Grice on 'some' and 'all'

--- by JLS
----- for the GC

The best way to explain a scale (as per Urmson, '', is via the natural numbers. There being a scale

<4,3,2,1...>

i.e. If I say I have three children I implicate that I don't have four.

A good reference here is Noel Burton-Roberts, "Modality and Implicature".
Linguistics and Philosophy 7 181-206 (1984).

Horn's refs include his early "Greek Grice: a history of protoconversational rules in the history of logic". Chicago Linguistics Society, and his later, "Why Gricean inference is Gricean". The Grice Legacy. Berkeley Linguistics Society, 16th Annual
Meeting, ed. K. Hall.

Horn writes in the Berkeley proceedings:

"It is by now widely accepted that the Gricean mechanism for the generation
of generalised conversation thru the exploitation of the maxim of quantity
("Make your contribution as required for the current purpose of the talk
exchange") PROVIDES A NATURAL ACCOUNT OF WEAK SCALAR OPERATORS ("some",
****"possible"****, "permitted", "or", "warm") as SEMANTICALLY ONE-SIDED,
LOWER BOUNDED BY THEIR TRUTH-CONDTIONAL MEANING ("at least some, ****at
least possible****, ...) WITH THE TWO SIDED understanding ("some but not
all, possible but not necessary) DERIVED BY AN UPPER BOUNDING SCALAR
IMPLICTURE:

utterance 1-sided reading 2.sided reading

It's possible she'll win "at least Poss" "Poss but not certain"

"This line provides a straightforward means for reconciling the apparent
TWO-MILLENIUM OLD CONFLICT between the mutual implications INTUITIVELY
RELATING THE MEMBERS OF SUB-CONTRARY PAIRS (some/some not,
******"possible"/"possibly not"******) and the desiderata of logical
consistency and parsimony that remain unattenable when these implications
are treated in semantic terms."

I'm using sub-contariety (in the header) as Horn uses: "I shall begin with
a tour of some of the highs and lows in the long history of sub-contariety
concentrating on those models that tend to prefigure the neo-Gricean
approach to the Square of Opposition." The assertoric square being

A E
I O

Horn quotes what Aristotle says to the effect that "not every man is white"
and "some men are white" are both true. (De Interpretatione 17b23):

"Verbally, while _four_ kinds of opposition are possible, really there are
only _three_, for the particular affirmative is only verbally opposed to
the particular negative"

(Aristotle, Prior Analytics 63b21)

Horn notes:

"Now, modal values can be superimposed onto the square of
opposition, with the A E I O vertices assigned respectively to the
necessary, the possible, the impossible and the not necessary (possibly
not)."

For Aristotle (as for Grice) the modal subcontraries are not only
MUTUALLY COMPATIBLE. They are -- on what Aristotle calls the "two sided
reading of possible - equivalent". "But" -- and this is Noel
Burton-Roberts's focus.

If, whatever is necessary is possible and whatever
is possible is possibly not (not necessary), whatever is necessary is not
necessary" (De Int. Ch. 13).

Horn writes:

"But, just as "Some S is P has been regarded since Aristotle as true so long as AT LEAST ONE S is P, so "S MAY BE P" has been taken -- since Theophrasus -- to be TRUE provided it is AT LEAST POSSIBLE for S to be P."

""Some" is compatible with "all", and
possible with necessary."

Horn expands on the in-between, and quotes from Jespersen's triangle of lexical variants:

A: necessity -- "must"
B: possibility -- "may"
C: impossibility: -- "must not"

Horn finds Jespersen interesting, for there seems to be a "triangle" at
play, and not a square. In Jespersen's triangle, the second category (B)
corresponds -- SEMANTICALLY -- to the conjunction of I and O vertices of
the traditional square, but it has only one lexical realisation ("may").

This lexicalisation gap Horn finds interesting: As for the scale ,
and with quantifiers, as there's no such English word as "nall" or "nand",
this extends to modals: "the missing O phenomenon in English modal idioms
is reinforced by the general tendency of "O -> E" drift, wherein items or
collocations associated by their compositional form or etymology with the O
corner of the square move inevitably northward toward E."

Now, Horn refers to further bibliography here

-- "the pragmatic inferential relation between the positive and negative subcontaries results in the SUPERFLUITY of one of
these subcontaries for lexical realisation, while the functional markedness
of negation assures that the superfluous, unlexicalised subcontary will
always be O."

Reaching Grice, Horn quotes from his early "Causal Theory of Perception" --
Section _not_ repr. in Studies in the Way of Words -- where, Horn notes, we
find Grice's own first shot at the relevant principle:

"one should not make a weaker statement rather than a stronger one unless there is a good reason for so doing". (Grice, 1961:132).

Here Horn quotes from FOGELIN, who turns the Modal Square into a Triangle

necessary impossible
possibly possibly not
necessary impossible
possible.

For Fogelin (he reviewed Grice's _Studies in the Way of Words_), unlike
Jesperen, though, the square becomes a triangle "only when the context allows". Horn writes: "Fogelin's triangles are pragmatically derived, not semantically given". Horn notes some Gricean influence (!) in this passage from Aristotle, as it concerns what Grice may have meant by "stronger" in terms of implication -- this Horn anachronisms can be tricky, but I confess I like them! --:

Aristotle writes:

"If one is to say of the primary substance what it is, it will be more INFORMATIVE and apt to give the species than the genus. For example, it would be more informative to say of the individual man that he is a man than that he is an animal (since the one is more distinctive of the individual man while the other is more
general). And more informative of the indivual tree that it is is a tree
than that it is a plant".

Categories, 2b10ff.

In Horn's lexicon, ""Nec. p" (A) UNLATERALLY entails P (A) which entails POSSIBLY P (I)". "The symmetry of the square belies an asymmetry of implicature".

"If you tell me something is POSSIBLY true, I will assume you don't know
it's true, but if you tell me that something is true (e.g. that all
bachelors are unmarried) I will not assume you don't know it is NECESSARILY
true."

"That is, the use the weak I or O form lincenses the inference that the
utterer is NOT in a position to use the corresponding intermediate (or
strong) proposition, but the use of an intermdiate form DOES NOT implicate
the negatin of its strong counterpart"

Russellian or Aristotelian? Seth Sharpless has discussed this, as if the opposition were between Aristotelian and Gricean. I would think the opposition is between
Aristotle and _Strawson_.

Grice tries to re-in-state (if that's the word) Aristotle in Oxford, as he had been criticised by Strawson (in Intro to Logical Theory and On Referring). The irony of it all, Grice thought, was that Grice was Strawson's _tutor_ in logic (in Oxford). _Some_ pupil!

Strawson has an example concerning "sleeping children" (in 'On referring',
now repr. in Logico-Linguistic Papers_) which ends with the famous -- well,
I read it a few times! --:

"Neither Aristotelian nor Russellian rules give the exact logic of any
expression of ordinary language, for ordinary language has no exact logic".

Russell replied (!) ub "Mr Strawson On Referring"! And of course Grice replied
on behalf of Aristotle!

That's why I like Horn's expression "Greek Grice" so much! Horn quotes this passage by Strawson and the example of sleeping children, and manages to mix all the examples in the literature, including one by Burton Roberts!

"The collapsing of Strawson's sleeping children into the sister of Stalnaker and Sadock who herself metamorphoes into Grice's aunt concert-going cousin who in turn mutates into the lunch-going sister of Burton-Roberts should remind us that in the evolution of pragmatic theory, all progress is relative!".

I quote that because it's a mention of Burton-Roberts! I hasten to share these notes, and I'll keep thinking about it! I still don't want to re-consult Burton-Roberts's essay not to be so influenced by him. As L. M. Tapper focuses on the fact that there are like GUARDED phrases in ordinary Language (i.e. one may say, "Chomsky is a nativist, but ("and" even) then maybe he isn't" -- I don't know!) I should mention that the topic _from the epistemic point of view_ (that Tapper probably favours being a fallibilist) is treated in detail by J. O. Urmson -- as antecedent
of Grice -- qua Oxford philosopher -- in 'Some questions concerning validity'.

In his Semantics, the Griceian Sir John Lyons distinguishes between epistemic and metaphysic modality. I think it is important to keep them apart! Also, it is important to know how language-relative all this is! ie. Northern England dialects, feature a form of "mustn't" qua metaphysic that is not found in the South of England. Or so the Northerners claim!