reading Postal intended with (49) (a). If we reconstruct Postal's ideas in this way - a fai r reconstruction, again, in my view - t hen his treatment is fatal for his previous analysis of Russell's ambiguit y . Once w e have the ACTUALLY- operator, we can explain the ambiguity by means of it alor.e without any recourse to a scope difference o f t he t-operator, the M O RE-predicat e, and the like. The ambiguity arising with belief-sentences is represented by the con trast o f (56) (a) and (b) :
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We fu rther assume t he following meaning rules - fair reconstructions o f
23
(56)
a. Bob believes (MORE x[Mary is old to x] y [ ACTUALLY (she is o ld to y)] ) b . Bob believes (MORE x [Mary is old to x] y [she is old to y ] )
The consistent belief (a) is d istinguished from t he inconsistent belief (b) simply by t he presence of the ACTUALLY-operator. In a language like German, a verb under an intensional operator not in the scope of t he ACTUALLY-operator can be in the subjunctive mood whereas a verb in t he scope of an ACTUALLY-operator is in the indi cative. (57)
Robert meint , da�Marie alter sei (subj .) als sie ist (ind .)
(58)
Unembedded verbs and verbs in the scope o f an ACTUALLY operator are in t he indicative. Verbs under intensional operators which are not in the scope of an ACTUALLY-operator can be in the subjunctive
This consideration shows that representations like (56)(a) and (b) are not without linguistic motivation. This explanation of t he ambiguity in our examples carries over in a straightforward way to counterfactuals. Since I don't want to defend Postal's WOULD-operator , which I believe to be misconceived for a number o f reasons, I return to the Stalnaker-Lewis-account o f counter factuals, which was sketched on p . 1 6. Postal's two readings (49)(a) and (b) are then represented in a much simpler way as (59)(a) and (b). (59)
a. MORE (x [Bob was tall to x] , y [ ACTUALLY (Bob was tall to y)] )o-+ Bob made the team b. MORE (x [Bob was tall to x] , y [Bob was tall to y] )o-+ Bob made the team
(a) is the reading with a consistent antecedent . According to the rule (SL) on p . 1 6, (a) is true in w0 , iff some world in which Bob's tallness was greater than his tallness in w0 and in which he made the team is closer to w0 t han any world in which Bob's tallness was greater than his tallness in w0 b ut in which he didn't make the team. And notice that our principle (58) predicts exactly the mood distribution o f (59)(a)'s German realisatio n :
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An u nembedded verb is in the indicative, of course. We t herefo re roughly have t he following correspondence between intensional operators and moods :
24 (60)
Wenn Robert gr6 {3er gewesen ware (subj .) als er war (ind.), ware (subj .) er in die Mannschaft aufgenommen worden
A cco rd ing to (58), (59)(b) is realized as (6 1): (6 1 )
Wenn Robert gro {J er gewesen w are (subj .) als er ware (subj .), ware (subj .) er in die Mannschaft aufgenommen worden
V. ACCOMMODATING DOUB LE INDEX ING INTO THE D I F FE R ENT THEO RIES
Once we use the ACTUALLY operator, t he relation between surface and logical form becomes rather simple, regard less whether we represent comparative-constructions in t he style o f Postal, Seuren, Cresswell or Hellan. We can assume t hat t he surface-structure of sentence (62) is some thing like (63): 1 3 (62)
Mary is taller than Bill is.
(63)
Mary is [ AP tall-er [5thai1j Bill is i-tall] ]
Let us assume that the than-phrase represents a property of degrees. I n Seuren's approach, t he than-phrase represents the two properties: 14
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Perhaps , the logical form underlying (6 1 ), viz. (59)(b) explains the ex treme oddness of (6 1 ): The antecedent of (59)(b) is contradictory. Person ally, I am inclined to say that (6 1 ) is not a grammatical sentence at all, b ut it seems hard to rule it out o n purely syntactic grounds. Let us summarize this discussion. Postal's t reatment of counterfactuals seems to require t he introduction o f an ACTUALLY-operator. Once we have gone so far, we don't need t he scope-device anymore for explaining Russell's ambiguity. A genuine scope so lution without t he use of t he ACUTALLY-operator was sketched in t he previous section (cf. p. 1 8). This solut ion, however, doe s not seem co mpatib le with t he syntactic con siderations leading Postal or Williams to t heir proposals. A scope solution has to b lock , fUJ;thermo re, unwanted readings (cf. (36)). Hellan's solution is certainly better than these. But it isn't co rrect either, because it doesn't yield the right truth conditions. On the other hand , I have shown t hat all t he ambiguities discussed so far can be explained by the presence or ab sence of t he ACTUALLY- operator, i. e. by a minimal difference in logical fo rm . I have further given some evidence that t his operator is reflected in t he indicative-subj unctive d istinction. It seems, t hen, that we have found an explanation of Russell's ambiguity which is simpler and better linguist ically motivated than explanations which work wit h scope-differences.
25 (64)
Ad [(ACfUALLY) (Bill is tall to at least d )] i i
(64) represents two properties, because t he ACTUALLY-ope rator may be present or not in English. (In German,
it .)
indicative, otherwise we don't have
it
is obligatory if the verb is in t he
I am assuming that a property is a
function from individuals into propositions. 15 In the above case, it is a function from degrees into propositions. (64)
is t hat property which is
true of a degree d in a world w iff Bill is tall to at least d in w (or w0 , if the ACTUALLY-operator is present in (64)).
I n Seuren's approach , the adjective phrase o f (6 3 ) will t hen express t he
properties Xx ( 3 d ) [x is tall to at least d
& -(64) (d)]
If we evaluate this, we get the properties (66): (66)
Xx ( 3 d [x is tall to at least d
& � [(ACTUALLY)
(Bill is tall to at least d)] ) So it is very easy to write a compositional semantics which combines the comparative A P in (6 3 ) with semantics in Seuren's style. The same ho lds
for t he other approaches. In Cresswell's theory, the than- clause [s t ha� Bill is i-tall] would
represent the fo llowing p roperties : (67)
A.d [(ACTUALLY) (Bill i
is tall to degree d i)]
And the whole AP in (6 3 ) would express the following propert ies :
Finally, in Postal's theory , the AP should express the properties (69): (69)
Xx [td (x is tall to d ) > td (67)(d)]
Thus, each of these approaches is compatible wi th the ACTUA LLY operator and it is very easy to write a compositional semantics for com parative adj e ctive phrases. In section I I I , I have said that Russell's and Postal's theory can live also without the ACTUALLY- operator. It doesn't increase their expressive power. And , fo r Hellan's approach, the introduction of the ACUT A LLY
operator does not make sense at all. So ,
if we
adopt the operator, con
siderations of conceptual economy speak in favo ur o f the approach of
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(65 )
26 either Seuren or Cresswell.
I
will, however, ignore metatheoretical argu
ments of this kind . I rather want to evaluate t he different approaches in the light of another observation,
viz.
that than-phrases are environments
which trigg e r so- called negative po larity items. Can each of t he above t heories, in its original or in its modified form, account for this phe nomenon?
VI. NEG ATIVE POLARITY One of the arguments Seuren gives fo r his analysis is that t he than-phrase
o f a comparative AP admits for negative polarity items but not fo r positive He concludes from this observation that
the
than
phrase must contain a (hidden) negative element , because negative polarity items require t hat . Negative polarity items are,
any, ever, much, be all that, lift a finger, cease to VP and others. Positive polarity items are, fo r in stance, already, rather, just as well, still. Consider t he following contrast s : • Any o f my friends could ever solve t hese problems faster than
(70)
Ede Ede could solve these problems faster than any o f my friends
(7 1 )
could ever do
(70) and (7 1 ) and ever. (72)
a.
i llustrate the behaviour of the negative polarity items
any
You have already got less support than he has
b . * He has got more support than you already have
(72)
illustrates the behaviour of the positive polarity item
already. 17
Now,
Seuren obviously assumes that a negative polarity item must be in the immediate scope o f a negation, whereas a positive polarity item is pre cluded from such an environment. This view goes back .to Klima and j ustifies, indeed , Seuren 's analysis
Lewis' or Kaplan's analysis, if we
(i. e.
want to be historically j u st). Consider readings are
(73)
e.g.
t he examples
(72).
Possible
(73):
a . ( 3 d) [You have
already got
at least d -less support
&
-(he has
got least d-less support)] b. ( 3d ) [ He has got at least d-much support got at least d-much support)]
& -(you have already
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po larity items. 1 6
27
(74)
If 0 is a sentential operator, t hen 0 is downward-entailing, if O(S) entails O(S'), for any S, S' such that S' is at least as informative as S (i e. S' entails S)
Clearly, negation is a downward-entailing operator. So the theory which says that negative polarity items have to occur in t he scope of a negation is subsumed under l..ad usaw's t heory which says that they can only occur in the scope of a downward-entailing operator. Let us consider a second example : (75)
A determiner Det is downward-entailing for the eN-position, if any sentence of form (i) entails any sentence o f form (ii) (i) Det eN VP (ii) Det eN' VP, where eN' is at least as informative as eN. 18
I am assuming that eN-phrases express properties. And a property p' is at least as informative as a property P iff for any x, the proposition p'(x) entails the proposition P(x). Defmition (75) enables l..ad usaw to predict the grammaticality of the following sentence: (76)
Every boy who has ever met Tania is delighted
The negative polarity item ever occurs within the eN-phrase, and every is downward-entailing with respect to the eN-position. This is seen from the following sentence pair:
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The explanation of (73){b )'s u ngr amma ticality is straightforward in Seuren's theory. In (73){b), the logical form of (72){b), already occurs in the immediate scope of a negation. Since already is a positive polarity item, this is not admissible and the sent�nce is bad . Similarly, we can ex plain the ungrammaticality of (7 1 ) (a). Here, the negative polarity item any is not in the scope of a negation. If an account along these lines were the only possible one, then Seuren's theory would be preferable to the competing ones we have discussed . Now, recently, Bill l..ad usaw has proposed a theory of negative polarity which generalizes the idea that negative polarity items can occur only in the scope of a negation. The generalization is this : Negative polarity items occur only in the scope of a downward-entailing operator. It is not possible to give the definition of a downward- entailing operator without going into technical details. I can't do this here and I therefore want to i llustrate this notion by means of examples. The frrst example is the following :
28 (76)
a. Every boy who likes potato- chips or Coca-Cola is welcome b. Every boy who likes Coca- Cola is welco me
Clearly the CN-phrase boy who likes Coca-Cola is more informative boy who likes po tato-chips or Coca-Cola and, therefore, a fortiori at
than least
as informative as the latter. Furthermore, (a) entails (b). This illustrates the fact that every is downward-entailing for the CN-argument .
Notice that t he old theory, which requires that negative polarity items
be
in
the scope of a negation, could explain the grammatically of
only by very artificial mo ves. It would have to analyse something like "-3
-"
few is downward-entailing
fo r t he CN
is downward-entailing for the complement position. A
theory that is not forced to introduce negations in logical form in o rder to explain these
cases is certainly preferab le. And it is more general. It
applies also for cases where there is no negation in logical for m . Com
parative constructions are possible candidates for an application of l..a
d usaw's theor y . The theory can, indeed , explain that negative polarity items can appear in than-phrases, even if we adopt the approach of Cress well, Postal or Hellan, where the
than-phrase
contains no negative ele
ment . It seems, however, that Seuren and Cresswell can do better than Postal or Hellan. Furthermore, it will tum out that Cresswell can do better than Seuren.
In the rest of t his section, I will estab lish these
claims.
Remember that the syntax of the comparative AP-s was something like this :
(77 )
[AP
Aer
["s than s] ]
Let us defme the following .
(7 8)
Aer in
(77)
is downward-entailing with respect to the S-argum ent
iff any sentence of form (i) entails any sentence o f form (i)
NP is Aer than S
(ii) NP is where s'
(ii):
Aer than S'
is at least a s info rmative as s.
It should be clear, by now, that any theory which says that
A er is down
ward-entailing for the S-argument is good , whereas any theory which doesn't say so is bad . 19 Only theo ries of the former kind can predict the
o ccurrence o f negative polarity items in than-phrases. Let u s check t he different approaches with respect to property following sentence-pair :
(78).
We consider t he
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regret
(76)
perhaps as
. But l.adusaw discusses <;ases, where such analyses
do not seem feasib le. For instance, position and
every
29 {79}
a. Ede b . Ede
is fatter t han Otto or Max is is fatter t han Otto is
Remember that, in the theories discussed , the than-phrase,
i e. ,
our S, ex
presses a property o f degrees. The than-phrase of {79}(a} expresses t he property {80}(a) and the than-phrase of {79}{b) expresses (80}{b ). {80}
a . Ad [Otto or Max is fat to d ] b . Ad [Otto is fat to d]
Oearly {b) is more informative than (a) : any degree satisfying {b) also satisfies (a). Therefore, in any t heory where fatter i s downward-entailing
different approaches with respect to this criterion.
In Cresswell's theory, {79}{a) and {b) express the propositions {8 1 ){a)
and {b) respectively. {8 1 )
a . {Vd 1 ,d 2 ) [Ede is fat to degree d 1
d 2 � d 1 > d2 ] b . (Vd 1 ,d 2 } [Ede is fat to degree d 1 d 1 > d2 ]
& Max or &
Otto is fat to degree
Otto is fat to degree d 2 �
Oearly (a) entails {b ). Therefore, fatter is downwa rd-entailing with res pect to t he than-phrase .
In Russell's approach, {79){a) and {b) express {8 2 ){a) and {b).
{8 2 )
a.
td [Ede is fat to degree d ] > td [Max or Otto is fat to degree d ]
b . td [Ede is fat t o degree d ] > td [Otto i s fat t o degree d ]
Also i n this case , (a) entails {b). This i s so , because (a) can only be t rue, if
Max and Otto have exactly t he same degree of fatness. Otherwise t he
defmite description td [Max or Otto is fat to degree d] wouldn't be t rue o f exactly one degree. Hellan has nothing to sa y to the problem we are discussing. He would analyze {79){a) and {b ) as {8 3 }(a) and {b) respectively. And t he latter two propositions a re logically independent from each other. {8 3 }
a . ( 3d 1 ,d 2 ,d 3 , d 1 =d 2 td 3 & d 3 > 0 & Max or Otto is d 2 -fat) [Ede is d 1 -fat ] b . { 3d 1 ,d 2 ,d 3 ,d 1 =d 2 td 3 & d 3 > 0 Otto is d T fat) [Ede is d r fat ]
Thus Hellan is ruled out, and Russell and Postal survive o u r test only if we
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with respect to the than-phrase , the proposition expressed by {79)(a) should entail the proposition expressed by {79}{b ). Let us check the
30 stick very closely to our criterion that the comparative adjective is down ward entailing with respect to its complement . There is, however , the problem that we also want the inference from {7 9)(a) to (b) if Otto and Max are not fat to exactly t he same degree. Seuren (and Lewis) can explain this, but Russell and Postal can't . There fore, t he frrst two theories are better in this respect .20 There is, however, another problem with Seuren's approach: it will license the following inference :
{84)
Ede is fatter than Otto :: Ede is fatter than everyone
{85 )
( 3d) [Ede is � d-fat & :{Otto is � d-fat)) ::( 3d) [Ede is � d-fat & -(Everyone is � d-fat ))
I have used , here, the notation "�" for "at least to degree". On the other hand, in Russell's, Postal's and Cresswell's theory, the argument (84) is only valid, if everyone means 'everyone else' and every one else has t he same degree of fatness. Intuitively, this is correct. That this is so , is clear for the frrst three authors, because in their analysis, the than-clause is represented as a definite description. In order to facilitate the understanding of my claim for Cresswell, I write down his formalization of (84). It is this:
{86)
� I e 2 )[Ede is d rfat & Otto is d 2 -fat => d I > d 2 i :. (Yd I ,d 2 ) [Ede is d rfat & everyone is d Tfat => d 1 > d 2 )
Thus, it seems that Cresswell is the winner of the game we played in this section. Most theories predicted the occurrence of negative po larity items, b ut Russell and Postal couldn't account for cetain intuitively valid in ferences viz. {7 9). On the other hand, Seuren's and Lewis' t heory licenses too many inferences, viz. (84). Cresswell did exactly right. In the example (84) we embedded a quantifier in t he than-clause. Quantifiers in than- clauses have some interesting properties. These we will study in the next section.
V II . QUANTIFIERS AND CONNE Cf NE S IN COMPARATIVE COMPLE M E NTS
It has been noticed by several people that one reading of {87)(a) entails {87 ) (b). 21
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This is seen at once if we write down Seuren's formalization of this ar gument :
31
(87)
a. Ede is wiser than Pericles or Socrates b. Ede is wiser than Pericles and he is wiser t han Socrates
Thus, the or seems to have t he force o f an and in the scope of a com parative adjective . The existential quantifier shows a similar behaviour. Let us assume with Ladusaw that the existential quantifier someone is realised as anyone in the scope of a downward-entailing operator. Con sider now the fo llowing pair of sentence s : (88)
a. Ede is fatter than anyone of us b . Each one of us is less fat than Ede
{89)
a. { 3 d) {Ede is wise to at least d & - (Pericles or Socrates is wise to at least d)) b. ( 3d)(Ede is wise to at least d & - (Pericles is wise to at least d)) and ( 3d ){Ede is wise to at least d & - (Socrates is wise to at least d))
(89)(a) entails {89)(b) and vice versa. This is so because of de Morgan's law, which can be applied to (a) and gives us the following proposition as an intermediate result between (a) and (b) : (89)
c. ( 3d){Ede is wise to at least d & - {Pericles is wise to at least d) & "' (So crates is wise to at least d))
{89){b) directly follows from t his. The equivalence of the sentence pair {88) is explained in an analogous way. (88)(a) expresses the proposition {90)(a): {90)
a. ( 3d){Ede is fat to at least d & "' ( 3x)(x is one of us & x is fat to at least d))
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Here , the existential quantifier in the than-phrase seems to have the force of a universal quantifier. In this section, I will be co ncerned with the question what the different comparative theories have to say about this phenomenon . I am assuming here that comparative adjectivals o f t he form [Aer than NP] are interpreted exactly in the same way as [Aer than NP is] . Consider now first Seuren's theory. Here, (87)(a) and (b) express the following propositions :
32 By the usual logical laws, this is equivalent to (90)(b ) :
(90)
b . ( 3 d) (Ede is fat to at least d & (Vx)(x is one of us => x is not fat to at least d (i. e. , x is less fat than d)))
(9 1 )
a. (Vd 1 ,d 2 ) [ Ede is d 1 -wise & (Pericles o r Socrates is d 2 -wise) => d 1 > d2 ] b. (Vd 1 ,d 2 ) [Ede is d rwise & Pericles is d 2 -wise => d 1 > d 2 ] & (Vd 1 ,d 2 ) [Ede is d 1 -wise & Socrates is d 2 -wise => d 1 > d 2 ]
A bit of reflect io n shows that (9 1 )(a) does indeed entail (9 1 ) (b). (The premises of (b) a re stronger). Postal's account will predict t he following t ruth-conditions for (87)(a) a nd (b): (9 2 )
a. t d [ Ede is d-wise] > td [Pericles or Socrates is d-wise] b. (td [ Ede is d-wise] > td [Pericles is d-wise] ) &{td [Ede is d-wise) & td [Socrates is d-wise] )
Now, (9 2 ) (a), in fact , entails (9 2 )(b). But the truth-conditions o f (a) are very weak. (a) is falsified if Pericles and Socrates don't have exactly t he same IQ. This is not what (87)(a) means. So this account doesn't seem right. Exactly the same objection can be raised against Hellan. If we have to choose among Cresswell and Seuren , it seems that Cress well's theory is p referable, because the following sentence is a problem for Seuren : (93)
Ede is fatter than Niko and Senta
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Now, this is exactly what (88)(b) means . If an accou nt predicts that a noun phrase o f the form [NP or NP] is 'co nverted' into a noun phrase of the form [NPand NP] in t he scope of a comparative adjective, then it will obviously also p redict that an existential quantifier is converted into a u niversal one. Therefore, I will hencefo rth consider the behaviour of the connectives or and arrl under the scope of comparatives only. If they are treated adequately, then 3 and V a re t reated adequately as well. To summarize the preceeding discussio n : Seuren's theory seems to be able to account fo r the phenomenon initially mentioned . Cresswell's t heory can do equally well. His account p redicts t he follow ing t ruth- co nditions for our sentences (87):
33 Seuren predicts that (93) means, among others, (94). (94)
Ede is fatter than Niko or he is fatter than Senta
I think , this is not correct. We certainly want to say that (93) entails (94), but it is not equivalent with it. The reading of (93) which is (94) is this : (95)
( 3d) (Ede is ;): d-fat & -(Niko and Senta ;): d-fat))
(96)
Ede is fatter than Niko am he is fatter than Senta
We get this by "quantifying in" t he NP Niko and Senta, as can be seen from the following representation : (9 7 )
Niko and Sent a Ax [ ( 3 d)(Ede is ;): d-fat & -(x is ;): d-fat ))]
Cresswell has no difficulties with these examples. He predicts the follow ing two readings for (93): (98)
a. (Vd 1 ,d ) [Ede is d I -fat & Niko and Sent a are d -fat => d I > d ] 2 2 2 b. Niko and Senta Ax [ (Vd i ,d ) [Ede is d r fat & X is d T fat => d I > 2 d ] 2
Both readings exist. So, this is another point for Cresswell. Another problematic point is the behaviour of neither-nor (or no one) in t he scope of a comparative adjective. Consider the fo llowing sentences. (99)
a. Irene is prettier than neither Ede nor Senta b. Irene is prettier than no one of us
These sentences are extremely odd and semantical theories of the com parative have to explain this fact . The theory o f Russell gives a straightfo rward explanation of these data. Fo r him, (99)(a) and (b) don't express propositions at all, as can be seen from his analysis of (99)(a):
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Thus, Seuren's (and Lewis' and Klein's) account faces the problem of barring this interpretation. I have no idea by which principles this could be done. We can, of course , also have the reasonable reading (96) for (93):
34 ( 1 00)
td [Irene is d-pretty) > td [ neither Ede nor Sent a is d-pretty)
This analysis uses t he tem1 td [ neither Ede nor Senta is d-pretty] , which, for abvious reasons, doesn't denote. Seuren would have to say that (99)(a) expresses a tautology, viz. (10 1 ): ( 1 0 1 ) ( 3d) [Irene is �d-pretty & --(Ede or Senta is � d-pretty)]
( 1 02) (Vd 1 ,d 2 ) [Irene is d 1 -pretty & -(Ede or Senta is d Tpretty) => d 1 > d2 ] This time it is even more difficult to find out what proposition ( 1 02) is. Each time, I am faced with (1 02), I have to draw a picture in order to convince myself that (102) is indeed a logical falsehood . Therefore, to my mind , Cresswell's t heory gives quite a good explication of t he oddness o f (99). Notice that we have to prevent the wide-scope reading for the NP neither Ede nor Senta, if we adopt the approach of Seuren or Cresswell. The wide-scope reading would yield the following propositions, (103)(a) in Seuren 's, (1 03)(b) in Cressw ell's system : ( 1 03) a. Neither Ede nor Senta Ax( 3d) [Irene is pretty to at least d & -(x is pretty to at least d)] b . Neither Ede nor Senta Ax.(Vd 1 ,d 2 ) [Irene is d rpretty & X is d Tpretty => d 1 > d 2 )
(I 03)(a) and (b) mean that neither Ede no r Senta does have the property
of being Jess pretty than Irene. This is a perfectly sensible proposition, but none that is intuitively expressed by (99)(a). Similarly, (99)(b) - here repeated as ( 1 04) - does not express the proposition (105). ( I 04) Irene is prettier than no one of us
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One might object against this solution that (99) is rubbish and should t herefore not express a tautology, i. e. something very precious to the philosopher or mathematician. On the other hand , it takes some time to figure out that ( 1 0 1 ) is in fact a tautology. In ordinary life, we calculate in real time. Perhaps we are not quick enough to perceive the logical st ructure o f (99), viz. (10 1 ). We stop at a certain point of conceptual complexity, hence the oddness of (99). The same kind of explanation is perhaps valid for Cresswell's account . He would predict that (99) expresses a logical falsehood, namely (1 02): 22
35 ( 1 05 ) No one o f us Ax{ 3 d){Irene is pretty to at least d & ""(x is pretty to at least d)
VOl. THE POSSIBI LITY OPERATOR IN COMPARATIVE CONSTRUCTIONS
In a way, modal operators are quantifiers. They quantify over invisible world variables. In the preceding section we found that definite com parative analyses (Russell and Postal) could not adequately t reat em bedded existential quantifiers. This result carries over in an obvious way to an embedded possibility operator 0. This operator has the usual se mantics, that is, we assume the rule {1 07):
{ 107) 0 S is true in a world w iff there is an (accessible) world w ' such that S is true in w ' One might think that it is clear from our comments on Russell's am biguity how 0 is treated. But this is not so. The believe-operator is, in a way, a universal quantifier and behaves quite differently from the pos sibility operator, an existential quantifier. Consider the following sen tence.
( 108) A po lar bear could be bigger than a grizzly bear could be24
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{ 1 05) means that no one of us is less pretty..than Irene, or that everyone of us is at least as pretty as Irene. Again, this is not what ( 104) means. Notice that the problem of distinguishing the behaviour of these NPs is not tied to Cresswell's or Seuren's approach. It arises with t he other theories as well. So this is a general problem which does not decide between the different theories. 2 3 Let me try to draw a conclusion from the discussion of this paragraph. Cresswell's and Seuren's theory can say so mething about the behaviour of or and the existential quantifier in the scope of a comparative adjectives. Seuren , however, makes the wrong predictions about and and the universal quantifier in that environment . The other theories can't deal with these facts at all. Co ncerning a negative quantifier like no one or neither-nor, the theories t reating the than-phrase as a defmite term seem to do best . But also Seuren and Cresswell can say something about the relevant phenomenon. If we take all this together, than Cresswell's theory seems to be the winner o f this paragraph. This is not so astonishing, because this section is closely related to the preceding one, where also Cresswell was the favourite.
36 I t is n o p roblem t o analyse this sentence by means o f Seuren's and Lewis' t heor y . On the other hand , it
other approaches. Prima
facie,
is
not possible to analyse ( 1 08) within the
t his is a strong point for Seuren and Lewis.
I will, however, show that the other theories can be repaired in such a way that ( 1 08) is no longer an insurmountable difficulty . This will have a positive effect concerning t he examples o f t he last two sections. Most
o f the difficulties encountered t here can be overcome. Let 's turn to Seu ren and Lewis first . a nalysed as ( 1 09): ( 1 09)
In
their system, ( 1 08) would be
( 3d) [ 0 (A polar bear is � d-big) & -0 (A grizzly bear is ;;;;. d-big)]
could
express e s
standard assumption.
Thus, ( 1 09) means ( 1 1 0)
( 3 d) [ 3w(A po lar b ear is ;;:.. d-big in w) & -{ 3w)(A grizzly bear is � d-big)]
exact ly as we would expect . Cresswell's t heo ry yields the wrong result, (I l l)
(Vd ,d 2 ) [O(A polar bear 1 d d ] => 1 > 2
is
viz. (I 1 1 ).
d rbig) &
0
(A g rizzly bear is d 2 -big)
These truth- conditions are too strong. We only have to fmd a po lar bear which is smaller than a grizzly bear in order to falsify t his proposition. This is very easy . Indeed, ( 1 1 1 ) is t rivially false , whereas I don't know whether ( 1 08) is t rue. We could try to give wide scope to one or two o f t he modal operators in (I 1 1 ). I leave it t o t h e reader t o check t hat such a move wouldn't help. Hellan's approach fails for similar reasons as Cresswell's. He would
analyse (1 08) as ( 1 1 2 ). I leave it to t he reader to check that t hese truth conditions are far too weak : ( 1 1 2)
( 3d ,d 2 ,d ) [O(A po lar bear is d rbig) & O(A grizzly bear is d 2 " 3 1 big) & d = d 2 +d & d > 0] 3 3 l
The straightfo rward representation o f ( 1 08) in
Russell's and
Postal's
t heory fails entirely, because the definite terms obviously don't denote anything :
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In order to get this we have to assume t hat the auxiliary
0, a
37 ( 1 1 3)
tdO(A po lar bear is d-big) > tdO(A grizzly bear is d-big)
Again , I leave it to the reader to convince himself t hat giving wide scope to both model operators could not save the situation . I t seems then that o u r example ( 1 08) gives strong support t o Seuren's and Lewis' account . Alas, this appearance is not cogent . I think that we should not be content with a failure of Russell's analysis. The reason is, that we need a deftnite analysis of comparative stat ements on quite in dependent grounds. Consider the following se ntence. ( 1 1 4) The size a polar bear can have exceeds the size a grizzly bear can have
( 1 1 5) The maximal size a polar bear can have exceeds t he maximal size a grizzly bear can have In Russell's t heory, we have to formalize this as so mething like ( 1 1 6): ( 1 1 6) the maximal d O(A po lar bear is d-big) > t he maximal d O(A grizzly bear is d-big) Take ''the maximal d . . . d . . " as short for "lrl [ Max(Ad [ . . . d . . . ] )(d)] " . Max i s a n operator modifying properties of degrees, having the following semantics: .
( 1 1 7) Max (P) is true of d iff P(d) a nd � ( 3 d ') [P(d ') & d ' > d] Given that degrees are linearly ordered , Max(P) is t rue of exactly o ne degree ; Therefo re, the defmite description td [ Max(P)(d)] will make sense, if P is the predicate XdO(A polar bear is d-big). Thus, t he more explicit spelling of ( 1 1 6) is ( 1 1 8):
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This is a perfectly u nderstandable English sentence which we have to t reat semantically anyway. Now, in ( 1 1 4), the modal can obviously must be within the scope of the definite article. A bit of reflection will show then, that ( 1 1 4) is a problem for any of our theories. This problem, however, is not caused by the semantics of the comparative morpheme. It arises to gether with the theory of descriptions. Once we have understood that, it is pretty obvious t hat formalization ( 1 1 3) is too naive. If we use the defmite article, we often leave certain parameters inexplicit . The book means 'the book at such and such place', the money means 'the totality of the money in my wallet'25 etc. , and , obviously, the intended sense o f ( 1 1 4) is something like ( 1 1 5):
38 (1 1 8) td [ Max (AdO(A polar bear is d-big))(d)] > td [Max (AdO(A grizzly bear is d-big))(d))
(1 1 9) (Vd 1 ,d 2 )((d 1 = the maximal d [OA polar bear is d-big] & d 2 = the maximal d [OA grizzly bear is d-big] ) => d 1 > d 2 ) This accommodation is not so obvious as in the previous cases, because, as said , Cresswell's analysis is not o f the defmite type. We can eliminate the definite article from Cresswell's account in view of t he fact that ''the maximal d" and "a maximal d" mean, in fact, the same thing. In other words, a better accommodation t han (1 1 9) would, perhaps, be ( 1 20): (1 20) (Vd 1 ,d 2 )( [Max(AdO(A polar bear is d-big))(d 1 ) & Max(AdO(A grizzly bear is d-big))(d 2 )] => d l > d 2 ) Here, Max is the operator we have described in ( 1 1 7 ). The difference between Cresswell's and the other t heories is t hat t he presence of the Max-operators is a natural outcome of the pragmatics of t he defmite article for Ru�II whereas it has to be stipulated in Cresswell's system, i. e. , it has to be built into the semantics of t he comparative. This seems to be a slight weakness of Cresswell's account . Hellan's theory can't be saved at all. The introduction of the Max-operator has a positive effect for all defmite theories in two respects. First. It obviously has t he impact that the comparative complement, i e. the than-phrase is the right environment for negative polarity, be cause the Max-operator is downward-entailing. I leave it to the reader to convince himself of the cor rectness of this assertion. Thus, the objections raised against Russell in section VI can be met now. Second, quantifiers appearing in the than- clause can be treated ade quately now by Russell. Consider first t he article case where a negative existential is in the scope of t he than-phrase.
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Thus, Ru�ell's theory is saved, and the object ions against his theory can be met on quite general grounds: Once we have a pragmatic theory which tel1s us with respect to which implicit parameters definite terms are evaluated , we obtain the correct readings. And it is clear that we need such a pragmatical theory anyway. This salvation procedure crucially hinges on the fact t hat Ru�ell's analysis o f the comparative is a defmite one. If we look at Cresswell's analysis, we fmd that it is not a defmite one. But , if we want to save him from the objection raised in this section, we obviously have to adopt t he same method. A correct analysis of ( 1 08) within an improved theory o f Cresswell would be t he following:
39 ( 1 2 1 ) *Ede drinks more than no one o f us
Ru�ll's analysis would predict the following reading : ( 1 22) the maximal d [Ede drinks d-much) > the maximal d fno one of us drinks d-much)
( 1 23) Ede drinks more than anyone of us ( 1 24) Ede drinks more than everyone of us
In Russell's system, these will be analyzed as ( 1 2 5)(a) and (b), respec tively: (125) a. The maximal d [Ede drinks d-much] > the maximal d [some one of us drinks d-much] b . The maximal d [Ede drinks d-much ] > the maximal d [every one of us drinks d-much ] ( 1 25)(a) means, indeed , (1 26) : ( 1 26) For everyone of us, it
is
the case that Ede drinks mo re than him
This is exactly the reading we were after in section VII. (125)(b) is correct, too . It means that Ede d rinks more t han everyone of us, in case we all drink the same amount. On the other hand, Lewis' and Seuren's system could not t reat ( 1 24) adequately. Cresswell's system was adequate with respect to these phe nomena, and nothing has changed with the introduction of the Max operator. So Lewis, Seuren and Hellan seem to be the losers of this game. There is, however, a negative effect for Russell's theory, which should be mentioned. The particular behaviour of the quantifiers is restricted to the than-phrase , whereas Russell predicts that we would fmd it also with respect to t he subject term. The same holds with respect to negative po larity. This, however, is not borne o ut b y the facts. According to Russell, there should be a reading of ( 1 27)(a) which means ( 1 27)(b) and
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As in ( 1 0 1 ), the second defmite term doesn't denote, because although there certainly are degrees d , such that no one of us drinks d-much, t here is no maximal degree of this kind , at least, if we assume that there is no upper limit of degrees, a reasonable assumption. On the other hand , it is no problem to embed existential or universal quantif.�ers within the than phrase :
40 ( 1 28) should, in o ne reading, expre� no proposition at all. Oearly, this
is inadequate .
( 1 27)
( 1 28)
a . Someone o f us
is
taller than Ede
b . Everyone o f us is t aller than Ede No o ne o f us
is t aller t han Ede
Cresswell's analysis is inadequate fo r exact ly t he same reason. The outcome of this section is t hat all the theo ries considered so far are
inadequate with respect to our dat a . It will be t he task o f t he last section to o ffer an alternative that can meet all the difficulties discovered .
So far we have assumed that comparative complements always go back to reduced clauses.
In
other words, we a�umed that t he comparat ive ad
jectival in ( 1 29)(a) is interpreted exactly as ( 1 29)(b ) : ( 1 29)
a. Aer than b . Aer than
NP NP is
This suggests t hat t he than-NP is always interpreted as the subj ect of a missing than-S. This is, however, not t rue without further qualificat io ns. Hellan [ 1 98 1 , p . 56] observes that : ( 1 30)
John thinks t hat Mary is taller than herself
could not mean the same as: (1 3 1 )
John t hinks that Mary is taller than she is
We would , however , predict this meaning, if we assumed that the under lying st ructure o f ( 1 30) were somet hing like ( 1 32): ( 1 32)
*John thinks that Mary
1
is t aller than herself1 is tall
Any of our systems would predict t hat ( 1 32) may report a consistent t hought of John's. Take, for convenience, Seuren's representat ion : (1 33)
( 3 d ) (John thinks t hat Mary
:;;>-: d -tall] ))
1
is > d-tall & � Actually [herselfi is
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IX . ARE COMPARATIVE COMPLEMENTS ALWAYS REDUCFD CLAUSES?
41 One might object that this reading is b locked o n independe nt grounds. 010msky's binding theory {cf. Chomsky [ 1 98 1 ] ) says that the reflexive herself must have its antecedent within the minimal governing category, here the than- clause. Since t here is no possible antecedent for herself in the than- clause, t he sentence is ungrammatical. But this would leave unexplained t hat there is a possible interpretation of { 1 30) viz. the case where John holds a contradictory thought about Mary. The only way out of this difficuhy seems to be t he assumption that t he construction ( 129)(a) does not go back to { 1 2 9)(b) but rather to (1 34): ( 1 34) Aer [ pp than NP]
( 1 35) John thinks that Maryi is [ AP taller [ pp t han herselfi ] ] Here, Mary can be an antecedent o f herself. because the two are in the same minimal governing category viz. the that-clause. This leaves open the question how (1 35) is interpreted exactly. I will assume that we proceed exactly as we did before. The PP than hersel� is interpreted exact ly as if it were t he reduced clause than herselfi is. This will give us the right reading, viz. ( 1 33 ) without t he ACTUALLY-operator. We have to say, of course, that t he ACfUALLY-operator may be present in logical form only, if the than NP goes back to a reduced surface clause. This stipulation will bar the unwanted reading (1 33). Notice that such a treatment is consistent with Chomsky's binding theory, because t he binding theory applies to the surface structure i. e. to ( 1 35) and not to the logical form, i. e. (1 33). Thus we obtain the following tentative conclusion. The NP herself in taller than herself is a subject on the level o f logical form but not the subject o f a reduced clause on the level of surface structure. Furthermore, it seems to me that an example like ( 1 30) supports Chomsky's view that the binding conditions apply on the surface and not on logical form.
X. MULTIHEAD COMPARATNES
In this section I will be concerned with the semantics of comparative con structions where the comparative complement is associated with more than one 'head '. These examples typically occur with plural nouns or mass nouns. I don't think that these cases represent genuine semantic pro blems. They can essentially be treated with the methods we already have
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A structure of this kind is advocated also in Chomsky [ 1977 ] . Thus, t he surface structure of ( 1 30) would be (1 35):
42 at our disposal. But it took me quite a while to realize tlm, because t he examples are conceptually rather complicated and are neglected in the literature. Furthermore, we can perhaps say something about the question of why such cases are restricted to plural or mass nouns. Chomsky [ 198 1 , p . 8 1 ] consider cases like the following : {1 36) a. [more silly lectures] have been given by [more boring pro feSS(>rs] - than I would have expected b .* [more silly lectures] have been given by [more boring pro fessors] - than I met yesterday
( 1 37) more silly lectures [than I would have expected] have been given by more boring professors [than I would have expected] As it stands, (1 37) is not yet sufficient for the semantic rules to apply. The bracketed S's lack an internal sentential complement. Each S must be reconstructed as a sentence of the form (1 38):
( 1 38) than I would have expected that silly lectures would be given by boring pro fessors Thus, the entire structure determining the interpretation of (1 36)(a) is ( 1 39): ( 1 39) More silly lectures [than I would have expected that silly lectures would be given by boring pro fessors] have been given by more boring professors [than I would have expected t hat silly lectures would be given by boring professors] I f we compare (1 39) with ( 1 3 6)(a) we see that greater explicitness is not necessa rily connected with better understanding. It would be interesting to invest igate the syntactic processes by which ( 136)(a) and (1 39) are related. I will say a few speculative words about some aspects of this problem. But let us ask first the following question: Which proposition does (1 39) express?
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Chomsky says that the first sentence is a case of construal whereas the second one is a case of unwarranted application of Move-a. (The than-phrase is naturally associated with the second bracketed NP. But, then, subjacency is violat ed . I will not go into the question of the correctness o f the latter explanation.) The construal process Chomsky assumes for ( 1 36)(a) associates the than-clause with the two b racketed NPs. Hence, the input for the se mantic rules is not (1 36)(a) but rather ( 1 37).
43 It is advisable to consider ftrst a simpler example o f the same kind , b e fore we answer the question. Consider the following sentence.
(I 40)
More dogs ate more rats than cats ate mice
I take it that ( 1 40) has the following truth-conditions (in its most easily available reading) : (141)
The number of dogs that ate rats cats t hat ate mice
&
is
greater than the number o f
the number o f rats that were eaten b y dogs is
greater than the numb er of mice that were eaten b y cats
( 1 40) is to check that other formulations found occasionally are no t correct. I have heard once the following truth-condition for ( 1 40): ( 1 42)
The number o f those <x,y> such that x is a dog and y
is
a rat and
x ate y is greater than the number o f tho se such that
z
is a
cat and w is a mouse and z ate w But this is too weak. Suppose three dogs ate the same rat (they share it) and one cat ate two mice . Then ( 1 42) would be satisfted because we would have more rat-eating dogs than mouse- eating cats. But, intuitively, ( 1 40) is false in this situation . This is so because the number of mice that were eaten by cats (=2) is larger than the number of rats that were eaten b y dogs (= I ) ,
i. e.
the second co nj unct o f ( 1 4 1 ) is no t m et .
Thus, I take it that ( 1 4 1 ) i s essentially correct . The question w e have to
answer is now : How can we obtain the information ( 1 41 ) from the surface ( 1 40)? Let us as<>ume, as Chomsky does in his comments on ( 1 36) (a), a rule o f construal that associates the than-phrase in ( 1 40) with both ( 1 43)
I
rmre NPs:
i i i [More dogs] ate [more rats] - [than cats ate mice]
have indicated this association by means of the 'association-index' i, an
a1 hoc-invention for the purposes of the present discussion. This notation is to be interpreted as if the than-phrase belonged to both NPs. So let us put it there, for convenience: ( 1 44)
More dogs [than cats ate mice] ate more rats [than cats ate mice]
The next step of construal involves considerations of parallelism : the sub-
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The best way to convince oneself that this is indeed the right reading o f
44 j ect
dogs o f t he mat rix-clause is correlated with t he subject o f the than cats and t he d irect object o f the matrix clause rats is correlated wit h
clause
t he direct object o f t he than- clause mice. We can expre&<> this correlation in t he following way :
( 1 45) More dogs SU [than catsSU ate mice
b0
DO [tha n cats ate mice ate more rats
]
Semantically, this correlation will have t he fo llowing effect : t he clause will express property perty
( 1 47):
first than (146) and t he second one will exp ress pro
( 1 47) Am [ cats ate m mice] We are now a&<>uming a semantics for comp arative NPs which parallels t he semantics o f comparative APs. Let us assume, for convenience, a meaning rule
in t he syle of l.ewis-Seuren .
( 1 48) [ NP more Ns S] is that higher-order property which is than
true o f a plural property p26 iff ( 3 x)( 3 n)
[x is a set of Ns & x has at least n-many members & P(x) & - (For at least n: S is true of n)] t han Let us assume now that t he
ate
in
( 1 48) is a two-place plural predicate.
Furthermore, we assume t hat we have a quantifier rule that raises the two
( 1 48) leaving a A-bound variable at t he original place. Thus we get ( 1 49) from ( 1 45):
NPs in
( 1 49 ) [More dogsS U than catsSU ate mice] Ax([more ratsDO than cats 00 ate mice ] Ay(x ate y))
If we evaluate t his according to our assumptions, ( 1 46 ) and ( 1 47), we get
t he following proposition:
( 150)
( 3 x) ( 3 n) [x is a set of dogs & x has at least n-many members
(3 y)( 3 m) [y is a set of rats & y has at least m-many members &
x ate y & "'(For at least m : cats ate m mice)] n cats ate mice))
& - (Fo r at least n :
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( 1 46) A n [ n cats ate mice]
45 I claim that (1 50) is exactly what we wanted to have. In order to see this, let us restructure { 1 50) a bit. This will give us the mo re readable formula (151 ): (1 5 1 ) ( 3 xy)( 3 nm) [x is a se t of dogs & y is a set of rats & x has at least n members & y has at least m members &x ate y & �(For at least n : n cats ate mice) & �(For at least m : cats ate m mice)] Not ice first ( 1 5 1 ) does not imply that cats ate mice. This seems to be correct to me because (140) More dogs ate more rats than cats ate mice
( 1 5 2 ) ( 3 xy)( 3 mn) [x is a set of dogs & y is a set of rats & x has at least n members & y has at least m members & x ate y & �(For at least n : n cats ate mice)] This means that the number of dogs that ate rats is greater than the num ber of cats that ate mice. This is the first half of condition ( 1 41 ). In o rder to obtain t he second half of ( 1 4 1 ), we leave away the condition �(For at least m : cats ate m mice). This will give us the second conj unct of ( 1 4 1 ) by analogous reasoning, as before. Let us return now to Chomsky's example ( 1 3 6)(a). We have asked what its t ruth co nditions are. We have gained a certain security from the t reat ment of t he simpler example (140) and can t herfore answer the question in a rather straight forward way. The truth-conditions of ( 1 36)(a) are the following ones:
( 1 53) The number of silly lectures given by boring professo rs is greater than the number of silly lectures such that I expected them to be given by boring professors and
the number of boring professors who gave silly lectures is greater than the number of boring professors such that I expected them to give boring lectures.
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is true, if, for instance, three rats were eaten by dogs but no mouse was eaten at all. In order to see that (1 5 1 ) is equivalent with our intuitive account of (140)'s truth-conditions , i. e. , with { 1 4 1 ), let us leave out from { 1 5 1 ) the last conj unct , i e. the condition �(For at least m : cats are m mice). This will give us (1 52):
46
We get ( 1 5 3) from (1 39) if we associate t he subject of ( 1 39) with the sub ject o f the reconstructed than-clause and by-NP of t he matrix with the by NP of the than- clause, as is indicated in ( 1 5 4): ( 1 54)
SU t han I would have expected t hat lectures] 1 SU would be given b y boring professors] [ s [Silly lectures] 1 Y have been given by more [boring professors] B t han I would have expected that [ silly lectures would be given b y [boring � 8Y] professors]
* More (silly
( 1 55) a. A.n[I expected t hat n silly lectures would be given b y boring professors] b. A.m [ I expected t hat silly lectures would be given by m boring professo rs]
Using the same procedure as before, t his t reatment will give us exactly the truth- conditions ( 1 5 3 ) for ( 1 5 4). Let us come back to t he question asked initially. Why is the phe nomenon of multiple head comparatives restricted to plural and mass nouns? Before answering t he question, let me give two more examples: ( 1 56) is a case where the heads of the 'extraposed' than-clause are mass nouns, ( 1 5 7) is a mixed case. ( 1 56) [ Le ss land] i produces [more corn] i [than ever before] i ( 1 57) No airline saves you more money in more ways than Delta. 2 7
Let u s compare (1 56) with (1 58) in order to answer our question, i.e. why is the former better than the latter? ( 1 58)
? [A greater man] i would be [a better man] i - [than Otto] i
As before, t he superscript indicates that t he than-clause has to be asso ciated with both b racketed NPs . Let us consider first (1 5 6). This sentence expresses the following pro position.
( 1 59) The amount of land which produces corn is smaller than the amo unt of land which produced corn ever before and
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We have to make sure t hat the two than 's express the following two properties, respectively :
47 the amount of corn produced by land is larger than the amount o f corn produced b y land ever before. We get this reading by familiar reasoning, if we associate the reconstructed than- clause with both head NP and if we 'link' the subject of the than clause to the subject o f the main clause and the object op the than-clause to the object of the main clause, as indicated in (160). -
( 1 60) [ Less land ] SU [than [land] SU ever before produced corn] produce [more corn] 081 [than land ever before produced [corn] 081 ]
(161)
[A greater man] i would be [a better man] i - [than Otto] i
We have two possibilities to fill up the than-clause : ( 1 62) a. than Otto is a great man b. than Otto is a good man If we choose the fust alternative, we get a co mplement that fits the first but not the second , and if we choose the second alternative, we have it the other way round . We would, of course, fust associate the than-clause in (1 6 1 ) with the two different NPs and only then complete it in different ways. But the low acceptability of ( 1 6 1) shows that our grammar doesn't work that way. It seems, then, that the restrictions for the reconstruction of a than-phrase are rather syntactic than semantic. As said initially, the treatment of multihead comparative constructions offers no new insight into the semantics of comparison . But they are a nice example of an application of the t heory. Rather simple principles enable us to analyse sentences which are at fust sight so complex that some people even doubt that they are semantically well-formed. 28 NP
XI. CAN DEGREES BE ELIMINATED? All the analyses we have considered so far rely on the notion of degree. We have not been co ncerned with the question, what degrees are. (For this question, cf. Cresswell [ 1976] and Klein [ 1980] .) Suffice it to say, what ever they are, they are highly abstract entities. Consider now the following two sentences.
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If we try to apply this method to (1 58) we see at once, where the differ ence is with respect to ( 1 5 6). Before associating the than-clause with the two head-NPs, we have to ask how we have to complete it. Let us repeat ( 1 5 8) as (1 6 1 ) for convenience :
48 ( 1 63) a. John is taller than Mary b . John's height exceeds Mary's height
( 1 64) Mary is tall is true with respect to c, if Mary is amo ng t he defmitely tall things in c with respect to c, false if she is among the definitely not-tall things in c wit h respect to c, and truth-valueless ot herwise. The sent ence ( 1 63) a. John is true
is
taller than Mary
with respect to c iff ( 1 65 ) ho lds:
( 1 65 ) ( 3 c '�c)(John is tall is true w.r.t . c ' & -(Mary is tall is t ru e w . r.t. c' )) It can be shown that , in Klein's theory, ( 1 65 ) is equivalent with (1 66): ( 1 66) John is tall is true w.r.t. I John, Mary I & "'(Mary is tall is t rue w .r.t. I John, Mary I )
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We have t he feeling that t he former is somehow more concrete than t he second . It states a relation between John a nd Mary, two concrete objects, whereas t he se co nd states a relation between John's height and Mary's height, i. e. between two degrees (abstract objects). Now , details aside, the semant ic t heories we have been considering in this article, treat ( 1 64)(a) and (b) exactly alike, viz. as propositions in volving degrees. It seems desirable to d evelop an analysis t hat does not involve the notion of degree for sentences like (1 63)(a). This is o ne o f t he motivations for E. Klein's theory of comparison (Klein ( 1980] ). In this sectio n I will show two things. First, in its actual form, Klein's analysis is incorrect , because it makes certain wrong p redictions. Second ly, degrees cannot be eliminated in t he general case. Therefore Klein's theory is necessarily incomplete. Now , what is Klein's theory? His main idea (which goes back to Wheeler [ 1 972] ) is that an adjective like tall has to be interpreted relative to a comparison class, called context. If c is a context, tall devides c into the definitely tall things (if there are any), t he definitely not-tall things (if t here are any) and those things which are neither defmitely tall nor defi nitely not-tall. Thus a sentence lik e :
49 ( 1 66) grasps the idea that ( 1 63)(a) is about John and Mary and that in order to verify this sentence we must compare the two . Let us make this more precise. I will restrict the discussion to an ex tensional version of an adjective semant ics incorporating these ideas. It is obvious how it carries over to an intensional frame-work. Let a pro[XJsition be a partial function from the set of comparison classes into the set of truth-values I 0 , 1 1 . The proposition p is true w.r.t. the comparison class c iff p(c) = 1 , and p is false w.r.t. c iff p(c) 0. Let us denote the denotation of an expression a by Ia I. Then, in Klein's semantics, the following is assumed : =
=
Now, Klein presumably identifies the defmitely not tall objects with the short objects (though he is not entirely explicit about this). Hoepelman [ 1982 : 1 1 ] remarks that this has the consequence t hat the following two sentences are treated alike, given Klein's interpretation rules for the connectives (Klein [ 1 980 : 1 1 ] ). (1 68) a. Mary is tall and short b . Mary is neither tall nor sho rt But, as Hoepelman correctly notices, there is a n intuitively given differ ence: (a) is always false whereas (b) is contingent . This criticism assumes the same meaning for not tall and short. In deed, if short where the same as not tall, then ( 1 68)(b) would mean the same as ( 1 68)(c): ( 1 68) c. Mary is not tall and she is not not-tall This can never be true. We could try to save Klein's adjective semantics against Hoepelman's criticism if we assume the following partition for any comparison class: ( 1 69) not tall short
zs
not short
(
tall )
The arrow symbolizes an ordering of the members o f c according to in creasing tallness.
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(1 67) !Mary is talll (c) = 1 iff Mary is definitely tall w .r.t . c and !Mary is talll(c) 0 iff Mary is definitely not tall w.r.t . c
50 Such a move would help Klein against the particular criticism of Hoe pelman. But this move seems rather artificial. For instance, we have to stipulate that t he extensions not tall and not short can overlap, because otherwise t he sentence ( 1 70) Mary is not tall and she is not short can't be true. It is not clear then, what t he general semantics of negation would be within that system. And an accommodation of Klein's theory along these lines would not save it from other objections . It seems to me that the following sentences co uld never be treated within Klein's frame-work :
I have no idea how ( 1 7 1 )(a) and (b) can be incorporated in Klein's system. I am inclined to think that this is not possible. I have t ried hard , b ut with out success . In order to convince the reader of the plausibility of my con j ecture, I should say a bit more about Klein's comparative rule, but I can't go into this for reasons of restricted space. Concerning ( 1 7 1 )(c), this example showx very clearly that degrees can't always be replaced by concrete obj ects. In order to fmd out whether (1 7 1 ) i s true, w e don't compare Ede with himself. We compare Ede's height with his breadth. It is reasonable to assume that this amounts to a co mparison o f two degrees. An other theory would be to say , that we compare two aspects of Ede. Ede qua tall and Ede qua broad. No one has, however, proposed a theory of the latter kind. And anyway, such a theory would involve abstract entities, height and b readth, exactly as before. The main conclusion of this section is that d egrees cannot be eliminated in the general case . Thus Klein cannot offer a unified analysis of comparative constructions. I don't know how strong this criticism is . 29 Perhaps a more concrete analysis in Klein's style (without the defect mentioned) should be upheld as long as possible. Only when this is impossible we will switch over to degrees. The second conclusion is that we have to respect the data of ( 1 7 1 ) for an adequate analysis of the comparative. Notice that the only theory which has treated cases lik (I 7 1 )(a) and (b ) explicit ly, is, to my knowledge Hellan [ 1 9 8 1 ] . It is not easy to treat these examples without more or less drastical changes in Lewis', Seuren's or Cresswell's system . On the other hand , it is precisely cases like ( 1 7 1 ) which motivate Hellan's analysis, which looks so complicated at fust sight . Hellan would analyse ( 1 7 I ) (a) and (b ) as ( 1 7 2 ) (a) and ( 1 7 2 )(b), respect ively :
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( 1 7 1 ) a. John is six inches taller than Mary b . Ede is twice as fat as Angelika c. Ede is more tall t han broad
51 ( 1 72) a. ( 3 d 1 ,d 2 ,d 3 )(John is d rtall & Mary is d Ttall & d 1 =ct 2 +d 3 & d 3 6 inches) b . (3 d 1 ,d 2 ,d 3)(E de is d fat & Angelika is d fat & d =d r T I 2 d3 & d3 = 2) =
•
The positive and equative arise simply as special cases: the 'differential' variable d 3 is specified by the context. It is a degree > 0 in the case of the comparative and it is the number 1 in the case of the equative. Thus ( 1 7 3 )(a) and (b) are analysed as ( 1 74)(a) and (b), respectively, in his system :
(1 74) a. ( 3d 1 ,d 2 ,d 3 ) (John is d rtall & Mary is d 2 -tall & d 1 d 2 +d 3 & d 3 > O) b . ( 3 d 1 ,d 2 ,d 3 ) (John is d rtall & Mary is d Ttall & d 1 = d 2 d 3 & d3 = I ) =
•
Thus, this extra complication is well motivated after all, and it must be in corporated in an adequate theo ry of the comparative.
X. ITE R ATED MODALITIES AND SCOPE OF THAN· CLAUSES
In section VIII, we found a way of justifying a theory that regards the than- complement of a comparative adjective as a definite description. Since the time has come to risk a p roposal which brings the loose ends of the previous sections together, I wa nt discuss the question of whether we should prefer such an approach or one working with double indexing. There is a classical argument , in Cresswell [ 1 97 3 : 1 49f] , that can help us decide this question: In certain cases, defmite descriptions have a greater expressive power than double indexing . Cresswell discusses the (ad mitted ly somewhat peculiar) sentence : ( 1 7 5) The major allowably presides necessarily If we treat the mayor as a Russellian description we can have a reading which is roughly represented as (I 76):
(I 76) Allowab ly (the mayo r Xx[necessarily (x presides)] ) This means something like (1 77):
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( 1 7 3 ) a. John is taller than Mary b . John is as tall as Mary
52 ( 1 77) In every permitted world w, the one who is mayor in w , presides in every world w', which is accessible from w The point is that the nominal the mayor is within the scope o f the modal operato r allowably b ut outside the scope of the model necessarily. If we t reat the mayor by means o f double indexing, that is, as a name where the mayor (w) denotes the mayor in w and the actual mayor (w) denotes the mayor in w 0, where w0 is the real world, we can't express this, because then, the mayor is either in the scope of both modal operators or it is so to speak, not in the scope of any modal operator. We can now try to carry this observation over to comparative con structions. Consider the following sentence.
I think there is a reading of (1 78) which can be rendered as something like ( 1 79): ( 1 79) For every world of my thoughts w, there was a world w' accessible from w, such that the degree o f Plato's boringness in w' exceeded t he degree of Plato's boringness in w We can represent this reading30 easily in a theory which treats the than complement of a comparative as a definite description. But we can't re present it in one o f our double indexing approaches. A Russellian account of ( 1 79) would be ( 1 80): ( 1 80) I thought (the d (Plato boring] > d')] )
is
d-boring] M ' [O(the d " [ Plato is d"
The only reasonable candidate for a representation of ( 1 79) in a double in dexing theory, say Seuren's, would be (1 8 1 ): ( 1 8 1 ) I thought 0( 3d)(Plato is > d-boring & -- ACTUALLY(Plato d-boring)]
is �
But this is not the reading (179). (1 8 1 ) rather means something like ( 1 8 2 ): ( 1 82) In the worlds of my thoughts it was possible that Plato was more boring than he really was One could try to express (1 79) by means of a more complicated para phrase, say (1 83):
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( 1 7 8) I thought Plato could have been more boring
53 ( 183) I thought 0 [(3 d)(Plato is ;;;<: d-boring & -(ACTUALLY(I thought [Plato is � d-boring] )]
XI. SYNTHESIS 1.
The comparative
Let us start with t he comparative. We use Montague's strategy and ge neralize to the worst case. Here is one. (1 84) Ede is at least 6 inches taller than Otto is We get t he right interpretation for this if we assume that the 'logical form' o f ( 1 84) is something like : ( 1 85 ) than how tall Otto is
I
at least 6 inches
I
NP· J Ede is ej more tall ei
I s
s s
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But such a move wouldn't help. Some reflection will show that (1 83) is inconsistent. The question is, of course, whether t he reading (1 79) exists for ( 1 7 8). I think it does. If (1 78) is not the right kind of example t hen it shows at least what kind of example is needed in order to show that t he Russellian approach enjoys a generality the double-indexing theories can't reach. On the other hand, we know that we can't take over Russell's solution in its existing shape. It will be the task of the last section to develop a proposal which is adequate with respect to all facts observed in this article.
54 Before I explain this picture let me give an idea o f the interpretation I have in mind for (1 8 5). It is this : ( 1 86) the d [Otto is d-tall] Xd i ( 3 dj ,dj > 6 inches) [Ede is dj + drtall] ) The wide scope o f the description doesn't matter in this case. Therefore, this amounts to : ( 1 87) ( 3 dj ,dj � 6 inches) (Ede is dj + the d [Otto is d-tall] -tall]
( 1 88) Ede is [ NP at least 6 inches]
� ; re ( tall [s than how tall Otto is]
The modifier more or -er is the comparative mo rpheme. The analysis of t he than- complement is inspired by Chomsky [ 1977] . I am assuming that the 'deep-structure' of the than-clause is : ( 1 89) than Otto is how tall By wh-movement we get (1 90)(a) or, perhaps, (b): ( 1 90) a. than [how tall] i Otto is e i b . than howi Otto is ei tall The than- complement might also be the clause ( 1 9 1 )(a) o r (b), possibilities discussed by Chomsky but immaterial for my purposes. ( 1 9 1 ) a. than what i Otto is e i b . [pp than Otto] The only thing that matters here is the following assumption : A1 .
The than- complement determines a p roperty of degrees.
The most plausible surface structure for illustrating this assumption is ( 1 90)(b). We may think o f the semantics of wh-movement simply as property abstraction. Thus, (190)(b) determines the property M [Otto is d-tall] . We can form this in a very sloppy way as a rule:
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This seems an adequate account of the truth-conditions of ( 1 8 4). Let me explain next how we get to ( 1 87) from the surface. I will give an informal account which is supposed to be precise enough for everyone to t ranslate into his favourite gramm atical frame-work. The surface of ( 1 85) is :
55 R1 .
Property abstraction how [ . . . . .i-A . . . ] expresses the property of degrees i
The idea is now t hat any
than-
Xd [ . . . d -A. . . ] .
o r as- complement is, semantically, a
nominal. Since nominals have scope, they must in general be raised in the
way indicated in ( 1 85). This holds for sentential complement s generally.
It is interesting to note t hat o nly very few people have noticed this, one o f
these b e ing Cresswell [ 1 973 : 1 6 5 ff] . But , a s far as I can se e , t h is far reaching idea has not entered into t he linguistic literature. A proper way of nominalizing the property of degrees expressed by a co mparative complement is to make a definite description out of it .
In the
case we are discussing here, the application of t he usual defmite article will
Vlll we know that
Thus the nominalization of the
than-
or as- clause can be described in the
following way :
R2 .
Nominalization of comparative complements.
Suppose , the "S" in
"than
S" or "as S " determines t he propert y of degrees
P. Then t he whole phrase determines t he nominal-meaning :
the (Max(P)) Let us repeat , for convenience t he defmition o f the functions , Max and { 1 92 )
the.
Let P , P2 be say fust-order properties. the(P )(P ) is the pro 1 1 2 position true in a world w if ( 3 x) (Vy) [ [w e P (x) � x = y] & 1 w e P2 (x)]
I am ·assuming an ontology like Cresswell [ 19 73 ] , i.e., I think of propo
sitions as sets of possible worlds and of properties as functions mapping
individuals into propositions. And I am assuming, of course, the usual
semantic vocabulary. Thus, ( 1 93)
the is j ust
Russell's defm ite description-operator.
Let P be any property o f degrees. Than Max(P)
is that property & -( 3 d ')
which is true of any degree d in a world w iff P(d) [ w e P(d ' ) & d '
> d]
This i s j ust a repetition o f ( 1 1 7). If w e take o u r rules together, then t he meaning o f our following way.
S than how tall Otto is
can be roughly described in the
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yield t he right resuh . But from the d iscussion in section
we have to 'maximize' the property of degrees to get the right resuhs.
56 ( 1 94)
Let P be any property o f degrees and let w be any world . Then
lfthan how tall Otto is 0 (P)
is true in w iff the maximal degree such
t hat Otto is d-tall has property P in w (If we spell that out properly according to
( 1 92) and ( 193),
the meta
linguistic locution gets much longer, of course.) There is a second nominal in
(1 85), viz. at least 6 inches.
If we disregard
its internal structure, its meaning can be described in the following way :
( 1 95) Uat least 6 inches U is true i n world ( 3 d)(d > 6 inches & w e P(d))
w o f a property o f degrees P i ff
means. I think o f the internal t hing like the following :
( 1 96)
Ede
is
NP
v
I
I
VP
s As Cresswe ll [ 1 976] and Hellan [ 198 1 ] , I am assuming, that tall denotes a
two-place relation connecting individuals with degrees,
i e.
we have t he
following rule:
R3 :
Let x be an individual and d a degree, then we have for any world w : w e
UtaliD (x,d) iff d
is a degree o f tallness
&x
has d in w .
For a p recise analysis o f the metalinguistic locution used in t he defmiens, vide Cresswell
[ 1976: 267 ) .
Before spelling out the meaning rule for
rmre it is
useful to reflect on
the logical type of its meaning. We can read it o ff from
( 196)
in the
following way. In Cresswell's o ntology, we would have t he following
correspondence between the syntactic categories assumed and t ypes :
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( 1 85 ) completely is to have an idea -er (which we represented as more) structure of the d eepest S in ( 1 85) as some
What we need in o rder to interpret what t he comparative morpheme
57 0 A
•
I A
<0, 1 , 1 >
<,I> 1 0 • <<,I>,> Hence, A /A 1 0 Since nvre t akes a degree and gives us a A /A , it must be o f t ype �<4f,I>,I>,>,I>. In what follows, I will denote t his t ype b y . Similarly for other co mplex t ypes. I don't think o f -+ as a •
function but as a relation . One category determines a lot of t ypes, in
general. Now, t he meaning of more (-er) is roughly this : R4 :
Comparative
, 1 >, re t 0 (d 1 )(A0) (d2 )(x) iffw w e I �:
0
e A (x,d +d ) 2 1
As is seen from a glance at the defmiens, this meaning rule is, in fact , very
simple. The complicated type of t he function llmore O i s due to t he particular descriptive frame-work I am assuming. In Montague's PTQ, more would even
be
of
t ype
t>>>>, I guess.
<�.e><�.<�.e>,<�.e>,t>>>,<�.e>,<�.e>,
In order to evaluat e ( 1 85) we need the generally accept ed assumption :
A2 .
Raised nominals are evaluated acco rding to the familiar quant i fying in rule (cf. Montague [ 1 974] ).
It is convenient to repeat { 1 8 5 ) in a way that reflects the logical structure which it has according to our assumptions: (1 97)
the maximal d .s.t . Otto is d-tall M 2 [at least
6
inches M
d +d tall] ] 1 T
1
[Ede is
According to our rules, t his proposition is t rue in a world w, iff {1 98) holds good . (1 98)
( 3 d ) [d ;a. 6 inches 1 1 s.t . Otto is d-tall in w]
&
Ede is d +d 2 -tall in w 1
& d2
= t he max. d ,
I f we look at t he meaning rule (R4), we fmd that Urmre D is a four place relation which has two degrees among its arguments.
In
the example we
have discussed , t hese arguments where specified linguistically. This is, however, often not the case. Take t he sentence :
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0 Let d ,d 2 be any degrees, A an appropriate relation o f type 1 x any individual and w any world . Then <0 , 1
58 ( 1 97) Ede
is
taller than Otto
Here, the 'differential' degree d 1 is not expressed . It has therefore to be supplied b y the context. Hence, the 'logical form' of ( 1 97) is something like : ( 1 98) For some degree d 1 > 0, Ede is d 1 +d 2 -tall, where d 2 is the d s.t . Otto is d-tall In ( 1 98), the nominal "For some degree d 1 > 0" has to be supplied by the context. There are cases, where also the second degree d 2 has to be re constructed from the context, for instance, if we say:
The present analysis follows the strategy that we make explicit those parameters in the logical analysis, which can be made explicit in a natural way linguistically. As ( 1 84) shows, both degree positions can be explicit . Thus, our rule (R4) is not artificial, it seems to me. 2 . The equative We can analyse the equative in a perfectly parallel way. The meaning rule for as is this :
Here, d 1 is a real number and the other parameters are as in (R4). Let us apply this. (200) Aristotle is at most half as boring as Plato The logical form of (2 00) is roughly : (20 1 ) the maximal d s.t. Plato i s d-bor ing ;\.d 1 [at most half (times) An [Aristotle is n d-boring) ] •
In order t o se e that this is right, w e only need a n appropriate meaning rule for at most half: (20 2 ) w
€
Gat most halj(times) O(P) iff ( 3 n)(n
�I& w
€
Here, w is any world and P is a property of real numbers.
P(n))
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( 1 99) Plato is more bo ring
59 I leave it to the reader to check that this semantics has exactly the desired effects. One of the nice features of this analysis of the equative is that we don't have to worry (as most authors have, e.g. Cresswell), whether sentence (2 03)(a) means (2 03)(b) or (c). (203) a. Tristan is as heavy as Randi b. Tristan is exactly as heavy as Randi c. Tristan is at least as heavy as Randi
3 . The positive We have to speak about the positive because the adequacy of an adjective semantics can be judged only if it covers in a natural way bo th the positive and the comparative adjective. Recall that fat is a relation between things and degrees (of fatness). The simplest way of representing (204) Ede is fat is to leave the degree variable open : (205) Ede is d-fat We would say than that it is the task of the context to specify the degree of fatness which Ede really has. In the same way, the context had to specify the d 1 -variable in the case o f the comparative (cf. section 1 ). This approach, however, would not be satisfactory. The meaning of (2 04) can't be satisfied by j ust any degree. Everyone is fat in some sense (cf. for this, Lewis [ 1 970: 65] ). So (204) would be trivially true. Since this is obviously not the case, (204) means something as 'Ede is positively fat'. The operator 'positively', call it pos, is invisible, which made E. Klein think that it doesn't exist . I will come back to this. Now, what should the semantics of pos be? From the literature we
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(20 3 )(a) can have both meanings. In one case the context supplies the quotient U (e.xactly) one (times)O and the second case it supplies Oat least one (times) n. Since ordinary language hardly ever makes the quotient explicit, equatives are vague with respect to the two readings. It would be wrong to build the 'exactly' or 'at least' into the meaning of as, I believe. In a way, as means simply multiplication and roo re means addition. It should be obvious from remarks at the end of section IX that I am indebted to Lars Hellan for this insight .
60
know that it is heavily context-dependent {cf., e.g. Cresswell [ 1 976] or Kaiser [ 1 979] or Aristotle [Categories) ). Take Aristotle's examples. (206) a. This co rn is big b . This mountain is small c. In the summer, there are only few people in Athens, but there are a lot of people in the village
=
(207) Ede is (a) pos {C/
d
/Ao
(man)
fat o
l
�
YJ c
I have used the label C for 'comparison class' (or 'common nouns'). Se mantically, C's are properties, i. e. functions of type <0,1>. Hence po s takes an adjective and makes a C-modifier out of it. We are now ready for a rough semantics of po s. R6.
Positive let A0 be any adjective meaning, C be any appropriate property, x be any appropriate individual ard w be any world. Then w € ftpos O (A0 )(C)(x) iff ( 3 d) [d is an A0 -degree & d > average [A0 ,C] & x has d in w & w € C{x)] .
I am not interested in analysing the notion "average [A0 ,C] ". If A0 = Dtal/1 and C = Dman D, then this can be read as "the average tallness for men". It is an empirical question how the notion "average" has to be analysed� it must depend o n t he parameters A0 and C, or perhaps even
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According to Aristotle, (a) means that t his corn is big with respect to other corns, (b) means that trus mountain is small with respect to other moun tains, and (c) means that the number of the people dwelling in Athens in summer time is small with respect to the number of people who stay in Athens during the w inter, but the other way round for the village. We can incorporate this insight into the semantics of the positive operator by stipulating that the degree determined by po s depends on a comparison class (vtle Cresswell [ 1976] for this). The comparison class can be given explicitly ( linguistically) or im plicitly (i. e. , by the context). These considerations suggest that the 'logical form' of (204) is something like (207)
61 o n w . Whatever the truth may be, I think the meaning o f the positive must be something like t he function descnbed in (R6). Let me make a brief remark about the difference between predicative and attributive adjectives. I think the semantic difference consists in the fact that the morphology indicates that in t he first case the comparison class is implicit whereas it is explicit in the second case. Thus, (208)(a) is analysed as (208)(b ), where C is a property variable the context has to specify . fat ] ] (208) a. Ede is [ AP[ A +pred b . Ede is [ [ C/C pos [ Ao fat] ] C]
(209) a. Ede
is
b . Ede is
a [N [ A fat ] man] +attr a [ [ C/C pos [ Ao fat ] ] man]
We can think of a positive adjective as modifying always the next common noun, simple or complex. This assumption would force us to assume an and in 'logical form' between appositive adjectives : (2 1 0) Ede is a fat young scholar The logical form (2 1 1)(a) determines the reading (21 2)(a) whereas (2 1 1 ) (b) represents (2 1 2){b) (2 1 1 ) a. Ede b . Ede
is is
a pos-fat (pos-young(scholar)) a [pos-fat and pas-young] scholar 3 1
(2 1 2) a. Ede is fat as young scholars go and he is a scholar b . Ede is fat as scholars go and young as scholars go and he is a scholar The positive operator specif�es in a way the degree variable of the ad jective. Therefore we can't have it if t he degree is . overtly specified, as in � 1 �: {2 1 3) Ede is 6 feet tall
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It is the impact of the feature [ + predicative] which requires the presence of the property variable C in logical form . The attributive adjective is analysed as (209)(a)- (b):
62 (2 1 3) will roughly have the logical form (2 1 4) tall (Ede, 6 feet) This creates a certain problem for t he interpretation o f (2 1 5) Ede is a 6 feet tall scholar
(2 1 6) Ede is a scholar who
is
6 feet tall
Thus, (2 1 5) requires oo new principles of interpretation. Let me conclude this section with a remark concerning the relation between positive and comparative. Ewan Klein [ 1 980 : 2] says that we should derive the meaning of Aer from the meaning of A, where A is the positive adjective. This must be so by the principle of compositionality. Obviously we have oot followed Klein's advice. I find Klein's argument oot convincing for the following reasons. I have assumed that the positive adjective may be regarded as A-stem + Positive roo rpheme whereas the comparative is analysed as A-stem + Comparative morpheme Since the positive is the unmarked form , the positive morpheme is not visible. Obviously, my analysis conforms the cornpositionality principle. Klein would admit this but he thinks that this is merely lip-service. He stipulates that a positive adjective should express a one-place property and that the comparative has to be shaped out of that . I have argued elsewhere, at length, that adjectives can't be one-place properties (cf. v. Stechow [ 1 982]). I think Klein's flaw is this : i f certain parameters are left implicit in t he language we should oot conclude from this fact that they are logically dispensable. The situation o f having to introduce extra parameters for the semantic analysis of language is not uncommon. Indeed, this is what almost always happens. Take, for instance, the medals
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"6 feet tall' is simply a p roperty and oot a relation between individuals and properties like ''pos tall". There are a number of possibilities for solving t he problem. The simplest one is to work with property conjunction, i .e. we make out of the two properties "6 feet tall" and "scholar" the complex property of ''being a scholar and 6 feet tall". We need this rule anyway, if we want interpret relative clauses, e.g.
63
must or can. Syntactically these take naked infinitives as complements and make VPs out of it. Think for convenience of them as sentential operators, i.e. as one-place functors. It is a common place that, semantically, these operators have to be two-place operators. lmustl (p) means something like "p follows from q " , where q is a proposition to be specified by the con text ( 'the modal backg round', cf. Kratzer [ 1 978]). Similarly, lcanl (p) means that p is compatible with the background proposition q. It would be hopeless to attempt to think of lmustl and lcanl as one-place functions simply because they are syntactically one-place connectives. If there were a straightforward connection between the positive and the comparative then it would be just the opposite of what Klein assumes: tall means "taller than x ", and the context tells you what x is.
POSITIVE
In this section I want to show that my t reatment of the comparative and
positive generalizes across the relevant categories: adjectives, mass nouns, plural nouns and certain adverbs. I will show in detail only how the analysis carries over to plural and mass nouns. It is obvious how adverbs have to be t reated . I am relying heavily on ideas found in C resswell [ 1 976] in o rder to formulate the relevant generalizations. Let me start with comparative plural (and mass) nouns: (2 1 7) At least 6 more toads than frogs croak (2 1 8) Ede owns at most 3 ounces more gold than Kurt The truth-conditions of (2 1 7) can be read off from the following formula. (2 1 9) the maximal n s.t. 3 X [X is an n-membered set of frogs who croak] Xd 2 [At least 6 Ad d 3 Y[Y is a d 1 +d 2 "member ed set of toads who croak]]] In order to see how we get these t ruth-conditions, it is useful to get an idea of how we analyse the nominal at least 6 more toads. C resswell's idea is that semantically, plural nouns (and mass nouns) are similar to adjectives. lltoads U is a relation connecting a set X of individuals and a cardinality n( 'set-degree') iff X is a set of toads and X has the cardinality n. It is pretty obvious now that we can apply the meaning of Umore U to lltoais 0, two cardinalities d 1 and d 2 and a set X. The only thing we have to make sure of is that at least 6 more toads is a nominal. This is achieved
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4. THE CROSs- CATEGORY GENERALIZATION OF THE COMPA RATIVE AND
64 by analysing at least 6 more as a complex determiner. Before stating t he relevant meaning rules, it is good to have an idea o f what t he logical structure of our nominal is. We illustrate this by d rawing a t ree which is, in a ll relevant respects, parallel to (1 96), i.e. t he tree motivating our rules (R3) and ( R4). This observation will allow an immediate understanding o f t he following meaning rules :
(2 2 0)
s
....,----
r
than frogs croak
�
NP 1
at least 6
------1
N 1
�
b r1l [=Det] �1 � I NP more toads I t N lt
�VP
N pl [= NP] S
I
I
pl
croak
t2
l
We have more or less the same category-type correspondence as in t he case of ( 1 96), i.e . :
�1
-
1 N pl - <, l >
� �1
N 1/
nrJre
-
-
_
b�
_
b
_
�t>
Let us indicate the meaning rules now. I will begin with t he plural rule (cf. Cresswell [ 1976; Def. 3 .6] ). A plural noun like toads has the follow ing st ructure: toad-pi, where pi is the plural morpheme. pi is interpreted as an operator of t ype <, >. It s meaning is t his: R7 .
Le t P b e a first-order property, X be a se t o f individuals, n b e a number, and let w be any world . Then w E �VJt n (P)(X,n) iff (Vx E X) [w E P(x) & the cardinality o f X is n] .
This rule presupposes t hat 'plural-degrees' are numbers with t heir usual
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I
S
65
ordering. Thus, '+' a nd have t heir ordinary meaning in this case. Ac cording to this rule, lltoads � i.e. llp!U ( Utoad 11) applies to <X,n> iff X is an n-membered set of toads. The meaning rule of our det erminer forming more is exactly parallel to adverb forming nvre ( R4). It is this : '·'
R 8.
w E ilmJre D (d 1 ) w E VPpl(X)] .
a11) (d 2 )(VPpl)
�
3 X [w E
� 1(X,d 1 +d2 )
&
�
R8.
!gold II is a two-place relation which holds good o f a mass x and an amount a iff x is gold and A is t he amount of t he totality of x.
It should be obvious that t his semant ics (Cresswell's) enables us to analyse (2 1 8) in a way which is exactly parallel to our analysis of (2 1 7 ). I don't want to spell this out here. Everything we have said carries over to t he analysis of positive plural and mass nouns. Since the details are messy I will content myself with a few remarks. Consider the following data. (22 1 ) a. b. c. d. e.
How much gold [ yp is in Ede's pocket ] ? Much gold VP At least 6 ounces (of) gold VP A large amount o f red gold VP Gold VP
(22 1 )(a) suggests that we should analyse the NP how nruch gold as (222). (222) d-much gold
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This rule presupposes that l is t he meaning of a plural noun, i.e. oome t hing like lltoads II. VPpl muSt b e t he meaning o f a plural-VP. The differ ence between singular and plural-VPs is simply t hat t he latter apply to set s o f individuals. Thus, llcroakpl H is t ru e of a set of individuals X iff each member o f X croaks. I don't want to spell this out here. For a detailed acco u nt , vide v. Stechow [ 1 980] . According to our rules, t he NP [t 1 nvre toads t 2 ] in (220) means AVP [ 3 X(X is a d 1 +d Tmembered set of toads which VP)] . I leave it to the reader to check that t he entire (220) does indeed mean (2 1 9). Constructions involving mass nouns are analysed in exactly t he same way. The only d ifference is t hat mass nouns are inherently relational. There is no need to apply an operator like llp/ 11 on t hem. Thus the meaning of gold is oomet hing like this.
66 with the following semant ics for t he determiner d-much : R9 .
w
€
nd-much 0 (Nmass)(VP) i ff 3 X [w € Nmass(X, d) & w
€
VP(X)] .
The logical form o f (22 1 )(c) is t he n roughly (22 3): (223) ( 3d,d ;;;, 6 ounces) [d-much gold VP] The determiner d-much is determined b y an appropriate rule from an amo unt degree d and the mass adje ct ive much whose meaning is :
RIO.
w
€
llmuch n (X,a) iff
a
This presupposes t hat X is a mass and a is an amount . Since much is an ordinary adjective stem, we can apply t he positive operator to it. This will g ive us [XJS much. Since this adj e ct ive occurs o n ly in determiner position, we have to describe its semantics analogously to t he determiner d-much Thus we arrive at the following meaning rule :
Rl l .
w € llpo s much II (Nmass )(C)(VP) iff t he maximal d [d is an Nmass degree & 3 X(w € N mass(X ,d) & w € VP(X))] > average [Nmass 'C]
According to t his rule, Much gold C is in Ede's pocket is t rue iff the maximal d such t hat d is a degree of gold in Ede's pocket which exceeds t he average of gold with respect to the comparison class C. If we assume an analogous rule for pos little with "<'' instead o f ">", t hen we obtain t he desired result t hat Much gold is in Ede 's pocket is incompatib le with Little gold is in Ede 's pocket. There is a great deal more to be said about this. For instance, what is the nature of t he comparison property C, which is practically never specified linguistically? The only t hing I have assumed is t hat it is a property of masses. Clearly, we want to know mo re about the relevant contextual parameters which determine C. I have nothing to say about this. But, deta ils aside , t he analysis of positive mass nouns seems correct . And it c arries over, of course, to positive plural nou ns. Here we have to work wit h the determin ers how many, n-many a nd {XJS many. It should be obvious t hat we can analyse positive and comparative adverbs in the same spirit : (224) a . Tristan yells loud ly b . How lo udly does Tristan yell? c. Tristan yells three times as loudly as Otto
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is the amo unt of t he tot ality o f X i n w.
67 I don't want to work out t he details for t hese cases. The general strategy is as befo re. The logical form of (224)(c) is roughly this. (22 5 ) [as how loudly Otto yells] 2 [three times] 1 Tristan yells d 1 loudly
·
dr
I leave it as homework for t he reader to develop an appropriate semantics for the adverb forming suffix-ly. If we have it we get t he right semantics, given t he assumpt ion that loud is an ordinary adject ive. Thus our se mantics of t he comparative and equative generalizes over all relevant categories.
Let me add some remarks about words like very or fairly. Wheeler [ 1 972] has proposed that the property very fat man gives us the individuals which are fat with respect to fat men. And a fairly fat man is a fat man but not a very fat man. This idea has b een taken up by Klein [ 1980] . I don't know whether Wheeler's view is correct , because this semantics seems too precise to me. But, if you want to adopt it , it is easy to build in. If you want another semantics, you can have it, too. The following is an ac commodation of Wheeler's and Klein's account . The complex noun very fat man has t he following logical structures: (226) very
pos-fat
man
A
N
I
I
A/A
-----------A
--
I
N
Here A is short for N/N, where N determines the t ype <0, 1 >. Hence, very is of type . And it has the following mea ning : R 1 2.
w E Uvery U (A)(N)(x) iff w E A (A(N))(x).
This presupJX>ses that A is a function of type N/N, i.e. somet hing like
{XJS-fat, that N is a function of type <0, 1 >, x is an ind ividual, and w is a world. According to our rules, (226) will express the property which is t rue o f an x in a world w iff ( 3d) [ d is a degree o f fat ness & d > average [fat , llpos-fat man II] & x is d-fat in w & w E Hpos-fat man U(x)] . If we evaluate this further we find that this holds good iff x is a man
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5. DEGREE MODI FIERS
68 in
w w ho is fatter
in
w than the average fat man. Thus ( R l 2) is no more
t han a t ranslation of Wheeler's idea into t his frame-wo rk. The meaning rule for fairly is now obvious.
6 . TOO : A COUNTERFACfUAL COMPARATIVE MO RPHEME
The word too has the most complicated semantics of t he comparative morphemes, as far as
know. Hence it
I
Consid er this sentence : (227)
worth describing semant ically.
This pack is at least ftfty kilos too heavy to lift
is :
s
----S--I I �VP NP at least j SO kg I � t his pack V AP I A� 1 is S �O I Op [PRO to lift t ] A A l /AO j j /'\ I NP.
too
NP
I
heavy
t
i
The idea fo r an analysis o f this structure is that it should express t he following propositio n : (229)
I f one could lift this pack, t hen it would be at least
50
kg less
heavy t han it actually is
Let us assume t hat the embedded
S
in (228) expresses a p roposition,
viz.
'One lifts itj ', where 'itj ' mea � 'this pack ' . 32 Accord ing to what we have said in previous sections, t he S should semant ically be a no minal. But in
this
S de too is o f t ype <<<<0, 1 >, O>,
p articular case we can ignore this. So let us assume t hat the
termines the t ype o f propositions 0. Hence
A0>, 1 >.
The difference with t he comparative morpheme is simply that
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The 'logical fo rm' of t his (228)
is
69 the S.complement of a too-adjective doesn't denote a property b ut a proposition. In the case o f (228) it is not obvious why this should be so, but the following example illustrates this point. (230) The weather is too good to stay at home Clearly, t he embedded infmitival does not express a property which applies to the weather. Instead of giving a full account of the meaning of too, I will simply write down a very sloppy meaning rule which hopefully makes the idea clear: lltoo li (d i ) (A0)(p)(x) 0 A (x,d r d i )J
=
0 t he max.d [ x i s d-A ] M 2 [p
o-+
Our semantic rules predict the following t ruth-conditions for (228): (23 I ) the d [this pack is d-heavy] Ad? [at least 50 kg Ad 1 [One lifts this pack G+ it is d r d rheavy] ) A little reflection will show that these truth-conditions are adequate.
7. REV IEWING THE RELEVANT DATA
In this section I will go again through the data considered initially. The claim is that my proposal can deal adequately with all o f them.
(RA) Russell's ambiguity
I thought you r yacht was larger than it was.
The two readings are analysed as (232)(a) and (b): (232) a. I thought (the max. d [your yacht is d-Iarge] M 2 [some positive degree Ad 1 [your yacht is d I +d T large] ] ) b . the max. d [your yacht is d-large] Ad :z [I t hought (Some positive degree Ad I [your yacht is d I +d 2 -Iarge J )J (232)(a) represents the inconsistent, (b) the consistent thought. (AC)
Ambiguous counterfactuals If Ed e had smoked less than he did , he would be healthier than he is
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RI 3 .
70 I will represent t he nontrivial reading o nly. It is clear, that we can have the uninformative readings, too. In order to improve readability I leave out the nominal some positive degree, which specifies t he open 'differential variab le' d I , and leave that variable free. (233) the max. d [ Ede has smoked d-much] Ad 2 [the max. d [he is d-healthy] M 2 [Ede has smoked d 1 +d T little D-+ he is d '1 + d 2healthy] ] Notice that our raising analysis prevents t he unwa rranted reading (36), which we discussed in section III. This is so because, in our account, the main clause is no t a description, which could have wide scope.
We have to show that the co mparative complement is an NPI-context , i.e. where S is a comparative complement, we can, sometimes, substitute a more informative S'. We show this for a special case. The following ar gument is valid : (234) Ede is fatter than Randi or Otto is :. Ede is fatter than Ra ncli is Here, S is Randi or Otto is d-fat and S' is Rami is d-fat. Clearly, S' is more informative than S. The relevant formalization of (234) in our theo ry is this: (2 35) the (Max (Xd [ Randi o r Otto is d-fat] ))M 2 [ 3 d ,d > 0) Ad I [Ede is d 1 +d Tfat] ] :. the (Max(M [Randi is d-fat])) M 2 [( 3d,d > 0) M 1 [Ede is d l +d T fat] ] Recall that the semantics o f the operators the and Max has been int roduced in ( 1 92) and ( 1 93). Clearly, this argument is valid . Not ice that it is es· sential that the 'differential variable' is bound by the appropriate existent ial quant ifier in order to make t he argument work. It is obvious that t he explanation of the validity of the argument : (Q &C) QuantiFter and connective embedding Ede is fatter than anyone [= someone] o f us :. Ede is fatter than everyo ne of us
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(NPI ) Negative polarity a. Ede is cleverer than anyone o f us b. Max is as well as ever
71 proceeds along exactly t he same lines. The relevant formalization is t he one where anyone is within t he scope of t he Max-operator but everyone is not, i. e. (236): (236) t he (Max (Ad [( 3 x, x is one of us) x is d-fat ] )) Ad 2 [ ( 3 d, d > 0) Ad 1 [ Ede is d 1 � 2 -fut ] ] _�������----�------���� :. Everyone Ax. [the (Max (Ad [x is one of us & x is d-fat ] )) M 2 [( 3d , d > O) :>..d 1 [Ede is d 1 +d2 -fat] ]
. (237) Ede Is as fat as
tndi or Otto �
anyone C! f us . as fat as Randi ... Ed e 1s everyone o f us
�
�
Let us see next how my analysis blocks unwarranted inferences like the following : (UI )
Blocking unwa"anted inferences Ede is fatter tha n Otto :. Ede is fatter than everyone
There are two formalizations of this argument , viz . (238) and (239). (238) the max. d [Otto is d-fat ] Ad 2 [ 3 d ,d > O) Ad dEde is d 1 +d 2 -fat ] ] :. the max.d [everyone is d-fat] :>..d2 [(3 d ,d > O):>..d l [Ede is d 1 +d 2fat] ] fat],_,_] (239) the max.d [Otto is d-fat] M 2 [ 3 d ,d > O)M 1 [Ede is d 1 +d 2 ·_ -=' :. Everyone Ax. [the max.d [x is d-fat] :>..d 2 [(3 d,d >0) :>..d dEde is d 1 +d Tfat ] ] ]
___
Clearly, (239) is invalid . (238) could be true if everyone did mean "every one except Ede" and everyone except Ede would be fat to the same degree. If Ede is fatter than Otto he must then be fatter than everyone except himself. I t hink t hese predictions are correct. We now explain the oddness of comparative constructions with em bedded negative quantifiers:
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Recall that the presence o f the Max-operator is essential for the soundness of t he last two arguments. Since t he Max-operator is present in any 'com parative' complement, i.e. also in complements of equatives, we pred ict exactly the same effects for equatives. This seems correct . We know that we fmd negative po larity items in as-clauses. Moreover, the quantifiers behave similarly, as the validity of t he following arguments shows :
72 Ed .
e
(NQ)
IS
�� mo re �� mte n·�gent s� than �5 no one o f us as as .
There are two formalizations of this. (240) does not express a proposition since t he description does not denote. (24 1 ), however, says that (NQ) expresses contingent propositions. I have no idea how this reading is to be barred . Yet, it should be clear from the discussion in section VII that any theory has a difficulty here. (240) the max.d [No one of us is d-intelligent] Ad 2 [
Ad 1 [Ed e is
(24 1 ) No one of us Ax. [ . . .x . . . ] Here, . .x . is (240) with x instead of no one of us. The next datum on our list is : .
(0)
. .
A polar bear could be bigger t han a grizzly bear could be
A satisfactory analysis is: (242) the max.d [0 3x [x is a grizzly bear & x is d-big] ] >..ct 2 [(3 d,d > 0) >..ct 1 [0 3 y [y is a polar bear & y is d 1 +d Tbig] ] ] So our t heory is adequate also with respect to this case. Let u s repeat
now the examples for the differential readings :
(DR)
a. John is at least six inches taller than Mary b. Ede is at most twice as fat as Angelika
These are analysed as (243) and (244), respectively. (243) the max.d [ Mary tall] ]
is
d-tall] Act 2 [ 3 d ,d ;;;., 6 inches) Ad dEd e is d 1 +d 2-
(244) the max .d [ Angelika is d-tall] }..d 2 [ 3d ,d � 2) }..d 1 [ Angelika is d t " d 2-fat] ] Iterated modality i s the last example o n our check list :
(IM)
I t hought Plato could have been more boring
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l � � �; � -intelligent] ]
�g� :� :�1 �
73 The interesting sense, which we were discussing in section X, is represented by t he following analysis: {245) I thought (the max.d (Plato is d-boring ] M 2 [(3 d ,d > O) M 1 [O{Plato is d 1 +d 2-boring)] ) Thus we can be happy in this respect as well. If we look back at our evaluation tabel (xv) of section I, we fmd that our proposal gets 9 points out of 9 possible points. ·On these assumptions the following statement is a t ruth: {246) My proposal is almost twice as good as Russell' s or Cresswell's.
NOTES L Cf. Russell [ 1905 : 489 ] . I am indebted to Horn [ 19 8 1 ] , who on his turn, is in debted to Abott, for pointing out that Ru ssell brought up this problem some seventy years before Postal [ 1 9 7 4 ] made it fashionable in linguistics. 2. There can hardly be any doubt t hat (2) and ( 3) are the correct 'proto formalizations' of Russell's analyses, because the paper where Russell's remark occurs is in fact his theory of descriptions, i e. t he birth of the idea that nominals have scope. What Russell calls a "size" is a special case of what is more commonly called a "degree of comparison" or just a "degree". In this paper I have nothing to say about the on tological status of degrees. I assume that degrees of the same kind form a scale so that we can say things like d 1 < d 2 . I also assume that in many cases degrees have a metric so that we can speak of d 1 + d 2 . (In the case of lengths for instance it is quite obvious that we can form a length which is the sum of two given lengths). Predicates like < or + are of cour!l! relative to the kind of degree in question, although this relativity is not usually indicated. I t is not clear when and how we can perform operations on different kinds of degrees. For instance if d 1 is a degree of length and d 2 a degree of c leverness it is not clear that there is any < for which d 1 < d 2 makes sense. 3. In an earlier version of this paper, I had included an extensive discussion of Horn's proposal (Cf. Stechow [ 1982 ] ). The usual restrictions in space forced me to sacrifice that section. 4. Williams' formulas are sl�htly more comp licated. I have simplif"Jed them by perform ing some ;\-conversions. 5. I am grossly simplifying. For the details of Cresswell's semantics for the com perat ive operator er than, see Cresswell ( 1976: 268]. 6 . This idea goes back to at least Jespersen aoo is made explicit in Ross ( 196 8: 294 ] . Cf. Seuren, p. 5 30ff. 7 . Cf. Lewis [ 19 7 2 : 6 4 ] . 8. Lewis' theory is a b i t nicer, because delineations are implicit parameters, l ike e.g. the world-and-t ime-parameter. I think, this is an attractive view.
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University of Konstanz linguistics Department P.O . Box 5560 77 50 Konstanz , BRD.
74 9. A t least, this is claimed in the literature. Cf. Postal, 392f. I n German, where we d istinguish between the indicative and the subjunctive of the past, it is not possible to have a counterfactual of this sort with an inconsistent antecedent or consequent. (i)
Wenn Maria weniger geraucht hiitte (subj.} als sie geraucht hat (ind.}, ware (subj.} sie gesilnder als sie ist (ind.}
Counterfactuals with t he subjunctive both in the main-clause and in t he a/s·clause of t he comparative construction are impossible: (ii}
*Wenn Maria weniger geraucht hlitte (subj .} als sie geraucht hiitte (subj.} wiire (subj . } sie gesiinder w sie wiire (subj.}
(ii} is felt as incomplete. We would expect further embedded wenn-clauses: Wenn Maria weniger geraucht hiitte, als sie geraucht hiitte, wenn sie eine ordentliche Arbeit gehabt hatte, wiire sie . . .
This cross-linguistic comparison makes it very hard for m e to believe in the am biguity of (26). For the purposes of the present discussion, however, my disbelief is i mmaterial. I am interested in the 'consistent' reading only. And t his is the one we have in German, too. 10. Cf. Lewis [ 1 9 7 3 a : 556 ] . 1 1. Postal, p . 392f. Our (48) is Postal's (76) (a) and our (49) i s his (7 7). 1 2. Cf., for instance, Stalnaker [ 1 96 8 ) . 1 3. Cf. Klein [ 19 80 ) . 1 4. The possibility of treating these cases b y means o f double indexing is mentioned in Lewis [ 19 7 3b ] . 1 5 . Cf. Cresswell [ 1 9 7 3 ) , for this u se of properties. 16. Cf. Seuren, p. 5 33 ff. 1 7. (7 2) is Seuren's (24). (7 1 ) goes back to Ross [ 1968, p . 294 ) , where a similar example is discussed. Notice that one might dispute the claim that any is a negative polarity item in view of ( 7 1 } alone. I am not going into this, here. 1 8. I t should be obvious that I am not using the symbols CN,VP etc. in the sense of nonterminals. CN denotes an aroitrary but f"tx ed common noun phrase. Similarly for the other symbols. 1 9. It will be seen later that this claim is too strong. Aer is only downward entailing for some S-atguments, as the next section will show. This suggests that we have to weaken Ladusaw's criteriotL 20. I n this connection it should be mentioned that it is very doubtful whether the (- operator should be regarded as genuitively downward-entailing with respect to its domain. I f we assume that the definite article is represented b y the .t- operator, then the definite article should be downward-entailing with respect to the CN-poSition. This, however, is not the case, intuitively. Thus, the def"mite article should not be down ward-entailing with respect to the CN-positions. But the CN-position of the def"mite term corresponds exactly to the S in Postal's analysis. i.e. we have the correspondence I.XCN "" vc:S. But then the (-operator should not be downward-entailing with respect to the S, This would rule out Russell's and Postal's theory on independent grounds. 2 1 . Vtl�. e.g. , Cresswell [ 1976 ) . 22. I n the original account o f Cresswell, which I have been simplifying throughout,
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(iii}
75 (99) doesn't express a proposition at all That's the reason why I gave Cresswell a "+" in the evalu ation in 1.2. 2 3. Similarly, (i) doesn't have the reading (ii}: • 1 ohn � taller than B ill is not
(i)
(ii)
John is not taller than Bill is
Clearly, these
are
examples which are related to our discussion.
point with Cresswell, bu t he claims that the wide scope readings
(I have raised this
are
possible. Since
my own theory doesn't block these readings either it would be good if he were r�ht).
24.
A sentence of t his kind was brought to my attention by David Lewis, though
in a rather d ifferent connection. R ich ard S harvey once gave a talk in Wellington, where he bu ilt in a totality
I am indebted to him fo r this
idea.
26. I e. , a property that applies to sets of individuals. Vide Stechow [ 1980 ] . 27. This example is taken from Chomsky [ 1 9 8 1 : 8 3 ] . Another nice example is:
"Never in the history of human conflict has so much been owed by so many to so few." (Churchill).
2 8.
So, for example, B. Partee, if I remember well a discussion we had in the Trianon
at N ij megen.
29. What worries me more with K lein's approach is that he thinks that the notion
of the comparative is essentially derived from the fact that the predicates in natu ral language are vague. This idea is in spired by Karnp
[ 197 3 ] . I believe that this idea is
mi!guided. We have comp arative notions in precise languages. Furthermore, in tu itively, comp arative notions like taller are always applicable without any problem
whereas this is not so for tall and short. So relation by two more obscure concepts.
30.
I see
no
reason to explain the clearer
The existence of this reading can
be made plausible by the following story : I had read Plato I thought him as boring as Spinoza (whom I rmd very boring). B u t when I was reading him I found him only as boring as Heidegger (whom I rmd less boring, than Spinoza). At this time, Plato had in every world w of my "Before
thoughts the same degree o f boringness as H eidegger had in w, but for every such worid w there· was
an
accessible world w', where Plato was
as
boring as Spinoza was
in w. Since for any world of my thoughts w, Spinozas boredom in w exceeds Heideg ger boredom in w, we can descnbe this situation as ( 1 79), whose linguistic expression is
( 1 7 8). I t is pretty obviou s that Plato 's "objective" boringness (if there is such a
thing), i e. his boringness in the actual world, plays no role in this comparison.
Perhaps the example is not well chosen. But the structure of the argument should be clear.
3 1 . I am assuming a cross-category generalization of and in the sense of v. Stechow [ 1974] or Partee-Rooth [ 1 983 ] . 3 2. The structure o f the pu rposive in (228) is the same as Chomsky [ 1981 , p . 205 ] assu mes.
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25.
condition for definite articles modify ing mass nouns.
76 REFERENCES Aristoteles, A ristotelis Categoriae et Liber de In terpretatione. Ed. L. Minio-Paluello. Oxford University Press, Oxford, 1963. B artsch, R. & Vennemann, Th., 1 9 7 2 : Semantic Stroctures. Atheniium, Frankfurt/M. Bresnan, J . , 1 97 5 : Comp arative deletion and constraints on transformations. Linguistic A nalysis 1 , 1 : 25-74.
Chomsky, N. , 1 9 7 7 : On wh-movement. In : P. Culicover, T. Wasow & A Akmajian (eds.), Formal Syntax. Academic Press, New York. Chomsky, N., 1 9 8 1 : Lectures on Government and Binding. Foris, Dordrecht . Cresswell, M.J., 1 97 3 : Logics and Languages. Methuen, London. Cresswell, M.J., 1 976 : The semantics of deg ree . In : B. Partee (ed.), Montague Gram mar. Academic Press, New York. pp. 26 1-292.
Hoepelman, J . , 1 9 8 2 : Adjectives and nou ns : a new calculus. In : R. Bauerle et a/.
(eds.) Meaning, Use and /nterpretati:Jn of Language. De Gruyter, Berlin. pp. 1 90-220. Horn, L, 1 9 8 1 : A pragmatic approach to certain ambiguities. Linguistics and Phi losophy 4: 3 2 1 - 3 5 8. Kaiser, G., 1 97 9 : Hoch und gut - Uberlegungen zur Se mantik polarer Adjektive. Linguistische Berichte 59: 1-26.
Karnp,
H., 1978: Two theories of adjectives. In: E. Keenan (ed . ) Formal Semantics ofNatural Language. Cambridge University Press, Cambridge. pp. 1 2 3- 1 5 5 . Klein, E., 1 9 8 0 : A semantics for positive and co mparative adjectives. Linguistics and Phibsophy 4 : 1 -45. Kratzer, A , 1 97 8 : Die Semantik der Rede, Kontexttheorie, Modale, Konditionale.
Scriptor, Kronberg/Ts.
I..ad usaw, W. A , 1 9 7 9 : Polarity Sensitivity as Inherent Scope Relations. PhD diss. Austin, Texas. Lewis, D.K., 1 9 7 0 : General Semantics. Synthese 2 2 : 1 8-67 . Lewis, D.K. , 1 973a: Causation. Journal of Philosophy 70 : 5 5 6-567. Lewis, D.K., 1 973b: Cou nterfactuals and comparative po ssibility. Journal of Philo
sophical Logic 2: 436-437. Montague, R., 1974a: Formal Philosophy. R.H. Thomason (ed.). Yale University Press, New Haven - London. Montague, R., 1974b : The proper treatment of quantil!cation in ordinary English (= PTQ). I n : Montague 197 4a, pp. 247-270. Montague, R., 1 9 74c: English pp. 1 88-2 2 1 .
as
a formal language
( EFL). In: Montague 1 9 74a, =
Partee, B. & Rooth, M . , 1 9 8 2 : Ge neralized conjunction and type ambiguity. In :
R. Bauerle, Ch. Schwane & A. von Stechow (eds.), Meaning, Use, a lrl Inter pretation of Language. De Gruyter, Berlin. Postal, P. M., 1974: On certain ambiguities. L inguistic lnquiry 5: 367-4 25 .
Ross, J . R . , 1 96 8 : A proposed rule of tree pruning. In : D.A. Reibel & S. Schane
(eds.), Modern Studief in English. Prentice Hall, Englewood Cliffs. pp. 288-299. Russell, B., 1 905 : On denoting . Mind 14: 479-4 9 3 .
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Gazdar, G. , 1979: A Phrase Structure syntax for comparative clauses. In : T. Hoek stra, H. v.d. Hulst & M. Moortgat (eds.), Lexical Grammar. Foris, Dordrecht. Hamann, C., Nerbonne J. & Pietsch, R., 1 980 : On the semantics of comparison. Linguistische Berichte 67: 1-22. Hellan, L , 1 9 8 1 : Towards an In tegrated A nalysis of Comparatives. Narr. Tiibingen.
77 Seuren, P. A.M., 1 97 3 : The comparative. In : F . Kiefer & N . Ruwet (eds.), Generative Grammar in Europe. Reidel, Dordrecht. pp. 5 28-564. Stalnaker, R, 1968: A theory of conditionals. In: N. Rescher (ed.), Studks in Logi cal Theory. B lackwell, Oxford. Von Stechow, A, 1974: �-;\.-kontextfreie Sprachen. Ein Beitrag zu einer natiirlichen formalen Semantik. Linguistische Berichte 34: 1-33 . Von Stechow, A . , 1 980 : Modification o f Noun Phrases. A challenge for compositonal semantics. Theoretical Linguistics 7 , 1 / 2 : 5 7- 109. Von Stechow, A , 1 9 8 1 : Topic, focus, and local relevance. In: W. K lein & W. Levelt (eds.), Crossing the Boundaries in Linguistics. Reidel, Dordrecht. pp. 95- 1 30 . Wheeler, S.C., 1 9 7 2 : Attributives and their modir�ers. Nous 6 : 3 10-3 34. Williams, E., 1 97 7 : Discourse and hgical form. Linguistic Inquiry 8, 1 : 1 0 1 - 1 39. Wunderlich, D., 1 97 3 : Vergleichsatze. In : F . Kiefer & N. Ruwet (eds.), Generative Grammar in Europe. Reidel, Dordrecht. pp. 6 29- 6 7 2
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Joumal o[&mantics 3 : 79 - 8 1
COMMENTS ON VON STECHOW
M .J. CRESSWELL
( I ) The degree of Arnim's ingenuity is amazing (2) Urs is even more ingenious than Arnim (3) The degree of Urs's ingenuity is even more amazing. The semantics of ( 1 ) and (3) seem to me clearly to involve degrees of ingenuity, and it is very difficult to see how this obviously valid inference could be explained without the involvement of degrees in the semantics of (2). Von Stechow raises the question of scope vs double indexing . This is a very vexing question in a whole range of situations, and seems to divide theorists into scopists and non-scopists. I think it is almost certain that, in general, both scope and double indexing are needed . Certainly I believe that defmite descriptions have scope. Beyond that I would hesi tate to venture . So it does not surprise me that in the case of the compa rative, as elsewhere, scope and double indexing might be involved. This certainly complicates the analysis presented in Cresswell ( 1 976), but not I think in a way incompatible with its spirit . One o f the most important features o f my 1 976 paper, at least in m y eyes, was that i t tries to give some account o f what a degree o f comparison actually is. A degree of comparison (see p . 266) is a pair >. where > is a relation and u is in its field . The point of this account is so that an
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My comments on von Stechow's paper will be extremely brief, and will solely concern relations between it and my 1 976 paper. I have not worked further on comparatives since then, except for a brief discussion of certain causative adverbs in Cresswell (I 979). By and large I am in agreement with most of what von Stechow says, or at least I see no reason for serious dis agreement, though of course I might not put things in just the same way myself. In particular, he has put forward powerful considerations for treat ing degree phrases as nominals. This seems to me to be right, if only be cause we can form explicit phrases like "the degree of Arnim's ingenuity". The use of such phrases also seems evidence for using a degree of com parison approach in the frrst place rather than one which does not involve degrees. Consider the following inference :
80 explanation can be given of when two degrees can be compare d , and what it is to compare them. Where > is a relation then > is a 'higher' degree than > iff u> v. The point of the > is simply to indicate how to compare them . Trouble comes when we have different relations if 1 > is a degree of height and 2 > is a degree of cleverness then how can they be compared? Strictly they cannot, because there are two scales involved. This makes sentences like
( 4) Martin is taller than Arnim is clever semantically uninterpretable . Perhaps this is as it should be. At any rate one of the unresolved questions of Cresswell
( 1 976), was what to do
with
a problem closely related to the ontological question of the nature of degrees. I t is problems of this kind, rather than problems of von Stechow's kind, which underlie the concerns of Cresswe ll
(I 976).
Some problems of
this kind were actually solved there . One concerns some interesting links between degrees of tallnes� and degrees of shortness. For instance , six feet, as a degree of tallness, m ight be represented as >, but, as a degree of shortness, as , in which < is the converse of > . Von Stechow assumes that it is m eaningfu l to say things like d 1 > d2 , without saying where > comes from . In particular the question of whether > is an ordering of all degrees, and what kind of an ordering it is, does not seem to me to be really faced . He even seems to think that degrees can be added . I n certain cases, such as heights or lengths d1
+
d2 does seem to
make perfect sense. But this may well be because of rather special proper t ies of the scale involved in these degrees. There are certainly difficult ontological problems here. A s von Stechow notes in Section XI , a sentence like (5) Ede is twice as fat as Angelika (this is his (
1 7 lb))
does seem to require that we can add degrees of fatness.
My problem would be to produce a defmition of degree which would en able this to be done when it can be done . Possibly one can extract the
appropriate metric from the scale. This was one of the problems I posed on p.
2 89 of Cresswell ( 1 976).
·In remarking that von Stechow does not tackle these ontological questions, I don't intend criticism of what he has done. He has probably produced the most thorough and comprehensive survey of truth condi tional accounts of comparatives, and has extracted from them a theory which is,
I
am inclined to think , better than the others. But the ontological
questions do remain - and it was those questions which formed a very
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situations in which this sort of sentences makes sense . This seems to me
81 large part of my own previous work. I t seems to me that von Stechow's work remains completely neutral on these issues and in that sense is in dependent of at least one of the principal concerns of my own work. Victoria University of Wellington Wellington, New Zealand.
REFERENCES
1 9 7 6 : The semantics o f degree. In : Partee, B . H . (ed.), Montague 26 1-292. Cresswell, M.J., 1 97 9 : Adverbs o f causation. In: Eikmeyer, H.-J , & Rieser, H. (eds.), Words, Worlds, and Con texts, De Gruyter, Berlin ; 21-37. Cresswell, M.J.
Grammar, Academic Press, New York;
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Von Stechow, A., this volume: Comparing semantic theories of comparison.
Journal of Semantics 3 : 83 - 92
NOTE ON SOME ISSUES RAISED BY VON STECHOW
LARS HELLAN
1.
Interaction with moda/s.
Von Stechow (this volume) notes that a sentence like ( I ) (his ( 2 6)) is not verified under the circumstances ( 2 ) (his (46)): (I)
(2 ) wo : w2 : w3 : w4 :
I f Mary had smoked less (than she does/did), she would b e health ier (than she is). C igarettes smoked by Mary 20 I5 IO 5
M ary's degree of health I I 2
The increase in health should have started already in w 2 , for ( I ) to be true . The same presumably applies if we consider w rw 4 as future real worlds, and change ( I ) to ( 3 ) : (3 )
I f Mary smokes less (than she does), she will be healthier (than she is).
In contrast, the sentences (4) and (5) are verified by ( 2 ), with w rw4 taken as possible and future worlds, respectively : (4)
If Mary had smoked less (than she does/did), she could be health ier (than she is).
(5)
If Mary smokes less (than she does), she can become healthier (than she is).
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Time prevents me from trying to asse ss von Stechow's unified analysis of the phenomena he addresses, and also from reflecting properly on some of the comments he makes on my analysis in Hellan ( 1 9 8 1 ) . My note is primarily confmed to the issue of representing semantic scope.
84 The relevance of (2 ) to ( 1 ) is thus not tied to the counterfactual content of ( 1 ), but rather to a contrast between willjwould on the one hand and can/could on the other: the former pair seems to involve universal quanti fication over the worlds (possible or future, real) in question, the latter existential quantification. A gross formalization bringing out this contrast between ( 1 ) and (3) is given in (6) and (7); note that in (6) (representing ( 1 )), also two degree variables receive universal quantification, whereas in (7), all quantification is existential. A similar difference will obtain in the representations of (4) and (5), the 'worlds'-quantification now being restricted to future, real worlds. 3 d 1 2 ,d 22 [Mary smokes d 1 2 much & Mary is d 22 healthy & w ¥ i R R • d l l ,d 2 1 [d u < d l 2 & d 2 1 > d 22 -4 w l R R [M ary smoke d 1 1 much -4 Mary be d 2 1 healthy] ] ]
3 d 1 1 ,d 1 2 ,d 2 1 ,d 22 , w lRR [M ary smokes d 1 2 much & Mary is d 22 healthy & d 1 1 < d 1 2 & d 2 1 > d 22 & w i RR[ M ary sm oke d 1 1 much -4 Mary be d 2 1 healthy]] ("w iRR p" means "p, with regard to the (non-real) world w i RR ".)
(7)
Both (6) and (7) represent non-trivial readings, neither claiming that for a given world (real or not, future or present), M ary has two degrees of health simultaneously (or smokes to two different extents simultaneous ly). In Hellan ( 1 98 1 ), the way generally chosen to represent which degrees go with which worlds involves the "Quantifier Raising" (QR) process, whereby degree-expressions pertaining to the 'real' world are situated out side the scope of whatever expressions introduce the 'non-real' (or future) aspect. The level of representation to which Q R applies is in most respects a syntactic level, and the result of Q R resembles an analysis tree of Mon tague-grammar or a Chomskyan "Logical Form", in Hellan op.cit. called DA (for "disambiguated representation"). (8), by this strategy, is an es sential part of the DA of ( I ) and (3), using the formalism in Hellan op.cit.:
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( 6)
85 (8)
- 1 --- Q - 2 ---- 1 -- o Deg Q 1 1 1 little
�
I
I
Deg
.I
er
1
1s
2s
�
-1 Q2 .-- - O � Q2 _...2 than she Deg 1 2 smokes t- 1 0 much 1 much D eg2 · -.. o---. Deg S 2 S
I
� than she is t-2 0 healthy
The 'counterfactual' morphemes had -d in 5 s and would/could in 6s are here left unexpressed. Hellan ( 1 98 1 ) has no treatment of such ex pressions, but we may assume that their effect on the logical translation of 3 s is t_9 provide an "unreal world" operator for the translation of the part of 3 s entered in (8), i.e. the bound occurrence of ' 'w i RR " in (6,7). In the further course o f translation given in this system , we obtain (9) for the node 1 S : (9)
wi RR [Mary smoke d 1 1 m uch -+ Mary be d 1 2 healthy] & Mary is d 22 healthy & d 2 1 > d 22 & M ary smokes d 1 2 much & d 1 1 < d 1 2
A final step remains, namely binding all the free variables. In Hellan ( 1 98 1 ), one single rule is given for this purpose, with two parts: adjoining an element B IND to the top S-node in DA , whose translation-effect is to prefix the translation of this S with existential quantifiers binding all the free variables in the translation of S ((1 9 ,2 0), p. 2 1 5 , op .cit.). As J said , forms like would and could were not addressed in· this system , but we note that this procedure yields exactly the right translation of (3) , namely (7). Now what about ( 1 )? Von Stechow correctly points out that the avail able system does not yield the right reading - represented as in ( 6), or
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I
er
86 by other mechanisms for counterfactuals. However, it is easy enough to devise an alternative operator to the above-mentioned BIND - let us call it WOULD - which converts (9) into (6) by the following convention :
{ 1 0)
s.
A similar convention would apply for WILL S, with w FUT instead of WI RR · At ftrst sight, this may look like a grossly ad hoc manoever just to ftt recalcitrant constructions into an inadequate analysis. However, the reader acquainted with Lewis ( 1 9 7 5) and Heim (I 982) will notice that what we are really doing here is to treat WOULD/WILL and COULD/CAN as a kind of "unselective" quantifiers, imposing their quantificational force on all free variables inside their scope , be it 'world' -variables or degree variables. The 'universal' force of WOULD is thus enforced in (I Ob ), while the 'existential' force of COULD is embodied in the above-men tioned translation of BIND S, which should then really be relabelled as "COULD S". The authors mentioned have argued for the adequacy of this kind of analysis for indefmite noun phrases, Heim in particular concluding that indefmite noun phrases have no quantificational force of their own . What we are suggesting is now that comparative expressions, which can be regarded as degree-denoting expressions, also have no quantificational force of their own. Modal verbs are on a par with adverbs in having the capacity of carrying the quantificational force . Thus, just as Heim (in the 'LF' in her chapter 2) 'raises' quantificational adverbs and quantifiers in NPs to the position under the top S-node, we must here conceive of WILL/WOULD and CAN/COULD as being raised to topmost position in
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Translation of [WOULD S ] : Let a dx b e any variable free i n the translation o f S which has an occurrence either inside the scope of w i R R ' or in a conjunct together with a variable free inside the scope of w iRR . [WOULD S ] then translates on the form (a) 3 dz , . . . ,d z [A & B ] 1 n where A is the conjunction of all those conjuncts in the translation of S lacking a d x , and B has the form (b) Vw iRRW ,d x , . . . , dx [C] n 1 Here C in tum is of the form (c) (D 1 & . . . & Dm -+ Dn where D n is initiated by the operator w iRR and none of D rDm is, and all of D 1 -Dn are originally conjuncts in the translation of
87 (8), with so m e kind of modal feature o n
s 3 as a 'vestige', to ensure intro
duction of the right 'world '-operator at this stage in the translatio n . In stead of (8), the DA of { 1 ) is thus { 1 1 ):
s
{1 1)
�S
WOULD
1
(as in (8), with the appropriate feature o n
s 3 )
Needless to say, many details will have to be worked out before we can claim to have combined the analysis of comparatives in Hellan { 1 98 1 ) with a Lewis/Heim-type approach to unselective quantifiers. Relating to Heim { 1 982), for instance, one question will be why WOULD in { 1 1 )
One upshot of this is then that the analysis of scope connected with quan tifiers presented in Hellan op.cit . may also be retained, in the face of the apparent problems raised by constructions like ( 1 ).
2. On "double indexing ". In his own proposal for how to deal with constructions like ( 1 ) , belief constructions and the like, von Stechow favours the use of an ACTUAL LY-operator over scope-representations of the type in (8)/{ 1 1 ) one alleg ,
ed advantage of this being that this logical representation comes closer to the surface syntactic form . By itself, this is hardly a substantive argu men t : either logical representations are a notational convenience for expressing truth-conditions and other semantically relevant properties,
in which case they can be chosen at wil l . Or they can be shown to be lin
guistically significant forms, in which case their formal properties are cru cially
not
something we can decide upon a priori. A more important con
sideration is whether such operators are required to attain empirical ade quacy. In the cases above, we have managed without a constant "AC TUALLY", but one may ask whether the w-subscripts "IR R " and "FUT" aren't really items of the same type . So let's consider what characterizes
this type of operator.
In the first place, ACTUALLY refers the evaluation to the 'real' world ,
or more generally, to a coordinate associated with the
speaker of the
sen 1 tence in question. Likewise for the NOW-operator (cf. Kamp 97 1 ).
Thus, construed as a predicate, "ACTUALLY" has the content " . . . . the speaker" as a crucial part . So, obviously, do "IRR" and "FUT". Secondly, and perhaps more importantly , ACTUALLY is exempted from the transitive relation "be inside the scope of' which most of the 'classical' operators take part in , along with categories in constituent
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leaves room for the existential quantifiers in { l Oa), despite its maximal scope. Still, it seems that such a combined approach is on the right track.
88 hierarchies. That is, for, e .g . , two 'classical' operators
0 1 and 0 2 and a 0 2 is inside the
constituent category C, if C is inside the scope of 0 1 and scope of
C,
then
02
is inside the scope of
01.
This conception of the re
lation "be inside the scope of' underlies both common logical notation and the disambiguated trees of DA/ L F . The point of ACTUALLY and
NOW
is that regardless how deeply embedded under other time- or world
operators they are structurally, they carry the speaker-oriented scope . Such 'non-transitive' behaviour is found also in the so-called "specific" use of indefmite NPs (called "snapping" use in· Hellan loading" in Barwise and Perry
( 1 983 )),
( 1 980), and
"value
in certain uses of past tense , and
p resumably in the time-related behaviour of certain common nouns, as explored in En�Y
(I 98 1 ) .
In the latter cases, the scope is not necessarily
the frrst . Looking now at the use of
"IRR"
in
(6,7),
we see that this use is
not
'non-transitive', since the operator is introduced in a non-embedded con text, i .e . in a context solely under the speaker's scope . Therefore , the re present ations
(6,7)
do not involve the full e ffect of the ACTUALLY
operator. This, of course, is made possible by our 'assembling' all the speaker-oriented material outside
3
8
in
(8);
the point now being made i s
only that we have avoided using both 'raising' processes i n DA and 'non transitive' operators in the logic . From this discussion, the general alternatives regarding the represen tation of 'scope' seem to be: (a)
Use of 'raising' in DA/LF, but no 'non-transitive ' logical operators.
(b)
Use of 'non-transitive' logical operators, but no 'raising' in DA/LF .
(c)
Use of both 'non-transitive' logical operators and 'raising' in DA/LF.
Concerning the 'non-transitive' operators, a notational alternative may be to have multiple representations which by themselves do obey the tran sitivity constraint , and which each represent one aspect of the total read ing. This is actually the format proposed in Hellan
( 1 980),
the 'aspects'
under consideration being quantifier scop e , 'snapping' vs. 'non-snapping', and 'responsibility', i .e . whether certain expressions are read as being un der the speaker's responsibility or some entity expressed in the sentence . The latter contrast can affect the choice between indicative and subjunc tive , like in the German example
( 1 2)
(suggested to me by Herbert Piitz,
personal communication), where the subjunctive form sei signals that the assertion of the weil-clause is to be ascribed to the children, not the speak er:
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speaker-oriented, so the second property of ACTUALLY is independent of
89 ( 1 2)
Die Kinder lachten iiber den Jungen, weil er so slecht angezogen sei. ''The children laughed at the boy because he was so badly dressed (according to them)"
That this aspect should be treated as independent of the quantifier scope aspect is suggested by examples like ( 1 3) cases were adduced in Fodor ( 1 976)) : ( 1 3)
(
=
( 1 5) in Hellan , op .cit . ; similar
John thinks that the chief U.S. spy has been murdered in five countries.
Here the characterization "chief U.S. spy" may be due to the speaker ,
the chief U S. spy is most naturally read as being inside countries, meaning that different persons have been mur dered in different countries. If then in five countries is inside the scope of thinks, which seems reasonable , chief U S. spy will be outside the scope of thinks with respect to responsibility, but inside with regard to quantifier
the scope of five
scope. One resolution of this· apparent conflict is then to represent res ponsibility and quantifier scope in different trees/formulas. Through some kind of 'double indexing', this effect could also be obtained in a unified representation, where one of the indexings would be 'non-transiti ve' at least with regard to the other. To the extent that this approach is correct , we then have some indepen dent support for the use of 'non-transitive' operators, which would direct us towards the alternatives (b) or (c) mentioned above . This counter to the upshot of our discussion of cases like
(1),
is a bit
which was that
(a) was sufficient in these cases. As a general conclusion , the latter would presumably be too strong also because of the 'snapping' uses of NPs and tense expressions (including the 'covert' ones in common nouns) . So it looks as if we are ultimately endorsing the 'richest' option (c), unless we settle for (b). Option (c) is interesting only if there is a principled difference between the cases calling for the 'non-transitive ' operators and those calling for
QR
in DA/LF (assuming of course that no phenomenon is subject to both
mechanisms). One such difference may be that 'snapping' and division of responsibility for expressions in a sentence are matters of which the
speaker
has almost unlimited control - it's like a light-ray which can be
directed against any part, independently of which other parts it has been directed against . (Some exceptions are clear: NPs like
no man, everyone
are hard to 'snap' with, and proper names uniformly require snapping. • I n contrast, scope-relations· depend very much o n syntactic structure and the m eaning of the operators involved, and it is reasonable to expect such
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John believing only that the office in question is that of ambassador. At the same time,
90 patterns to be subject to a transitivity requirement . This is rather loose
and speculative, of course , but quite likely true . If so , we notice that what the constructions
(1 ,3,4,5) involve is only scope of quantifiers, and
neither
snapping nor responsibility , and so we expect the analysis of these con
structions to be phraseable exclusively in terms of 'transitive ' operators,
that is, in the way we have proposed . With this elaboration, thus, (c)
is an interesting option after all, and the one we will settle for .
T o the claimed 'rigidity' of the transitivity-constrained representations,
it may be objected that they differ in some cases radically from surface
syntactic form , enjoying a freedom with regard to rearrangements which
harmonizes badly with the claimed rigidity . However, leaving open to what limits the 'semantic' scope structure can differ from surface constituent
sentation constrained by transitivity of the relation "be inside the scope
of'', once we stick to quantifiers, negation and constituent structure .
When snapping and responsibility are taken into account , in contrast , there is no such representation .
3. On the formalism of "multiple indexing ". Let us say that
Y
is
subordinated to X
in the following cases:
1 . X and Y are both logical operators, and Y is inside the 2 . Y is an expression read a s being under the responsibility X is either an NP or the speaker.
scope of
of
X,
X.
where
A convenient way of annotating syntactic structures with regard to these subordination-relations is to provide the item Y with an index to
X, expressing also which type of subordination-index will contain the
pointing
subordination is in question . Such a
token -index of
X,
together with the
mark of the subordination-type . A special index should b e reserved for
"speaker", say "0". In a language like German , verbs marked as subor
dinated not to speaker are now candidates for receiving subjunctive
mood . 2
In the case of quantificatio n , the subordination-indexing with
regard to two quantified NPs A and B is either " A . . . B t or '\A . . i j j B " , where indices to the left are token-indices and those to the nght j subordination-indices. A third option , though, is simply ' \A . . . . B "
l
- i.e . neither subordinated to the other. With large intervening texts, his is of course the usual situation, but it may :L ;o obtain in an example like
( 1 4), ( 1 4)
a newspaper headline before the annual mousse-hunt (in Norway): M ange jegere jakter pa
ta elger.
'Many hunters are hunting few mousse s'
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structure, our claim here is only that for each reading, there is a repre
91 The preferred reading here is neither that for many hunters x , x is hunting few mousses, nor that for few mousses y, y is being hunted by many hunters; rather , the set of hunters is simply claimed to be large and the set of mousses to be small, by some standard of comparison. Similar annotations can be used to express binding (of anaphors and traces), predication, attribution and government, with the anteceden t , predication-subject ,
attribution-kernel
and
governor
a s superordinate
items. Part of this annotation is then purely syntactic , part of it is syntac tic with a semantic interpretation in many cases (binding and predication), and part of it is mainly semantic, but with syntactic effects (responsibili ty). Such an annotated structure does not serve as a representation of the semantic properties per se - they will be encoded in som e kind(s) o f
i.e. as 'inputs' to syntactic rules. With such indexed
structures, the
DA/LF
representing quantifier
scope may be superfluous, as long as representations like
(6,7)
(or their
model-theoretic interpretations) are obtained ( e .g . through a translation procedure with 'storage' of the type proposed in Cooper
( 1 975) and later
works), where the transitivity of "be inside the scope of" holds. As for the semantic representations of the phenomena involve d , they need not constitute a unified object . Som e , e .g . , may require some kind of 'form'-level (see Hellan , ms, for some suggestions), while others will be captured in the model-theoretic interpretation itself, for instance the distribution of negative polarity items, according to the theory of Ladusaw
(1 979),
which says that negative polarity items can only occur within
the scope of 'downward entailing' operators, a notion defmed exclusively in model-theoretic terms.
A
fmal remark can now be made with regard to the latter issu e . Von
Stechow quite correctly points out that the analysis in Hellan
( 1 98 1 )
has nothing to sa y about negative polarity items. I n terms o f the model just proposed, though, a conjecture could be that in syntactic represen tation, negative polarity items have a subordination-index pointing to the " putative downward entailing operator, which gets 'filtered ' in the m odel theoretic interpretation through a checking of whether the operator is really downward entailing with regard to the constituent containing the negative polarity item (which may be a comparative clause , for instance) . I f i t is, the indexing i s accepted, and therewith the negative polarity form . 3 Crucially, now, this filtering procedure need not make reference to the logical form of the containing constituent itself, which makes it irrelevant whether this form , in the case of comparative clauses, contains a negation operator or not . The complete absence of such operators in my analysis of comparative constructions thus need not entail that the
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'real' representations against which the annotated structure i s checked . The annotation only encodes these properties for syntactic purposes,
92 analysis is not compatible with an adequate account of negative polarity items. Since this issue is otherwise unresolved in so many respects, I will not venture into it. 4 The University of Trondheim College of Art and Science 7055 Dragvo/1, Norway.
NOTES are
1.
I.e., they
2.
And in m any other languages as weU, of course. Being subordinated to a counter
"rigid designators", foUowing Kripke ( 1 97 2).
effects, the "non clause-bounded" reflexives in Icelandic seem to be a case in point. Cf. Thrainsson ( 1 976).
3.
This is somewhat analogous to the procedure proposed in HeUan, ms, for check
ing whether a seK-reflexive is correctly distributed with regard to that such reflexives be contained in a constituent
4.
predicated
requirement
of the antecedent.
For further discussion of the issue, apart from the contributions in this volume,
see Hoeksema ( 1 983).
R EFER ENCES Barwise, J. Cooper,
R.,
and Perry, J. 1 98 3 :
Situations and A ttitudes. M IT-Press, Cambridge. Montague 's Semantic Theory and Transformational Syntax ,
1 97 5 :
Ph .D. diss., Univ. of Massachusetts, Amherst. En�, M . , 1 98 1 :
Tense Without Scope: An Analysis of Nouns as Indexicals,
Ph . D .
diss., Univ. of Wisconsin, Madison. Fodor, J . D . , 1 976 :
The Linguistic Description of Opaque Contexts,
Indiana Univ.
Linguistics Oub, Bloomington, Indiana. Heim, I., 1 98 2 :
The Semantics of Definite and Indefinite noun Phrases,
Ph .D. diss.,
Univ. of Massachusetts, Amherst.
HeUan, L., 1 980: On semantic scope. In : Heny F. (ed.),
Contexts,
Ambiguities in Intensional
Reidel, Dordrech t ; 4 7-8 1 .
--
. . 1 98 1 :
--
. ms:
Towards an Integrated A nalysis of Comparatives, Narr , Tubingen . Reflexives in Norwegian and Theory of Grammar. Monograph. Hoeksema, J ., 1 98 3 : Negative polarity and the comparative, Natural Language and L ingu istic Theory 1 . 3 ; 403 4 34 . Kamp, H . , 1 97 1 : Formal properties of 'Now', Theoria 3 7 ; 227-2 7 3 . ·
Kripke, S . , 1 97 2 : Naming and necessity. In : Davidson, D . and Harman, G . (eds.),
Semantics of Natural Language, Reidel, Dordrech t ; 253-3 5 5 . Polarity Sensitivity a s Inherent Scope Relations,
Ladu saw, W . , 1 97 9 :
Ph.D. diss .,
Univ., of Texas, Austin. Lewis, D . , 1 975 ; Adverbs of quantification . In : Keenan, E. (ed.),
ofNatural language,
Cambridge Univ. Press , Cambridge : 3 - 1 5 .
Formal Semantics
Thrainsson, H . , 1 97 6 : Reflexives and subjunctives i n Icelandic. N E L S VI. Von Stechow, A . , this volume: Comparing semantic theories of comparison.
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factual m odel often has a similar effect, which will be captured by the quantifier scope-indexing proposed below. Among items apart from verbs being subject to such
JoUI7Ull of Semantics 3 : 9 3
-
107
TO BE CONTINUED : THE STORY OF THE COMPARATNE
J. HOEKSEMA
ABSTRACT
Some aspects of Arnim von Stechow's analysis of comparatives (this
of this distinction are provided and some prima facie difficulties consider ed. In addition, Von S techow's analysis of the amb iguity of comparison in intensional contexts is critically examined ; a quantifying-in solution is argued to be inferior to an operator approach .
1 . If the realm of language is seen as a cosmos, vast, largely unexplored and sometimes bewildering, then the comparative construction must be a
microcosmos, reflecting all the complexity of the whole. It is no wonder that some of the central topics of syntactic discussion in the 1 970's were closely linked up with the analysis of comparatives. These topics
included the controversy about the status of Wh-movement versus un bounded deletion (Chomsky 1 977, Bresnan 1 977), the status of com
plementizers (Den Besten 1 978), and deletion rules (Sag 1 976, Williams 1 977), X-bar syntax (Selkirk 1 977) etc. At the same time, the semantics of the comparative construction has occupied the minds of many investi gators, notably Cresswell ( 1 976) , Kamp (1 975), Klein (I 980, 1 98 2) , Hellan ( 198 1), and S euren ( 1973) . All except Seuren adopt a Montague style approach to semantics. The issues involved in these studies have
proved to be sufficiently complex and diverse to preclude all hope of pro viding a complete and unified account of all the data to be accounted for in a single paper, or even a single volume . Nevertheless, a valiant attempt is sometimes made to capture as many properties as possible of the comparative construction and intregrate them in one analysis, and as such the paper by Arnirn von S techow in this issue of the •
Journal of
This research was supported by the Foundation of Linguistic Research, which
is funded
by
the Netherlands Organisation for the advancement of pure research ,
ZWO, grant no. 1 7- 24 - 04 .
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volume) are criticised, especially his failure to make a semantic distinction between oblique and sentential comparatives. Several arguments in favour
94
Semantics
should be very welcome indeed . And yet, even though the
number o f problems von Stechow is addressing is quite large , it is clear, that he is dealing with no more than half of the matter, since he does not really look into the syntactic peculiarities of the comparative . This is not necessarily a drawback of the paper, but as
I will try
to make clear below,
a closer examination of the syntax might lead to a reconsideration of some o f the semantics proposed.
2. I
have argued elsewhere (cf. Hoeksema 1 983), following Hankamer
( 1 97 3 ) , that a syntactic distinction should be made between comparatives with a noun phrase complement (let us call these oblique comparatives) comparatives) . Consequently, we must distinguish b etween the compara t ive construction in example in
(I )
below, and the comparative construction
(2):
(I)
Bill i s taller than Mary.
(2 )
He is bigger than we are .
The distinction between the oblique comparative and the sentential com parative is more obvious in some languages than in English. For instance , Seuren (this issue) mentions Italian as a language t hat has separate comple mentizers for the two comparative constructions : struction and
che
di
for the oblique con
for the sentential construction. Since English has the
same complementizer
than
in both comparative constructions, and since
the clausal comparative is subject to a rule of ellipsis , one might conclude that all comparatives are in fact sentential, and that English does not make the distinction in question (the same argument would hold for Dutch). However, there are strong arguments in favour of Hankamer's position, many o f which are summarised in Brame (1 983). Brame mentions 1 0 tests i n which the N P- complements o f comparative
than
pattern like other
NP complements, such as objects o f transitive verbs and objects of pre positions, and not as NP constituents o f sentential complements. The first test that Brame mentions is also discussed by von Stechow : '1blique comparatives allow reflexive pronouns whereas sentential complements do not allow the occurrence o f reflexive pronouns whose antecedents are o utside o f the comparative constructio n : (3)
She can't be smarter than herself.
(4)
She can't be smarter than she is.
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and comparatives with a sentential complement (let us call those sentential
95 • She
( 5)
can't be smarter than herself is.
This is the pattern we expect, if we take the NP- complements of than
to be like any other NP-complement, and do not derive it from an un derlying sentential complement.
The second test uses multiple wh- terms:
(6)
Who is taller than who?
(7)
*Who is taller than who is?
Compare this with: Who looks after who?
(9)
Who is kidding who?
Again , the oblique comparative patterns like transitive verbs and verb
preposition combinations, and differently from the sentential comparative. The third test is Wh-movement1 : ( 1 0)
Who is she taller than?
(1 1 )
*Who is she taller than is?
The fourth test is modification by but:
(I 2)
She is taller than but few friends.
( 1 3)
*She is taller than but few friends are.
The fifth test
I
will skip.
2
The sixth test uses idioms :
( 1 4)
He seemed larger than life.
(1 5)
* He seemed larger than life is.
The other tests will be granted. Brame concludes from these arguments,
that the form
taller than me,
which is frowned upon by some grammar
ians, is indeed the correct form, and that
taller than I
is in fact the un
happy result of drilling and correction by prescriptive schoolmasters. He
adduces as e vidence for this point of view the fact "that children naturally acquire
she is taller than him
and
she is
as
tall as him , but have to be
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(8)
96 drilled or instructed or tortured to produce as
as tall
he" .
she is taller than he and she is
From my own experience , I know that on Dutch elementary
groter als mij is indeed not considered correct, whereas groter dan ik is t aught to be the only gramma tical variant. Apart
schools the form the form
from language acquisition , it should be clear that there is abundant syn
tactic evidence for making a principled distinction between the oblique comparative and the sentential comparative . In the next section I will show how this bears on some of the semantic questions that von Stechow has discussed.
3. I f there is a syntactic dichotomy between sentential and oblique com well, since there is often a close fit between syntactic and semantic struc t ure . And indeed, such evidence can be given (cf. Hoeksema 1 983). The semantic evidence I am about to present, is provided by the different in ferential behaviour of the two comparative constructions. As von Stechow has correctly argued , the sentential comparative must be a downward entailing construction3 in the sense of l..a dusaw ( 1 979), since it licenses negative polarity items such as ever or
could help . The following examples
are taken from von Stechow's paper (his (7 1 )) and Seuren's (his (4) f), respectively : Ede could solve these problems faster than any of my friends
( 1 6)
could ever do . ( 1 7)
My urge to steal was stronger than I could help.
And it is indeed possible to show formally that the sentential compara tive is a downward entailing construction (cf. Hoeksema 1 983) . Let me
Adj-er than S is more informative than Adj-er than S ' informative than S . By the way, this formulation is more
j ust note here that iff
S'
is more
correct than the formulation von Stechow gives, since he requires that for any
than S '
NP iff
we should have that NP is
S ' is
Adj-er than S entails NP is Adj-er S . However, it should be clear whenever NP itself is downward
more informative than
that such entailments are overruled
entailing (cf. the discussio n of the replacement theorem in Curry ( 1 963): 1 03 ) . For example , the predicate
predicted is more Bill had predicted.
more interesting than John or Bill had more interesting than
informative than the predicate
However, sentence ( 1 8) below does not entail sente nce
( 1 9) . The reason is, of course, that
phrJ se :
nothing is
a downward entailing noun
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parative, we would expect to fmd semantic evidence for this dichotomy as
97 ( 1 8)
Nothing was more interesting than John or Bill had predicted .
( 1 9)
Nothing was more interesting than Bill had predicted.
To see that ( 1 8) does not entail ( 1 9), consider a situation in which Bill predicts that the things which are going to happen will be utterly de void of interest, whereas John predicts that some things will be mildly interesting. Now suppose that some of the things that happen have a modest degree of interest, but nothing is more than mildly interesting. In that case, ( 1 8) is true, whereas ( 1 9) is false.
(20)
A cheetah runs faster than a lion.
(2 1 )
A cheetah runs faster t han a hungry lion .
Examples like these are flawed, however, since they involve generic ex pressions. If we exclude a generic reading of the expressions involved, the inferential pattern changes:
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4. Transitive verbs and verb-preposition combinations are usually not downward-entailing. I f I kiss a woman, it does not necessarily follow that I kiss a tall woman. Only the few downward-entailing verbs would permit such an entailment . A good example is the verb lack : if the zoo lacks a unicorn, then certainly it will lack a red unicorn. Transparent verbs are upward-entailing. If I kiss a tall woman, then I kiss a woman . I f your father punishes naugJtty children, then he punishes children . This follows from the fact that transparent verbs and verb-preposition combinations can be construed semantically as homomorphisms from the algebra of noun phrase denotations to the algebra of verb phrase denota tions. All homomorphisms are upward-entailing (by the fact that upward entailing constructions are semantically functions preserving the subset ordering of their domain in a set theoretical frame-work ; homomor phisms preserve the boolean structure of their domain and consequently the subset ordering). For some discussion of these notions, cf. Keenan ( 1 98 1 ), Keenan and Faltz (to appear). Given the syntactic similarities between transitive verbs and the oblique comparative , and the fact that the comparative construction is trans parent (i.e . not opaque), we expect to find that the oblique compara tive is upward-entailing. Is it? Some examples suggest , that it is, in fact, not . For example, from (20) below we conclude (2 1 ) :
98
(22)
Yesterday, a cheetah ran faster than a lion .
(23)
Yesterday, a cheetah ran faster than a hungry lion.
Surely , (23) does not follow from (22). On the other hand, (22) follows from (23). The different b ehaviour of examples (20) and (2 1 ) is accounted for when we note that we can make the genericity more explicit by using the universal quantifier a// : 4 (24)
All cheetahs run faster than all lions.
(25)
All cheetahs run faster than all hungry lions.
This entailment follows from the downward-entailing character of the determiner all , also noted by von Stechow (section VI of his paper). In examples like these, it is clear that the comparative construction must be upward-entailing, for if it were otherwise, the combination of a down ward-entailing determiner and a downward-entailing comparative con struction would yield an upward-entailing environment , since two down ward-entailing operators cancel one another's negative force. 5 (Just like double negation is equivalent to affirmation .) Only an odd number of downward-entailing operators can form a downward-entailing en vironment. Consequently, the oblique comparative cannot be anything but upward-entailing in examples such as (24). Examples in which only upward-entailing operators occur lead to the same conclusion. Consider: (26)
Some girls are taller than some boys.
Downward entailments are not allowed. In other words, from (26), we are not allowed to conclude that (27) m ust be true as well : (27)
Some girls are taller than some boys from Morocco .
On the other hand, it is clear that (27) entails (26). So, again, we see that the oblique comparative must be upward entailing, since we may replace the expression boys from Morocco by the less informative com mon noun boys without loss of truth. This section can be summarised by the following statement :
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This sentence entails (25) bdow, which is the near equivalent of (2 1 ):
99 Thesis The oblique comparative is an upward-entailing construction.
{28)
Ede is fatter than anyone of us.
This kind of example seems to contradict not only the upward-entailing character of the oblique comparative but even the entire theory of the distribution of negative polarity items proposed in l..a dusaw {1 979). Fortunately, both can be maintained, by noting that anyone in {28) may be an occurrence of so-called free choice any (cf. Ladusaw 1 979, Carlson 1 98 1 ), which is not a negative polarity item at all . Free choice any differs fro m negative polarity any in that it is a universal quantifier , whereas the latter is a n existential quantifier. Compare for instance the following examples: {29)
Anyone can solve that problem.
(3 0)
There wasn't anyone left .
In (29) we have a clear case of free choice any : we may paraphrase this sentence as (3 1 ) : (3 1 )
Everybody can solve that problem.
It does not make sense to treat anyone as a narrow-scope existential quan tifier in this particular example , since paraphrases such as (32) are ob viously inadequate : {32)
It is possible that someone solves that problem.
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5. In the previous sections, I have argued that the sentential compara tive construction differs from the oblique comparative in that it is a down ward-entailing construction, whereas the other construction is upward entailing. In this respect I disagree with von Stechow, who claims that the two constructions are equated on the level of logical form (section IX o f his paper). I will now address a problem that arises in connection with the ana lysis of negative polarity items. If the oblique comparative construc tion is upward-entailing, we expect to fmd that negative polarity items are excluded as objects of comparison. Nevertheless it appears that any can occur here . Consider von Stechow's example
1 00 On the other hand, it is equally clear, that anyone in (30) must be ana lysed as a narrow-scope existential quantifier, since there only allows existential noun phrases:
(33)
There is some cake left.
(34)
*There is
all
cake left .
Like other universal quantifiers, free choice any
almost or nearly :
Almost anyone can solve that problem.
(36)
Nearly anyone can ride a bicycle .
be modified by
Existential quantifiers (except for numerals) cannot, in general, be modi fied by these expressions:
(37)
• Almost some of the boys disappeared.
(38)
*Nearly a school burned down.
As expected, negative polarity any does not allow almost or nearly either :
(39)
* There wasn't almost anyone left.
(40)
*There wasn't nearly anyone left .
Let us now take a look at the oblique comparative . W e are i n a position to determine whether anyone in (28) is indeed an occurrence of free choice any , as our present account predicts, or an instance of polarity sensitive any .
(41 )
Ede is fatter than almost anyone of us.
The grammaticality of (41 ) indicates that our prediction is correct. Harder to account for is the behaviour of or. In upward-entailing positions, we may substitute A or B for A without loss of truth. For instance, sen tence (42) below entails (43) :
(42)
This man killed his father.
(43)
This man killed his father or his mother.
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(35)
can
101 So we expect that (44) entails (45): is
(44)
Spain
(45)
Spain is larger than Portugal or Malta.
larger than Portugal .
However, in one o f its readings, (45) does not follow from (44). The two readings of (45) can be paraphrased by the following sentences: (46)
Spain is larger than Portugal or larger than Malta.
(47)
Spain is larger than Portugal and larger than Malta.
(48)
Bill or Sam can help you with your home-work.
And indeed (48) has a reading in which it is equivalent with (49) below, instead of (SO) : (49)
Bill can help you with your home-work and Sam can help you with your home-work.
(50)
Bill can help you with your home-work or Sam can help you with your home-work.
A scopal analysis of the ambiguity of (48) will not work for the same reason as in the case of free choice any. 6 To be sure, this is just a partial solution, for the problem of how to account for the distribution of free choice any still remains to be solved. For a survey of this rather messy area, see Carlson ( 1 98 1 ) .
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Naturally, only the reading represented by (46) follows from (44), whereas the reading represented by (47) is not entailed by, but entails (44). If the oblique comparative is interpreted as a boolean homomorphism, as I argued in Hoeksema (1 983), it is predicted that (45) is equivalent with (46). On the other hand, if the oblique comparative is treated as a downward-entailing function, more precisely an anti-additive function , the equivalence o f (45) and (47) i s predicted . I n the latter case, the read ing represented by (46) can be derived by quantifying in . I will now propose an alternative solution to this problem, which is reminiscent of the analysis of any presented above. Let us assume that there is a free choice variant of or. In other words, let us assume that A or B may sometimes mean anyone of A and B, or A or B, no matter which one . We expect to fmd this or whereever we fmd free choice any , for example in the neighbourhood of modal expressions :
1 02 6.
In the previous sections, I have argued that the syntactic distinction
between sentential and oblique comparatives is reflected by their in ferential properties: the former are downward-entailing, the latter are upward- entailing .
or
Putative
evidence
to
the
contrary
from any
and
has been reanalysed to make it compatible with this claim . Now I will
present some examples that purport to show that the semantic distinc tion between the sentential and o blique constructions is not a weird pro perty of the comparative , but can be found among several verbs as well . Consider the Dutch verbs
weigeren
'to refuse ' and
ontkennen
'to
deny ' . These verbs are clearly d ownward-entailing with respect to their sentential complements, since they licence the occurrence of negative polarity items : Hij weigert
een vinger uit te steken
He refuses a
fmger to lift
"He refuses to lift a finger"
(52)
Zij onkent
oak maar iets
gezegd te hebben
S he denies anything at all said
to have
"She denies that she has said anything at all" Yet , the same verbs are upward- entailing with respect to their noun phrase complements, since they do not licence the occurrence of negative polar ity items here :
(53}
* H ij weigert oak maar een boek He refuses whatsoever any boek "He refuses any book whatsoever"
(54)
*Zij ontkent oak maar een bewering She denies whatsoever any claim
"She denies any claim whatsoever" The semantic distinction between the two constructions can also be shown by their inferential behaviour, but I will refrain from doing so here . My only point is that the analysis o f comparatives proposed above is quite natural
in
that it does not postulate any properties of the comparative
not found e lsewhere .
7.
In this fmal section, I will d iscuss a problem that is very prominent
in von Stechow's paper. The well-known ambiguity of sentences such as
(55)
below is handled in von Stechow's paper by means of quantify
ing-in the comparative clause :
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(5 1 )
1 03
(55)
John seems taller than he is.
The 'illogical' reading, according to which it seems that John is taller than himself, is obtained by a normal derivation, whereas the 'consistent' reading, according to which John's height is less than it seems to be, is obtained by quantifmg-in . There is, however, another type of solution to this problem, also men tioned by von Stechow, but rejected for reasons I do not fmd very con vincing. The other solution would b e to postulate an 'actual world' oper
ator, comparable in all respects to Kamp's ( 1 97 1 ) 'now ' operator. As
von Stechow notes, this operator can be motivated by the behaviour of mood in languages such as German, where the actual world operator
With this operator, w e could represent t h e t w o readings of
(55)
as
follows :
(56)
Seems(John is taller than he is)
(57)
Seems(John is taller than Act he is)
The semantic defmition of the Act operator is rather straight- forward. We evaluate every expression with respect to a possible world w , a moment of time t , and a context c. We now defme :
(58)
Definition [Act S ]
w ,t ,c
=
[S]
c
W'
t ,C
' where c
w
is the actual world
A
context c is an n-tuple, consisting of a time of utterance c , a world t , a speaker, a place of utterance etc. The w above definition is similar to the one given in Kaplan ( 1 9 79).
of utterance (or actual world) c
Let us assume that the Act operator is in fact an overt expression o f the mood of the verb . I n that case w e expect it to appear i n clauses, but not in noun phrase complements. This explains quite neatly, why (59) below is not ambiguous in the same way as (59 )
(55) is.
John seems taller than himself.
The quantifying- in approach can handle this fact equally well, since it is clear that the binding conditions of reflexive pronouns prohibit quanti fying-in . For that reaso n , ambiguity will not arise . Von Stechow argues that his theory is superior in that it can handle more readings than the operator-approach. When there are
n
iterate d
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corresponds to indicative moo d in opaque contexts, whereas the absense of this operator corresponds to subjunctive moo d .
1 04 modal o perators, the quantifying- in a pproach predicts
n+l
readings .
The o perator a pproach can handle no more than two readings, the one with the
Act
operator, and the one without the
Act
o perator. Von Ste
chow o ffers the following example as evidence for the correctn ess of his theory : (60)
I thought Plato could have been more boring.
The relevant reading of (60) is formulated thus : (6 1 )
For every world of my thoughts w , there was a world w ' acces sible from w, such that the degree of Plato's boringn ess in w' ex
This is t h e reading in which the comparative clause has narrow scope
with respect to the o paque o perator to
could. This
thought
and wide sco pe with respect
example, however, fails to convince me, since it involves
a truncated comparative clause. Because of the ellipsis of this clause , (60) can mean a lmost anything ; for example, i t might mean that I thought Plato could have been more boring than Thomas Aquinas, or more boring than I was told to expect, etc. 7 This very vagueness or context-depend ency can a ccount for the reading represented as (6 1 ) . The quantifing-in a pproa ch adopt ed b y von St echow comes to grief in such examples as the following: (62)
We expect that every schoolboy thinks he is brighter than he is.
The relevant reading of this sentence is the one according to which it is the case in every world consistent with our expectations that the degree of brightness that every boy a scrib es to hims elf is less than his degree of brightn ess in the a ctual world .
This reading can hardly b e obta ined b y quantifying-in the compara
than he is , since that would mean that he cannot be bound by every schoolboy , unless that expression is quantified-in as well. But there is a perfectly plausible reading of (62), a ccording to which every schoolboy has narrow scope with respect to expect (consider for example tive clause
a situation in which the set of schoolboys in every world consistent with our ex pectat ions is a subset of the set of schoolboys in the a ctual world). Since th e o perator a pproach does not have any d ifficulties with such ex amples as (62), I take it that it is su perior to the quantifying-in solution . There is anotht:r reason a s well to prefer the o perator a pproach , which is of a more th eoretical nature. If we restrict quantifying-in to those expressions that are traditionally considered to be quantifiers, i.e. noun
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ceeded the degree of Plato's boringness in w .
1 05 phrases like every girl and adverbs like sometimes , we can stay with a much more restrictive theory of interpretation than we would have if we adopted the more liberal approach advocated by von Stechow and allowed quantifying-in for clauses as well. Groningen University
Institute of Dutch Language & Literature Grote Kruisstraat
9 712
2/1
TS Groningen
Netherlands
NOTES Cf. also Hankamer ( 1 9 7 3).
This test involves the behaviour of no one. It is interesting to note that Brame considers (i) to be correct, whereas von Stechow (section VII) feels that similar ex amples are "extremely odd":
John is taller than no one.
(i)
3. Downward-entailing constructions are interpreted as monotone decreasing [unc tions, i .e . functions that reverse the subset ordering of their domains. Formally : f is
monotone decreasing iff xs_y implies that f(y)s_f(x). The subset ordering of do mains corresponds to von Stechow's notion "at least as informative as". An expres c [ B ) , i.e., if the sion A is at least as informative as another expression B iff [ A I interpretation of A is a subset of the interpretation of B. Cf. Ladusaw ( 1 9 7 9 , 1 983) and Zwarts ( 1 98 1 , 1 9 84) for a discussion of the rele vance of these notions for the semantics of natural language and the analysis of nega tive polarity items. 4. Naturally, I am aware of the fact that generic expressions tend to be much more vague than straightforward universal quantifiers. Therefore, the entailment relation between (20) and ( 2 1 ) is present only in the event that the generic expres sions involved have universal force. 5 . Formally, if f and g are monotone decreasing functions (i.e. downward-entailing functions, cf. note 3), the compound f(g(x)) is upward-entailing in the x-position. Proof: x s_ y implies g(y) S g(x), which implies f(g(x))s_f(g(y)). 6 . An interesting additional example is (i), borrowed from Carlson ( 1 98 1 : 1 7) : (i)
John likes dogs or cats.
This sentence has a reading equivalent to (ii) :
(ii)
John likes dogs and John likes cats.
Again, a scopal analysis of the ambiguity of (i) wou4l be hard to motivate, if possible at all. Note, by the way, that free choice any may occur here as well: John likes any dog.
(iii) 7.
To
see
this more clearly, consider contexts such as :
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1. 2.
1 06 (i)
They told me that Thomas Aquinas could be very boring. However, I thought Plato could have been m ore boring.
R EF E R ENCES
Ladusaw, W., 1 9 8 3 : Logical form and conditions on grammaticality. Linguistics and Philosophy 6 . 3 ; 3 7 3-392. Sag, I .A., 1 976 : Deletion and Logical Form . Ph.D. Dissertation MIT. Distributed 1 9 7 7 by the Indiana University Linguistics Club, Bloomington, Indiana. Selkirk, E.O., 1 9 7 7 : Some remarks on noun phrase structure. I n : Cull cover et a/ . , (eds.) ; 285- 3 1 6 .
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Besten, H . den, 1 9 7 8 : On the presence and absence of Wh-elements in Dutch com paratives. L inguistic Inquiry 9; 64 1 - 6 7 1 . Brame, M .K ., 1983 : Ungrammatical notes 4 : !!marter than me. Linguistic Analysis 1 2 .3 ; 323- 3 3 8 . Bresnan, J .W., 1 9 7 7 : Variables i n t h e theory of transformations. I n : Culicover, P . et a/. (eds.) ; 1 57-196. Carlson, G . , 1 98 2 : Distribution of free choice any. Papers from the 1 7th Regional Meeting of the Chicago Linguistic Society , Chicago ; 8-23. Chomsky, N., 1 9 7 7 : On Wh-movement. In: C ulicover, P. et a/. (eds.); 7 1- 1 3 2 . Cresswell, M . , 1 976 : The semantics of degree. I n : Partee, B . (ed.), Montague Gram mar, Academic Press, New York; 26 1-292. Culicover, P . , Wasow, T. and Akmajian, A . (eds.), 1 9 7 7 : Formal Syntax. Academic Press, New York. Curry, H .B., 1 96 3 : Foundations of Mathematical Logic . Reprint 1 9 7 7 , Dover, New York. Hankamer, J . , 1 97 3 : Why there are two than 's in English. I n : Papers from the Ninth Regional Meeting of the Chicago L inguistic Society , Chicago Linguistic Society, Chicago ; 1 78-1 9 1 . Hellan , L., 1 98 1 : To wards an Integrated A nalysis of Comparatives . Narr Verlag, Tilbingen. Hoeksema, J ., 1 9 8 3 : Negative polarity and the comparative. Natural Language and L inguistic Theory 1 .3 ; 403-434. Kamp, LA.W., 1 97 1 : Formal Properties of 'Now'. 7heoria 3 7 ; 227- 2 7 3 . Kamp, J .A.W., 1975 : Two Theories about Adjectives. In : Keenan, E . L . (ed.) , Forma/ Semantics of Natural Language, Cambridge University Press, Cambridge ; 1 23-1 5 5 . Kaplan, D., 1 979: O n the Logic o f Demonstratives. Journal of Philosophical Logic 8 . 1 ; 8 1 -98. Keenan, E.L., 1 98 1 : 'A Boolean Approach to Semantics'. In: Groencndijk, J . , Stok hof, M . & Janssen, T. (eds.), Formal Methods in the Study of Language , Mathe matisch Centrum, Amsterdam ; 343- 3 7 9 . Keenan, E.L . & faltz, L., t o appear: Logical Types of Natural Language . Reidel, Dordrecht. Klein, E . , 1980: A Semantics for Positive and Comparative Adjectives. Linguistics and Philosophy 4 . 1 ; 1 -4 5 . Klein, E., 1 9 8 2 : The Interpretation of Adjectival Comparatives. Journal of Linguis tics, 1 8 .1 ; 1 1 3- 1 3 6 . Ladusaw, W., 1 979 : Polarity Sensitivity as Inherent Scope Relations . Unpublished Ph.D. dissertation, University of Texas. DIStributed 1 980 by the I ndiana Uni versity Linguistics Club.
107 Seuren, P .A.M . , 1 9 7 3 : The Comparative. In : Kiefer, F. and Ruwet, N . (eds.), Generative Grammar in Europe. D. Reidel, Dordrecht ; 528- 564. Seuren , P.A.M . , this volume: The comparative revisited. Stechow, A. von, this volume : Comparing semantic theories of comparison. Williams, E . , 1 9 7 7 : Discourse and logical form. Linguistic Inquiry 8 ; 1 0 1 -1 39. Zwarts, F . , 1 98 1 : Negatief polaire uitdrukkingen I . CL OT 4 . 1 ; 35-1 3 3 . Zwarts, F., 1 9 84 : Dissertation o n Quantifiers and Determiners i n Modern Dutch. To appear.
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Jounud ofSemantics 3 : 1 09 - 1 4 1
THE COMPARATIVE REVISITED
PIETER A.M. SEUREN
''La verite n'est que rarement simple, et elle n'est jamais pure." (Marguerite Yourcenar)
(1)
3e: extent [Jim i s tall to e A � [Joe i s tall to e ]]
(With von Stechow, I will often use the notation "e-tall" for "tall to e"). This analysis is based on two main considerations. First, there is an inti mate relationship of the comparative in English and mo st other European languages with negation. This appears from the etymology of than , which derives (Joly 1 967) from Old English pon-ne {"by which not"). The French comparative particle que, as well as its Romance cognates, derive from Latin quo (via Vulgar Latin quod), meaning "by which". The missing element of negation crops up after comparative que when there is a second finite verb: (2)
Il est plus grand que je ne pensais. (He is taller than I thought.)
Many English dialects have nor for than , as is well known. Again it fmds a non-negated counterpart in West Flemish of (Bergrnans 1 982) or An cient Greek e, both meaning "or". Then, in those English dialects that have Negation Copying, such as Cockney, one finds copies of the under lying negation after than :
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Amim von Stechow's critical appraisal of various theories of the compar ative in the present issue of the Journal of Semantics provides a welcome opportunity for me to look at my 1 973 paper again and give my com ments. It is clear that that paper falls short of what it wanted to realize. Many extremely interesting observations were not made. Certain trouble some environments (such as counterfactual constructions) were not con sidered. The paper was definitely poor on the semantics of the compara tive . And, finally, hardly any notice was taken of the various ways in which the semantic notion of comparative is expressed in the languages of the world. In the following I shall recapitulate my own position as given in 1 973 . I shall then give my own comments and suggestions for improve ment. Finally I shall discuss von Stechow's critique. On the whole, how ever, I shall maintain the principles on which the 1 973 analysis was based. The analysis in my 1 973 paper of the comparative proceeds in two stages. First, a comparative like "Jim is taller than J oe" is analysed as:
1 10 (3)
She did a better job than what I never thought she would.
Moreover, so-called negative polarity items (NPI) 1 seem to feel quite at ease in than-phrases. Among the examples listed in the 1 973 paper are : (4)
The italicized items are all NPI (including need with bare infinitive) . Yet they seem happy in than -phrases. Positive polarity items (PPI), on the other hand, are excluded in than -phrases: (5)
a. b. c. d.
* He has got more support than you already have . * He carries more than I would rather do . *You eat less than I could just as well do . * He has more money than he would be far better off with .
Yet it is possible to read the sentences o f (5) with an extent paraphrase and "and - not" for than . We can say, for (Sa), "there is an extent such that he has support to t hat extent and you do not already have that amount of support". But now the second conjunct has the characteristic 'echo' of negated sentences with PPJ's. Apparently , the negated second conjunct has to remain without such an echo.1 The second consideration behind the analysis given in ( 1 ) is to do with the quantification over extents. Such quantification is profitable in view of sentences of the type: (6)
Planes are safer now than thirty years ago .
Sentence (6) is ambiguous between a reading in which the same planes have become safer, and one in which whatever was a plane thirty years ago was less safe than whatever is a plane now. The analysis of generic plurals (planes) is problematic. In 1 973 I committed the error of analys ing such plurals as a form of universal quantification ("all planes"). But the argument is not affected by this. Let us, for lack of a better solution, analyse planes as "if you take an x : plane, then x ... " . If we apply this analysis to (6) as it stands we can only get:
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a . That amou nt of spaghetti was more than I was all that keen to eat. b. The fifth glass was more than I cared to drink. c. John runs faster than he needs run. d . He was a greater bore than I could possibly put up with. e . He went further than I had the slightest intention of going. f. My urge to steal was stronger than I could help .
111 (7)
If you take an x: plane , then x is safer now than thirty years ago .
The second , and more obvious reading is then lost. Jf, however, we quan tify over extents as illustrated in (1 ), as in:
(8)
3e:extent [planes are e-safe now A � [ planes were e-safe 30 years ago]]
and if we then apply the analysis of generic plurals , we get two readings:
(9)
A small number of transformational and morphological rules then con verts the analytical structures into the desired surface structures. This is the first stage in the analysis of the comparative as presented in my 1 973 paper. It is the analysis figuring in von Stechow's rendering of that paper. There is, however, also a second stage , regrettably neglected by von Stechow. The reason for the second stage is that analyses of the type ( 1 ) are inadequate for cases like: (1 0)
Jim is taller than six feet.
which contain a compared measure phrase (CMP) as the filler of the than-phrase . If we apply the analysis as given in ( 1 ) to (10) , we get:
(1 1 )
3 e :extent [Jim is e-tall A � [6 ft i s e-tall]]
But this is semantically inadequate , since one does not say felicitously "six feet is not that tall". Moreover, if (1 1 ) were correct , we would expect Jim is taller than six feet is tall to be a possible. sentence of English, just as Jim is taller than Joe is tall is a possible sentence (albeit marginally possible). Also , if the expression six feet functions exactly the way Joe does in ( 1 ) , we would expect the following ungrammatical sentences to be grammatical:
(1 2)
a. b. c. d. e.
*Six feet is less tall than John . *Six feet is as tall as John . • John is not so tall as six feet. *Six feet is smaller than John . *Six feet is not so tall as John .
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a . if you take an x : plane, then 3 e :extent [x is e-safe now A � [ x was e-safe 30 years ago. b. 3e:extent [if you take an x : plane now, then x is e-safe A � [if you took a y :plane 30 years ago , then y was e-safe]]
1 12 And we would expect the following grammatical sentences to be ungram matical :
(13)
a. b. c. d. e.
Six feet i s less than John i s tall . Six feet is as much as John is tall. Six feet is not so much as John is tall . Six feet is more than John is tall. John is more than six feet tall.
( 1 4)
3e : extent [the f:extent [Jim has tallness to f) is much to e A [the g: extent [Joe has tallness t o g) is much to e]]
We are now in a position to formulate an adequate, semantically trans parent analysis of (1 0):
( 1 5)
3e : extent [the f:extent [ Jim has tallness to f) is much to e A - [ six feet is much to e]]
The analysis thus corresponds intuitively to something like "Jim's tallness is more than six feet is much". At fust sight it looks as though it is a long way from ( 1 4) to Jim is taller than Joe . Yet the way is hardly longer than from ( 1 ) to the same surface sentence, and there are some extra bonusses. In Seuren 1 973 and in later publications it is argued that there is a rule, called Relative Raising in 1 973 , but Predicate Lowering later (1 974) , which has the following effect :
( 1 6)
the
X
s[ . . .x . . . ) be Pred .N6minal => s[ . . .Pred.Nominal ... )
That is, any underlying structure of the form "the x s [ . . .x ... ] be Predicate Nominal" will receive sentence nuclear accent on the predicate (i.e., the predicate nominal), and can be reduced to just the relative clause s [ ... ), but with the higher (accented) predicate i n the posit ion of the variable x . The higher predicate carries its accent along to the lower clause , which thus carries a nuclear accent on a constituent which itself is not the sur face predicate. Thus, from "the x [John wrote x 1 he the Jetter" we get "John wrote the letter" (with contrastive acce n t ).
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It is quite clear that CMP-comparatives are different from 'ordinary' com paratives, and this must be reflected in the analysis while the two types should be kept as similar as possible. To this end a refinement is brought about in the analysis, whereby all comparatives are reduced to compara tives of quantity (much). Instead of (1 ) we now read:
1 13 It is argued, furthermore, that a sentence of the underlying form "the x:Nominal s [ . . .x ... ] be Predicate" can be changed into ''the x s [ ...x ... ] be Predicate Nominal". Thus an u nderlying "the x :car S [I sold x] be red", or: ''the car I sold was red", we get "the x s P sold xj be a red car", and hence, by rule ( 1 6) , "I sold a red car". The rule of Predicate Lowering is optional or obligatory, depending on the language and the construction in which it occurs. Its range of application is wide. In English and many other languages it is used for the purpose of contrast or emphasis. 3•4 It is used in WH-questions: "Who killed Johnny Ray?" is derived from ' 'the X s [X killed Johnny Ray) be whO " by means of rule ( 1 6), plus, if necessary, WH-preposing.5 It is used for the analysis of comparatives of the type: a . Jim bought a faster car than that Ford (is). b. Jim bought a faster car than Joe (did).
which are analysed in the ftrst-stage terms of ( 1 ) as, respectively : ( 1 8)
a . 3 e :extent [the x : car [Jim bought x] is e-fast A � [that Ford is e-fast ] ] b . 3e:extent [the x : car [Jim bought x] i s e-fasi A � [the y : car [Joe bought y] is e - fast ] ]
The structures of the type ' 'the x : car [Jim bought x] i s e-fast'' are ftrst transformed to "the x [Jim bought x] is an e-fast car", and then, by rule ( 1 6) to "Jim bought an e-fast car". We then get : (1 9)
a . 3 e :extent [Jim bought an e-fast car A � [that Ford is e-fast] ] b . 3e:extent [Jim bought an e-fast car A � [Joe bought a n e-tast car]]
The standard treatment of English comparatives then yields ( 1 7a) and (1 7b). Going back to ( 1 4) and ( 1 5) now, we see that the structural bits of the type : ''the f:extent [Jim has tallness to f] is e-much" is converted ftrst to : "the f [Jim has tallness to f] is an e-much extent" a n d t h e n , by rule ( 1 6) of Predicate Lowering to :
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( 1 7)
1 14 "Jim has tallness to an e-much extent" . Morphological rules (discussed in Seuren 1 978) reduce this t o "Jim is e-tall", so that we are now where we were at stage 1 in analysis ( 1 ) . In order t o facilitate the discussion I shall operate from now on with the first stage analysis illustrated in ( 1 ). But it must be remembered that it is, in fact , a reduction from second stage analyses of the type illustrated in ( 1 4) and (1 5).
2.
(20)
a . Paris is as quiet" as ever. b . Two glasses was as much as I cared to drink. c . That was as much as he was willing to lift a finger to do. d. Jim is as competent as anybody here could possibly be .
Both Ross and McCawley feel that observations such as (20a-d) speak against my analysis since "as-clauses would not contain an underlying negative". Clearly, the value of this argument depends upon the plausibility of the assumption that equatives do not involve negation. Ross and McCaw ley seem to take this for granted. Yet a closer look at equatives quickly shows that this is not a foregone conclusion . Von Stechow, in his article in the present volume , points out (his ex. 203) that a sentence like: (2 1 )
Jim is as tall as Joe (is).
can be interpreted in two ways. It means either (22a) or (22b) : (22)
a. Jim is e xactly as tall as Joe is. b. Jim is at least as tall as Joe is.
Von Stechow touches here o n a difficult point, for which none of the existing theories of comparison has a satisfactory answer. Let me illustrate the point by giving some data . We note that (21 ) has two negations: (23)
a. Jim is not as tall as Joe (is). b . Jim is not so tall as Joe (is).
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I n the light o f this resume o f m y 1 973 analysis, I shall now discuss a criticism that has been levelled against it . The criticism in question derives from J .R. Ross (and is published in McCawley 1 98 1 : 1 9 1 ). Ross observed that NPI's also occur in equative sentences of the type:
1 15 The former means that the e xtent of Jim's tallness and the extent of Joe's tallness are not identical; the latter that the extent of Jim's tallness is less than the extent of Joe's tallness. It might be thought that a sentence like: (24) is
Jim
is
6 foot tall.
likewise interpretable as either (25a) or (25b ):
(25)
a. Jim is exactly 6 foot tall. b . Jim is at least 6 foot tall.
(26)
J im
is
not six foot tall.
must be considered true if Jim's height e xceeds 6 ft as well as if it stays below 6 ft. This would indicate that (26) is the negation of (24) only in the reading (25a), which is the reading it most clearly has. On the other hand, a sentence like: (27)
Jim
is
that tall.
can also mean that Jim is at least that tall . And its negation : (28)
Jim is not so/that tall .
again clearly means that Jim is less tall than the measure indicated by that/so . It thus appears that the equative relation expressed by as. . . as is not always symmetrical. The relation specifying extents by measure phrases, as in (24), however does seem to. be symmetrical (Jim is exactly as tall as 6 ft is much, and 6 ft is exactly as much as Jim is tall) . On the other hand, if an extent is specified by means of a deictic expression, as in (27), the relation is not symmetrical (Jim is at least as tall as 'that' is much, but not vice versa). It is far from clear what the ultimate rationale is for this play between symmetricity and non-symmetricity. We should notice that very similar phenomena occur with verbs that are commonly classified as being symmetrical, such as meet, equal, or resemble : (29)
a . Jim met Joe. b . Jim equals Joe in height . c . Jim resembles Joe in the way he walks.
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Yet , if this is so, it is much less clearly the case than with (2 1 ) . Anyway , the negation of (24):
1 16
(30)
a. • Jim is exactly as competent as anybody here could possibly be. b . Jim is at least as competent as anybody here could possibly be.
But they do occur, as in (30b), in non-symmetrical equatives. This would suggest that non-symmetrical equatives do contain an underlying nega tion, contrary to what Ross and McCawley believe . Let us see what happens if we analyse (2 1 ) , in the non-symmetrical reading (22b) , as follows: (3 1 )
\fe[the f [Jim has tallness to f) is much to e V "' [the g [Joe has tallness to g] is much to e ] ] (where e , f, and g are extents)
Intuitively this reads as something like "for all extents of tallness, if Joe has it , so has Jim". This is reduced by Predicate Lowering to : (32)
ve [Jim is e-tall V - [Joe is e- tall]]
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It has often been observed that such sentences are not necessarily sym metrical . If (29a) is said to assert that Jim met Joe at the airport, then surely the predicate is not symmetrical. If (29b) or (29c) are said in a situation where Jim is Joe's father and Joe is an adolescent son, then they are incorrect . For then we feel we must say that Joe equals Jim in height, and that Joe resembles Jim in the way he walks. (We may say that these predicates give rise to a presupposition that the subject (Jim) has been subject to change prior to reaching the state or event described by the sentence . But this aspect will not be pursued any further here .) The best we can do, with these data in hand, is to posit a real ambiguity between two different readings for equatives like (2 1 ) . One reading is_ sym metrical, the other is non-symmetrical. This solution is not satisfactory in every respect , mainly because the ambiguity posited is not of the usual type . Usually, ambiguities differ greatly from language to language since their occurrence in the grammar results from the rules of grammar, which differ from language to language , and their occurrence in the lexicon is usually haphazard. (There seems to be no reason other than historical accident why, e .g., loom in English means "weaving machine" or "shaft or handle of an oar" or "indistinct and exaggerated apperance of land at the horizon , seen through mist or darkness" (OED)). If we adopt, there fore , a solution involving an ambiguity between symmetrical and non symmetrical equatives, we must be prepared to live with ambiguities that are lexical but not haphazard .6 We now observe that NPI's do not occur in equatives of the symme trical type:
117 This analysis by itself is not sufficient, because it does not enable us yet to extract the correct truth-conditions. We still need a semantics that makes sure that bits like "- [the g [Joe has tallness to g] is much to e ] " ,
or "- [Joe is e-tall]" are considered true only
if Joe
is
less
tall than the
degree indicated by e . We shall come to this in a moment . Now , assuming the right semantics, we see that the negation of (3 1 ) gives the right result . If we place the whole of (3 1 ) under negation, we get : (33)
3e [- [Jim is e-tall] A [Joe is e-tall]]
which entails that Jim is less tall than Joe, provided we have the right semantics for " - [Jim is e-tall]"
(34)
Ve [Jim is e-competent
V - [anybody
here could possibly be e
competent ]] or, intuitively, "for all extents e , if anybody here could possibly be e-com
petent , then Jim is e-competent " . We now have the negation which is in any case needed if we want to maintain the generalization that NPI's occur only in negative environments. Depending on the general tenability of this whole approach, we may now say that the Ross-McCawley ob jection has been met. But we cannot say that we have explained the phenomena at hand. One reason is that we still have very little under standing of the behaviour of NPI's. We may posit the condition that any NPI must occur in the scope of some negation in underlying structure , but that condition is hardly enough. Notice, for example, that (20d) lacks the negation form that is typical for non-symmetrical equatives, as in (23b) : (3 5)
• Jim is not
so competent as anybody here could possibly be.
(There is a negation for (20d), but with
as... as,
and with radical
not
and
an echo : (36)
! Jim is NOT as competent as anybody here could possibly b e .
where the exclamation mark i s used to indicate the echo .) The only serious attempt at explaining the occurrence and behaviour of NPI's is l..a dusaw 1 979, but it is couched in terms of a semantics that is totally alien to this study, and, moreover, as we shall see below, it is inadequate in several respects. In any case, the objection raised by Ross and McCawley is either not valid , or it has to be supported by arguments why the assump-
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I f we apply this analysis to (20d) above , we get :
1 18 tion of an underlying negation in non-symmetrical equatives is impossible . The symmetrical reading of the equative structure (2 1 ) can be rendered as follows: (3 7)
the e [1 im has tallness to e]
=
tlre f [ 1 oe has tallness to f]
Likewise , if (24) has the symmetrical reading, we read : (38)
the e[Jim has tallness to e]
=
6 ft
(39)
the e [Jim has tallness to e] is much to 6 ft
provided we give a correct semantic description of the predicate be much to , as we shall do in a moment. If these structures are negated, we get the right results, provided again that be much to is given a proper semantic defmition . A remarkable detail with all this is that the negation used with symme trical equatives smacks of the radical negation and provokes an 'echo', as in (23a), (26) or (36). On the other hand, there is a feeling of minimal negation when non-symmetrical equatives are negated . In fact, the con struction so - Adjective - as is a negative polarity item , whereas as - Ad jective as is a positive polarity item. I do not venture an explanation of these phenomena here. -
3.
So far , we do not seem to be faring too badly with our analysis of the comparative . It is time , therefore , to try and find some weaknesses, and this is not too difficult . First of all, the 1 973 proposal is poor on the semantics of comparative constructions. The analysis is based on the notion that surface structures are transforma tionally related to seman t ically transparent underlying structures, - whereby the rules of transfor mation must be well-motivated and have a fair load of explanatory value. B ut nothing is said about what lies beyond the semantically transparent underlying structure . In other words, there is no real semantics yet in that paper. This in itself is not surprising, considering the total lack of real semantics in linguistics till quite rece ntly . The possible world, or model theoretic, semantics adopted by von Stechow has it origin in the formal semantics for logical languages, and penetrated into linguistics proper only
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where it is to be noted that the expression "6 ft" is the name of an extent (of tallness). If it is felt that (24) can, after all, also mean what is expressed by (25b), we read :
1 19 quite recently . Since my
1 973
paper was firmly rooted in the world and
the tradition of linguistics, it would have been strange if there had been a well-developed semantics available in that paper. The situation is a great deal better now. There now is a theory of for mal semantics, which is model-theoretic in the sense that it defmes func tions for the computation of truth-values of sentences given certain in dependently defined states of affairs (or 'possible worlds'). It is this form of semantics that von Stechow adopts in his study . Against this, it may be observed that existing standard formal semantics suffers from certain central weaknesses. Among these is the fact that the functions provided do not seem to be implementable within the constraints of any reasonable psychological theory : they are cognitively implausible to a very
high
tence-based, and fails to take into account the central role of context or discourse in processes of understanding and interpretation. Many re searchers today feel that a reasonably plausible psychological model of linguistic comprehension should incorporate the factor 'discourse' and assign it a central place, while the role of logic should be considered in dispensable but marginal . I reckon myself to belong to this group of researchers. I therefore do not accept the semantics used by von Stechow.
This means that some of his comments or inferences regarding my 1 973
analysis lack relevance, as will become clear below.
Another important respect in which standard formal semantics fails to do justice to linguistic reality is the area of presuppositions. Presupposi tions tend to be relegated to an ill-defmed 'pragmatics ' . In the seman tics I am developing (Seuren (forthcoming)) presuppositions are a semantic property of sentences: they are presupposed in previous discourse, and
therefore entailed. As was said in note
2,
two negations are distinguished
in natural language , the minimal, presupposition-preserving negation and the radical, presupposition -cancelling negation , which provokes an 'echo'. Consequently, there are three truth-values, one for truth, one for minimal falsity (whereby the presuppositions are still entailed), and one for radi cal falsity (where all entailments are cancelled). Presuppositions originate from predicate conditions, i . e . , conditions to be fulfilled by term deno tations for the application of the predicate to result in truth . Two kinds of predicate conditions are distinguished : preconditions (whose non-ful filment resuhs in radical falsity), and satisfaction conditions (whose non fulfilment results in minimal falsity). I shall now give an outline sk etch of the way in which a cognitive , discourse-base d , presuppositional th eory of semantics might handle the analyses of comparative and equative constructions provided above . In doing this I must ask the reader to keep in mind that it is not really feasible to pre�nt a complete and e x plicit th eory at this stage. First , the
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degree. Moreover, present-day standard formal semantics is strongly sen
1 20 theory itself
is
if
still very much in development , and then, even
the
general theory were available in a sufficiently elaborated and e xplicit form , its application to comparison constructions is likely to be far from trivial . We know that the grammatical description of these constructions
ex
is
traordinarily complex ; the same may b e expected for the semantic descrip tio n . In what follows I shall aim directly at an account of the predicates
have tallness to
and
be much to .
The account
is
'mixed' in that it is
couched in truth-conditional terms as well as in terms of mental correlates of expressions occurring in grammatically underlying structures. We must first postulate a cognitive parameter T of tallne ss , which starts fro m the value zero and extends one- dimensionally without any upper limi t . The term "extent " applies to parts of parameters. Extents case they are called
finite ,
and
positive,
or they are limited by a lower
value other than zero, and are unlimited upwards. These are
infinite
and
negative . (In Seuren 1 978 it is argued that positive gradable adjectives (tall, heavy, old) are translatable in terms of positive extents, and negative gradable adjectives (short, light, young) in terms of negative extents.) We furthermore postulate an operation of projection , whereby a gradable property of some entity
is mapped onto
some parameter. Projection
is thus
a function which gives a value for a (mental representation of) an entity on some parameter. The value provided
is
the limit of the extent asso
ciated with the entity of the parameter. If the extent is positive , it upper limit ; if the extent is negative , it
is
is
the
the lower limi t . Projection is
easily demonstrated by means of a diagram . I f we project Jim ' s tallness
on the parameter T, we get the extent
(40) 0
I �
e of Jim's tallness :
:
---· T -----------+ ---� -1 im 's
ll ne ss
And likewise , if we project Jim's shortness on T, we get the extent which Jim
0
to
is not tall : e
(41 )
e'
I
r------+--� T
the complement o f J i l ll ' s L <J l l n css We arc now in a position to understand w h a l
1s
J nca n l hy an e xpression
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are either limited by the value zero and by some upper limit , in which
121 like "Jim has tallness to the extent as saying that
e
e".
This e xpressio n must be interpreted
is the projection of Jim's tallness on the parameter T.
More generally , we specify the predicate conditions of the predicate
have tallness to as follows: 7 (42)
"X have tallness to Y " is true iff:
preconditions:
X is the name o f an entity that can be said to have tallness ; Y is the name of an extent on the parameter T ;
satisfaction condition : Note that for
(42)
Y is the projection of X o n T.
to make any sense it is necessary that projections have
of projections for granted and rely on intuitive processes of grasping the truth-conditions of cognitive representations. Our next step is the defmi tion of the predicate conditions for the predicate
be much to ,
since
sentences of comparison are derived from underlying forms typically containing structural elements of the form "the e [Jim has tallness to e ) is much t o Y " , where
e is an extent variable, and Y" stands for any extent
variable or extent name . The subject phrase , i .e . , " the e [Jim has tallness to e)", is now defmed as the projection of Jim's tallness on the parameter T . What remains i s a defmition of the predicate
be much to . This
defmition
must be such that its negation generates the entailment that the extent expressed by the subject phrase is
less
than the extent expressed by the
object phrase . We have taken care that this predicate does not occur in symmetrical equatives, so that these do not run the risk of non-sym metricity. Let us now defme
(43)
be much to as follows:
"X be much to Y " is true iff:
precondition :
There is a parameter extents on
satisfaction condition :
P;3
P
such that X and Y are
V v [v E Y => v E X ] , where ranging over values on
''v"
is a variable
P.
It is clear that the negation of this predicate , "- [X be much to Y]", now has the desired entailment that the extent X is
smaller
than the extent
Y, since the negation of the satisfaction condition is equivalent with the statement that there is a value
v
on
P
such that v E Y but v
t X. G iven the
way in which we have defined extents and projections, this simply means
t ha t whatever is projected o n P to yield X is smaller on the P-sralc than t he e x t e nt Y .9 This i s as much as I can say here about the sema nt ics of compariso n l"l l l lsl ruct ions.
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truth-values. In the context of this paper I shall take the truth-conditions
1 22 4. Another severe limitation of m y
1 973
paper consists in the fact that,
whatever its merits or demerits, it can claim validity only for a highly restricted class of languages, let us call them than - languages . In Stassen
1 984
it is shown that quantitative comparison of unequal entities is ex
pressed in many different ways in the languages of the world . Without any claim to completeness , we can distinguish the following types (largely based on Stassen
1 984):
"Jim and Joe , Jim is tall" (Malay)
(b)
"Jim is tall, Joe is not tall" (Nahuatl)
(c)
"Jim is tall, Joe is short" (Samoan)
(d)
"Jim exceeds Joe in tallness" (Hausa)
(e)
"Jim tall exceed Joe " (Yoruba, Cambodian)
(f)
"Jim is tall to Joe" (Breton , Masai)
(g)
"Jim is tall from Joe" (Japanese , Korea n , Hindi)
(h)
"Jim is tall o n Joe" (Georgian).
Furthermore , there are the than -languages, which have a semantically
non-transparent particle to link up the two terms of comparison, as well
as a morphological or lexical marking expressing the notion "more" or
the notion "less". The languages of the types (e)-(h), moreover, some times have a "more" - marking o n the adjective . Sranan (Surinam Creole), for example , has besides a than -comparative, also a comparative of type
(e), i .e ., with the serial verb
psa
("exceed"), but with the adverb
moro
("more") to modify the adjective . The categories (a)-(e) are fully transparent sema ntically , in that these languages do not have a separate construction for the comparative but make use of existing means to express what the comparative expresses in languages that have a special category for it . The most one can say here is that the construction· types shown are the conventional means for expressing the comparative notio n . In (f)-(h), on the contrary, there seems to be a stronger form of conventionalization in that metaphors of place are used conventionally to express the comparative . Type (e) is intermediate
in
that a serial verb construction is used,
which makes these languages particularly prone to conventionalization and even reanalysis. In many West African languages, for example , as well as in many Creoles whose speakers o riginate from West Africa , one fmds a rich and productive use o f serial verb constructions alongside with frequent reanalyses of seruil verbs into prepositions, adverbs and particles. Thus, in Sranan (and analogously in most Caribbean Creoles) the sentence
A ton
gwe, derived historically from a ("he") run
go away ,
simply means
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(a)
1 23
(44)
a . Luigi e piu alto che non pensassi. ("Luigi is taller than 1 thought")
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''he ran away", and the originally serial verb gwe is no longer felt to be verbal but adverbial. Typically, in serial verb languages the dative preposi tion is identical with or derived from the verb for "give". And many other examples could be cited. (A clear indication, in these languages, that re analysis has taken place is that the 'new' adverbs, prepositions, particles can no longer be combined with indicators of tense and aspect .) The than-languages are the least transparent of all, which probably explains why their constructions of comparison are so complex. What is known of the history of the comparative constructions in at least the Germanic and the Romance languages indicates that older stages of the construction in these languages were more transparent. Germanic than sentences as well as Romance que-comparatives derive historically from a construction of the type "Jim is tall to an extent to which Joe is not tall", or "Jim is tall to some extent and Joe is not tall to that extent". This appears from the etymologies of than and its Germanic cognates (from pon-ne meaning "by which not"), of Romance que (from Latin quo meaning "by which", whereby the negation has not been lexicalized into que but crops up again in the comparative clause as was shown in ex. (2) above), of the English dialectal form nor ("and not") for than . The occurrence of particles meaning "or" for than in certain languages (West Flemish, Ancient Greek) might be explained by the assumption that those comparatives derive from historical predecessors meaning "for all extents e, either Jim is e-tall or Joe is not e-tall", i.e . , the equative, with some semantic shift towards the comparative in the course of histor ical reanalysis. Although many, perhaps even most, historical details are shrouded in mystery and may even remain that way forever, enough is known to assert with some confidence that the European than-comparatives derive histor ically from semantically more transparent constructions. An interesting confirmation is provided by Italian, which has two comparative particles, di (from Latin de meaning "from") and che (from Latin quo , the Italian counterpart of French que) . These two particles are in complementary distribution : di is used whenever the than-phrase consists of a noun phrase ; che is used before a than-clause , i.e., with a finite verb. However, instead of che followed by the comparative clause it is also possible to have di quello che ("from that which", where che is not the com para tive particle but the relative pronoun "which"). In formal standard Italian the negation non (together with the use of the subjunctive) is required in the than -clause whenever its complementizer is the comparative che . But when the clause is relativized by means of di quello che there is no negation and no subjunctive:
1 24 b . Luigi e piu alto di quello che pensavo. ("Luigi is taller from what I thought")
(45)
a . Jim is taller than me (•I). b . Jim is the one nobody is taller than.
In the closely related Dutch construction, with the particle dan for than , this is not so :
(46)
a . Jim is grater dan ik (•rnij). b. • Jim is degene waar niemand grater dan is. 1 1
Against this partially fuzzy and blurred background of historical" develop ment, the question now arises what historical reanalysis means in terms of synchronic description . What exactly happens when a ·semantically transparent construction jells into a new category or is shaped into the form of an existing category thereby affecting the semantic transparency of the latter? This question, again , is not easy to answer .U Clearly, any answer to this question will necessarily have to be heavily theory-de pendent . In my theory, I would be inclined to say that reanalysis in the case of comparative constructions in the European languages means that the lexicon has been enriched with a ready-made bit of computation, so that it is no longer necessary, psycholinguistically, to go through the whole semantic computation of the comparative, as it was in the seman tically transparent construction type. Computationally there is an ad-
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This difference is confmnation for the hypothesis that the che-compar ative in Italian derives historically from a construction involving the nega tion, whereas the di-comparative does not . In general, howe_ver, the evi dence is relatively messy, and a great deal of mixing of construction types seems to have been going on.10 The overall conclusion is that we must seriously reckon with the pos sibility that comparatives are the result of historically preceding seman tically transparent constructions into either new construction types or already existing grammatical categories. Than-comparatives by themselves typically form new construction types in the languages where they de velop. Yet certain elements of this construction type fall in with existing categories. Thus, the deletion rules for comparatives show non-trivial similarities with deletion rules in conjunctions. Closely related languages may differ in details of reanalysis. In English, for example, than turns into a preposition when it is followed by a noun phrase , as appears from the oblique form of personal pronouns ( 45a) as well as from the possi bility of stranding than , as in (45b) :
1 25 vantage in that a system with a larger inventory of ready-made but seman tically more complex building blocks for sentences is more efficient in terms of processing than a system with fewer ready-made items and less complex internal analyses :
single lexical items ate grammatically easy
to handle 1 and can still carry a considerable load of semantic information. Such storing of semantic information into ready-made lexical items occurs generally when the semantic information in question is of a typical, recurring nature . This answer, however, is deceivingly simple . In actual fact, there are a great number of complications associated with
this
'jelling' of semantic
information into single lexical items . In language, as in all other areas o f nature , the truth i s rarely simple , and never pure.
I n this section I wish t o expand a little o n the complexities of lexicali sation, in particular with regard to a serious problem raised by von Ste chow in his paper in this volume .
1 973
The analysis of the comparative that I presented in my
paper
was entirely in the tradition of what was then called 'generative semantics' (or 'semantic syntax', as I have always preferred to call it) . This tradition was characterized by the notion that a grammar of a language is a set of rules mapping underlying structures and surface structures of sentences onto each other (i .e ., the traditional idea of philosophical grammar), and by the idea that the deepest syntactically underlying structure (deep structure or DS) is identical with the semantic analysis (or SA) of a sen tence . At the same time it b ecame clear that at least some lexical items lend themselves to internal analyses along lines strictly parallel to syntactic analyses found for 'open' syntactic constructions . The most successful illustration of this type of analysis was McCawley's analysis of causative verbs (in particular
kill,
which was analysed as "cause to become dead'') ,
as proposed i n many publications. The central rule operative i n bringing together "cause to . become dead" under one single
V -pode
is the rule
of ·Predicate Raising, which has since been shown to occur in the open syntax of many languages in the world (Seuren
1 972 ;
Evers
1 975) . Given
the assumption that DS equals SA, it was assumed as well that complex lexical items were best described in syntax by inserting them into syntactic trees as part of the overall transformational process. This is also what is done in my
1 973
paper: a DS-cum-SA is assumed (what I have called
"analysis" in this paper), and the bit "and -not" is replaced by
than
at
some stage in the derivation. Since then we have grown a little wiser. First , it became clear that
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5.
1 26 many lexical items that lend themselves for decomposition also carry
a great deal of 'extra' information over and above the information con
tributed by the internal syntactic analysis.
assassinate
Thus,
for example , the item
in the English lexicon not only contains the bit "cause to
become dead", but also a great deal extra which is not open to such clear cut quasi-syntactic analysis. For it to be true that A assassinates B, B must
not only be killed, but the killing must be a case of murder (i .e . , unlaw
ful and with malice afore-thought), and B must be a person of public
importance , and the killing must take place on account of B's public
importance . All this infonna tion is part of the meaning of
assassinate ,
but not conveyed by any motivated form of prelexical syntactic analysis.
Many linguists drew the conclusion that , therefore, the whole theory of
tence containing the predicate stages: one stage (the
assassinate had better be presented in two DS) where the item itself is left unanalysed, and one
further stage which has no effect on the syntax but which unravels the
lexical meaning of the word, partly in terms of "cause to become dead".
This means that it makes sense to distinguish between a deepest syn
tactically underlying structure
DS,
which only provides a partial semantic
analysis, and a full semantic analysis 'underneath' the
This
DS.
is all right for a numb er of semantically complex lexical items .
It explains, for example, why they are impenetrable for quantification.
This is an important point : if kill is analysed as "cause to become dead" (or, for ease of reference, "cause to die") , then, one might ask, why is
it that :
(47)
Harry killed someone.
can only mean s(3 x5[Harry cause s[ x die ] ] ] , and not s[Harry cause s [3 x
S (x
die ] ] ] . In the 'primitive' semantic syntax theory there is nothing
that could exclude the latter reading, since cyclic treatment will first
transform s ( 3 X s( X die]) into s(someone die], and further cyclic Predicate Raising will give s[Harry y[ cause-die] someone] and hence
someone.
But if quantification
is
Harry kill
made to operate on structures with all
lexical items filled in, we can avoid this awkward consequence without any extra cost .
The attractiveness of this theory is illustrated by a case like French
de[endre,
which is analysed as either "not allow to take", i .e ., prohibit ,
or "not allow to be taken", i .e ., defend, with an extra passive thrown in.
A sentence lik e : (48)
1 ean a defendu le vin a un enfant .
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lexical decomposition was worthless, but that conclusion was a little pre
mature . What does follow, however, is that a semantic analysis of a sen
1 27 can only mean "there is a child such that Jean forbade it wine" , and not
"there is no child that Jean allowed to take wine" or "Jean did not allow
there to be a child that took wine ". If all complex lexical items behaved in such orderly manner, theory-building would be relatively easy. Un fortunately, however, matters are more complex . For there are proposi tional �perators, such as
almost,
which do penetrate into complex items.
Morgan
( 1 969) made the famous observation that :
(49)
Harry almost killed
can mean
"Harry
Bill .
almost caused
it almost to happen that
Bill
Bill
to become dead", or "Harry caused
became dead", or "Harry caused
Bill
to
the quantifiers :
(50)
Harry did not kill
Bill .
cannot mean "Harry caused it not to happen that Bill became dead" or
"Harry caused Bill to become not dead".
Moreover, some complex lexical items do allow for certain quantifiers to 'penetrate', but never the 'open' quantifiers class, and never the negation penetrate are unstressed
a
not.
some, all, every
and their
The quantifiers that do sometimes
and any with its class
(ever, the slightest),
the latter requiring a negation somewhere in the complex item. Thus,
if we analyse look for as something like "try (for) to find", a sentence
like :
(5 1 )
Harry is looking for a secretary .
is, as is widely known, ambiguous between a specific reading where Harry is looking for a specific secretary (3 x: secretary [Harry is trying to fmd xD, and a reading where what Harry wants is a secretary (Harry is trying for 3 x: secretary [Harry fmds x]) . Likewise , the item
lack,
decomposed as
"not have" , with the presupposition that the subject could do with what it does not have, clearly allows for internal quantification with a or any :
(52)
a. She.lacks any charm. b. He lacks a sense of humour.
It thus seems that we must distinguish between two kinds of operators
(including quantifiers). On the one hand we have the class of 'external'
operators, such as not, some, all, every , which never penetrate into a lex ical item , and the 'internal' operators, such as almost, a, the zero article ,
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become almost dead"Y On the other hand, the negation behaves like
1 28 any, ever,
which can penetrate into some lexical items , but not into all.
And we must distinguish between the 'closed' items which are entirely impenetrable , and the 'open' items which do allow for penetration by the internal operators . I 'm not sure that this picture is adequate, but the distinctions mentioned seem inevitable in any theory of gramma tical and
semantic description. They are not a peculiarity of the theory of semantic
syntax , but have the status of facts that need a description and an ex planation . For the theory of semantic syntax these and similar observa tions have far-reaching consequences, the details of which transcend the limits of this paper. It must be mentioned, however, given the immediate relevance to the present context, that the notion of 'penetration' into a complex item negation stands at the extreme right of the analysis. Von Stechow notes
(his exx .
(84) than everyone
ff.) that
Jim is taller than Joe
would entail
Jim is taller
in my theory . His reasoning is as follows . Assuming that
proper names may denote only existing individuals , my analysis of this sentence , as given in
(53)
( 1 ) above, entails:
3 e : extent [Jim is e-tall A 3 x - [x is e-tall]]
which again is equivalent with:
(54)
3 e : extent [Jim is e-tall A - 'r/x [ x is e-tall]]
which would have to be convertible into the comparative :
(55 )
Jim is taller than everyone .
Von Stechow touches on an important point here, but it is not , as he
presents it, a point that affects my theory in particular. On the contrary, we have here a fact that needs a description and an explanation in
any
theory of the comparative .
Let us have a closer look. Sentence says.
(54)
(55)
does not mean what
means that not everyone is as tall as Jim , l4 but
(55)
(54)
means
that for every x it is the case that J im is taller than x. So the problem does not lie in the logic that gives
(54)
as an entailment from
the grammar that must prevent the derivation of gramma r must make sure that
whole sentence.
quantifiers after
In
in
(55)
from
( 1 ) , but in (54). The
is given scope over the
fact, the gramma r must make sure that all external
than
can have scope under
has largest scope :
everyone
(55)
have largest scope. Only the internal quantifiers
than . In all of the
following sentences the quantifier
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extends to the position just after any incorporated negation , even if the
1 29 (56)
a. Jim is taller than someone. b. Jim is taller than no-one here . c . Jim is taller than many people .
Not so with the internal quantifiers: (57)
a. Jim is taller than anyone here. b . Jim is taller than you will ever be. c . Jim is taller than a six-year-old .
(58 )
a. 3 e :extent [Jim is e-tall A "' 3 x [ x is e-tall ]] 3 e :extent [Jim is e-tall A "' 3 t [at t [you will be e-tall]]] (where ''t" is a variable over time moments).
Notice also that ( 57b) is ungrammatical when ever is replaced by some times or by al-ways (i.e., by external quantifiers) : (59)
a. *Jim is taller than you will sometimes be. b . *Jim is taller than you will always be .
The reason for this ungramma ticality is simple (in semantic syntax) . Both sometimes and always would have to take large scope, i .e ., preceding the initial existential extent quantifier. But then these words will ine vitably end up in the main clause :
(60)
a. Jim is sometimes taller than you will be. b . Jim is always taller than you will be . 1 5
As has been said , we have here a problem, not noted before, to my know ledge, in the literature, which is general and exists for any theory that assumes a clause (always or sometimes ) after than at any structural level that is input to the semantics. And, of course, there is no theory that does not make such a claim. The problem is that a sentence like :
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Here the quantifier scope is, or may be, limited to the clause under than . Note that it would be wrong to propose that , e.g., (57a) should b e read as "for everybody here it is true that Jim is taller than him " , since that analysis fails for (57b) , which clearly cannot mean "it is always the case that Jim is taller than you will be", The proposal that any in (57 a) should be taken as the universal quantifier with large scope thus fails on account of the analogous case (57b) where this analysis is blocked . The sentences (57a-b) are to be analysed as, respectively :
130 (6 1 )
Jim is taller than everyone thinks.
6.
In this last section I will discuss the main remaining points in von Ste chow's paper that affect my comparative analysis. 6.1 Ambiguous counterfactuals
Von Stechow points out that a sentence like: (62)
If Jim had worked harder than he did, he would have passed.
has at least the following two readings: (63)
a. If, at the time under discussion, "Jim works harder than he does" had been true, he would have passed. b . If, at the time under discussion, Jim had worked harder than he actually did, he would have passed.
The former reading is somehow absurd, since it entails that a condition for Jim's passing is that he does and does not work hard to some extent,
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requires overall scope for everyone, and excludes any interpretation with the scope of everyone limited to the than-clause . (6 1 ) means unam biguously "for every x, Jim is taller than x thinks", and not "not everyone thinks Jim is as tall as he is". Since there is a clause after than , any theory recognizing this clause will have to account for the fact that this type o f clause i s subject t o the constraint that it does not allow for quantification under an external quantifier. Only internal quantification is allowed there . We must be grateful to von Stechow for coming up with his problem of "unwarranted inferences", since without that we would not have noticed this troublesome and therefore interesting fact. This is not the right place to venture a theoretical explanation and a descriptive frame for the distinction between external and internal oper ators, and the distinction between those items that do and those that do not allow for operator penetration. It must suffice here that these distinc tions are real, and are , apparently, at work in the comparative as well as in other cases of complex lexical items. From this viewpoint, the com plication at hand, though unsolved in the general theory of linguistic description and explanation , is a further argument in favour of the decom position of than into "and - not".
131 which will make it wellnigh impossible for him to pass . The second reading
is the reasonable one . Von Stechow points out as well that any adequate
theory of the comparative must allow for an account of both readings, in particular reading (b) , which is the more difficult to achieve . Up to this point I have no quarrel with von Stechow. But he then proceeds to present an analysis of counterfactuals in terms o f a possible world semantics and Lewis-operators, using this account of counter factuals as a touchstone for the various theories he discusses . In doing so he seems to take
it
for granted that his account of counterfactuals
(and the wider semantic theory of which it forms a part) is
the
correct
theory . It must be observed, however, that some comparative analyses may perhaps not easily lend themselves to a von Stechow-type account be naturally compatible with other semantic
"ambiguous counterfactuals" says little about the comparative theories discussed as long as there
is
no agreement on the intrinsic quality o f
poSsible world semantics. On the other hand, however, t h e challenge
posed by (62) must be met , and if a possible worlds account is rejected, it would be good if it could be shown how an alternative account would work .
All I can do here is give a summary sketch of the alternative theory.
(For details see Seuren (forthcoming).) I envisage an incremental se
mantics, whereby each new utterance adds a bit of structure to a discourse domain D. Additions to D (i.e . , increments) are of two kinds: they either
add to the bulk of D or they add to D an instruction constraining subse quent developments of D. The conjunction
if is ana)ysed in
deep structure
as a predicate taking clauses as arguments. Its contribution to any given D consists in an instruction to the effect that, given
ifA then B, all subse A is add�d,
quent developments of D are subject to the constraint that if
8 is added as well . So far there is no difference between ordinary con
ditionals and counterfactuals. Counterfactuals differ, however, from or dinary conditionals in that the instruction says "for all subsequent de
velopments of D', if A is added so is 8,
-
where D'
=
D except that D e n
tails not-A and D' lacks that entailment " . (In actual fact , I would stipu
late that for counterfactuals the predicate
if presupposes
that D entails
not- A and asserts for D' what ordinary conditional if asserts for D .)
The important point now is that it must be possible for any clause
proposed for incrementation to D' to contain e xpressions referring to elements in D. If the means for doing so is secured, there is in principle no obstacle left for a solution to the problem posed by (63b ). Tech nically this is easily achieved in discourse semantics. Increments to non truth domains must be marked anyway, as well as definite descriptio ns, for a number of reasons. Thus, e .g . , any theory of semantics must account for the non-contradictory readings of sentences lik e :
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of counterfactuals but
theories and counterfactual accounts. In other words, the criterion of
1 32 (6 4)
The girl with brown eyes has blue eyes.
This sentence is true if the subject-NP refers to a girl with brown eyes who , for example, has been represented in a painted portrait as having blue eyes, - or vice versa , if the subject-NP denotes a portrait of a girl painted with brown eyes who, in fact, has blue eyes . (Cp. Fauconnier 1 979) . For increments to non-truth domains we can use subscripts indicating the domain to which a clause is to be added. For (63b) we get something like: (65)
This analysis takes
if to
e-hard] 1\. -
o[ Jim has worked
be a deep structure predicate , as was said a little
earlier, taking clauses as arguments. 1 6 As was said in Section 3 above,
extents are interpreted as parts of parameters. They are thus domain-in dependent . Projections, however, as well as clauses indicating or specify
ing their quantity (by means of the predicate specific . Thus,
"o•[Jim
be much to) are
domain
has worked e-hard]" is a quantity specification
in D' of the intensity of Jim's work by means of the permanently avail able intensity parameter. The same clause indexed for D is the same in D .
(A
parsimonious notation would leave out all indexings for D and mark
only subdomains that are not intended to be held up for truth-testing.) (65) thus says that for any addition to D' where an intensity extent
e
is identified for the projection of Jim's working on the intensity parameter in D' such that
e
is larger (greater) than the truthful specification of the
intensity of Jim's working in the truth-domain D, for any such addition to D' it is required that "Jim has passed" be likewise added to D'. The presupposition that there is no intensity extent
e
fulfilling the same con
ditions but involving only D-increments is trivially satisfied, since no domain can contain a contradiction.
6.2 Downward entailment In his Section I V , von Stechow discusses the use made in Seuren ( 1 973) of negative polarity items (NPI), and rejects the support value of their occur rence in than - phrases and than- clauses for the assumption that
than
contains a negation on the grounds that, according to von Stechow, it is shown in Ladusaw 1 979 that NPI's occur typically in
entailing
downward
contexts, i .e ., roughly , in positions where a replacement of the
constituent filling that position by another constituent denoting a proper subpart of the extension of the original constituent results in an entail-
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o•[Jim has worked o•Pim has passed]
I F(3 e : extent e-hard] ] ,
1 33
(66)
*The child must be left alone more than can be helped .
The sentence becomes grammatical when it is negated : (67)
The child must not be left alone more than can be helped .
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ment of the original sentence. This allows us, still according to von Ste chow, to give up the hypothesis of underlying negation in than . I am afraid I disagree entirely. First, even if Ladusaw's theory were adequate, there would not be any good reason for giving up the hypothesis of underlying negation. For the theory that says that NPI's occur typically in downward entailing contexts does not say anything about the reasons for the downward entailments. If indeed, as I assume is the case for many downward entailing positions at least , the downward entailments can be seen to result from underlying negations, negation being the prime dow ward entailment generating operator, then both Ladusaw's and my the ories are helped . In other words, there is no contradiction between Ladu saw's account and mine. There would be a contradiction if it was claimed that all NPI 's always require an underlying negation and if it could be shown that there are cases where an underlying negation is impossible . Von Stechow seems inclined . to read such a claim into Seuren ( 1 973), but without reason. I have never made that claim about NPI's (though it would be nice if it were found to be viable). My inference from NPI's after comparative than to underlying negation is of a tentative kind, intended to lend further support to the analysis, not to 'prove' it . Moreover, where von Stechow mentions downward entailing positions that also allow for NPI's such as the common noun position after every, then to claim that the assumption of an underlying negation would make no sense , one does not have the im pression that he has looked very hard for a viable analysis with underly ing negation. One can easily do better than analysing the universal quanti fier as ...:., 3 � just in order to let negations jump out of the logical hat . All one would have to do is apply , one way or another, the standard analysis of the universal quantifier in predicate logic, i .e . , through an im plication. And the implication "A ::J B" is equivalent with "� A V B", which makes the desired negation jump out of the hat rather more ele gantly . Not that I intend to defend this analysis here, but it is an obvious thought , which might well be usable in a theory of semantic syntax coupled with discourse semantics. There are, moreover, independent problems with Ladusaw's theory . First, it is by no means the case that all NPI's behave similarly. Many, but not all , occur in than-environments. To give an example, the NPI can be helped is out of place in :
134 I wish I knew why , but I don't know. No-one t o m y knowledge has so far made any kind o f representative survey of English NPI's and the en vironments
in
which they can occur. It has been done for Dutch, how
ever (Hoppenbrouwers
1 983),
and it is immediately obvious that Ladu
saw's theory does not cut ice . It o
nly
cuts some ice for the extremely
limited class of NPI's considered in his study. Even for those, however,
there are problems .
Every,
for example , is downward entailing with
regard to its common noun, and it allows for NPI's in that position. But
each
is likewise downward entailing
in
that way and it
does not
allow for NPI's there :
(68)
*Each boy who had ever read any science fiction was hooked on it .
every ,
but it is not downward entailing with respect to that position (contrary to what von Stechow says):
(69)
Few animals fled � Few dogs fled.
Likewise , it
is not
(70)
be surprised
allows for NPI's in its complement clause , but
downward entailing:
She was surprised that Harry came to the party � She was sur prised that Harry and Rita came to the party .
It seems to me, therefore , that my analysis is not seriously threatened by l..a d usaw's theory, and that the latter will need a great deal of refme ment and correctio n , if it does not tum out to be a blind alley altogether.
6.3 Negation and quantifiers In connection with his exx.
(93)
and
(94),
von Stechow states that sen
tences of the type:
(7 1 )
Jim is taller than Joe and Steve .
are a problem for my theory , since my theory would make the obviously false prediction that at least in one of its readings
(7 1 )
same as:
(72)
Jim is talle r than Joe or Jim is taller than Steve .
which is, of course , not so .
should mean the
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Then, few allows for NPI's (some at least) in its CN-position, like
1 35 There is some justification for this objection, since under the assump tions of classifical calculus an analysis like : (73)
3 e : extent [Jim is e-tall A - [Joe is e-tall A Steve is e-tall]]
which would correspond to (7 1 ), is equivalent with : (74)
[ 3 e :extent [Jim is e-tall A - [Joe is e-tall] ]
f-tall A - [Steve is f-tall]]]
V
3f:extent [Jim is
which corresponds to (72). In my 1 973 paper there is no indication that I wish to deviate from classical calculus, so that any critique solely based are, however, later papers which make it clear that I entertain unorthodox notions regarding the logic underlying natural language use. In my paper 'Negative's travels' (1 974) I draw attention to the fact that
De Morgan's laws seem to apply only asymmetrically in natural
language . It is observed there (pp. 201 ff.) that (75a) and (75b) 'feel' equivalent, but (76a) and (76b) do not : 1 7 (75)
a. He doesn't like tea and he doesn't like coffee . b . He doesn't like tea or coffe e .
(76)
a . He doesn't like tea or he doesn't like coffe e . b . H e doesn't like tea and coffee.
In a footnote on p . 203 it is pointed out that this phenomenon is found
again in comparatives. The two sentences
in (77) 'feel' equivalent , but
those in (78) do not : (77)
a. Jim is taller than Joe and Jim is taller than Steve. b. Jim is taller than Joe or Steve .
(78)
a. Jim is taller than Joe or Jim is taller than Steve . b. Jim is taller than Joe and Steve .
In Seuren 1 979 , 1 980 , and (forthcoming) , I argue that the logic found
in natural language is three-valued, with the values 'true', 'minimally false' , and 'radically false' , and that there are two negations, the minimal negation (-), and the radical negation
(::::.) , 18
as indicated in note 2 above .
I feel entitled, therefore , to claim that my comparative analysis should be seen in the light of the published papers, which means, at least , that it should be clear that I do not share all assumptions of classical logic .
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on that paper is fully justified in drawing attention to this point . There
136 It does not mean, however, that I have all the answers ready. But one observatio n can be made, which may be sufficient to show that this par ticular problem of
and
and
or, at
least for the present, does not constitute
a serious threat. The observation is that the conj u nction operator and seems to be a positive polarity item, which means that when placed under
negation , that negation m u st be the radical negation , so that an 'echo' is provoked or anyway some special intonation is called for, as in (76b ). I f this is so, then (73) is a n impossible structure since it has the minimal negation over a conjunction . That negation should be the radical one. But then there is no longer a conversion into than . Consequently, (73) cannot be an analysis of (7 1 ) , and, in fact, in my comprehension of English (7 1 ) must be interpreted either with large scope for and, so that Steve taken together, for which reading I am hesitant to propose an analysis . It will be evident that there is no problem in relating (77a) and (77b).
6.4 Differential measure phrases A neglected aspect o f the comparative question is the analysis of dif ferential measure phrases (DMP), such as six (79)
inches in :
Jim is six inches taller than Joe.
At the end of my 1 973 paper I mention the problem of DMP's and pro
pose a very tentative solution in sketchy outline. The idea put forward there is that DMP's should be anlaysed as metaphorically interpreted extension-phrases, more or less like "Jim is tall to an extent to which,
over a stretch of 6 in, Joe is not tall". This analysis is called "speculative"
t here (p. 56 1 ). In any case it seems that DMP's are most naturally analysed as modifying phrases taking scope over the than-clause. (In deep structure these phrases function as predicates.) If we are prepared to fall back on the notion of reanalysis, it is not even very important any more what kind of semantically transparent modification is taken to underly DMP's, since they have become a specialized category in their own right , used just to function as differential measure phrases. It may also b e that the historically underlying mo difying phrase is not necessarily the same in
all than -languages. What I had not noticed in the 1 973 paper is that , in English, the preposition
by
seems to lurk j ust beneath the surface of
DMP's:
(80)
a. She was his elder by fifteen years. b . I 'll make you shorter b y the length of one head. c. He beat me b y two minutes.
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( 7 1 ) is the same as (77a), or as meaning that Jim is taller than Joe and
137 A similar modification seems t o u nderlie Latin DMP's which are placed
in the ablative case . If by underlies DMP's, tall to an extent to which, by The semantics of DMP's
is
6
(79)
would read as
"Jim is
in , Joe is not tall", at least historically.
clear : DMP's result in cognitive extents on the
relevant parameter representing the parameter extension covered by the comparing entity and not covered by the compare e , - more or less as proposed by Hellan
1 98 1 .
In any case , it
is
is
clear that we haven't seen the
end of the day yet in comparative analyses.
Nijmegen Univerrity Philosophical Institute
Netherlands
NOTES
1.
"Negative polarity items" is the term commonly used for lexical items or com
binations of them, or grammatical constructions, which (for largely unknown rea
sons) require either a full negation (not) or a negative word, such as hardly , or only , in declarative main clauses, on pain of ungrammaticality. Examples are at aU, all that (+ adj.), in the least, ever, any, so adj . - as, any more, as much as (+ VP) , can possibly, bat an eyelid, etc. Positive polarity items are items which, when placed under negation, provoke an 'echo'. Examples are relatively/absolutely/eminently etc. (+ adj.), still, not, splendid, some. far from (+ adj .) , perhaps , etc . . . . -
2. In work I have done after 1 973 (e.g. 1 979, 1 980) I argue that a distinction must be made between two negations in natural language, the minimal negation ( - ) ,
which i s presupposition-preserving, and t h e radical negation (::::): , which cancels pre
suppositions. The negation required by NPI's is the minimal one, whereas PPI's
allo w for only the radical negation, which is the source of the 'echo' observed by
many linguists in negative sentences with PPI's. Moreover, if a negation is morpho logically or lexically incorporated, it can only be the minimal negation. It thus follows that the negation of the comparative is the minimal negation, not the radical
one. The ungrammaticality of the sentences of (5) is thus explained. For a more
complete account
see
Seuren (forthcoming).
An obvious problem is formed by those cases where the contrasted element is not a syntactic constituent but, e.g., a morphological element, as in :
3.
(i)
I didn't DEcode it; I ENcoded it.
Note that contrastive accent is a problem for all existing theories of grammar. One way or another, they all encounter difficuhies here. In particular those theories
which proclaim that any grammatical element can always be adorned with con
trastive accent fail to explain why, e.g., (ii) For
*I don't suppose Harry has arrived yet ; BILL has. cases
like (i) I would suggest that they should be treated
elements, more or less as:
as
contrasting quoted
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P.O. Box 9108 6500 HK Nijmegen
1 38 (iii)
not [the x [ "!past x-code it") is "de " ; the x [ "I past x-code it"] is "en".
It is noteworthy, anyway, that in French constrastive Predicate Lowering is not allowed when the contrasted element is a full nominal constituent, but obligatory when it is something else. Thus, French has (iv) but not (v) : (iv) (v)
Dieu DISpose ; il ne PROpose pas. C'est DIS que Dieu pose; ce n'est pas PRO.
Clearly, a thorough general study of the relation between (pseudo)clefting and Predicate Lowering in various languages would be extremely useful. 4 . Montague grammarians often use a variant of Predicate Lowering in order to account for contrastive accent. Their analysis is cast in terms of lambda-calculus: AX [John wrote x] (the letter)
Lambda-conversion then yields the surface sentence John wrote th� Jett�r. It should be noted, however, that this is a spurious use of lambda-calculus. Lambda-formulas are simply logically equivalent with their conversions ; their usefulness lies in the fact that a semantic function named as a lambda-formula can 'anticipate values in certain argument positions provided 'higher up' in the categorial tree. However, the use of lambda-formulas. as underlying structures in syntactic descriptions is
entirely different, and the difference should be noted. 5 . This analysis of WH-questions has interestingly correct consequences for mul tiple questions of the types (Baker 1 970) : (i)
(ii)
(iii) (iv)
Who Who Who Who
bought what? remembers what we bought? remembers that we bought what? remembers where we bought what?
But we cannot go into this question here. 6. The situation is somehow similar to what we fmd with negations (see note2) . In the case of negation, however, there is a principled explanation for the ambiguity, as is explained in Seuren (forthcoming) . 7 . We can, on the basis of (42), defme derived predicates such as have ta/lness to
half- Y. The satisfaction condition is then "Y is half the projection of X on This will produce the correct semantics for cases like Jim is half as tall as John . 8. There are cases such as: (i)
T".
The corridor is longer than the room is wide.
where two parameters with a common measuring system are collapsed into a single parameter of that measuring system. Besides, there are cases of 'sloppy' comparison, such as :
(ii)
He has more clothes than cupboards to put them in.
which means something like "he does not have enough cupboards to put all his clothes in". Or:
(iii)
he talks more than he has money.
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(i)
139 which is even further removed from the ordinary m eaning of comparatives. 9. This analysis is, in fact, a provisional follow-up of note 1 7 in Seuren ( 1 9 7 3 : 5 6 1 ) .
1 0 . I am intrigued by t h e fact that German and Ancient Greek, which have com parative particles (als and !, respectively) that do not historically incorporate a
negation, allow for negative verbs in a way that English and Dutch, whose com parative particles do incorporate a negation, do not. We fmd, e.g., in Ancient Greek (Plato, Sophist 258c) : (i)
Pleion e 'keinos apeipe skopein ... (lit: "More than he forbade to look ... ) "
or in ordinary standard German (in a TV-play) :
(ii)
whereas they mean, respectively, "more than he allowed to look " and "that went faster than I had sulf{Jected ". 1 1 . Preposition stranding is not the same in Dutch and in English. Some forms of colloquial Dutch, however, come pretty close to standard English in this respect. Yet even in these forms of Dutch no equivalent of (45b) is ever possible. 1 2 . The main author in the linguistic literature on questions of diachronic reanalysis and grammaticalization is T. Giv6n ( 1 979a; 1 9 79b), who is a severe critic of 'estab lished' syntactic theory . 1 3 . Remarkably, the three readings are distinguished in French. The frrst corre sponds to something like Harry aurait tul Bill; the second is rendered as HQ/"ry a
failli ruer Bill; the third is Harry a pre!que rue Bill. (I am indebted to Lance Ridley of Sydney University for this observation.) 14. (i)
Notice that, in the terms of the equative analysis given above, the sentence: Not everyone is as tall as Jim.
is analysed. as:
(ii)
-
'rl e :extent [ 'rlx [ x is e- tall) V
-
[Jim is e- tall l l
which is eq uivalent to (54). 15. Hoeksema (this volume) maintains that anyone as in (5 7a) is indeed the uni versal ( 'free choice') any, and not, .as I maintain, the (negated) existential any. The point is of considerable weight for his analysis, since he defends the thesis that NP comparatives are u pward entailing and S-comparatives are downward entailing. (I reject the thesis, as well as the grammatical distinction beyond anything deeper than shallow structure: the semantic differences are all accounted for by operator scope.) Hoeksema's argument is that any in NP-comparatives can be modified by almost or netzrly : (i)
Jim is taller than almost/nearly anyone here.
whereas (negated) existential any cannot :
(ii)
*There wasn't almost/nearly anyone here.
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Das ist ja schneller gegangen als ich befiirchtet hiitte. (lit : "That went faster than I had feared.")
1 40 However, it must also b e noted that
(iii)
There almost/nearly wasn't anyone here.
i5 a fmc sentence, where almott/nearly takes not in its scope. Note that (i) does the same semantically : "Jim is taU to an extent to which almost/nearly no-one here is ". In much the same way I know takes not in its scope in, e .g. :
(iv)
Jim is taller than I know his brother is.
which is "Jim is taU to an extent to which I know his brother is not". Hoeksema's argument is too weak altogether. Note, for example, that universal any always requires a modal or 'irrealis ' context : (v)
O ne would expect this condition t o b e present i n NP-comparatives with any, but it is not:
(VI)
Bennie drank more than any of the teachers at the party.
O ne would moreover expect, on Hoeksema's account, that the inverted comparative should be acceptable, but it is not :
(vh)
"'Any of the teachers drank less than Bennie at the party.
Finally (for now), Dutch quite clearly shows the untenability of Hoeksema's position
in this respect, since Dutch has a clear lexical distinction between 'free choice' any
( wie dan ook) and existential any ( ook maar iemaru:f). We now see that the latter =
=
is perfectly normal in NP-comparatives:
(viii)
Hij weet meer dan ook maar iemand van om. He knows more than anyone of us
submit, therefore, that Hoeksema's argument is insufficient. I submit, moreover, that this point is crucial. 1 6 . The lexical analysis of if will reduce it to a structure with the analysis " - A V B" (for "if A then B'') as a central element. This will then be the basis for an ex planation of the occurrence of many NPI's in if-clauses. 1 7 . The difference is described there as a result of and being a Negation Raising predicate, whereas or is not. Though I still hold that view, more is needed to explain this whole complex of phenomena. 1 8 . For the properties and proof theory of this three-valued propositional calculus, see Weyters 1 98 2 .
REFERENCES Baker, C . L . , 1 9 7 0 : Notes on the description of English questions: the role of an ab stract question morpheme. Foundations of Language 6 . 2 ; 1 9 7- 2 1 9 .
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"' Any teacher drank a lot at the party f.J Any teacher will drink a lot at the party .
1 41 Ballweg, J. & Glinz, H ., (eds.) 1980:
Grammatik und Logik .
Jahrbuch 1 979 des
Instituts ffir deutsche S pmche. S chwann, DUsseldorf. Bergmans, L., 1 9 8 2 :
Language!.
Semantic Aspectll of Comparison in Dutch, English and Other
Ph.D thesis, University of Louvain.
Evers, A . , 197 5 :
The Transfomuztional Cycle in Dutch and German .
Ph.D thesis,
University of Utrecht. Fauconnier, G . , 1 9 7 9 :
Mental Spaces.
cennes.
Givon , T ., 1979a: On
Unpublished. Universite de Paris VIII, Vin
Underrtanding Grammar.
Academic Press , New York-San
Francisco-London.
Givon, T . , 1 9 7 9b : From discourse to syntax: grammar
as
a processing strategy. I n :
Givon (ed.), p p . 8 1-1 1 2 .
Discourse and Syntax. (
Givon, T . , (ed.) 1 979 :
=
Sy ntax and Semantics, Vol. 12) .
Academic Press, New York-San Francisco-London. Hellan, L . , 1 98 1 :
Toward$ an Integrated Analysis of Comparatives .
Narr, Tilbingen.
Hoppenbrouwers, G., 1 9 8 3 :
Poliuiteit. Een literatuiUOnderzoek .
N.l .S . Working
Papers No. 2. Nijmegen Institute of Semantics. Joly, A., 1 967 :
Negation and the Comparative Particle in English. Presses Universite
Laval, Quebec.
Kiefer, F. &Ruwet, N. ( eds.) 1 9 7 3 : Generative Grammar in Europe. Reidel, Dordrecht. Ladusaw, W.A., 1 9 7 9 :
Polarity Sensitivity as Inherent Scope Relations .
Ph.D dis
sertation, University of Texas at Austin.
Everything that Linguists Have Always Wanted to Know ashamed to ask . Blackwell, O xford. Morgan, J .L., 1 96 9 : On arguing about semantics. Papers in Linguistics 1 . 1 ; 49-7U Seuren, P .A .M . , 1 9 7 2 : Predicate Raising and dative in French and sundry languages. McCawley, J .D., 1 98 1 :
about Logic• •but
were
Magdalen College, Oxford. (LAUT, Trier). Seuren, P.A.M., 1 9 7 3 : The comparative. In : Kiefer & Ruwet
(eds.),
pp. 528-564.
Seuren, P .A.M., 1974: Negative's tmvels. In: Seuren (ed.), pp. 1 8 3-208 . Seuren, P .A.M., (ed.) 1 974 :
Semantic Syntax. Oxford
University Press, Oxford.
Seuren, P.A.M., 1 978 : The structure and selection of positive and negative gmdable adjectives. In :
Papen from the Parosession on the Lexicon .
Chicago Linguistic
Society, April 1 4 - 1 5 , 1 9 7 8 . pp. 3 36-346. Seuren, P.A.M., 1979:
The logic of presuppositional semantics.
Unpublished paper,
Filosofisch lnstituut, Nijmegen University. Seuren, P .A .M ., 1 980 : Dreiwertige Logik und die Semantik natiirlicher Spmche. I n : Ballweg & Glinz (eds.), pp. 72-103.
Discourse Semantic$. Blackwell, Oxford. Comparative and Conjunction. An Essay in Universal Grammar.
Seuren, P.A.M., (forthcoming) : Stassen, L . , 1 9 84 :
Ph.D thesis, Nijmegen University.
Von Stechow, A., 1984 : Comparing semantic theories of comparison. This volume. Weyters, T.,
Presuppositional propositional calculi.
Nijmegen Institute of Semantics.
N J .S . Working Papers No. 1 .
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Hoeksema, J ., This volume: To be continued : the story of the comparative.
Journal of Se17Uln�s 3 : 1 4 3 - 1 8 2
THE COMPARATIVE COMPARED
LEON STASSEN
1. INTRODUCTION
In the recent literature that has been devoted to the syntactic and seman of this construction type have been largely left out of the discussion. In
this
paper, my aim is to argue that this
is
an unfortunate situation, and
that from a universalist survey of comparatives valuable insights as to the
nature of this construction type can be gained. In particular, I want to
make a case for the claim that , from a universal point of view , the compa
rative construction should not be looked upon as a 'primitive ' or 'auto nomous' construction type ; rather, its particular formal manifestation in a given natural language can, to a significant extent, be predicted from the formal manifestation of other syntactic patterns occurring in that language .
In this
way, the universal investigation of comparative construc
tions may be of interest to syntacticians, semanticists and cognitive psychologists alike . As far as formal syntactic theory is concerne d , our claim has as a consequence that, in universal grammatical theory , we do not need construction-specific rules to generate comparative constructions; these constructions will be derived automatically by rules which are in dependently needed for the syntactic derivation of certain other construc tion types. From a semantic (or perhaps better: cognitive) point of view, our investigation leads to the contention that the mental operation by which two entities are compared to one another is not an independent, 'primitive', mental operation ; at least as far as its codification into natural languages is concerned , the mental act of comparison must be seen as a conceptual extension (a 'cognitive metaphor', so to speak) of certain other mental operations, which must be viewed as more 'basic' or 'fundamental' to the human cognitive system . The data upon which the present cross-linguistic survey of comparatives is based are gained from a sample of
1 1 0 languages, chosen from genetical
ly diverse language families. In each of these languages, the linguistic mani festation of the comparative construction is identified . A categorization of the various ways in which natural languages may encode the mental act
of comparison gives rise to a typology of comparative constructions in
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tic properties of the comparative construction, universal characteristics
1 44 which at least five categories can be distinguished clearly. After this typ ology has been established , we face two interrelated questions of an ex planatory nature ,
viz.
a) the question o f how t o explain the attested occurrence and non�c currence of categories. That is, we will have to provide a principled answer to the question of why it is just these attested categories that flgure in the typology, instead of other, equally thinkable , alternatives. b) the question of how to explain the distribution of languages over the attested categories in the typology. That is, we must ask ourselves why a given language
L
in the sample belongs to category X in the typ
ology of comparatives, and not to category Y. In other words, we start from the assumption that the grouping of languages which emerges
natural classes, and hence our task will be to identify the determining factor or factors of this naturalness. In section
3
of this paper I will present the typology of comparative
constructions which I have constructed on the basis of the data in my language sample . Following that , the two explanatory questions mention ed above will be dealt with in section
4 and section 5 . However, before we
can start out on the actual typological investigation of comparatives, there
are a few preliminary points which must be cleared b eforehand . These points are both of a general methodological and of a merely practical nature . 2. PRELIMINARY REMARKS
At the very start of the execution of any typological linguistic research project, the researcher is bound to be confronted with a major methodolo
gical
issue, namely, the problem of cross-linguistic identification. It goes
without saying that natural languages can be expected to show formal variation in the ways in which they codify a certain relevant linguistic property such as comparison; indeed, the very existence of this variation
is the reason why cross-linguistic typological investigation is a feasible
enterprise at all . However, this formal variation among languages also
poses the problem of how to decide which structural configurations in
each of the languages of the sample must be rated as the primary expres sion of comparison. In other words, we need some criterion for the cross linguistic identification of comparitive structures, so that we will not make the category mistake of comparing essentially uncomparable items. The solution to this problem of cross-linguistic identification of com parative constructions evidently calls for a definition of the notion "com parative construction" that is stated in terms which are independent of the characteristics of single languages or groups of languages. In modem
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from our typology of comparatives is the reflection of a grouping into
1 45 universalist gramm a r, recognition of the need for language-independent definitions has generally led to the use of semantic (or cognitive) defini tional criteria ; that is, the feature upon which the typology is to be based is defmed in terms of its semantic content or function , rather than in terms of its alleged formal characteristics. This semantic solution to the problem of cross-linguistic identification has been employed succesfully in a number. of recent typological publications, such as the prestigious study on relativization by Keenan and Comrie ( 1 977). It can be noted that, in this study, the typology of relativization is based upon a semantic definition of the notion "relative clause", and that in this definition no reference is made to the formal manifestation of relative clauses in specific languages.
of the comparative construction across the language of my sample . Stating the defmition somewhat informally, we will say that - a construction counts as a comparative construction (and will therefore be taken into account in our typology), if that construction has the semantic function of assigning a graded (i.e . non-identical) position on a predicative scale to two (possibly complex) objects. In this connection, it should be pointed out that , with regard to the semantic/cognitive definition of comparative constructions, a certain tradi tion of graphical representation appears to have developed in the linguistic literature on comparison . Such diverse authors as
Valin
( 1 95 2) , Joly
( 1 967), Doherty ( 1 970), Klooster ( 1 976, 1 979) and Seuren ( 1 978) all represent the cognitive structure of a case of comparison in the form of a spatial configuration .
In
this configuration, the parameter of the compa
rison (that is, the property with respect to which the comparison is made)
is pictured as an axis, which is marked for positive-negative polarity. On axis, the two objects which are to be compared are juxtaposed in such
this
a way that the object which has the higher degree of the quality in ques tion
is placed farther to the positive side of the parameter. In this way,
the positions of the two compared objects on the axis define extents, which represent the degree to which the compared objects possess the quality at issue , and which are juxtaposed to the effect that one of these extents envelops the other. Given this way of representation, the cognitive struc ture underlying a comparative construction like "A is bigger than B" can be graphically pictured as the following diagram , in which it must be understood that the axis represents the gradable quality of "being big":
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In conformity with this strategy currently favoured among universalist linguists, I have chosen to use a cognitive criterion for identifying cases
1 46
B
{1)
_ _ _ _ _ _ _ _ _ _ _ ___
A
!
- - - - - - - - - - - - - - - - - -- - - - - - ·
j
+
As noted , this way of representing the cognitive content of comparative constructions assumes that such a representation is basically spatial in character: relative degrees of intensity with respect to a certain quality are represented in terms of relative distances on an axis. Independent motivation for taking this spatial point of view of comparison is presen ted by, among others, Klooster { 1 979: 1 98) and by a number of psycholin guistic studies discussed in Bergmans ( 1 982 : 1 5 2 - 1 54) . In keeping with
derlying comparative constructio!ls. Thus, our problem now is to describe and explain the variation in the ways in which natural languages map this cognitive structure onto their linguistic surface structures. Given this defmition of comparison, we should be able to identify the cross-linguistic
codification of this concept, thereby establishing the
data base of our typology. However, before we can present an expose of the attested typological variants of the comparative construction , we must ftrst point out a number of complications connected with the definition of the notion "comparative construction", and mention several practical decisions which further restrict the scope of our inquiry . First, our cross-linguistic investigation of comparative constructions will be limited exclusively to cases of the comparison of inequality. That is, the only comparative constructions with which we will be concerned are those in which the two objects that are involved in the comparison differ in the degree of intensity to which they possess the quality at issue. A s a result of this practical limitation, constructions which are the equivalents of the English sentences in (2) will not form a part of our data base : (2)
ENGLISH: a.
The dog runs as rapidly as the bird flies
b.
John is a s tall a s his brother
Within the class of inequality comparatives (henceforth to be referred to simply as "comparatives") I will impose a further restriction on the data which will be included in our typology . I have found it useful to confme my typology to those cases of comparative constructions in which two objects or individuals (typically expressed by NP's) are being graded against each other. The reason for this decision is entirely practical ; where-
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these insights, I will adopt a configuration like the one depicted in ( 1 ) a s an approximation o f the language-independent cognitive structure un
1 47 as all sources on the languages in my Sl111ple indicate the way in which NP
comparatives are fonned , they do not, in general, provide for sufficiently reliable data on constructions in which other elements (say , adjectives, verbs, or sentence s) are involved . Thus, the prototypical sentence for our inquiry will be a sentence along the lines of those in in
(3), and not
of those
(4):
(3)
(4)
ENGLISH: a.
The tree is taller than
b.
I like Pamela better than Lucy
the house
ENGLISH: The general was more cunning than
b.
The president i s smarter than you
brave think
Constructions like those in ( 4) will be taken into account only when we look at some language in detail. In particular, they will provide evidence for our analysis of the comparative constructions in English and Dutch . As a last point, it must be realized from the outset that our· typology may suggest a division among languages which looks more defmite and neat than it actually is. For one thing, we must concede that a number of languages in our sample have comparatives which do not seem to fit neat ly into one of our established categories. These languages appear to have a 'mixed comparative' , that is, a comparative construction in which the fun damental features of two typological variants are combined . Another phenomenon that weakens the strictness of our categorization is the fact that quite a few languages appear to have more than one alternative to express NP-comparison. Thus, for example, in Latin the grading of two objects against each other is typically expressed by means of a construc tion like the one in (5), which contains the comparative particle (5)
quam :
LA TIN: Cato
eloquentior
est
quam
C.
more�loquent
is
than
"Cato is more eloquent than Cicero"
Cicero
c.
However, as i s noted in Kuhner-Stegmann ( 1 95 5), Latin also has the pos sibility of a comparative like the one in
(6). In this case, the particle quam
is no longer present, and the NP which serves as the standard of com parison is put into the ablative case :
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a.
148 (6)
LA TIN: Cato
Cicero-ne
C.
C.
''Cato
·ABL
eloquentior
est
more�loquent
is
is more eloquent than
Cicero"
Faced with this double option of comparative type choice , I have chosen to categorize the languages in my sample in two different ways. I take it that for each language there is a basic comparative construction , which is somehow more 'natural' or 'unmarked' than its possible alternatives. I n the typical c ase , this basic comparative can b e u se d more widely than any of its alternative options; thus, for example, it can be shown that the ablative comparative in Latin is restricted in its use to cases of NP-com will be classified primarily as a language of Type
6
(a so-called Particle
Comparative), and the ablative comparative will be rated as the secondary comparative option for that language . It can be argued , incidentally , that a language is not completely free in the choice of its secondary compara tive s ; this choice can be shown to be governed by the same principles that determine the choice of its basic, or primary , comparative form . 3. THE TYPOLOGY OF COMPARATIVE CONSTRUCTIONS
3. 1. In
Terminology
this
section, I will discuss the parameters of our typology of compa
rative constructions, that is, those features of comparative constructions which constitute the basis of our categorization Of comparatives into types. Throughout the discussion I will adopt the following terminology . The linguistic codification of the predicative scale in a comparative con struction will be termed the
cate;
comparative predicate,
or simply
the predi
in the majority of the examples, the predicate of a comparative
construction will have the form of a predicatively used adjective . The two objects which are involved in the comparison are typically encoded in the form of noun phrases (NP's). Of these two NP's, the NP which indica tes the object that serves as a yardstick for the comparison will be referred to as the
standard NP.
The other NP in the construction , which refers to
the objective of the mental operation of comparison, will be called the
comparee NP. Thus, in a sentence (7)
like
ENGLISH: John is taller than Bill
the NP
Bill is
the standard NP, and the NP
John
the comparee NP. The
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parison , whereas the quam-comparative is not. For this reason, Latin
149 predicative adjective
tall, which names
the scale on which the comparison
takes place, is the comparative predicate in this particular constructio n .
3.2.
Parameters in the typology of comparatives
Once the comparative construction has been identified for each of the lan guages in the sample, we are in a position to start the actual work of typological investigation, viz. the construction of a typology. At this
stage , the sampled comparative constructions are classifie d into a number
of categories, on the basis of differences and similarities in the way in which the cognitive structure of comparison is formally expressed by them . Now, it is a well-known fact of general methodology that, in such
against one another for their theoretical relevance and utility. In our case , this evaluation of possible starting-points for a cross-linguistic typology of comparatives has led to a categorization in which
standard NP
the encoding of the
{and the variation which can be observed in that encoding)
is taken to constitute a highly significant factor. _ . With regard to the encoding of the standard NP in comparative con structions, a ftrst dichotomy involves a split between ratives and
fixed-case
derived-case compa
comparatives. In the rrrst class, the standard NP in
the construction is not put into one single case form in all the instances of the comparative construction in the language at issue . Instead , it appears to derive its case assignment from the case into which the comparee NP in the construction has been put . Thus, if the comparee NP in the construc tion happens to be a subject, and is therefore put into the nominative case , the standard NP in that construction will also have nominative case ; if the comparee NP is in the accusative case , the standard NP will also be marked for accusative ; and so on. In short , derived-case comparatives ex hibit a parallelism in case assignment to the two NP's in the construction , to the effect that the case assignment of the comparee NP appears to de termine the case assignment of the standard NP. In contrast to this, ftxed-case comparative constructions always put the standard NP into one and the same oblique case form , no matter what the case form of the comparee NP in the construction may be. In other words,
in ftxed-case comparatives the case assignment to the standard NP is in dependent of the case assignment to the comparee NP . The opposition between instances o f derived case and ftxed case can be illustrated by the two comparative constructions in Latin mentioned a bove . The Latin quam-comparative can be shown to be an instance of de rived case: as the examples in (8) demonstrate, the case form of the stan dard NP in this comparative must be parallel to the case form that has been assigned to the comparee NP. Cp . :
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categorizations, the choice of parameters is not completely theory-inde pendent ; objectively possible parameters will always have to be weighed
150 (8)
LA TIN: a. Brutum ego non minus amo quam B .-ACC I-NOM not less love-JSg than "/ love Brutus no less than you {love Brutus)" b. Brutum ego non minus amo quam B .-ACC I-NOM not less love-/Sg than "I love Brutus no less than (I love) you"
tu you-NOM te you-ACC
(9)
LA TIN: Brutum B .-ACC
non minus ego I-NOM not less
te you-ABL
amo love-JSg
For both categories distinguished so far, further typological divisions readily present themselves. As far as fixed-case comparatives are concern ed, a natural parameter to employ is the particular type of case form into which the standard NP is to be put . Applying this criterion , we fmd that fixed-case comparatives can be categorized into direct-object comparatives and adverbial comparatives. In the latter category, the standard NP has as its fixed form a marking which is employed in the language to encode adverbial constituents; the Latin ablative comparative (which structurally expresses the standard NP as an instance of an adverbial source-phrase) is a case in point. Opposed to this adverbial codification of standard NP's, other fixed case comparatives encode their standard NP's by the same structural means which the language in question employs to encode direct objects. In such comparative constructions, a special transitive verb is in cluded, which has the general meaning of "to surpass" or "to exceed", and which takes the standard NP as its syntactic direct object . Thus, in comparative constructions of this particular type, the surface structure typically contains two predicates, one of which represents the scale of comparison, and another which provides the syntactic means to represent the standard NP as a direct object. The comparee NP in the construction
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On the other hand, the ablative comparative in Latin is an instance of fix ed case. The standard NP in this construction is invariably put into the ab lative case, regardless of the case form of the comparee NP. As a result, a sentence like {9), which is the fixed-case counterpart of the sentences in (8), is ambiguous, due to the fact that it can be either the subject-NP ego or the object-NP Brutum which may be taken to be the comparee NP ; the fixed ablative form o f the standard NP does not give u s any clue as to the right choice of the comparee NP for this construction. In other words, sentence (9) may have either the reading which we assigned to (8a) or the reading of (8b) (at least according to Kuhner & Stegmann 1955 ; vol. 2 : 466):
151 is
encoded as the subject of this latter transitive verb . An example of a
direct-object comparative is the following sentence from Duala :
( 10)
DUALA : Nin
this
ndabo
e
kolo
house
it
big
ouka
exceed
nine that
"This house is bigger than that"
While direct-object comparatives constitute a terminal category in our typology (i.e . a category that cannot ·be split up into further subclasses), adverbial comparatives do allow for further subcategorization . In this case , the relevant parameter involves
is
the semantic type of adverbial phrase
used as the codification of the standard NP in comparative con
structions. As it turns out , languages which possess an adverbial compara tive typically represent standard NP's in the form of an adverbial phrase which has a clearly recognizable
locational interpretation. In other words,
most languages in this category model the codification of their standard NP's on one of the options which they have in the formal expression of the semantic system of
spatial relations.
Given this fact , it becomes pos
sible to introduce a further typological subdivision within the category of adverbial (ftxed-case) comparatives, based upon the particular locational option which a language chooses for the representation of its standard NP's. To be exact , the application of this parameter to the class of ad verbial comparatives gives rise to
a tripartite distinction .
First , we encounter adverbial comparatives in which the standard
is
codified by means of a
separative
NP
marker. In this case, the prototypical
device for representing the standard NP appears to be a marker (i .e . a case
affix , or an adposition) with a meaning that is e quivalent to the meaning
of English
from .
Semantically speaking , one might say that in these con
structions comparison seems to be 'metaphorized' as a movement in which the object represented by the standard NP is conceived of as the point of
origin .
Examples of this type of adverbial comparative include the Latin
ablative comparative mentioned earlier , and the following construction from Japanese:
(11)
JAPANESE: Nihon-go
wa
Japanese
TOP German from
doits-go yori
muzukashi difficult
"Japanese is more difficult than German" Diametrically opposed to separative comparatives are those adverbial com paratives in which the object represented by the standard NP appears to be conceived of as the
goal
of a movement. Languages which select this
a/-
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which
1 52 lative
relation as the metaphor for the expression of comparison typically
choose to mark their standard NP's by means of a marker with a meaning that
is equivalent
to .
to the English preposition
Allative comparatives are
not very frequent ; clear examples of languages which have this type of adverbial comparative as their primary option are Maasai and Nuer. Cf. :
( 1 2)
MAASAI: Sapuk
ol
-kondi
to
1
is-big
the
-deer
to
the-waterbuck
-kibulekeny
"The deer is bigger than the waterbuck"
( 1 3)
NUER : ne
gao
ke
ji
am
I
to
you
"I am bigger than you" The third class of adverbial comparatives, the
locative
comparatives, may
be regarded as the 'neutral' case between allative and separative compara tives. In the case of the locative comparative , a spatial configUration
is
selected in which no movement at all seems to be implied, either to or from the object represented by the standard NP. Instead, the comparative construction seems to be modelled upon the expression of a situation in which two objects are at rest and in contact with one another. Hence , the prototypical marker for the standard NP in this type of comparative is an element which
is
semantically equivalent to the English items
on
or
at.
Examples of this type of construction can be found in Chuckchee and
Latvian:
( 1 4)
CHUCKCHEE: Gamga-qla'ul-ik
qetvu
all
strong
men
on
"I am stronger than
( 1 5)
LA TVIAN: smukaka Anna A .-NOM
-ci
-ium
more 1 Sg
all men"
prettier-Fern.
aiz on
Trinas T.-GEN
"Anna is prettier than Trina" With the distinction of direct-object comparatives and the three subtypes of adverbial comparatives, we have established the terminal categories of the class of fixed-case comparative constructions. To conclude our discus sion of the parameters which we employ in our typology of comparative constructions, we must now pay attention to the other major class of
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Diid · big
1 53 comparative constructions, viz. those comparatives in which the case form of the standard NP can be derived or determined from the case form of the comparee NP. One might say that, in such constructions, the case of the standard NP is 'parasitic' on the case assignment which the comparee NP has received. Within the class of derived-case comparatives, we can single out one highly typical subcategory , which can be identified very easily across languages. For this category, a defming characteristic is that the compara tive construction consists of
two structurally independent clauses ;
one of
these clauses contains the comparee NP, whereas the other contains the standard NP. Furthermore , the two clauses in question show a
structural
to the effect that the grammatical function of the comparee
NP in one of the clauses is reduplicated by the gr ammatical function of the standard NP in the other clause. If, for example, the comparee NP func tions as the gramm atical subject in its clause, the standard NP will also have subject status in its. clause . Since the comparative construction at issue consists of two independent clauses, it follows that such a construction will also have to contain two independent predicates. In other words, a further feature of this type of comparative is that
the comparative predicate is expressed twice. There are
two ways in which this double reference to the comparative predicate can
be effected in this comparative type. On the one hand, we find a subtype
in which the two clauses contain antonymous predicates (e .g. "big-small" , "tall-short") ; on the other han d , there are cases i n which the comparative predicates in the two clauses exhibit a positive-negative polarity (e .g. "big-not big", "tall-not tall"). As a last point, we should note that the semantic relation between the two independent clauses in this type of comparative is usually to b e des cribed as
adversative coordination : its literal interpretation is so mething p, but B is q (c.q. not-p)". Thus, one might say
along the lines of: "A is
that , in this type of comparative , there is no direct measuring of the two objects against each other, but the non-equal gradation of the objects involved can be inferred from the fact that they are contrasted in an adversative coordination . T o quote two examples of this type o f
conjoined comparative,
sider the following sentences from Kobon and Hixkaryana. Cf. : (
1 6) KOBON: U
kub ,
u
pro
that small this big "This is bigger than that "
con
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parallelism ,
1 54 ( 1 7)
HIXKAR YANA : Kaw-ohra naha
Waraka, kaw
naha
Kaywerye
tall-not
W.
he-is
K.
he-is
tall
"Kaywerye is taller than Waraka" Conjoined comparatives o f the type discussed above form a very typical subclass of derived-case comparatives, but they are by no means the sole representatives of this category . In addition , we f"md a considerable num ber of comparative constructions in which the standard NP has derived case , but which cannot be called instances of conjoined comparatives,
since in these constructions comparee NP and standard NP are not constituents of separate independent clauses in surface structure ; and b)
there
is
no (or at least n o obligatory) double reference to the
parameter of comparison in surface structure . In short, these instances of derived-case comparatives do not have the structural form of an (adversative) coordination in surface structure , at least not from the point of view of synchronic syntax . Quite commonly, the standard NP in these comparatives is accompanied by an element which we may call the
comparative particle ; this
particle cannot be iden
tified as a case marker, since its presence is independent of the particular case form which the standard NP happens to have . A derived-case compa rative construction in which such a comparative particle is present will be called an instance of the
particle comparative.
Examples of particle
comparatives which have already been introduced in the foregoing text are the Latin quam-comparative and the Dutch dan-comparative . While particle comparatives share at least one common feature (namely , the fact that their standard NP's have derived case), there are also indi cations that the particle comparative is not a homogeneous category . The internal diversification of this set of comparatives is brought out by the fact that the comparative particles which are involved in the various con structions cannot be shown to have the same origin or categorial status for all of the languages in this class. In a number of cases, we f"m d that the
connective item of some kind, either baino , Ilocano ngem), or a disjunctive or a negative conjunction (Gaelic na
comparative particle is in its origin a an adversative conjunction (Basque conjunction (Classical Greek e),
"nor") or a conjunction with the basic meaning "and" (Javanese
karo).
Other languages employ as their comparative particle an item which is
adverbial subordinating conjunction (Hungarian mint, Malagasy noho and perhaps
also in use as an
with the meaning
"like"
also Albanian
se).
A third group of languages has chosen as its comparative particle an ele-
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a)
1 55 ment which also functions as a thereafter" (Toba Batak
asa,
temporal adverb , typically meaning
''then,
perhaps also Dutch dan). Fourthly, there are
languages in which the comparative particle can be identified as having its etymological origin in the stem of a
relative/inte"ogative pronoun , chem ,
which has been "frozen" into a n adverbial case form (Russian
que,
French
quam). Finally, there is some evidence for negative element has somehow come to be incor comparative particle (Hungarian mintsem , perhaps also
perhaps also Latin
some languages that a porated into the
than).
English
In short , the class of particle comparatives (in so far as it
can rightly be said to form a class at all) seems to have assembled its mem
bers from a large variety of sources. This suggests that, within the typology of comparative constructions, particle comparatives should be assigned a
will receive some further attention in section
3.3.
6.
The typology of comparative constructions
If we apply the above parameters to the cross-linguistic data base of our typology of comparative constructions, we arrive at a classification into five clearly identifiable typological variants; in addition, there is a type of comparative construction (viz . the particle comparative) of which the status as a homogeneous category is open to some doubt. In this section , I will briefly introduce each of these variants in turn, and list the lan guages which have a comparative construction of the type at issue as their primary option. Furthermore , I have included some comments on the basic word order of the languages involve d ; as will become clear, we can observe some degree of correlation between basic word order type and choice of comparative type.
Type 1: the separative comparative. The separative comparative is an instance of fixed-case comparative con structions, in which the standard NP is invariably encoded as a constituent part of an adverbial phrase with a separative ('source') interpretation .
A list of languages which exhibit this construction as their primary option
reads as follows: Amharic
Andoke
Arabic (Old)
Aranda
Avar
Aymara
Bedauye
Bilin
Burmese
Burushaski
Carib
Coeur
Eskimo
Finnish
Guarani
Hebrew(Old)
Hindi
Japanese
Jurak
Kashmiri
Korean
Lamutic
d 'Alene
Khalka
Laz
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status which is essentially different from the other comparative types which we have distinguished. The phenomenon of particle comparatives
1 56 Manchu
Mundari
Nama
Piro
Tibetan
Tupi
Turkish
Vayu
Quechua
Tajik
Furthermore, a separative comparative as a secondary o ption can be esta blished for Albanian, Basque, Old French, Old English, Classical Greek, Latin, Russian and Tamil. From the above listing, w e may conclude that the se parative compara tive is very w idely spread indeed: more than
30%
of the languages in the
sample choose this type as their primary o ption. A striking characteristic of this category is that the languages which it contains a ppear to have a very strong preference for S OY word order. Of the
34
languages w ith a
primary separative comparative, only five (viz . Arabic, Coeur d'alene,
Type 2: the allative comparative Like the separative comparative, the allative comparative is an instance of a fixed-case adverbial comparative type, but, in this case, the standard NP is invariably marked as a constituent part of a goal-phrase. Listing the primary languages in this class, we get : Breton
J acaltec
Siuslaw
Tarascan
Kanuri
Maasai
Nuer
An allative comparative a s a secondar y o ption can be encountered in Mandingo , Mangarayi and Tamil. We can n ote here that, at least as far as the primary o ptions in this category are concerned, the allative comparative a ppears to be limited almost exclusively to languages which have basic VSO word order. Kanuri, an SOY-language, is the only exception here.
Type 3: the locative comparative The third instance of fixed-case adverbial comparatives is the locative comparative ; in this construction, the standard NP is invariably encoded as a constituent part of an a dverbial phrase which is marked by an element
w ith the basic meaning "on" or "at". The following twelve languages are primary members of this class: Chuckchee
Cebuano
Latvian
Naga
Salinan
Tamazight Tamil
Mandingo
M a puche
M iwok
Tubu
Ubykh
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Finnish, Guaran i and Hebrew) are contradictions to this tendency.
1 57 Secondary locative comparatives are documented for Basque, Dakota , Gumbainggar, Hungarian, Maori, Nama and Samoan . As for word order, the absence of SVO-languages in this class is a strik ing fact, even if we make allowance for the relatively small size of this class. Thus, it seems that a predilection for either SOV-order or VSO order among the languages of this category may be stated with some confidence: our sample contains no counter-example to this tendency, neither for primary nor for secondary members of this type.
Type 4:
the exceed comparative
Banda Gbeya Margi Yagan
Bari Cambodian Hausa lgbo Nguna Swahili Yoruba
Dagomba Jabem Thai
Duala Fulani Kirundi Mandarin Vietnamese Wolof
A secondary exceed comparative can be found in Aymara, Maasai, Que chua, Sika, Sranan and Tamazight . The exceed comparative is the second largest category in our sample . We can observe that for this set of languages SVO word order appears to be mandatory, at least as far as the primary members of this category are concerned.
Type 5: the conjoined comparative The conjoined comparative is the most conspicuous manifestation of de rived-case comparative constructions. NP-comparison is typically effected by means of the adversative coordination of two clauses, which exhibit a structural parallelism. A list of the nineteen primary languages in this class reads as follows: Abipon Hixkaryana Miskito Pala
Cayapo Kobon Mixtec Samoan
Dakota Mangarayi Motu Shipibo
Ekagi Maori Monumbo Sika
Gumbainggar Menomini Nahuatl (Class.) Yavapai
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The exceed comparative is the fourth and fmal variant of fixed case comparative constructions. Its main characteristic is that the standard NP is invariably constructed as the direct object of a special transitive verb , the meaning of which can be glossed as "to exceed", "to surpass" or "to excel"; furthermore , the comparee NP always functions as the gram matical subject of this "exceed"-verb. Our sample contains twenty lan guages which have (some variant of) the exceed comparative as their primary choice . These languages are the following:
1 58
Type 6: the particle comparative Particle comparatives have in common that they are predominantly 2 instances of derived-case comparison ; unlike conjoined comparatives, however, they do not have the structural form of a coordination of claus es. A second feature shared by all particle comparatives is the presence of a specific comparative particle accompanying (usually, preceding) the stand ard NP. However, as we saw in section 3 .2 . , these particles vary widely as to their etymological origin, so that the mere presence of such a particle does not, in all probability, constitute sufficient reason for treating par ticle comparatives as a natural, homogeneous class. A primary particle comparative of some type can be attested for the following sixteen languages in the sample : Albanian Gaelic Javanese Toba Batak
Basque Goajiro Latin
Dutch Greek (Old) Malagasy
English French Hungarian Ilocano Sranan Russian
Furthermore , a particle comparative occurs as a secondary option in Bari, Finnish, Latvian and Classical Nahuatl. Looking at the list of languages with a primary particle comparative , I think it is safe to say that particle comparatives are, to a considerable extent, to be rated as an areal phenomenon. No less than ten of the sixteen languages at issue are members of the European "Sprachbund ", while four others belong to the Austronesian family. As for word order, this list makes it clear that basic word order patterns do not seem to con stitute a determining factor in the choice for a particle comparative. As
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A secondary option for a conjoined comparative can be found in Banda, Mapuche, Ilocano, Kirundi, Nuer and Swahili . A first thing to note about this class is that the languages which it contains appear to exhibit a certain degree of geographical grouping. The primary languages in this class are predominantly Australian, Papuan or Polynesian, or else can be situated on the American continent . It thus looks as if the choice for a conjoined comparative is (at least to a certain extent) influenced by the characteristics of certain. linguistic areas. As regards basic word order, no defmite statements can be made for this class. Basic word order does not seem to be a determining factor in the choice for or against a conjoined comparative ; all major word order patterns are represented in this category and, what is more , they occur in proportions which do not differ greatly from those which one would ex pect to fmd in a random selection of languages.
1 59 with conjoined comparatives, all major word orders are represented here , in proportions which one would expect to encounter in a random selection
of languages . All in all , then, we may conclude that there is no corre lation between derived-case comparison and preference for certain word
order types, while for the various -sub-types of fixed-case comparison such a preference can be established with some certainty. 4 . A N EXPLANATORY FRAMEWORK FOR COMPARATNE TYPE CHOICE
4. 1.
Sequencing as a determinant factor
Now that our description of the data on the comparative constructions in logy, our next task will be to fmd a principled way to account for the distinctions which this typology offers. As we noted in section
1,
such a
principled account presupposes that we are able to fmd an explanation for the attested occurrence and non-occurrence of the categories which figure in the typology , and for the attested distribution of languages over the options which the typology offers. A natural way to provide answers to these questions is to search for a second typological parameter which can be identified as the determining 'outside' factor of our original typology of comparatives. That is, we will try to categorize the languages in our sample in an additional typology, in such a way that the categorizations in this second typology match the distinctions which we have attested in the typology of comparatives; this matching can be laid down in a set of implicational universal statements. In as far as the parameter of the second typology can be argued to be more 'basic' or 'fundamental' to language systems than the frrst (i .e . than comparison), we can call this second typo logy the
determinant
of the typology of comparative constructions; it
serves as the basis upon which the non-randomness of variation
in
the en
coding of comparatives can be accounted for , and hence it can , in some sense , be said to constitute an explanation of that variation . Looking at the data on comparative constructions which we have dis cussed so far , we can distinguish at least two 'outside phenomena' which seem to be correlated to some extent with the typological variation in the encoding of compariso n . First of all, we have noted that, at least for some types of comparatives, a correlation with a certain basic word order pattern could be established . Thus, our data enable us to formulate uni versal statements o f the following kind : ( 1 8)
a.
I f a language has a separative comparative , then it is SOV .
b.
I f a language has a n allative comparative , then i t i s VSO .
c.
Jf a language has a n exceed comparative , then i t is SVO.
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our sample has resulted in the establishment of a cross-linguistic typo
1 60 d.
If a language has a locative comparative, then it is either SOV or VSO.
( 19)
a.
Languages with a separative comparative belong to type A in typology X. b. Languages of type A in typology X are typically SOV. c. Therefore: languages with a separative comparative are typical ly SOV (= ( 1 8a)).
Now, the data on comparative constructions which we presented in sec tion 3 appear to give us at least some clue as to the nature of this interme diating typology X . To be specific, we have noted that, at least for some types of comparatives, there is an apparent relation between the codifi cation of comparison and the structural procedure of sentence-coordina tion. This relation is, of course, completely transparent in the case of conjoined comparatives; here one might say that, formally speaking, the comparative construction is a sentence-coordination. Other pieces of evidence for the relation at issue stem from the etymology of various comparative particles in particle comparatives; as noted, these items have, in a number of languages, developed from coordinating elements, be it adversative conjunctions, disjunctions or negative conjunctions. These facts suggest that it might be worthwhile to take a further look at sen tence-coordination as a possible determinant of comparative type choice. In this connection, it should be added immediately that it cannot be the formal notion of sentence-coordination which is of relevance to us here. If we were to defme the notion of sentential coordination in struc tural terms (for instance, as a configuration in which two clauses or sen tences are embedded at the same level of structure ; see Dik ( 1 968)), the
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While these four statements clearly represent valid universal tendencies in our data, it must also be admitted, however, that correlations of this kind can be formulated only for part of the categories in the typology of comparative constructions. To be exact, correlations between word order type and comparative type hold only for the subclass of fixed-case compa ratives ; for derived-case comparatives (i.e. conjoined comparatives and particle comparatives) no correlation whatsoever with a particular type of basic word order can be defended. For this reason, it seems better to assume that the relation between basic word order type and certain com paritive types, while undoubtedly real, is of a more indirect nature. If we accept this, it follows that we should be able to track down a parameter which intermediates between comparative types and word order types, so that statements like the one in ( 1 8a) can be replaced by a syllogism of the form illustrated in ( 1 9):
161 relation between sentence-coordination and comparative formation would break down at once for a large number of languages ; for one thing, quite a few languages simply do not have the possibility to form syntagms in which two sentences or clauses are constructed at the same level of embed ding. Thus, we must conclude that , in this case too, it is the
semantic
function of a coordinated sentential structure , rather than its specific
formal
manifestation, which must be invoked to defme the feature upon
which the intermediate typology X is to be based. In order to avoid con fusion, I will use the term
temporal sequencing
to refer to the semantic
content of coordinated (and semantically equivalent) constructions.
Temporal sequencing
can be defmed as the cognitive process by which
overlapping, preceding or following each other" (Traugott,
1 975 : 208).
The result of the mapping of this process onto the language system is a
temporal sequence,
i .e . a semantic configuration in which two tensed pro
positions (representing states or events) are presented successively . Now, natural languages may vary in the ways in which they choose to formally encode these semantic configurations. This variation gives rise to a typolo gy of
syntactic sequences,
and it is this typology which we will argue to
be the determinant of comparative type choice . One of the best-known and major ways in which temporal sequencing can be formalized in natural languages is the application of the structural procedure of (sentence) coordinatio n . However, sentence coordination is by no means the only option in syntactic sequencing constructions across languages; I hope this will become clear in the next sectio n , where the parameters in the typolo gy of syntactic sequences will be discusse d .
4.2.
Types of syntactic sequences
In the previous section, we defmed the notion of syntactic
sequence
as the
formal encoding of a temporal sequence in a natural language . In other words, a syntactic sequence is the result of the mapping of a semantic con figuration which contains two tensed propositions onto the surface struc ture of a given natural language . Since it can be empirically attested that this mapping does not yield the same type of surface structure for all natural languages, it is possible to establish a cross-linguistic typology of syntactic sequences. In this section, we will be concerned with the para meters that appear to be crucially involved in the variation which this typology embodies. A first typological factor which influences the actual surface man ifes tation of temporal sequences in natural languages has to do with a split in the ways in which the two propositions in the temporal sequence are represented in surface structure with respect to ran k . On the one han d , a
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the mind establishes " . . . the relation between two events, A and 8 , as
162
(20)
ENGLISH: John jumped out of his chair and grabbed a gun
(2 1 )
GUARANI: Oi-ke ka-agwi pe ha o-henu petei in and he-heard one he-went forest "He went into the forest and heard a noise"
avu noise
Thus, the defming characteristic of balancing languages is that their syntactic sequences are structurally coordinations. As a result, syntactic sequences in balancing languages are subject to the Coordinate Structure Constraint formulated in Ross ( 1 967), as can be seen from the ill-formed ness of (22) and (23) : (22)
ENGLISH: * What did John jump out of his chair and grab(bed)?
(23)
GUARANI: • Ma?e pa what Inte"og.
oi-ke ka-agwi pe he-went forest in
ha and
o-henu he-heard
Rather than keeping the balance, however, a language may also choose to represent the two predicates in a syntactic sequence by reducing one of these predicates in rank. In such a case , only one of the predicates in the sequence retains its finite form, whereas the other is represented as a subordinate, usually non-fmite verbal construct. Languages of this type I will call deranking languages, and its syntactic sequences I will call
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language may choose t o express those two propositions in surface struc ture by means of two independent clauses or sentences. In this case , the important thing is that the two predicates which express the two relevant actions remain structurally of the same rank ; that is, they are embedded at the same level of structure . Hence , if the total sequence is not embedded, both predicates in the sequence will have the form of a fmite main predi cate . If the predicates happen to have the same subject, coordinative reduction of one of the subjects may take place, but this will not result in a 'de-balanced ' structural configuration: a coordinated verb remains a finite verb , even if it has lost its subject, and it remains equally ranked to the other verb in the sequence. Sequential constructions in which predicates remain of the same rank I will call balanced constructions, and languages which choose this kind of encoding option I will call balancing languages. Examples of balanced sequential constructions are the following:
1 63 deranked sequential constructions. From a strictly syntactic point of view , one may say that deranking languages do not have sentential coordination at all , since their surface structures do not permit sequential predicates in configurations which embed them on an equal level of structure . That there is indeed subordination involved in deranked sequences can be shown from examples in Tamil, a language in which syntactic sequences are deranked obligatorily. Thus, in Tamil we fmd the following construc tion (taken from Annamalai, 1 968): (24)
TAMIL : Avaru he-NOM
kavide poetry-ACC
erudiitu write-Perf Gerund
naaval novei-ACC
In (24), one of the predicates in the sequence (viz. moripeyarttaaru "(he) translated") is represented as a fmite main verb in the Indicative Past, while the other predicate (viz. erudiitu "having written") has the non-fmite, subordinate form of the Perfect Gerund . Now, it can be shown that such Tamil sentences cannot be regarded as structural coordinations. In particular, the Coordinate Structure Constraint no longer applies; as the well-formed example (25) illustrates, it is possible to relativize the complement of the fmite verb in sentence (24):
(25)
TAMIL : A varu he-NOM
kavide poetry-ACC
erudiitu wr ite -Perf Ger.
moripeyartta translate-Partic.Past
naaval novel "lit. the novel which he wrote poetry and translated" Now, while syntactic sequences in balancing languages show a great deal of structural uniformity (in that, basically, they are all coordinate struc tures), the category of deranked syntactic sequences is in need of further subcategorization. If we take a look at the various languages in which deranking of one of the predicates in a syntactic sequence is permitted or required, we note that, for a number of these languages, the application of the deranking procedure appears to be restricted by specific structural conditions. In particular, we fmd that there are languages which can de rank a sequential predicate only in cases where the two predicates in the
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moripeyarttaaru translate-Past. Indic. 3Sg. "He wrote poetry and then translated a novel"
1 64 sequence have identical subjects; if different subjects are involved, the construction must remain balanced. Such a situation we encounter in Wolof (see Rarnbaud, 1 903). In this language, syntactic sequences with identical subjects derank the second predicate into a subjunctive form , which is characterized by the presence of a specific particle a and special rules for the placement of pronouns. If the subjects in the sequence are not identical, t he only option is the use of a coordinate construction, which may be asyndetic, but can also contain the coordinative particle te "and". Cf. (26)
0
call-Subj.
ko
him
WOLOF: na Nyeu o n mu te wakh on na rna ko come Past Indic. he and tell Past Indic. I him "He came and I told (it to) him"
In what follows, the group of constructions in which this specific identity condition on deranked predicates holds will be referred to as conditionally deranked sequences, and the group of languages which exhibit this possibi lity will be termed languages with conditional deranking. In o pposition to those languages where the deranking procedure is sub ject to a structural condition on subject identity , we also fmd deranking languages in which no such condition seems to obtain . That is, these lan guages may derank one of the predicates in a syntactic sequence regard less of whether the predicates in the sequence have identical or non identical subjects. As a consequence, such languages can have syntactic sequences in which both the deranked predicate and the finite main pre dicate have their own overt subject. I n keeping with traditional termino logy, I will use the term absolute construction for a construction type in which a deranked predicate has its own overt subject ; hence , languages in which such a structural possibility exists will be called instances of absolute deranking languages. An example of a language in which absolute deranking is clearly possible is Tamil . Judging from sentence (28), it ap pears that, in this language , the deranked predicate (i.e . the gerundial form kuduttu "having given") and the fmite main predicate (poonan "(he) went") may each have their own subject (viz. naan "I" and avan "he", respectively). Cf.: (28)
TAMIL : kuduttu avan sinimaa-vukku panam Naan Ger. he-NOM movie -to I-NOM money-ACC give Perf -
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(27)
WOLOF: Demal a go-Imper. Subj. "Go and call him"
165 poonan go-Past. Jndic. 3Sg. " I gave him money and he went to a movie" For the sake of clarity, it should be stressed here that our notion of absolute deranking is defmed so as to include the possibility of conditio nal deranking. That is, languages which permit deranking of sequential predicates under non-identity of subjects will always allow deranking to take place in cases of subject identity, but the converse does not hold . Alternatively, we may state as a universal fact of natural language that there are no languages in which deranking under non-identity of subjects is possible while at the same time deranking under identity of subjects is cute than deranking under non-identity of subjects; hence, given the plau sible principle that one can perform a difficult task only if one has master ed all the easier ones, it is only to be expected that the possibility of absolute (i .e . non-identity deranking) will necessarily imply the ability to achieve deranking under identity of subjects . To sum up our discussion so far , we can state that a categorization of languages with respect to the question of whether or not they derank their syntactic sequences gives rise to a three-way typology . We can distinguish : a) balancing languages, i . e . languages which do not derank their syn tactic sequences at all ; b) conditionally deranking languages, i . e . languages which derank their syntactic sequences only if the subjects of the predicates in the sequen ce are identical ; c) absolutely deranking languages, i .e . languages which derank their syn tactic sequences under any circumstances. Now, in addition to the typological parameter which is based upon the op tions that languages have in the application of deranking , we will assume here that there is a second parameter which is operative in the linguistic formalization of temporal sequences (and hence, given our hypothesis, in the codification of comparative constructions). This second type of rele vant grammatical procedure may be referred to as
identity deletion .
The concept of identity deletion employed here is meant to cover all those instances of syntactic sequence formation in which lexical material has been omitted or suppressed on the basis of the identity of that mate rial with lexical material that is present elsewhere in the string. Using a somewhat different, but essentially equivalent terminology, we may say that identity deletion is meant to cover all those cases in which lexical material has been reduced to a null-anaphor under conditions of formal
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forbidden. Apparently, conditional deranking is, somehow, easier to exe
1 66
(29)
a. b.
(S (V
V) S)
( s ( v
v )
s )
Given this situation, the only cases of identity deletion which are of relevance to us are cases in which subjects may or may not be deleted under identity, and cases in which predicates may or may not be deleted under identity. Now, if we consider the options of natural languages with respect to the application of S-deletion and V -deletion , we fmd that the typology of identity deletion parallels the typology of deranking options in an interesting way, in that both typologies can be shown to admit a three-way variance. As it turns out, a first typological split in the options of identity deletion involves a simple yes-no decision . In the same way as there are languages which do not allow any deranking, we can fmd languages in our sample in which no form of identity deletion at all (i.e. neither subject deletion nor predicate-deletion) is permitted. In these languages, it appears
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identity. Thus, the well-known phenomena of Coordination Reduction and Gapping, which have been discussed extensively in recent gramm atical literature , will be taken to be instances of a case in which (some specific variant of) identity deletion has applied to a string. On the other hand, cases of contextual ellipsis (see Shopen , 1 973), and cases of Pro-Drop, are not subsumed under our concept of identity deletion ; in these cases, lexical material may be omitted in any construction where its reference is recoverable from the general context, and therefore this left-out material . does not have to be subject to conditions of identity with material that is explicitly mentioned elsewhere in the string. Given the above demarcation of the concept of identity deletion, we can now ask ourselves what the options are which languages have with respect to the application of this procedure in the derivation of the surface structures of temporal sequences {and hence of comparative construc tions). For our specific purpose, we can confme ourselves to a rather limit ed range of input structures for identity deletion. As it happens, the tem poral sequences which are the models of comparative constructions in natural languages typically consist of propositions which contain only a one-place predicate (such as BIG or SMALL) and its argument . Assuming that, in the linguistic codification of such sequences, these one-place predicates will be expressed by intransitive verbs or adjectives (V), and that the arguments of these predicates will be expressed by a subject-NP (S), this means that the typical underlying string to which the procedure of identity deletion may apply in the derivation of comparative construc tions will be a structure which has the general form of either {29a) or (29b):
1 67 to be impossible to have null-anaphors that are bound by identity ; these languages require that every configurational position be filled lexically, either by a full lexical constituent or by a pronominal element . An ex ample of a language which belongs to this type is Hixkaryana (see Derby shire,
1 980).
As sentence
(30)
illustrates, there is, in general, neither a
deletion of identical predicates nor a deletion of identical subjects in this language:
(30)
HIXKAR YANA : Mawu
wono
howler-monkey he-shot-it
Waraka, horoto
w:
xarha
spider-monkey
also
he-shot-it
w.
"Waraka shot a howler-monkey and a spider-monkey" Opposed to this class of languages with no identity deletion, we also fmd languages in which
some form of identity deletion
can be document
e d . For languages which belong to this group, it will be clear that there are three logically possible subtypes, namely: a) languages which may delete subjects under identity, but which do not ·
have the possibility to omit identical verbs;
b) languages which may delete identical verbs, but which do not possess the possibility to omit identical subjects; c) languages
in
which · both identical subjects and identical verbs may
be reduced to null-anaphors. However, if we look at the facts which are provided by the languages in
our sample, we observe that one of these categories, namely, the second
one , does not occur in reality . That is, it appears that there are no natu ral languages in which verb-deletion is possible while at the same time deletion of identical subjects is forbidden. It seems that
the option of verb-deletion always automatically includes the option of subject-deletion;
in this respect , identity deletion presents an interesting parallel with the procedure of deranking, where - as we have seen above - the option of absolute deranking always includes the option of deranking under identity of subjects. Given this state of affairs, we can conclude that the typological op
tions in the application of identity deletion allow for a three-way variance among languages , viz. : a) languages which have
no identity deletion , such
as Hixkaryana ;
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Waraka
wono
1 68 b ) languages which have limited identity deletion , i.e. languages which pennit reduction of identical subjects, but not reduction of identical verbs in a sequence. Examples of this class are Mandarin and Thai ; both of these languages " . . . totally resist deletion of verbs" (Mallin son and Blake, 1 98 1 :2 1 8) . On the other hand , deletion of identical subjects in these languages is quite common. The following sentence from Thai may be an illustration of this point : (3 1)
THAI: Mali Somchaj top kh:i : Damrong lae? M. s. slap kill and D. "Somchaj slapped Mali and killed Damrong"
(32)
JAPANESE: Sumie wa inu o o mita , Norio wa ki S. TOP dog ACC N. TOP tree ACC see-Past "Sumie saw the dog and Norio the tree"
4.3.
Optimal and non-optimal sequencing types
The discussion in the previous section has resulted in two categorizations of syntactic sequencing constructions, on the basis of the applicability of the gramm atical procedures of deranking and identity deletion . Now , I take it to be evident that every language will have to combine one of the options in identity deletion and one of the options in deranking ; that is, every natural language system will have to contain some pairing of a par ticular deletion variant and a particular deranking variant . Since both deranking and identity deletion give rise to a three-way categorization , the number of logically possible pairings o f these variants amounts to nine. I think, however, that it can be argued that, in reality, the number of pairings is restricted ; to be particular, some of these pairings should be rated as more 'natural' or 'optimal' than others. As we remarked above, the categorizations that can be established on the basis of deranking and identity deletion parallel one another in a number of significant respects. For one thing, both of these categorizations allow for a three-way variance. Moreover, both categorizations have a yes-no decision as their primary distinction : on this basis, balancing and no dele-
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c) languages which have total identity deletion , i.e. languages which can delete both identical subjects and identical verbs. English, Dutch, French and Latin are all members of this category. The same goes for Japanese ; as sentence (32) shows, in this language it is possible to apply Gapping, that is, deletion of identical verbs in a syntactic sequence :
169
5 . SEQUENCING-BASED UNIVERSALS O F COMPARATIVE TYPE CHOICE
Now that, in the previous sections, a cross-linguistic typology of syn tactic sequences has been established, we can return to our main concern, viz. the explanation of the attested variation in the linguistic codification of compariSon. As may be recalled , our central hypothesis is that the typo logy of syntactic sequences must be seen as the determinant of the typolo-
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tion are set apart from the other options. And fmally , within the remain ing variants (i.e. those options where at least some degree of applicabili ty of the procedure in question is warranted) we fmd in both cases a dis tinction between an unconditional variant (absolute deranking and total deletion, respectively) versus a variant in which the application of the rele vant procedure is limited by certain conditions (conditional de ranking and limited deletion, respectively). Thus, it looks as if both categoriza tions can be viewed as scales, on which the applicability of the procedure at issue is marked in three degrees: the procedure may either be disallow ed, or allowed only under some specific circumstances, or generally ap plicable . Given this remarkable parallelism, I venture the following hypothesis. I will assume that the optimal pairings of variants from the two categori zations are those in which the two variants involved are at the same level of 'extremism' on their respective scales. Thus, if a language does not have any deranking at all, it will tend to have no identity deletion at all, and vice versa. Opposed to this, we claim that languages which have the most 'far-reaching' form of deranking (viz. absolute deranking) will tend to have the most extreme form of identity deletion (viz. total dele tion) as well. Lastly, we claim that languages which have the more "mode rate" form of deranking (viz. conditional deranking) will tend to pair this option with the more limited form of identity deletion. In short , our claim is that, of the nine logically possible pairings of procedural variants, three are to be singled out as the optimal alternatives. It should be added here that the concept of 'optimal type', which rests on the assumption that gramm atical procedures tend to adapt themselves to one another in their degree of applicability, is not completely without empirical support. On the linguistic side, the data in my sample confum that the three types of pairings which I have rated as optimal are by far the most frequent pairings attested ; taken together, these three pairings cover 94 of the 1 1 0 languages in the sample . In addition, the concept of 'optimal type' employed here can be illuminated by invoking a number of general cognitive and functional princples, for which there seems to be a certain amount of independent evidence . For a full discussion of these points the reader is referred to Stassen ( 1 984, chapters 1 1 and 1 2) .
1 70 gy of comparative constructions, so that it might be said that the expres
sion of comparison in natural languages is 'modelled upon', or 'borrowed from', the expression of temporal sequencing. This modelling relation which we claim to exist between comparison and temporal sequencing can be brought out explicitly in a set of implicational universals. These universals can be called "sequencing-based", since the various types of syntactic sequences form the determining factor in the implication. As a first set of implicational universals of this kind, I would like to advance the following three statements:
As will be clear, this set of universals correlates the three major types of comparative constructions established in section 3 .2 . with the three optimal types of syntactic sequences that were developed in section 4.3 . Of these three universals, Universal 1 is in need of further specification since the class of adverbial comparatives - unlike exceed comparatives and conjoined comparatives - does not form a terminal category in our typo· logy. In this connection, we must draw attention to the fact that the se mantic notion of "temporal sequence", as defmed in section 4 . 1 ., allows for two semantic subtypes. In one of these subtypes, the events referred to in the sequence are taken to occur at the same point in time: we will call these temporal sequences instances of simultaneous sequencing. In con trast to this, we also encounter temporal sequences in which the two events must be conceived of as occurring in a successive order: temporal sequences of this kind will be referred to as consecutive sequences. As for the codification of these two semantic subtypes, we can observe that the large majority of languages adhere to a principle of parallelism , in that they select the same procedural option for the expression of both simultaneous and consecutive sequencing. In a number of languages, this parallelism in the choice of procedure type has even led to the 'radical' consequence of neutralization ; here the options which are selected for the codification of consecutive and simultaneous sequences are not just paral· lei, they are identical. Neutralization of this kind is particularly common in balancing languages and in languages with conditional deranking. Thus, for example , it can be noted that the distinction between simultaneous and consecutive interpretation is formally neutralized in the following balanced surface structure from English, which is therefore semantically ambiguous:
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UNIVERSAL 1 : Languages with an adverbial comparative are languages with absolute deranking and total identity deletion. UNIVERSAL 2: Languages with an exceed comparative are languages with conditional deranking and limited identity deletion. UNIVERSAL 3: Languages with a conjoined comparative are languages with no deranking (i.e . they are balancing) and no identity deletion.
171 (33)
ENGLISH: John played the lute and Mary recited a poem by Yeats
A similar semantic ambiguity can be attested in the following conditional ly deranked structure from Mandarin :
(34)
MANDARIN: Ta
kan
diclnying
chi
p ingguo
he
saw
movie
eat
apple
"He saw a movie and ate an apple�· T urning now to languages with absolute deranking, we can note that the
ing in the formal expression of its consecutive sequences, it will generally choose absolute deranking to codify its simultaneous sequences, and vice versa. However, in this case we can also note a discrepancy between the codification of the two semantic subtypes, which is related to conditions of
directionality
imposed on the deranking procedure . More specifically ,
we can note that absolutely deranked
consecutive
sequences can be
divided into two classes, on the basis of whether it is the anterior predicate (i.e. the predicate which expresses the earlier event) or the posterior predi
cate
(i.e. the predicate which expresses the later event) that gets affected by
the deranking procedure . As sentence
(28)
shows, Tamil is an absolutely
deranking language which deranks anterior predicates in consecutive sequences. Absolute deranking of posterior predicates in consecutive sequences is the option which is chosen in Maasai ; cf.
(35)
MAASAI: E -iput-a
emoti
n
she-fill-Past
pot
Depend. Tns.
.
-a-pik
en-kima
-1-put
on-frre
In contrast to this two-way split in the codification of absolutely deranked
consecutive sequences, there is no reason to subcategorize absolutely
deranked
simultaneous
sequences on the basis of this type of directional
ity. Since , in simultaneous sequences, the two events involved are taken to occur at the same point in time, the anterior-posterior distinction is not relevant here . This semantic state of affairs is mirrored formally by the fact that, in absolutely deranked simultaneous sequences, both predicates are equally eligible for the application of the deranking procedure . Given these considerations, we can conclude that , within the class of
absolutely deranked sequences, there are three options upon which the
choice of a comparative construction might be modelled . In our hypoth-
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procedural parallelism mentioned above generally holds for these lan guages, too. That is, if a language selects the procedure of absolute derank
1 72 esis, this tripartite distinction is matched by the three-way division of ad verbial comparatives which we discussed in section 3 .2. The relevant cor relations are expressed in the following three implicational universals, which must be looked upon as further specifications of Universal 1 :
Taken together, the two sets o f universals presented above must b e con ceived of as an operationalization of our claim that the choice of a parti cular comparative type in a language is determined by the possibilities in the formal expression of temporal sequencing in that language . Obviously , these universals are, as they stand , nothing more than hypotheses, which should be validated by confronting them with the actual data of the lan guages in the sample . It turns out , however, that the set of universals pro posed here can be shown to be adequate to a considerable degree, both as a set of empirical predictions and as an explanatory framework of cross linguistic comparative type choice . Concerning the empirical accuracy of our set of sequencing-based uni versals, cross-linguistic testing reveals that the cQll nter-evidence to the correlations formulated here is very sparse . I hope I can be absolved from the obligation to present the full linguistic evidence by which the set of sequencing-based universals is confirmed in the sample ; interested readers may consult Stassen ( 1 984, chapters 6 to 1 0). At this point , it may suffice to state that the counter-examples to the various universals in the set can rightfully be rated as incidental, and that they do not disturb an over-all clear picture . This state of affairs holds for the predictions of the primary comparative options in the various languages, as well as for the predic tions of the options which languages may have in the selection of a secon dary comparative . As a second poin t , it can be demonstrated that the set of sequencing based universals offers not only correct predictions as to the possibilities of comparative type choice : it also accounts for the correlations between word order types and some of the types of comparatives, as laid down in section 3 3 . These predictions of preferred word order are made possible by virtue of the fact that some particular sequencing types (which are taken to be the determinants of some particular comparative types) can
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UNIVERSAL JA : Languages with a separative comparative are lan guages with absolute anterior consecutive deranking and total identity deletion. UNIVERSAL JB: Languages with an allative comparative are languages with absolute posterior consecutive deranking and total identity dele tion. UNIVERSAL J C: Languages with a locative comparative are languages with absolute simultaneous deranking and total identity deletion .
1 73 be shown to be correlated with a specific word order option . For instance ,
it can be demonstrated that languages with absolute anterior deranking of
consecutive sequences have a preference for SOV word order, and this fact enables us to set up the following syllogism :
(36)
a.
Languages with a separative comparative are languages with
b.
Languages with absolute anterior consecutive deranking typi
c.
Therefore:
absolute anterior consecutive deranking (Universal I A) ;
cally prefer SOV word orde r ;
Languages with a separative comparative typically
prefer SOV word order .
deranking and VSO word order, and between conditional deranking and � SVO word order ; hence, the orrelations between allative comparatives
and VSO order, and between exceed comparatives and SVO order, can be
accounted for in a straightforward fashion . The fact that locative compara
tives are correlated with either SOV order or VSO order is immediately explained by our model, since it is, in general, only SOY-languages and
VSO-languages which have the possibility of absolute deranking. Finally , our model can account for the fact that conjoined comparatives are not
correlated with a preferred word order type , on the basis of the empirical
fact that the option of balanced (i.e . coordinate) sequential structures is not in any way restricted to a specific word order type.
As for the explanatory value of our proposed set of universals, we can
make the following comments. As we have stated earlier, this set of univer sals must be conceived of as the expression of the claim that, in natural
language systems, the codification of the concept of comparison is deriva tive of the codification of the concept of temporal sequencing. In other
words, we claim that the correlations laid down in the universals are the way
they are by virtue of the fact that comparative constructions are not
an 'independent', 'autonomous' construction typ e ; their syntactic expres
sion has been modelled upon the way in which the 'deeper-lying' concept
of temporal sequencing has been formalized in natural languages. In this
way , our set of sequencing-based universals lays claim to an
explanation
of the facts in the typology of comparative constructions.
In this connection, it should be added that the view of temporal se
quencing as a more 'fundamental' concept than comparison does not seem
to be implausible ; it is certainly more plausible than the view that the
modelling relation should be the other way around. The perception of tem
poral ordering between events is certainly a very elementary psychological
process, and the conceptualization of temporal relations is one of the pre
requisites for such fundamental human faculties as memorizing and d e -
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Similar correlations can b e attested between absolute posterior consecutive
1 74 ductive reasoning. Moreover, the intuitive view that, of comparison and temporal sequencing, the latter is the more basic concept has been affirm ed by a number of psychological and psycho linguistic experiments. 3 Speaking more generally, we should remark that the 'structural reductio nism' argued for here is not unknown in recent linguistic theory . Es pecially those authors which can be said to be a part of the so-called 'lo
calist' tradition have argued that various more or less 'abstract ' concepts (such as grammatical functions, possessivity , causativity and existence)
receive a linguistic formalization which is modelled upon the expression of the more 'fundamental' concept of spatial location. In this sense , our approach to comparative constructions can be said to be sympathetic to the localist viewpoint .4
The major remaining problem for our analysis of comparative type choice concerns the status of the so-called particle comparatives. As we saw in section
3 .3 .,
this type of comparative construction must be rated in prin
ciple as an instance of derived-case comparison . However, unlike the other class of derived-case comparatives, particle comparatives do not have the surface form of a coordination of independent sentences. Furthermore, particle comparatives are characterized by the presence of a special com parative particle which accompanies the standard
NP.
Finally, we re
marked that particle comparatives cannot be associated with a preferred word order type, and that their occurrence is, in all probability, an areal phenomenon . The first thing that can be noted about this class of particle compara tives is that the following sequencing-based universal can be confirmed in our sample without any exception :
UNIVERSAL 4 : Languages with a particle comparative are languages no deranking (i.e. they are balancing) and with total identity deletion. with
Thus, within the framework which we have adopted , we might say that particle comparatives are modelled upon a sequencing-type which is
optimal
(in the sense in which we defmed this notion in section
non 4.3.).
There i s some (admittedly, rather scanty) historical evidence which sug gests that most of the languages with a particle comparative used to belong to one of the optimal sequencing-types, viz. the type with absolute de ranking and total identity deletion . It seems that, in some areas, languages of this optimal type gradually lost the deranking option, while the option of total identity deletion was retained. In this connection, it is a telling
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6. PARTICLE COMPARATIVES
1 75 fact that a considerable number of languages with a particle comparative have an adverbial comparative as their secondary option, and that, in all the cases for which historical evidence is available , the adverbial compara tive appears to be the older of the two. For a few of the languages with a particle comparative, the relation of the comparative construction with a balanced sequencing construction is still transparent in synchronic surface structure. Such a case is, for example , presented by Javanese; in this language the particle
karo , which marks the
standard NP in comparatives, is also _employed as a conjunction or adverb which marks balanced (simultaneous and consecutive) sequences. The par allelism is clearly illustrated in the following examples:
JA VANESE: Gede
djaran-mu
karo
djaran-ku
is-big
horse -your
Part.
horse -my
"Your horse is bigger than my horse"
(38)
JA VANESE: Bapaq menjang ing-desa karo sirnboq menjang ing-desa uga father go
to-field
and
mother go
to-field
too
"Father went to the field, and mother went to the field too" In other languages , however, the development of the particle comparative seems to follow a more complex pattern. For these languages one is led to postulate a historical process of "grammaticalization" (Lehmann , "syntactization" (Giv6n,
1 984) or 1 979), that is, a diachronic process by which" . . .
loose, paratactic, 'pragmatic' discourse structures develop - over time into tight, 'grammaticalized' syntactic structures" (Giv6n,
1 979 : 208). As a
result of this diachronic process, an erstwhile semantically transparent construction (in our case, a balanced temporal sequence) may 'jell' into a new and separate construction type , which is then no longer transparent. Since the process of syntactization is gradual, the situation may arise in which a construction type must, at a certain stage , be classified as 'hybrid', so that it may be the object of "multiple analyses", in the sense of Hankamer
( 1 977).
Such a hybrid status can be assigned to the present
day particle comparative in Dutch. On the one hand, there are various good reasons to rate the comparative clause in this construction (i.e. the clause which follows the comparative particle dan "than") as subordinate . Thus, on the face of it, it looks as if the Dutch comparative clause should be viewed as an instance of adverbial complementation, in which the ele ment
dan
functions as a complementizer. Perhaps the most telling argu
ment in favour of this analysis is the fact that comparative clauses in Dutch have verb-fmal word order, a feature which in Dutch, as in German, is restricted to subordinate clause s :
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(37)
1 76 (39)
DUTCH: dan Ik zag hem eerder I than saw him earlier "I saw him earlier than he saw me"
hij he
mij me
zag saw
On the other hand, however, there are also data which suggest that Dutch comparative clauses should be considered to have main clause status . Ar guments to this effect can be derived from the fact that such clauses allow sentential modifiers like eerlijk gezegd "to be honest", which can occur only in main clauses, and from the fact that Dutch comparative clauses can undergo Gapping, an operation which is generally defmed only for coor dinate structures. Cf.: DUTCH: Hij beweert meer dan hij , eerlijk gezegd , kan bewijzen he claims more than he honestly said can prove "lit. He claims more than he, to be honest , can prove"
(41 )
DUTCH: Ik koop meer boeken dan Jan platen I buy more books than J. records "I buy more books than Jan buys records"
In this connection, we may also point out the uncertain status of the item dan in cases of Dutch NP-comparison. While in formal, written Dutch the comparative particle does not require a fixed case form of its following NP (cf. (42)), colloquial Dutch gradually develops into a situation in which NP-complements of dan invariably have accusative case , i.e . the normal case form for complements of Dutch prepositions. Cf. : (42)
(43)
DUTCH: Hij is een betere schaker dan he is a better chess-player than "He is a better chess-player than I (am)"
ik I-NOM
DUTCH: Hij is een betere schaker dan mij he is a better chess-player than me-ACC "He is a better chess-player than me"
In other words, it seems that, in Dutch, the process of syntactization in the formation of the comparative construction gradually leads to a situa tion in which the originally reduced coordinate clause dan + NP comes to
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(40)
1 77 be reanalyzed as an adverbial modifying phrase , in which
dan
plays the
role of a preposition . Now, it can be observed that this process has started to apply earlier in English than in Dutch. As Visser
( I 963: 249)
notes,
instances o f accusative case for underlying subjects in English compara tives can be attested from the first half of the sixteenth century onwards. The process has developed into a situation in which a sentence like rated as good usage, while the variant and old-fashioned:
(45)
(44) is
is considered to be stilted
ENGLISH:
(44)
You are stronger than
me
ENGLISH:
(45)
I
The difference in the extent to which English
than
and Dutch
dan
have
been syntacticized into prepositions in NP-comparatives can also be shown from the differences in the application of movement rules. As Hankamer
(1 973: 1 8)
states, there is an increasing possibility in at least some English
dialects to apply WH-Movement to standard NP's in comparatives ; in sentences where this rule has applied, the particle
than
is treated as a
stranded preposition . In Dutch, however, the application o f. WH-Movement to standard NP's is completely forbidden , even in colloquial and non standard speech:
(46)
ENGLISH: Who is he bigger than?
DUTCH:
(47) *
Wie is hij grater dan?
In summary, I think that the above comparison of Dutch and E nglish comparative constructions demonstrates that the process of syntactiza tion must be seen as a gradual process; this process has the effect of trans forming an erstwhile coordinate clause into a subordinate clause, allowing for intermediate stages in which the comparative construction exhibits hybrid characteristics. Apparently, the process has progressed further in English than in Dutch. While the modern Dutch comparative construction
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You are stronger than
1 78 still retains some of its original coordinate traits, the English compara tive has been syntacticized to such a degree that the connection with its coordinate origin has disappeared almost completely. As a result of this development, the English NP-comparative has come to be fitted into the mold of a different construction type already available in the language ; as we have seen above , English NP-comparison is gradually allying itself to the prepositional phrase construction . Assuming that the p article comparatives in English and Dutch (and pre sumably also in other languages) are the result of a diachronic syntacti cization of coordinate structures, we can now ask ourselves what the grammatical operations are of which this diachronic process consists. As instance, Javanese) it seems sufficient to postulate the operation of ellip tical rules to the original balanced input structure . However, for languages like Dutch and English, the process of syntactization must be thought of as more complex. First, there is strong evidence for the claim that, in a number of par ticle comparatives, an
underlying negative element
is present . This nega
t ive element may either be incorporated into the comparative particle (as in Gaelic na "nor" or Latvian
ne
'nor"), or may crop up in comparatives
as an independent item, given certain specific circumstances (as in French
and Italian ; see Seuren,
1 973).
For Dutch and English, the intimate
relation between negation and comparatives has been argued for repeat edly,
both on syntacto-semantic grounds (see Seuren ,
Mittwoch, (see Joly,
1 974; 1 967).
Napoli and Nespor,
1 976)
1 973 , 1 984 ;
and on etymological grounds
Secondly, it can be demonstrated that the process of syntactization of comparative clauses sometimes involves a process which shares essential features with the process of
relativization .
Straightforward evidence for
such a process can be derived from those languages in which the compara tive particle is historically an adverbial case form of the relative pronoun (Russian , Italian, French, F innish). Also, for English it has been argued repeatedly that the particle
than
is, in its etymology, closely related to
a demonstrative/relative pronominal stem, it being either an oblique case form of this stem (Campbell,
1 959) or a combination of such a case form 1 967). In addition to these etymological
and the negative particle (Joly,
data, there are also several structural arguments which point to a close simi
larity between Relative Clause Formation and Comparative Formation in English (see Bresnan,
1 97 1 , 1 973;
Hankamer,
1 979;
Kuno ,
1 98 1 ). One
of
the most telling arguments in favour of such an analysis is the fact that , in some non-standard varieties of English, this relativization even shows up overtly in surface structure :
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we stated earlier, for some languages with a particle comparative (like , for
1 79 (48)
ENGLISH: John is a lot smarter than what you'd think (he is)
It thus seems plausible to conclude that, for English at least, the formation of comparatives involves a set of syntactic procedures which is essentially
similar to the rule system needed in the formation of relative clauses. As I
see it , this conclusion holds independently of the S{!ecific formulation one
chooses for the rule system in questio n .
If we accept the above conclusio n , w e must ask ourselves what the form of the 'input structure' for the particle comparative in English should be assumed to be . As an approximation of a solution to this problem , I will adopt here the analysis of the English comparative proposed by Seuren In this proposal, English comparatives are analysed in terms
of an underlying structure which crucially involves existential quantifica tion over extents. Thus, for instance , a comparative like "Jim is taller than Joe" is analyzed in the following way:
(49)
3: e : extent [Jim is tall to e A � [Joe is tall to e ] ]
or - to rephrase this analysis i n a non-logical form - : "There i s an extent e such that Jim is tall to e and Joe is not tall to e." As Seuren points out , there are several independently motivated arguments for the correctness of an analysis of this typ e . Apart from the fact that this analysis accounts for the underlying negation which must be assumed to be present in Eng lish
comparative
clauses (see above), the quantification over extents
which is embodied in this proposal provides a framework for the descrip tion of the phenomenon of positive and negative connotations of English gradable adjectives (see Seure n ,
1 973: 535-537), and
enables us to account
for the occurrence of a dverbial measure-phrases in comparative clauses (see Seuren,
1 984).
Furthermore , it can be shown that this analysis is able
to deal with the ambiguity observed in a sentence like forward fashion (Seuren,
(5 0)
1 973 : 5 2 8-5 2 9 ; Seuren, 1 984):
(50)
in a straight
ENGLISH: Planes are safer now than they were thirty years ago
From the point of view of the present study, the main attractiveness o f Seuren's proposal lies in the fact that this analysis i s able t o reconcile two seemingly contradictory requirements on the 'input structure ' for the particle comparative in English. On the one hand, we have argued that the input structure for all particle comparatives should be conceived of as basically a coordinate structure; this requirement is met by the pres ence of the and-conjunction in
(49).
On the other hand, we have also con-
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( 1 973 , 1 984).
1 80
eluded that the fonnation of the English comparative involves some pro cedure of relativization . Structure (49) provides a possibility for the ap plication of this procedure , in that it specifies an existentially quantified antecedent for a constituent of the comparative clause. This constituent (viz. the extent-phrase e) becomes thereby eligible for relativization. 7 . CONCLUSION
The main theoretical point which is argued for in this paper is that the following insight should be incorporated into our conception of the notion "natural language":
I n other words, our claim is that comparison is one more case of "abstract location" in the sense of Lyons ( 1 977 : 7 1 9), at least as far as its linguis tic codification is concerned. In the majority of natural languages inves tigated here, the modelling of comparatives on syntactic sequences turns o ut to be fairly straightforward and transparent . However, in one particu lar class of comparative constructions, viz. the particle comparatives, the direct relation between the two construction types can be argued to have been obscured by way of a diachronic process of syntactization. This research result is, I think , of particular relevance to those inves t igators who occupy themselves with the development of a fonnal seman tic theory for comparative constructions. I feel that attempts in this area have, up to now, been hampered considerably by the fact that they are commonly based upon an analysis of the English comparative . As we have tried to demonstrate , this is an unfortunate place to start , given the highly marked status of the particle comparative in English and other European languages. Thus, cross-linguistic work of the type illustrated here may contribute to the insight that the English comparative , when seen in the light of more general universal facts, is a hybrid construction, which combines characteristics of various different construction types available in the language. It may be expected that this insight will have its repercussions on the fonn which a semantic theory of comparison in English should be assumed to take . Nijmegen University Institute of General L inguistics Erasmusplein I Nijmegen - Holland
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The linguistic expression of the concept of comparison is modelled on the linguistic expression of temporal sequencing.
181 NOTES 1 . The research reported in this paper was completed during a stay at the Nether lands Institute for Advanced Science (NIAS) in Wassenaar, The Netherlands. Thanks are due to Pieter Seuren, John Hawkins, Melissa Bowerman, Joan Bybee, Lachlan McKenzie, Ekkehard Konig and Ad Foolen, who commented upon various earlier stages of the project. Unfortunately, nobody among these kind people is responsible for errors that may remain in the final version. 2. English is exceptional in that the particle than has developed into a preposition (see below, section 6). 3. See , among others, Sherman ( 1 969), Clark (1 970), Higgin s and Huttenlocher ( 1 9 7 1 ), and Baron ( 1 973). 4 . A survey of the basic assumptions in the localist tradition is presented in Lyons ( 1 9 7 7 : 7 1 5-722).
Annamalai, E. 1 97 0 : On m oving from coordinate structures in Tamil. In: Papers from the Sixth Regional Meeting of the Chicago Linguistic Society , Chicago, lli . ; 1 3 1-146. Baron, J . , 1 973 : Semantic components and conceptual development. Cognition, 2; 299-3 1 7 . Bergmans, L . , 1 9 8 2 : Semantic Aspects of Comparison in Dutch, English and Other Languages. Ph.D. Dissertation, University of Louvain. Bresnan, J., 1 9 7 1 : On "a non-source of comparatives". Linguistic Inquiry 2; 1 1 71 25 . Bresnan, J ., 1 9 7 3 : Syntax of the comparative construction i n English. Linguistic Inquiry, 4 ; 3-40. Campbell, A. 1 959. Old English Grammar. Oxford. Clark, H. 1 9 70. Comprehending comparatives. In : G .B . Flores d'Arcais and W.J.M Levelt (eds.), A dvances in Psycholinguistics, Amsterdam/London; 1 94-206. Derbyshire, D., 1 9 79: Hixkaryana. Amsterdam. Dik, S., 1 96 8 : Coordination. Its Implications for the Theory of General Linguistics. Amsterdam. Doherty, M., 1970: Zur Komparation antonymer Adjektive. ASG-Bericht 6, Berlin . Giv6n, T., 1 97 9 : On Understanding Grammar. New York. Hankamer, J., 1 97 3 : Why there are two than 's in English. In : Papers from the Ninth Regional Meeting of the Chicago Linguistic Society, Chicago, III . ; 1 7 9-1 8 8 . Hankamer, J . , 1 9 77 : Multiple analyses. In : C.N.Li (ed.), Mechanisms of Syn tactic Change, Austin ; 602-620. Hankamer, J., 1979: Deletion in Coordinate Stmctures. New York. Higgins, E. and Huttenlocher, J. 1 97 1 : Adjectives, comparatives and syllogisms. Psychological Review, 7 8 ; 487-504 . Joly, A., 1969 : Negation and the Comparative Particle in English . Quebec. Keenan, E. and Comrie, B . , 1 97 7 : Noun phrase accessibility and universal grammar. Lingu istic Inquiry, 8; 6 3- 1 00 . Klooster, W . , 1 9 7 6 : Adjectieven, neutraliteit e n comparatieven. In : G . Koefoed and A. Evers (eds.), Lijnen van taaltheoretisch onderzoek, Groningen; 2 29-25 9. Klooster, W., 1979: Opmerkingen over de comparatief. In : Handelingen van het XXX/lle Vlaams Filologencongres. Louvain ; 1 97-206.
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REFERENCES
1 82 R. and Stegmann, C. , 1 95 5 : Ausfiihrliche Grammatik der /ateinischen Sprache. Darmstadt. Kuno, S . , 1 98 1 : The syntax of comparative clauses. In : Papers from the Seventeenth Regional Meeting of the Chicago Linguistic Society, Chicago, ill . ; 1 36-15 5 . Lehmann, C . , 1 984 : Der Relativsatz. Tiibingen. Lyons, J . , 1 9 7 7 : Semantics. Cambridge. Mallinson, G. and Blake, B., 1 98 1 ; Language Typology . Amsterdam. Mittwoch, A., 1 974: Is there an underlying negative element in comparative clauses?, L inguistics, 1 2 2 ; 39-4 5 . Napoli, D . and Nespor, M., 1 976 : Negatives i n comparatives. Language, 5 2 ; 8 1 1838. Rambaud. J-B., 1903 : La Langue Wolof. Paris. Ross, J . R . , 1 9 6 7 : Constraints on Variables in Syntax. Ph . D . Dissertation. Cambridge, Kiihner,
Mass . MIT.
Ph.D. Dissertation, Nijmegen.
1 975 : Spatial expressions of tense and temporal sequencing. Semiotica, 1 5 ; 207-230. Valin, R., 1 95 2 : Esquisse d 'u ne theorie des degr�s de comparaison. Quebec . Visser, F . , 1 96 3 : A Historical Syntax of the English Language. Leyden.
Traugott, E . ,
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1 9 7 3 : The comparative. In : F . Kiefer and N. Ruwet (eds. ) , Generative Grammar in Europe. Dordrecht, Holland ; 5 28-564. Seuren, P., 1 978: The structure and selection of positive and negative gradable ad jectives. In : Papers from the Parasession on the L exicon, Fourteenth Regional Meeting of the Chicago Linguistic Society, Chicago, ill . ; 3 36-346. Seuren, P . , 1 984 : The comparative revisited. This volume. Sherman , M., 1 96 9 : Some Effects of Negation and Adjectival Marking on Sentence Comprehension . Ph.D. Dissertation , Harvard. Shopen, T., 1 97 3 : Ellipsis as grammatical indeterminacy. Foundations of Language, 1 0 ; 6 5-77. Stassen, L., 1 984 : Comparative and Conjunction. An Essay in Universal Grammar, Seuren, P.,
Joumal ofSemantics 3 : 1 83 - 1 9 9
MY REACTION TO CRESSWELL'S, HELLAN'S, HOEKSEMA 'S AND SEU REN'S COMMENTS
ARNIM VON STECHOW
1. EXPLANATORY PRINCIPLES IN SEMANTICS?
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I would like to start my reply to the many valuable comments on my article with some more principled remarks on the methodology of the kind of semantics I adhere to. Obviously, it is not possible to take up all the critical points raised against my proposal. My reaction will be highly se lective, dealing with only those arguments which concern the essence of the enterprise. Noam Chomsky would presumably call the type of semantics I am ad vocating "a type of descriptive semantics, except that I think it is not semantics really, in the sense that it does not deal with classical questions of semantics such as the relation between language and the world . . . . . It does not lead very far into the frightening area of general explanatory principles, and therefore it has a lot of appeal, as descriptive phonetics does." (Chomsky 1 9 82 : 46f.) I am not sure whether I agree with the first statement, because I am interested in the truth-conditions of statements. And if truth-conditions have nothing to do with the relation between language and the world, then I don't know what they are . But I certainly agree with Chomsky on the second statement. Most of what I have done is descriptive semantics. And the same is, to my mind, true of the other theories I have discussed . And it is also true of Hoeksema's reaction. It was, however, my aim to develop a number of fairly simple principles of interpretation which could be in tegrated in a more principled modular theory of grammar. I have carefully tried to avoid merely descriptive manoeuvres. Now, it is hard to say what explanatory principles are, without com mitting oneself to a particular theory of g rammar. Chomsky certainly would say that explanatory principles in semantics must be related to cognitive psychology (1982 : 93). An explanatory principle of grammar will have to explain, for example, why a child never commits certain errors when it learns a language. This is a very ambitious concept of explanation, leading ultimately to the concept o f universal grammar. I would like to subscribe to this idea. For the purposes of this discussion it is, however, convenient to rely on a
1 84
2. N EGATIVE POLARilY ITEMS (NPis)
Hoeksema and Seuren accept Ladusaw's thesis that NPis occur in the scope of a downward entailing operator. Although I took the same line of reasoning, I must confess that this theory is rather mysterious. Why should NPis occur exactly there, whereas positive polarity items should not? Perhaps this is an irreducible property of these items. One has, how ever, the feeling that a functional explanation is in order here. Perhaps the distinction [ ± NPI] helps to reduce ambiguity in downward entailing con texts. Seuren's distinction between external and internal operators points in this direction. Be that as it may, for the moment, Ladusaw's theory merely seems to be a descriptive generalisation , though a very interesting one. Let me now come to the treatment of NPis as it is proposed by my opponents. Consider Hoeksema first. His main thesis is this.
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more innocent concept o f explanation. I t is this: i f a number of highly complex and apparently unrelated facts are reducible to a few simple p rinciples, then t hese principles explain these facts. I take it that this concept of explanation is present in a lot of current work in generative grammar. Take, e.g., Chomsky's binding principles A, B and C. These subsume a larger number of classical constraints. Clearly, this kind of reductionism, even if modular in some sense, con veys a rather weak notion of explanation. It is very similar to what is sometimes called internal evidence. We should not hesitate to give up very elegant rules, if external evidence speaks against them, i.e., if it can be shown t hat they are not 'psychologically real'. For example, both internal and external evidence speaks in favour of a rule of final devoicing in German or Russian. But only internal evidence speaks for a rule of final stop deletion in Maori. External evidence speaks against such a rule. Con siderations of the same kind apply, in p rinciple, to semantics. What else could then be an explanatory principle in semantics? I have no general answer to this but I will venture to say a few things. First I want to argue in a purely negative way by pointing to some accounts which I take to have t he flavour of being pure descriptions of the facts. This discussion will be mainly concerned with accounts dealing with negative polarity items (NPis). Then I will reflect on the role of transparent constructions in a possible explanation of opaque constructions. A further section takes up t he question of the division of labour between quantifier scope and double indexing. All these sections will be mainly concerned with the comments of Hoeksema, Seuren and Hellan. The last section deals with Cresswell's point. I also try to elaborate a bit on Seuren's ideas about the ontology o f extents.
1 85 There are two kinds of comparative constructions, the oblique compa rative as in ( I ) and the sentential comparative as in (2):
(I)
Ede is smarter [ ppthan me]
(2)
Ede is smarter
fsthan I am]
(3)
x is A-er [ ppthan y] iff x >A y (cf. Hoeksema [82, def.3 ] )
(4)
x is A-er
fsthan S]
iff (Vy)( fs than S] (y) => x >A y)
Here , fsthan S] is a property of degrees. (Cf. Hoeksema 1 983 ; def.8). It is obvious that the first "x is A-er than" is not downward entailing with respect to the complement, because it is simply a two-place relation. But the second is, because the definition is in the essential respects similar to Cresswell's, i.e., we are allowed to strengthen the antecedent of a conditional. Now, my worries with this account are these. It is absolutely mysterious to me why we should have two semantic rules, one interpreting structures of the form (3), the other interpreting structures such as (4). It seems to me that the alleged semantic difference between (3) and (4) should be the outcome of the same kind of interpretation rules plus the structural difference. Thus, even if Hoeksema's account were descriptively adequate, it would merely describe the facts but not explain them. Now, I also have strong doubts as to the descriptive adequacy of Hoeksema's proposal. Remember that he claims that oblique comparatives behave exactly like transitive verbs. But then we would expect the follow ing two sentences to be alike in grammatical status: (5) (6)
Senta likes none of us ?? Ede is smarter than none of us
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Cblique comparatives are said to behave exactly like transitive verbs, i. e. they are not downward entailing with respect to the complement, hence do not admit for NPis. Sentential comparatives, on the other hand, are downward entailing with respect to the complement . Hoeksema's objection is that I fail to see this distinction, since I t reat the two constructions alike semantically. Suppose for a moment that Hoeksema's objection is valid. It is inter esting, then, to see how he treats the semantic difference between (I ) and (2). Trivializing grossly the semantics given in Hoeksema {1983), his account is this. There are two semantic rules, i.e. :
1 86 At least some English speakers accept
(6).
For me,
(6) is
almost ununder
standable , because my intuitions come from German. And the German counterpart of
(6),
viz. (8):
viz. (7), is as bad as the Dutch translation of
(7)
•Ede ist khiger als niemand von uns ( .. ist)
(8)
•Ede is slimmer dan niemand van ons ( .. is)
(6),
If we add the copula, the sentences get even worse . It seems to me that an explanation for the oddnes cannot rely on semantic considerations alone, because we have no conceptual problems with these sentences. An entirely
For none of u s is it the case that Ede is smarter than him .
(9)
For some reasons, we don't get this interpretation in the German and Dutch examples. I have a partial answer to this problem , i .e . , I can say why - (8) are odd on one reading. Cf. XI, 7
(6)
however, that I cannot block
(9).
(240)
of my article. I admit,
Hoeksema does not even seem to ac
knowledge that we have a problem here. Let me now turn to another objection made by Hoeksema. He criticises my position t hat comparatives are always downward entailing with respect to their complement. Now, my comments on (78) indeed suggest such a view . But the latest stage of my proposal is much more subtle. It is com patible with the following position, which I actually hold :
( 1 0)
Whether a comparative is downward entailing or not depends on the presence of a downward entailing operator. This has nothing to do with the PP- versus S- complement d istinction.
Let me show that my proposal is indeed compatible with this position. Hoeksema claims that I cannot treat cases like
(1 1 )
and
(1 2),
where a
comparative is upward entailing with respect to its complement :
(1 1 )
All cheetahs run faster t han all lions
(1 2)
All cheetahs run faster than all hungry lions
(1 1 )
e ntails
(1 2).
But this is no problem for my t heory . Disregarding the
all and every, the (1 2) are (1 3 ) and (1 4), respectively :
difference between
relevant formalizations of
(1 1)
and
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reasonable interpretation is this :
I 87 ( 1 3)
Every lion Ax. [the d [x runs d-fast] M 2 [( 3 d i > 0) [Every cheetah runs d I + d 2 -fast]
( I 4)
Every hungry lion Ax. [the d [x runs d-fast] M 2 [ 3 d i > 0) [Every cheetah runs d I + d 2 -fast} ] ]
(I 5 )
a. • J im is exactly as competent as anybody here could possibly be b . Jim is at least as competent as anybody here could possibly be
In order to explain this difference, Seuren postulates a systematic lexical ambiguity for as. . . as. On one reading the equation is symmetric, on the other it is not . The second reading is the one where we expect NPis in the complement. Again , this seems to me to be a purely descriptive manoeuvre. It seems to me that it is pretty obvious that the equative as. . . as has exactly the same meaning in both cases. The sources of the [ ±NPI] environment must be the operators exactly and at least. The relevant syntactic form which determines the scope of these operators is presumably very similar to the one which Chomsky assumes in Aspects, viz. ( 1 6):
(I6)
Jim
is
{
exactly at least
}
- as anybody here could possibly be-competent
The account of the equative I propose in section Xl. 2 does not proceed exactly along these lines. But it is obvious that it can easily be rearranged in such a way that it is in accordance with the general p rinciple (I O). I should add here that I do not maintain that it is always the MAX-operator which creates an NPI environment . It is not even necessary that the MAX operator be p resent. Before I leave the equative, let me mention a curious fact for which I have no explanation at the moment : ( 1 7)
a. Ede ist so klug wie keiner von uns b. • Ede is as smart as none of us
For me and some speakers of German I have asked, ( 1 7a) is fairly normal
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Clearly, ( 1 3 ) entails ( 1 4). Thus, contrary to what Hoeksema assumes, these sentences do not raise a problem for my theory. I fmd the position ( 1 0) particularly appealing when we turn to an analysis of the equative. This brings us to Seuren. Seuren correctly remarks that an equative modified by at least admits for NPis in the complement, whereas we cannot have an NPI, if the modifier is, e.g., exactly. Consider Seuren's sentences (30Xa) and (b), here repeated as (I SXa) and (b):
1 88 and has indeed the reading that Ede is more clever than any of u s . ( 1 7a) becomes bad if we add the
at least
or
at most. (17)
German counterparts of modifters like exactly,
might be a case where a construction is non
sensical when interpreted literally . There are o ther such cases. Take, for instance , the French sentence :
( 1 8)
La
tour Eiffel est tro
� fois plus haute que la tour de Pise
It is hard to see how we could construct semantic rules such that the
literal meaning of this sentence conforms to our intuitive understanding.
The same happens with Wason's famous sentence : No b rain injury is too trivial to be ignored
We u nderstand this sentence immediately, but not in the sense the se mantic theory predicts. Or compare our increasing difficulty in under standing the following sentences : (20)
a . I am too stupid to be sacked b . Everyone is too stupid to be sacked c . No- one is too stupid to be sacked
Sentences like
( 1 9 ) and
(20c) are almost totally opaque.
The interesting problem is to explain why we have such difficulties with these apparently simple constructions. These examples lead me to some general remarks about transparency vs. opacit y .
3. SEMANTIC ARCHEOLOGY : THE SEARCH F O R TRANSPARENCY If I understand Seuren correctly, then one motivation for the analysis of the comparative consists in looking at a period where the construction was still transparent . Seuren's particular analysis strongly relies on the fact t hat
than
is historically derived 1 from
pon-ne
"by which not ". What
worries me about this argumentation is this : How should the speaker know that
than is derived in
this way and has the meaning and
+ not?
You can of
course say that there is indirect evidence for this decomposition, viz. the presence of NPis in the
than-S.
But this would be a circular argument ,
since the point at issue is precisely w hether NPis are conditioned by a negation or b y a more general feature of operators. Another argument would be to say t hat the se mantics for the compa rative was ftxed at a time when the construction was transparent and that it has been fossilized since. I think that no-one holds such a view, because
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( 1 9)
1 89 it would make the sense of the construction practically unlearnable. It is not even clear to me that a language With an o ccasionally overt negation like Italian has to be analyzed along Seuren 's lines. Consider his sentences (44) , here repeated as {2 1 ) :
{2 1 )
a . Luigi e piu alto che non pensassi b. Luigi e piu alto di quello che pensavo
We
add a third variant, one with a WH-phrase :
can
{22)
c . Luigi e pill alto di quanto io pensavo
{23)
Timeo ne veniat
where the ne goes together with the subjunctive . There is no reason to suppose that the negation plays any part in the truth-conditions of this sentence. Of course it is interesting to look at different transparent constructions for the comparative, as Seuren does in section 4. For example, the Malay and the Nahuatl example, i . e. :
{24)
a. "Jim and Joe, Jim is tall" {Malay) b . "Jim is tall , Joe is not tall" {Nahuatl)
are quite compatible with E. Klein's theory of the comparative . The Samoan example :
{24)
c. "Jim is tall, Joe is short"
conforms to Hoepelman's theory. And
{24)
d . "Jim is tall from Joe"
is the type we also find , in addition to the languages Seuren mentions, in most Balcanic languages and in Hebrew. In biblical Hebrew we occasional ly even fmd constructions like : {24)
e. "Noam is tall from our thinking"
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The variants {2 1 ){b) and {22) are them ore common ones. The Hrst one w ith the negation is elevated style. I am not sure that the negation has much to do with the comparative. The subjunctive + negation somehow marks the unexpected . The situation is similar to Latin
190 I t is a n achievement to construct semantic theories which start from different transparent constructions and choose different primitives. The important question then is whether these theories make different pre dictions for a particular language . Ifso , we have . a way of making a choice
b etween them. This is basically what I have done in my article.
It is interesting to see what happens if t he transparent constructions are
grammaticalized , thus possibly becoming opaque. It might very well be the case that the original conceptual strategies are then replaced by something else . Lexical material may be reanalyzed and thereby change its semantics. Or the literal meaning may be overruled by other necessities. For example, it may be the case that differential m easure phrases
(DMPs) are
not even
compatible with the semantics of the Nahuatl-t ype, i.e., the semantics such a case. This last remark leads me to some comments on
DMPs.
4. DIFFERENTIAL MEASURE PHRASES (DMPs)
For a long time I was happy with a semantics for the comparative in the style o f Kaplan-Lewis-Seuren-Klein . (I hope I can be forgiven for putting these four into the same quartet .) One of the main reasons why I gave up this semantics in favour of an analysis in Hellan's style was that I was not able to see how
DMPs
could be incorporated into this theory. Now,
Seuren says that this is no problem. In his section
6.4,
Seuren says that a
sentence like
(25 )
Sue is si x inches taller than Ed e
h as to be analysed via t h e paraphrase
(26)
Ede is tall to an extent to which, over a stretch of 6 inches, Sue is not tall
He says that the
DMP
operates on the entire than- clause and his para·
phrase suggests that the negation is t hat the semantics for
DMPs
result
in
DMPs
in
the scope of the DMP. He thinks
is obvious: ''The semantics of DMPs is clear :
cognitive extents on the relevant p aram eter representing
the parameter extension covered by the comparing entity and not covered b y the comparee, more or less as is proposed by Hellan
198 1 . "
I simply fail t o see that a semantics in Hellan's style i s compatible with Seuren 's, particular analysis. Everything depends, of course, on how we formulate the semantics for the sentential adverb
inches,
for short :
over 6 inches.
over a stretch of six
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which Seuren assumes for English. It is unclear to me what happens in
191 The only thing I have been able to figure out is something like this. I assume that Seuren has in mind the following logical form for
(27)
( 3 e) [Sue is > e-tall � "'
& (Ve ')
Ede is � e'-tall] ]
(25):
[(e minus 6 inches) .;;;; e' < e
We may hope to get this reading if we assume the following semantics for
over 6 inches: (28)
U over six inches 0 (P)(e)
�
� P (e')]
Ve' [(e minus 6 inches) :< e' < e
First: (27)
means that Sue is
intended ; we want of the
at least.
exactly
at least 6
instead of
inches taller. This is not the reading
at least.
I don't see how we get rid
This seems to be a feature which is built into Seuren's
semantics. In other words,
(27)
would be true under the following conditions :
6
inches
Ede's tallnes Sue's tallness
Second: In order to get the reading (27), the over 6 inches must be between and and "' : (29)
. . and over 6 .
If we place
inches "' . . .
over 6 inches
under the negation, the resulting reading be
comes too weak . It is unclear to me how this can be remedied. I admit, however, that I am perhaps not inventive enough to fmd the
right solution for this proble m . So my objection is perhaps not a crucial
one . It is just a question I direct to Seuren.
5 . SCOPE AND INDEXING
In my approach, than-phrases have scope. Hoeksema does not like thil> and disputes my example
(29)
(1 79), here
repeated as :
I thought Plato could have been more boring
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There are two problems with this proposal.
1 92 The second thing he does is to offer a sentence whose intended interpre tation could not be obtained by quantifying in , anyway :
(30)
[
=
Hoeksema's 6 2 ]
We expect that every schoolboy thinks he is
b righter than he is These two points are enough for him to claim that an operator-approach,
i .e . , o ne working with double indexing, is superior .
M y reaction is this. I concede t hat (2 9) i s a badly chosen example. But
Hoeksema is wrong in disputing the point behind it . As fo r the operator
Double indexing is double indexing. It may be the
approach, I t hink the problem is much more general. not enough. We need a sort of generalized
if we take that line
of analysis. Hoeksema's own method is, however , no t sufficient .
I agree with almost everything Hellan says about double indexing in
section 2 of his response , though I d isagree with him on the particular
move by which he t ries to save his system from my criticism. I will come to this at t he end o f t his section.
Let me fust try a better example than (2 9). I hope the following
sentence will do :
(3 1 )
Max believes that any Martian is obliged to speak faster t han any Vulcanian speaks
I think t hat it is hard to deny that the following is a reasonable interpre tation of
(32)
(3 1 ):
Max believes [the max d [Some Vulcanian speaks d-fast] M2
[( 3 d 1 > 0)
Any Martian is obliged to speak d
1
+ d 2 -fast] ]
This is a case where the content of the comparative complement, i.e. , "the max d [Some Vulcanian speaks d-fast] " c annot be evaluated with
respect to the real world , since Vulcanians do not exist there. And this complement is not in the scope o f t he obligation-operator either. Hoekse ma cannot get this reading. Let me tum now to Hoeksema's (6 2 ), here repeated as
(33)
(33 ) :
W e expect that every schoolboy thinks he i s cleverer than h e is
The intended reading is the o ne where every
schoolboy
is in the scope o f
expect b u t than he is is not. Hoeksema correctly points o u t that I cannot
get this reading.
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case that we can dispense with scope fo r than-phrase s,
193 I t seems to m e that se ntences of this type point t o a rather general problem which is not tied to the comparative in particular. The problem is this. In most of the current approaches, an operator o p 2 cannot be interpreted transparently with respect to an opacity-creating operator op , if op is in the scope of op 1 . But exactly this o ften seems to be 2 1 wanted . Let me illustrate this point by means of an example from Bauerle ( 1 983): (34)
Max thinks that George believes that no student knows every book by Chomsky
Suppose that Max is responsible fo r the u niversal description
every book
responsible for the universal negative words, George holds a belief about a
set of books which are the books by Chomsky
according to Max 's belief
only, i.e., not necessarily in t he real world. This means that the quantifier every book has to be evaluated with respect to Max's belief worlds and it must nevertheless be in the scope o f no student, which by supposition is in t he scope o f George believes. Clearly we cannot have this in either a scope approach or the usual double indexing approach. The intended reading o f (3 4) is rat her something like : (3 5 )
' (Vw,B ) (Vw ' ,Bc ') (No x ) [ student x in w M w w o ' (Vy)(bo k y in w => x k nows y in w )]
&
' and Be ' mean that w and w are belief-worlds o f Max and Here, B M w w ' Geo rge, n! spectively. I do not want to go into the question o f how we get (3 5 ) from the surface . Several proposals exist. Vide Ioup ( 1 97 7), Enc; ( 1 9 8 1 ) and Bauerle ( 1 9 83). Thus, it seems to me that we have to do something along these lin es. Hellan's remarks in section 2 of his response point in the same directio n . The usual method of double indexing, where one index always points to the actual world , has to be replaced by the more general re quirement that one index points to the worlds created by some other operator. It seems to me that we can, indeed, treat (3 1 ) acco rding to this metho d . Thus, Hoeksema m ay actually be right with his claim that we should treat examples like these b y an operator approach, but he is not right in disputing t he point behind my example (29). Let me conclude this section by saying a few words about Seuren's and Hellan's treatment of ambiguous counterfactuals. Seuren's reaction is to attack t he Stalnaker-Lewis semantics of counter factuals on the grounds that it is based on possible world semantics. I think that a rejection on these grounds is not very fruit ful . I like the
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.
by Chomsky, whereas George is description no student. In other
1 94 frame-work of possible world semantics, but I really do not care if some one has a viable alternative like situation semantics, discourse semantics or whatever. Any framework will do for me provided it yields the correct t ruth-conditions. A worrying attack would have been to show that the Stalnaker-Lewis semantics yields the wrong truth-conditions. It is impossible for me to evaluate Seuren's own p roposal for am biguous counterfactuals, since I do not know his discourse semantics. However, I want to mention one thing. He tries to account for the reason able reading o f (36)
[ = Seuren's 6 2 ) I f Jim had worked harder than he did , he would have passed
(37)
[ = his 65) IF ( 3 e :extent p ' [Jim has worked e-hard)/\"' [Jim has worked e-hard) ), D ' [Jim has passed] D
If I look at this, I see a striking formal similarity with double indexing. D corresponds to the actual world , i. e. to the ACTUALLY-operator and D ' corresponds to the counter factual worlds. If this is correct, then what I have said about the weakness of double indexing applies here, too. Let me now say a word about Hellan's actual solution of ambiguous counter factuals. The essential point seems to me to b e this. He has a semantic interpretation rule, viz. his convention ( 1 0), which is able to convert the ''intermediate" meaning : (3 8)
[ = Hellan's 9) wi RR [Mary smoke d 1 1 much � Mary be d 1 2 healthy] & Mary is d 22 healty & d 2 1 > d 22 & Mary smokes d 1 2 much & d 1 1 < d 1 2
into the meaning : (3 9)
[ = his 6)
3 d 1 2 ,d 22 [Mary smokes d 12 much & Mary
is
d 22
healthy & Vw i RR• d 1 1 , d 2 1 [d 1 1 < d 1 2 & d 2 1 > d 22 � w i RR [Mary smokes d 1 1 much � Mary be d 2 1 healthy) ) ) I d o not want to go into the question o f whether (39) [ = Hellan's 6) is a reasonable representation of the meaning of the sentence in question. My point is this : there cannot be a rule converting (38) [= 9) into (39) [= 6] . This rule would violate virtu ally any reasonable constraint on semantics. I take it that (3 8) is an open proposition, i.e., a set of worlds which
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by the formula
195 depends o n the values for the free variables. But w e cannot 'look into' a proposition, identify parts like "d
< d 1 2 ", rearrange them, replace con 11 nectives etc. If (1 0) were part of a theory of translation i.e., if ( 1 0) were
a rule relating two 'mental representations', then we should expect some reasonable constraints, too . It seems to me that (10) rule, even if it were theoretically possible.
is
not a learnable
6. ON THE O NTOLOGY O F EXTENTS
Cresswell is entirely right that I did not want to commit myself to a particular ontology of degrees. I think, however, t hat this
is
the place to
Every ontology of degrees has to meet some linguistic criteria of adequacy . Cresswell mentions some. We cannot make literal sense of:
(40)
* Martin is taller than I am clever
There are other odd sentences, whose oddness seems to have purely con ceptual reasons : (4 1 )
Ria
(43)
Ria is twice as tall/*short as Alain
(44)
Ede is 20 em taller/*smaller than Ria
is
1 .50 m tall/*short
And , of course , we expect the following argument to be valid : (45)
(46)
Ede
is
(20 em) taller than Ria. Therefore, Ria
than Ede
is
(20 em) shorter
Ria is (twice) as t all as Alain . Therefore , Alain is (half) as tall as Ria .
In a talk which Manfred Bierwisch gave in November 1 983 in Konstanz, he mentioned some further , more subtle data . But I think that sentences like these represent the minimum t hat a good ontology of degrees should ex plain . It is p retty obvious, that the oddness of the starred sentences cannot be explained on syntactic grounds.
In section 2 of his response Seuren makes some extremely stimulating
remarks on the ontology of extents. I will follow the line of his remarks
and try to develop the outlines of an ontology which fits exactly the data mentio ned in this section .
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risk some speculative remarks.
1 96 According to Seuren, Ria's tallness is a [XJsitive extent, an extent beginning with 0 on the dimension of tallness (= T) and ending with some positive value n on T, whereas her shortness is t he rest of the dimension T, i .e., the stretch beginning with n and ending nowhere, since t here is no upper limit fo r tallness . Such an open-ended stretch is called a negative ex tent. (47)
t----+-- . . T .
n
0
00 Ria's tallnes
Her shortness
Let us write , as usual, A(x,e) for ''x is A to extent e". We can t hen define the relation o f antonymy A in t he following way : (49)
A(x ,-e) iff A(x ,e)
The idea is t hat A denotes short iff A denotes tall and similarly for other antonymous pairs. Thus, (50) is t he case iff (5 1 ) holds good : (50)
Ria is -tall
(5 1 )
Ria is <1 .50 m ,00>-short (=-t ifl)
Now, we express by "1 .50 m ", whereas we do not have a name fo r <1 .50 m,oo>. Generally, measure phrases always denote positive extents. Therefore, we cannot express statements that involve measures o f shortness like t h e starred version o f (43). What we have to do next is introduce an operation of concatenation or 'addition ' for extents. The idea is, that we can concatenate an extent to a positive or a negative extent only ''in the middle", because t here is no space left on t he left or the right end o f the relevant dimension parameter. It follows from this intuition that we can only concatenate a positive
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Let us call an (indexed) ordered pair of the form a positive extent. An ordered pair o f the form is a negative extent. Here, A stands for an appropriate adjective, indicating some dimension. The dimension index will mostly be ignore d . Only pairs o f t his form are extents. We can define negation ofpositive extents as :
197 extent with either a positive or a negative extent. I f w e were t o t ry to concatenate a negative extent with a negative one then the result would not be an extent . I nstead of elaborating a model from which these in tuitions follow I will simply describe the admissible concatenations : (52)
(!)
(53 )
@
=
(54)
Ede is 20 em (±) the e [ Ria is e-tall] -tall
Let us represent 20 em by <0 ,0.20 m>. Let us further assume that Ria's tallness is represented by <0 , 1 .50 m>. Then, (54) amounts to : (55)
Ede is <0,0 .20 m> (±) <0, 1 .50 m>-tall � Ede is <0,1 .70 m>-tall, by (52) � Ede is -<0 ,1 .70 m >-short , by (49)
(56)
Ede is <1 .70 m ,oo>-short , by (48)
Now, we know that : (57) Ria is <1 .50 m ,00>-short , since she is <0 , 1 .50 m>-tall From this and (56) it follows immediately that (58) holds good (by (53)): (58)
Ria is <0,0.20 m> 0 < 1 .50 m ,oo>-short
(5 8) is , however, t he meaning of (45)'s conclusio . This we wanted to show. Multiplication of extents is analyzed according to the same intuitions. This operation must be even more restricted. We carmot multiply a negative extent because the result would never be an extent : it would be too big or not even intuitively defmed . What remain s is multiplication of positive extents. And this operation is defmed in analogy to concatenation : (59)
8 n
: =
·
n>
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I assume that (±) is a symmetric operation. Notice, that (53) may be un defmed. This will happen if m is greater than n. This o ntology enables me already to account for the argument (45). Let us see how it works.
1 98
This accounts for the datum (43). As to the operation of division, it is obvious that it should not be d efmed for negative extents, because these are infmitely long stretches. On the other hand, it is obvious how it can be defmed for positive ex tents: (60)
Q n :
=
We express division linguistically by multiplicative statements, i .e., we analyse : (6 1 )
Alain is half as tall as Ria
(62)
Alain is
� 8 the e [Ria is e-tall] -tall
Formally, it is perhaps not very nice that t hese operations are not de fmed in a more uniform way. But formal elegance is not my concern at the moment . The o perations defmed here fit t he data exactly. It is clear that my remarks are only the crude outlines of an ontology of extents. But it seem s to me that an ontology along t hese lines, Seuren's lines, is on t he right track. It is obvious t hat I have not answered every question that Cresswell raised . For example, I have not said yet why we can concatenate extents of length and depth but not , say, length and intelligence. But, whatever anyone will say to this question, I hope t hat it is compatible with the view put forward here . 7. IN QUEST OF EXPLANATORY PRINCIPLES AGAIN
In the discussion, I have been following the practice common in linguistics. I started with the quest for explanatory principles and went straightaway to t he discussio n of details. Let me, therefo re, come back to the question of what the simple principles1 might be which could be integrated into a possibly explanatory , modular theory of grammar. The following are some hopeful candidates. First. More and -er mean (B , i.e. � e. the concatenation of extents. Second. as . . . as means 8 , i.e. the multiplication of extents or frac tions o f extents. Third. The source of NPis are downward entailing operators like at least o r M AX .
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as:
199 Fourth. Comparative and equative complements either denote pro perties o f degrees o r descriptions of degrees. These principles are very simple. The amazing complexity of com parative constructions arises, if we consider their interaction w ith other relevant principles of syntax and semantics. This is precisely w hat we would expect in a modular approach to grammar.
REFERENCES
and H. van RiemfJiijk. Foris Publications, Dordrecht. En((, M . , 1 9 8 1 : Tense without scope: A n analysis of nouns as indexicals. Unpu blished
PhD-dissertation, University of Wisconsin, Madison. Hoeksema, 1 ., 1 98 3 : Negative Polarity and t he Co mparative, Natural Language aoo L inguistic Theory 1 ; 403-434.
loup , G.,
1977:
Specifity and the interpretation o f quantifiers, Linguistics and
Philosophy 1 ; 2 3 3 - 4 5 .
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Bauerle, R., 1 9 8 3 : Pragmatisch-�mantische Aspekte der NP-lnterpretation, in M. Faust et a!. (eds.), Allgemeine Sprachwis:renschaft, Sprachtypologie u nd Text linguistik, Festschrift fii r Peter Hartmann, Tiibingen. Chomsk y , N., 1 98 2 : The Generative Enterprise. A discussion with R. Huybregts
