LINGUIST List 2.571

Fri 27 Sep 1991

Disc: Compositionality

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1. Paul Saka, RE: compositionality; disjunctions
2. Geoffrey Russom, Re: 2.554 Compositionality

	In a recent posting I claimed that we cannot represent
the meaning of an ambiguous expression E as a set of readings
{M1, M2...}. This has provoked two respondents to ask
why we can't interpret "{M1, M2}" as a disjunction rather than
as a conjunction [LINGUIST 2.551]. Here is my answer.
	My original formulation was cast so as to sound like
readable English rather than hair-splitting logic, but I guess
I simply ended up creating confusion. In ordinary language
(altho not in academic logic), the expression "the set {M1, M2}"
is ambiguous between a collective reading and a distributive
reading.
	In neither sense can we say that the set {M1, M2}
is the meaning of E.
	In the collective sense, if we say that {M1, M} is
the meaning of E, then we say that the meaning of E is a
set, a SINGLE abstract object which itself contains two
different meanings. But this is precisely what we want to avoid
because, pre-theoretically, ambiguous expressions are just
those expressions that possess MORE than one meaning. Further,
this proposal implies that M1 and M2 are ontologically different
from {M1, M2} -- that they are different kinds of thing. Either
M1 and M2 are not meanings, which is contrary to the stipulated
hypothesis; or {M1, M2} is not a meaning.
	In the distributive sense, to say that {M1, M2} is
the meaning of E is the same as saying that the ELEMENTS of
{M1, M2} are meanings of E (cf "the set of green things is/are
colored"); which is just to say that EACH element of {M1, M2}
is a meaning of E, ie M1 AND M2 are meanings. This follows
from the very concept of set.
	Margaret Fleck says that AI people treat sets as having
disjunctive significance. What I suspect is going on is the
following. Let us suppose that you specify set A = {a, b, c}.
Then you can command: "if x is an element in A, print YES;
otherwise print NO." The result is the same as commanding:
"if x=a OR x=b OR x=c then print YES; otherwise print NO."
But this doesn't really mean that the curly brackets signify
disjunctions; it is still the case that a is a member of A
AND b is a member of A AND c is a member of A. If AI people
are TRULY using curly brackets to signify disjunction, then
they are not really talking about sets.
	In response to Robert Goldman:
>What makes it difficult to have "a theory that says an ambiguous
>expression means M1 OR M2?"
My INITIAL point was only that it is difficult for those theories
which assume COMPOSITIONALITY. But since you ask, I believe that
that point holds for all truth-conditional theories: unless you
talk about speech-acts, there is no way to distinguish between
the disjunction of ambiguity (E sometimes means M1 and sometimes
M2) and the disjunction of uncertainty (the translator thinks
that E always means M1 or always means M2, but isn't certain
which). For further details on this, please write to me.

Message 2: Re: 2.554 Compositionality

In a discussion of English compounds, Laurie Bauer has pointed out that
one cannot divide them tidily into "lexicalized" and "non-lexicalized"
categories. Some compounds are lexicalized semantically
(having a meaning not predictable from the meanings of the parts) but
not phonologically (retaining full stress on the root syllable of the
second constituent). In other cases compounds can be lexicalized
phonologically even though the secondary constituent seems to retain its
semantic identity. Aren't idioms also matters of degree, even from
a synchronic point of view? The journey from phrasehood to wordhood
is one that involves several stages, and it seems best to concede the
native speaker an ability to deal with intermediate forms in which,
for example, elements partially or wholly drained of semantic content
retain syntactic identity. Undergraduates in critical theory classes
frequently use, under more or less appropriate conditions, phrases
containing words they don't understand at all well. The claim that
a phrase is either an idiom or not would appear to presuppose that
we usually know exactly what we're talking about, whereas it seems
that we usually don't (ordinarily, for example, people learn words from
context rather than looking them up in a dictionary and memorizing
their meanings perfectly). The study of idioms may be one area in
which strong idealization to an ideal speaker-hearer (of the sort
useful in syntactic theory) begins to cause more problems than it
avoids.
 -- Rick Russom