The Implicature Projector: No Problem!

The trouble with much of the argumentation you find by neo- rather than palaeo-Griceans is that it _confounds_, first, general problems_ (of the very existence of _generalised conversational implicatures_ as a species of inference -- and Grice's joke in calling these things 'generalised'), second, the alleged pragmatic intrusion into truth-conditions (cfr. Grice on quasi-demonstratives and his avowed 'artificial' sense of 'say'), third, the general nature of semantic representation ('logical form') before the alleged pragmatic enrichment, fourth, so-called 'metalinguistic' uses of operators like negation, finally, last but not least, the alleged

projection problem for implicatures.

And it confounds all this with the rather _specific_ difficulties associated with the English number words ("one, two, buckle my shoe").

The specific difficulties boil down to a few facts. But some scholars consider that there are a number of _other_ fatal flaws in the implicature account of numeral expressions. For example, Seuren (Western Linguistics, p.409) thinks that

1. Grice has exactly 2 children.

would then incoherently mean

2. ?Grice has exactly at least 3 children.

But the solution to this is given by Kadmon's PhD (ch.4) who shows how an
'at least' semantics is _compatible_ with modifiers like "exactly" (&
_non-redundant_ with "at least") within a Discourse Representation
Theory framework.

Essentially, Kadmon's solution works by treating '3 children' in

3. Grice has 3 children.

_like_ an _indefinite_ phrase: "3" introduces an _exact cardinality_, _but_, there is _no commitment_ that the _set_ of 'three children" is _exhaustive_ [cfr. Koenig's remarks on proper sets and improper sets in "Re: More Grice Bashing"]. Kadmon points out that such a view is compatible with any further constraints on interpretation that may arise from either:

i. predicative uses or

ii. rhematic positioning

An observation that has led other scholars, like Scharten -- in his PhD -- to abandon the implicature account)

It seems the non-implicature account is especially popular in Netherlands and
Belgium. Which is odd, since Levinson is now teaching in the Netherlands. Thus,
B. Bultnick, whom Tapper quotes in his post, has now supplied for the
LINGUIST listers the following review of Kadmon's book with Blackwell.

In math-literate cultures, there will be possible confusion bbetween
English "three" and the numeral "3", with a consequent _bias_ towards an
'exactly 3' interpretation for "three".

This may be associated with the fact that, in some cases, the number
words are associated with upper-bounding specifications that are _not_
easily defeasible (Kadmon 1984:30ff, Horn, Natural History, p.251). For
example, compare (20), which seems to stipulate "only one" with (21)
where the upper bounding implicature is more easily lifted:

4 Grice has 1 child

5. Grice has a child.

This may well be due however precisely to a Manner-Implicature ("be
brief (avoid unnecessary prolixity)") associated with that opposition.
Similarly, (4) more strongly suggests an upper bound than (5). Cfr.

6. I have $203.
7. I have $200.

which can again perhaps be attributed to a manner-implicature: to
bother to say "203" -- in English,

_"two hundred _and three_"

where the _shorter_

"two hundred"

alone _might_ be sufficient suggests that _there _is_ a
reason to be precise, and the speaker is acting in accordance with that
reason.

As Horn (Natural History, p.252) points out (see also Brown/Levinson,
p.258ff), all implicatures are potentially subject to a process of
_conventionalisation_, and the number words _may_ be under pressure to
_lexicalise_ the 'exactly' reading: Where 'three' is _lexically
incorporated_, as in

three-sided

triple

three-ply

triumvirate

no 'at least' reading is _possible_, (Horn, 'Neg-Raising', Atlas 1983) a
fact already clear in the ORDINALS, like

-- Karen was Grice's second child.

There are, perhaps, genuine differences in interpretive freedom
between
number words in different _syntactic_ and _thematic_ positions, as Atlas
1983, Kadmon 1987, Fretheim (essay in Kasher), Kuppevelt, and Scharten
argue, which might be expected if the "partial conventionalisation"
account is correct.

These four complicating factors are sufficient, I think, to
make the number words _not_ the correct test-bed for the whole theory of
scalar implicature (as, e.g. Kempson 1986:86 seems to suppose).

Horn
1992b:172-5 indeed _abandons_ the classic scalar approach to just the number
words, pointing out a number of _additional_ special properties. Still,
when due allowance is made for the special _role_ of number words in
math-literate cultures, and consequent possible conventionalisation of
the 'exactly' readings, there are a number of reasons to HANG ONTO A SCALAR
interpretation of ordinary language numeral expressions in general. One
central piece of evidence is provided by those languages that have a
FINITE series of numerals. Many Australian languages, for example, have just
_thre_ number words, which are glossed as "one", "two", and
often "three".

The scalar _prediction_ is clear in these cases: we have a finite scale:
or the perfectly Gricean scale:

(35) Guugu Yimithirr

not all).

Thus, although in these discourse contexts an implied contrast is
required, the 'at least' interpreation fails to come to mind for both the cardinal
and the quantifier case, where it would be most relevant. This suggests
that in both cases there is a generalised conversational implicature
biasing interpretations in the same direction, regardless of the
different discourse biasing (a pattern impossible to account for in a
nonce-inference account)."