Intermediate syntactic meaning
Andreas Nolda
andreas.nolda at CMS.HU-BERLIN.DE
Tue Jan 11 20:56:51 UTC 2005
Dear IL-List subscribers,
I would like to draw your attention to some shortcomings of the
conception of intermediate syntactic meanings and to propose a
partially different conception for them.
According to Lieb (1983, chap. 19 and 20), intermediate syntactic
meanings typically are of the same formal type as basic syntactic
meanings: they are pairs <Z, b>, with b being an n-place potential
concept and Z being an m-place 'contextualization set'. Let us
consider two examples, taken from (Lieb 1983).
First example. The intermediate meaning for _american student_ is (1)
("e" and "i" denote the element relation and the intersection
operation, respectively; "V" typically stands for an utterance from
the point of view of the linguist and "V1" for a speaker from this
point of view; as a rule, numerical indices are to be read as
subscripts):
(1) <Z1, .american student.>
where
(2) Z1 = {<x, V, V1> |
x e reference-basis(_american_, V, V1, .american.)
i x e reference-basis(_student_, V, V1, .student.)}
The intension of .american student. is defined as the union of the
intensions of .american. and .student..
Second example. The intermediate meaning for _in London_ is (3) ("A"
denotes the universal quantifier):
(3) <Z2, .in London.>
where
(4) Z2 = {<x, V. V1> |
A x1 (V1 refers by _London_ in V to x1
-> <x, x1> e reference-basis(_in_, V, V1, .in.))}
The intension of .in London. contains the intensional relation (5) as
its only element ("L" denotes the lambda-operator):
(5) L x V V1: A x1 (V1 refers by _London_ in V to x1
-> <x, x1> e extension(.in.))
Now, (5) is a 'hybrid' relation as far as the ontologies the arguments
are taken from are concerned: it relates one entity of type x from
the speaker's ontology to two entities of type V from the linguist's
ontology. When we assume that such a relation (of type d) is contained
in the intension of a concept, we have a problem. Recall that
according to the definition of "(potential) concept" (e.g. Lieb 1983,
208 f.), the elements in the intension of a concept are part of the
content of a perception or conception. According to Lieb (1983, 210),
"we may then require that every speaker of idiolect system S _has_
the non-empty concepts that are lexical meanings in S". Thus, the
elements of the intension of a potential concept should involve
entities from the speaker's ontology only.
This problem was already pointed out in the IL colloques (e.g. Lieb
1999/2000, SS 2000, 36). As a remedy, Lieb proposed to replace
intermediate syntactic meanings like (3) by single intensional
relations like d1 in (3'):
(3') d1 = L x V V1: (V1 refers by _London__ in V to x1
-> <x, x1> e reference-basis(_in_, V, V1, .in.)
i extension(.in.))
In other words, the pair <Z1, .in London.> is collapsed into d1.
This change also solves an empirical problem with Lieb's (1983, 318)
semantic analysis of example (6), where _in London_ occurs as a
prepositional object:
(6) _The student has arrived in London._
According to him, the proposition for (6) is the following intensional
relation ("E" denotes the existential quantifier):
(7) L V V1: A x1 (V1 refers by _the student_ in V to x1
-> E x (a. <x, x1, Z2(-, V, V1)>
e reference-basis(_has arrived_, V, V1,
.arrive.)
b. <x, x1, extension(.in London.)(-, V,
V1)>
e extension(.arrive.)
...))
Formulae of the form "M(-, V, V1)" abbreviate "{x | <x, V, V1> e M}".
The problem with (7) concerns condition (7 a). The set Z2(-, V, V1)
contains, according to (4), all first components of pairs consisting
of x and the referent of _London_ such that the pair is an element of
the reference basis for .in.. A pair is in the reference basis for
.in. if the speaker V1 is willing to assume that '.in. applies to it'
or to assume that '.in. does *not* apply to it'. Thus, in a given
utterance situtation, Z2(-, V, V1) will typically contain a large
number of spaces in London as well as of spaces which are *not* in
London.
Now, it is quite probably that the triple <x, x1, Z2(-, V, V1)> is not
at all an element of the reference basis for .arrive.: the 'monster
set' Z2(-, V, V1) may be simply too large for V1 to consider it. This
effect, however, is not intended. Therefore, the contextual
restriction by condition (5 a) is too strong. (As far as I know, that
problem has not yet been noted anywhere.)
Note that this problem does not arise when (3) is replaced by d1:
(7') L V V1: A x1 (V1 refers by _the student_ in V to x1
-> E x (a. <x, x1, d1(-, V, V1)>
e reference-basis(_has arrived_, V,
V1, .arrive'.)
i extension(.arrive'.)
...))
Here, "d1(-, V, V1)" denotes not a set, but the corresponding property
"L x: <x, V, V1> has d1". (As we are now relating a property --
instead of a set -- to the verbal concept, we also have to replace
.arrive. by its intensional variant .arrive'.)
There is no problem with (7') because the set of entities to which
d1(-, V, V1) applies is much smaller than Z2(-, V, V1): d1 is a
property of spaces in London only.
Alas, d1 cannot generally be substituted for <Z2, .in London.>.
Consider the following example, where _in London_ functions as a
non-complement modifier of a referential expression's nucleus:
(8) _The hotel in London was splendid._
Presupposing d1 as the intermediate meaning for _in London_, the
existential-doxastic referential meaning for _the hotel in London_ in
(8) would run as follows:
(9) L V V1: a. E! x (V1 refers by _the hotel in London_ in V to x)
b. A x (V1 refers by _the hotel in London_ in V to x
-> (x e reference-basis(_the hotel_, V, V1,
.hotel.)
& x has d1(-, V, V1)))
c. ...
d. V presupposes that:
A x (V1 refers by _the hotel in London_ in V to x
-> (x e extension(.hotel.)
& x has d1(-, V, V1)))
As can be seen from (9), "d1(-, V, V1)" occurs twice. In addition to
the presupposition in (9 d), it reappears in (9 b) outside of any
presuppositional context. (9 b) should involve only reference bases or
contextualizations, though. d1, however, also involves the extension
of .in.. As a consequence, (9 d)'s presupposition that x has d1(-, V,
V1) is invalidated.
In view of these problems with the conceptions of Lieb (1983) and Lieb
(1999/2000), I'd like to propose the following solution. _In London_
has an intermediate meaning of the following sort:
(10) <Z2, d2>
where
(11) d2 = (5)
If _in London_ is used as a modifier, the components of its
intermediate meaning can be processed separately. Consider, for
example, the revised existential-doxastic referential meaning for
_the hotel in London_ in (8) is (9'):
(9') L V V1: a. E! x (V1 refers by _the hotel in London_ in V to x)
b. A x (V1 refers by _the hotel in London_ in V to x
-> (x e reference-basis(_the hotel_, V, V1,
.hotel.)
& x e Z2(-, V, V1)))
c. ...
d. V presupposes that:
A x (V1 refers by _the hotel in London_ in V to x
-> (x e extension(.hotel.)
& x has d2(-, V, V1)))
If _in London_ is used as a complement, the components of (10) are
'fused' into a set (or a property), as, for instance, in the the
proposition of (6):
(7'') L V V1: A x1 (V1 refers by _the student_ in V to x1
-> E x (a. <x, x1, M>
e reference-basis(_has arrived_, V,
V1, .arrive.)
i extension(.arrive.)
...))
where
(12) M = {x2 | x2 e Z2(-, V, V1)
& x2 has d2(-, V, V1)}
Andreas Nolda
References
Lieb, Hans-Heinrich (1983). _Integrational Linguistics_. Current
Issues in Linguistic Theory 17. Amsterdam: Benjamins. Vol. 1:
_General Outline_.
Lieb, Hans-Heinrich (1999/2000). Integrative Sprachwissenschaft: Der
Sprechaktaspekt in der Integrativen Sprachtheorie. Authorized minutes
of a colloquium at the Freie Universität Berlin in the summer
semester 1999, the winter semester 1999/2000, and the summer semester
2000.
--
Andreas Nolda http://www2.hu-berlin.de/linguistik/institut/nolda/
Humboldt-Universität zu Berlin
Philosophische Fakultät II
Institut für deutsche Sprache und Linguistik
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