One, Two, Buckle My Shoe: Grice on numerals

Absolute cardinality. L. M. Tapper is not pacified (but then he would _not_
be, would he) by the attempts and considerations for serious pragmatic
analysis provided by that important philosopher (I am elongating this
sentence because it's silly for "Speranza" to feature in the first line of
a post by ME) called "Speranza".

Murphy writes (in reply to Larry Tapper's inability to understand the
meaning of _three_). Interesting. Now that I have access (because I bought it) to Levinson's _Presumptive Meanings: The Theory of Generalised Conversational
Implicature_, MIT, 2000, paperback, 480 pages) (I collect books with 'implicature' in their title) I think I learned what numbers mean. One example (due to my brother, J.J. Speranza -- and zillion linguists, such as Stubbs.

1. A: What month has 30 days?
B: All (except February?)

Levinson discusses this (although he fails to attribute it to my brother).
Re: Murphy example I think we have to distinguish between

2. A: Bobby [as the Early Larry was called]
Tell me something true about the things you see
on the table
B: There are three apples.
A: Good. Try now something slightly more interesting.
B: Like what colours they are?

versus:

3. A: Tell me the _exact_ (or "optimally informative" if you
will) cardinal as it applies to the number of apples on
the table, and be maximin optimim informative.
i.e. in other words, I want to know if you can tell me
the TOTAL number of fruits you see on the table, Bobby.
It's for some IQ thing, Bobby.
B: Three.
A (to psychiatrist). Did you take notice of _that_?
Psychiatrist: I did, sir.

I'm appending what writes about this -- Boultinck being a Dutch linguist
discovered by Tapper on --

http://ccat.sas.upenn.edu/~haroldfs/dravling/levinson.html
(see Tapper, "Grice Lessons", THIS FORUM).

Boultinck writes:

"The cardinal numerals are actually the best example to demonstrate the
terminological and conceptual-architectural confusion that is unavoidable
if empirical data are disregarded to the advantage of a largely theoretical
and highly debatable distinction between truth-conditional semantics and
Gricean pragmatics. LR Horn has actually admitted that his classical
Gricean treatment of the cardinal numbers (Horn 1972, 1989) runs into
trouble, and subsequently restricted his neo-Gricean approach to other
scalar items (Horn 1992). Also Levinson argues that "the number words [are]
not the correct testbed for the whole theory of scalar implicature" (p.90).
Nevertheless, the numerals figure prominently in the evidence that Levinson
presents for a number of claims. In his discussion of indexical resolution
(p.178), ellipsis unpacking (p.183), the conditional (p.206),
metalinguistic negation (p.213), negation in general (p.255), and Sag's
model for pragmatic intrusion (p.247) the numerals are called upon to
demonstrate certain allegedly Gricean phenomena. In this line of thinking,
numerals like three have 'at least three' as literal, "semantic" meaning
and the 'exactly three' interpretation is the result of a Gricean
Q1-implicature. This concrete example makes the question that was posed in
general terms above even more acute: where does this 'at least'-meaning
come from? Corpus data reveal that "bare numerals" as in

4. John has 3 children

always have 'exactly'-interpretations. It is not economical to explain this
meaning via a scalar implicature that transforms the "actual" 'at
least'-meaning into an 'exactly'-meaning, if this supposedly happens every
time. If generalized conversational implicatures are so general that they
occur every time, it is simpler to accept the 'exactly'-reading simply as
the meaning of numerals. The data are overwhelmingly against 'at
least'-meanings, to the extent that this 'at least'-meaning can only be
expressed when the language user explicitly modifies the numeral by using
the phrases

5. _at least_ 3

6. 3 _if not more_

etc. The monotonicity phenomena that are deemed so central can thus be
easily explained as nuancing or correction phrases". Of course Speranza
disagrees with this. (Since Levinson's chapter III is about anaphora and
I'm currently devouring his book, I've started to refer to myself in the
third person to avoid anaphoric problems for the non-Gricean).

Enough to want to say, 'buckle my shoe' and skip the 'one, two'.