Grice as essentially monist

By JLS
--- for the GC


"Two Gricean mathematicians meet in the street"

A: What is 2 + 2?
B: 27
A: Correct."

This contradicts S C Levinson,
_Presumptive Meanings: The Theory of Generalised Implicature_. MIT Press.

It's Section 2.2.2.2.2: The Number words.

Contextualisation. The nice result, "2.2.2.2.2" is: Ch. 2: the phenomena.
Section 2:

Grice's second submaxim of quantity: do not be more informative
than is required.

Subsection 2: L. R. Horn's "entailment" scales.

Sub-sub-section 2: "entailment scales over NON-Logical predicates" (I find
this controversial, since, as G. Koenig has pointed out, "3" _is_ a logical
predicate in that it can be defined only in terms of (Ex) and "=").

Sub-sub-sub-section 2: the number _words_.

Levinson speaks of _words_ here
since he's trying to argue that "3" is _not_ a word. "Three" is. Levinson
writes: "The Number Words. One kind of scale that has exercised analysts is
that formed by the _infinite_ series of number words or numerical
expressions in English, viz:

(4) <...,5,4,3,2,1>.

L. R. Horn (in "The Properties of Logical Operators in English" UCLA PhD,
distributed with the Indiana Club) assumed that the numerical expressions
should fall within his scalar approach. Thus, an assertion,

(5) John has 3 children.

should implicate, but not _entail_

(6) John has _no more_ than 3 children.

In general, the reasons for assuming that there _is_ such a scale in
English with corresponding generalised conversational implicatures still
seems good. The assertion of (5) would have the semantic content (or
truth-conditions) paraphrased in (7):

(7) John has _at least_ 3 children.

(the lower-bound "at lest 3" is entailed -- (such a paraphrase is _not_ of
course an _analysis_ of the relevant _semantic representation, which might
be formalised in various different ways) ((cfr. at this stage the version
proposed by G. Koenig:

(8) (Ex)(Ey)(Ez). CHILDx & CHILDy & CHILDz & x/=y &
x/=z & y/=z and John has Them.

--and the generalised conversational implicature (8):

(9) John has _at most_ 3 children.

-- the upper-bound is _implicated_, as in scales generally. The normal
suspension tests apply, as in:

(10) John has 3 children, if not 4
(11) John has 3 children, & perhaps more.
(12) John has 3 children, or possibly 4.

which shows that the content of (9) can_not_ be _entailed_. Also, in the
right context, where an _exact_ specification is _irrelevant_, the
impicature is _implicitly_ cancelled, as in:

(13) A: Does John qualify for the Large-Family Benefit?
B: Sure: he has 3 children all right.

Despite these attractions, there are a number [how many? JLS] difficulties
with a scalar approach to the number words.

1. Mathematics would be in danger (Sadock). When we assert

(14) The square root of 9 is 3.

we do _not_ "_mean_"

(15) The square root of 9 is _at least_ 3.

Otherwise, we could as well say

(16) The square root of 9 is _2_.

Special conventions are in force, of course. and we may want to distinguish
sharply between i and ii:

i. natural language numerical expressions

ii. cardinal numbers.

(Atlas 1993, Pragmatic analysis: Logic, meaning, and conversational
implicature, Oxford UP, ch. 2).

2. Horn (in his PhD) himself drew attention to the fact that in certain
_specific_ circumstances, the scales could be _inverted_. For example in
tallying golf scores, where the _higher_ score is the _lesser_ number one
might _felicitiously_ say:

(17) John can do the round in 72, if not 70.

This possibility of scale reversal does _not_ appear to arise with other
quantifiers (Sadock, p.143), and indeed otherwise seems restricted to
pragmatically defined scales. This raises the general issue of the extent
to which all scales are in the last resort pragmatic in nature, an issue I
address at a later stage. [his discussion of J Hirschberg's _ranks_: e.g.
based on the fact that P. Newman is more famous than J.
Woodward, discussed in my 'Themes from Grice', THIS FORUM]. But this
possibility of scale reversal, coupled with the fact that the implicature
can evaporate in contexts like (13) -- the Large Family Benefit context --
has led some analysts to abandon the scalar approach to numerical
expressions. One position is to claim that the number words are just
_ambiguous_ between an 'exactly' reading and an 'at least' interpretation,
perhaps disambiguated in specific linguistic contexts. For example, an
'exactly n' when acting as _determiners_ (see Kempson, Presupposition. This
is Kamp's position reported in Kadmon). But the prospect of _infinite
ambiguities_ not only here but then elsewhere too is very _unattractive_
(especially compared to the scalar approach where the two _uses_ of numeral
expressions follow from _general properties_ of any scalal series
whatsoever). Another approach is to assume that the meaning of, say, _3_ is
simply _indeterminate_ at the _semantic_ level between 'at least 3' and
'exactly 3', and is then further _specified_ by a _particularised_
conversational implicature in context as appropriate, or perhaps restricted
by semantic constraints in particular constructions. Thus, Atlas
(Ambiguity) suggests that _collective_ noun phrases have the 'exactly'
interpreation. Kempson 1986 and Atlas 1993b take this approach but for
different reasons: Kempson because she wishes to reduce generalised
conversational implicatures to _particularised_ conversational implicatures
compatible with relevance theory. (She also introduces the issue of
examples like:

(18) He doesn't have *_3_* children. He has _4_.

rejecting Horn's account in terms of metalinguistic negation. These issues
are taken up later [I note that Tapper has identified this manoevure by
Horn: put the blame on _meta-linguistic_ negation, if you _must_]). Atlas,
because he wishes to assimilate the _unspecified_ nature of cardinal
semantics to his account of "not" which has a similar property. Carston
(UCL MS) took a similar line, arguing that "3" is semantically
_unspecified_ between _3_ readings:

i. at least 3

ii. at _most_ 3 (as in the reverse scale case above)

iii. _exactly_ 3

particular contexts being responsible for our understanding in each case.

The trouble with much of this argumentation is that it _confounds_

A. _general problems_ (of the very existence of _generalised
conversational implicatures_ as a species of inference),

B. pragmatic intrusion into truth-conditions.

C. the general nature of semantic representations
before pragmatic enrichment.

D. so-called metalinguistic negation.
and

E. the projection problem for implicatures with the rather _specific_ difficulties associated with the English number words. The specific difficulties boil down to the following facts:

(Note: 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 'John has exactly 3 children'
would then incoherently mean

(19) ?John 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
(5) "John 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) ((INTERLUDE. by JLS. 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. Review
appended below))).

1. 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".

2. 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:

(20) He has 1 child

(21) He has a child.

This may well be due however precisely to a Manner-Implicature ("be brief
(avoid unnecessary prolixity)") associated with that opposition. Similarly,
(22) more strongly suggests an upper bound than (23):

(22) I have $203.
(23) 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.

3. 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

(24) three-sided

(25) triple

(26) triple

(27) three-ply

(28) triumvirate

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

(29) _fourth_ prize.

I discussed this with Horn! and wasn't I convinced. Our topic then was

(30) "bisexual"

Being the libertine I am, I tried to show Horn how this meant

(31) homosexual.

My argument: "if you are a bisexual, you are a homosexual". Horn pointed
out to me that the scale would then be symmetrical: "if you are a bisexual,
you are straight". I said mmmpff, and we decided that I was a _purist_:
i.e. one _minimal_ homosexual orientation and you are bisexual. Same, he
said, with some racists in USA who say that if you have _one_ drop of Black
blood, you are _black_. His point was however, that while

(33) John is attracted to men & John is attracted to women.

_does_ entail (via a Horn scale)

(34) John is attracted to men.

(and he would be, in my book, a homosexual) ("But then, what IS your book?" Horn asked). Horn noted that "bisexual"
lexicalises -- he said "semanticises" as I recall, see below -- the
_double_ inclination. Like "bicycle", he added -- a word he had dealt with
in his PhD. His reply in appendix II]

4. 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 [my conversation
with him was later, so I'm not the one to blame! JLS] 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


where 'one' or 'two' will implicate, _ceteris paribus_, an upper-bound.
But, because there is no stronger item, "four", the cardinal "three" shuold
LACK this clear upper bounding by generalised conversational implicature.
And this is clearly the case in, for example, Guugu Yimithirr: "nubuun" can
be glossed "one"; "gudhirra", "two", but "guunduu" _must_ be glossed "three OR MORE, a few"

(These data are from my own field notes, but independent confirmation can
be found in the glosses of Haviland, p.176). And this is the general report
(Dixon, p.108). Finally, Cruse, p.69-70 points out that by certain tests
for the better establishment of one sense over another, the 'exactly'
interpretation of the Engish number words are psychologically more
_salient_ than the 'at least' intepretations and by the same tests it can
be seen that this corresponds with the favoured interpretations of the
quantifiers (those with doubts about the very existence of generalised
conversational implicatures mayfind this bia interesting)(Compare (38)
where in B 's utterance the cardinal has the normal generalised
converational implicature, which thus contrasts, rhetorically, with A's
utterance which lacks; with (39) where B's utterance still has the
generalised conversational implicature despite the fact that an 'at least'
interpretation would contrast better rhetorically but is _obscured_ by the
generalised conversational implicature:

(36) A: I could earn at least $10 there.

B: Well, you will earn $10 dollars.
(+> no more than $10)

(37) A: I could earn only $10 there.

B: Well, you will earn $10 here.
(+> no more than $10).

A similar pattern holds for the classic scalar implicatures:

(38) A: He stole at least some of the money there.
B: Well, he stole some of the money here.
(+> not all)

(39) A: He stole only some of the money there.
B: Well, he stole some of the money here
(+> 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)."

===

APPENDIX I: B Bultinck's review of N. Kadmon. Formal Pragmatics:
Semantics, Pragmatics, Presupposition and Focus. Blackwell, 2001. "This is a major contribution to the nascent field of formal pragmatics. I will not summarize each of the 21 chapters. I will limit myself
to _one_ discussion of a specific problem presented in the book, namely
her discussion of numeral determiners in NPs. The interpretation of numeral
determiners is one of hotly debated subject in the
last three decades of pragmatics and it is no exaggeration to say that
Kadmon offers the most convincing analysis of numerals that is available
today. Criticizing Horn's original (1972, 1989) analysis
of numerals in terms of an 'at least' semantics and an 'at most'
implicature as well as Kamp's analysis starting from an 'exactly' meaning
of numerals, she proposes that the difference between "3 cats" and
"at least 3 cats" lies in the scalar implicature, which may be created by
uttering the first, but not the second. The difference with Horn's account
is subtle, but crucial. because Kadmon treats noun phrases
with numeral determiners just like indefinites of the form a CN (Common
Noun) the 'at least' meaning that is postulated by Horn as the meaning of
the numeral itself, arises as the consequence of an existential operator
ranging over the whole discourse, and not just over the numeral. The
advantage of Kadmon's approach is that it is no longer necessary to accept
counter-intuitive 'at least' meanings for numerals, while her approach
still manages to explain crucial arguments in favour of such an 'at least'
analysis (e.g., the combination of negation and numerals). Even if Kadmon
does not state this very explicitly, her analysis leads to the powerful and
intuitively acceptable claim that numerals have 'absolute value' semantics
and that all sorts of phenomena (grammatical, such as the English
restrictors, as well as pragmatic, such as discourse positions) can alter
this basic meaning. Throughout this book, she shows that she is aware of the
overwhelming importance of contextual influence on meaning creation, and
also in her discussion of numerals she rightly points out a number of
common sense reasons why numerals almost invariably appear to have
'exact' semantics.

APPENDIX II.

Horn's intuitions in favour of a partial English
conventionalisation. Horn writes ('The Diaries of JLS"):

"My _intuition on
this one_ [Note his unrefutable appeal to his intuitions. It was a blessing
to find L. M. Tapper whose intuitions are more intuitive to me than Horn's]
is that 'John is bisexual' does _not_ entail 'John is homosexual',
although having sex (or having the disposition/orientation/preference to
have sex) with those of members of one's own and/or members not of one's
own sex does indeed entail having sex (or having the
disposition/orientation/preference to have sex) with members of one's own
sex. That is, if John is oriented toward sex with men and women, he's
oriented toward sex with men, but if John is a bisexual, it doesn't follow
that he's gay/a homosexual. Essentially, these latter terms semanticize the
"only" that may be implicated by saying "John is oriented toward (or has
sex with) {only} men." To be gay, or of course het, you must have an
orientation to exactly one sex; to be bi, it must be to exactly two. This
is not unique; as discussed in my PhD, a bicycle is not a vehicle with two
wheels (and possibly three), or with at most two (and possibly one)-- it is
a vehicle with EXACTLY TWO wheels. Unicycles and tricycles don't count. In
the same way, a bisexual must be oriented toward members of EXACTLY TWO
sexes (not one or three). There are really two issues to disentangle here,
though; it could be the case that while there is no scale
as such, it might be maintained that "bisexual" outranks "gay" in strength,
as "general" outranks "lieutenant" (although a general isn't a lieutenant)
or "full house" outranks "flush" (although a full house isn't a flush) or
"full professor" outranks "assistant professor". The following diagnostics
(again, using my own intuition) come into play here:

[SCALES]

(1)a. Not only is it warm, it's hot.
b. #Not only she an assistant professor, she's a full professor.
c. #Not only is she a lieutenant, she's a general.
d. #Not only is she gay, she's bisexual.

[RANKS]

(2)a. It's not just warm, it's hot
b. He's not just an assistant professor, she's a full professor.
c. He's not just a lieutenant, he's a general.
d. %He's not just gay, he's bisexual.

While being bisexual doesn't entail being gay (the way being hot entails
being warm), there are contexts in which being bisexual is like
being-gay-only-more-so (the way being a full professor is like being
an-assistant-professor-only-more-so). Consider the attitude of a Christian
right-winger--call him Pat--for whom homosexuality is a sin, but
indiscriminacy is even more perverse (in that at least homosexuals are
consistent). Not inconceivable, right? So for such a Pat, someone who
conforms to (2d) is particularly reprehensible. But by the same token, I
could imagine another right-winger -- call him Dan -- who believes that
"homosexuality is a choice, and it's the wrong choice, and that therefore
homosexuals are worse than bisexuals, who at least some of the time get it
right. For Dan, (2d) would be nonsensical, but (2d') would be perfectly
plausible as grounds for consignment to perdition (Maybe "gay" wouldn't be
the label of choice, but that's a different issue. (2)d'. %He's not just
bisexual, he's gay. Of course, we could equally well imagine someone with
the opposite political ideology; the point is that it's the context that
determines which attribute outranks the other (Hirschberg deals with
similar cases, though not with this one.)"

===

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