Talk by Fred Landman
Degree Relatives
Carlson 1977 observes the difference between (1) and (2):
- (1)
- #I took with me every book which there was on the table.
- (2)
- I took with me every book that there was on the table.
In (1), the trace of the relativizer which is in a there-insertion context and (1) is
infelicitous, (2) is the same as (1), except that (2) has relativizer that (2) is
felicitous. Furthermore, Carlson notes that sentences like (2) are only felicitous if the
determiner is every or the. (3) I took with me every book/the books/the three books/#some
book/#three books/#most books/#no book that there was/were at the table. Carlson, and,
following him, Heim 1987, have a nice explanation for the facts in (1)-(2). They assume
that which-relatives involve abstraction over an individual variable, while that-relatives
can involve abstraction over a degree variable. (1) has infelicitous interpretation (1a):
individual variable u is bound by existential quantification in the there-insertion
context (the definiteness effect), but then the set abstractlon is vacuous.
- (1a)
- # BOOK n {u s u: Eu: OT(u)}
In (2), the relative clause denotes a set of degrees, rather than a set of individuals, the
headnoun book is interpreted as a sortal inside the relative clause. (2) involves a
degree-function d from plural individuals (sums) to numbers such that Vu E $ SUM ¡(u)= |
u|. The there-insertion context binds an individual variable, but the abstraction is over a
degree variable, which is not in a position that the definiteness effect applies to. That
is why (2), as a degree relative, is ok:
- (2a)
- {d E DEG: 3u E *BOOK: o(u)=d A OT(u)}.
While we think that this explanation is right in essence, there are two serious problems
with it.
- 1.
- the analysis has nothing to say about the facts in (3).
- 2.
- Carlson und Heim assume that the degree relative denotes a
set of numerical values (this is why the headnoun is interpreted inside).
This predicts that at the level of the sentence only those degrees, but crucially not the
entities that they are degrees of are available. This predicts that degree relatives can
only get a pure degree interpretatlon. Heim claims that this is exactly what we find: (4)
does not express (5), but (6):
- (4)
- It would take us the rest of our life to drink the wine
that she spilled at the party.
- (5)
- The wine that she spilled at the party is the wine that
it would take us the rest of our life to drink.
- (6)
- The amount of wine that se spilled at the party is
the amount of wine that it would take us the rest of
our life to drink.
We will argue that this is a wrong prediction.
Heim's example involves a special interpretation, which is available in certain cases,
often sentinces involving a modal or a generic element, or certain other cues, but this
degree interpretation is normally not available at all. For instance, (2) means that I
took the actual books on the table, not the same amount of books as there were on the
table. Thus Carlson and Heim's analysis makes the right predictions concerning the felicity
of (2). but assigns it a wrong interpretation.
We will propose an alternative analysis that deals with these two problems. Our analysis
incorporates the main insights of Carlson and Heim. In particular, we assume that (2)
involves abstraction over degrees and that the headnoun is interpreted internally. We
present our analysis by describing how the degree-relative DP in (2) is build up. Up to the
CP level, we build up the same semantic representation as Carlson and Heim, (2a). But our
ontology is different: we assume that degrees do not lose the information about what they
are degrees of: a degree is a pair of a plural individual and its numerical value n in N:
- d: SUM -> SUMxN such that for every u e SUM: d(u)=< u, |u| &rt;.
Of course, that makes no difference for the explanation of why (2) is ok, while (1) is not.
Here we make the same predictions as Carlson and Heim.
We can simplify (2a) to (2b):
- (2b)
- {<u, |u|&rt;: u e *BOOK A OT(u)}
A second plank of our theory is the assumption that degree relatives contain an implicit
operation. MAX, of maximalization of degrees, which takes place at the CP-level. Support
for this operation can be found in other degree constructions as well (MAX licences
polarity items in sentential comparatives (Hoeksema 1983), and ever in free relatives). MAX
is given by:
- MAX(D) = {d E D: Ve E D: [d]2 ³ [e]2}
(where D is a set of degrees, [d]2 is the second element of d).
Except in cases where the relative clause contains a modal element, the interpretation of
degree relatives after maximalization will be a singleton set, (2c):
- (2c)
- {&\t; U{u e BOOK: on the table(u)},t |U{u e BOOK:OT(U)}l|&rt;}
or shorter: {<U{u e BOOK: on the table(u)}, max&rt;}.
At the NP-level, the headnoun is already interpreted downstairs. Here one of two
operations take place. The default operation is DOMAIN, giving the normal interpretation
of the relative clause as a set of sums of individuals (the domain of our set of pairs).
Under special condition, we may get Heim's interpretation, by applying the operation RANGE.
In the normal case, then, we get as the interpretation of the noun-relative clause complex:
- (2d)
- {U{u E BOOK: on the table(u)}},
where |U{Ue BOOK: on the table(u)}| = max
(2d) is a set of sums of individuals, not a set of numerical values. We will show that this
solves problem nr. 2. Problem nr. 1 ls solved by what happens above the NP node. We will
argue that in degree relatives, numericals can only specify max, not restrict the NP (as
they would do usually). Using Bittner's 1994 semantics for OPs, we will show that MAX is
incompatible with weak determiners. For the remaining strong determiners, we will show
that the only strong determiners that preserve the information that is specified by max in
the NP meaning are every and the. A constraint that max needs to be preserved in the DP
meaning will then predict the facts in (3).
Finally, we will extend the discussion to some related phenomena concerning event-
relatives.
(This lecture presents joint work with Alexander Grosu.)
Paul Dekker, November 2, 1995