Grice on ix, "the" (WoW:22)

-- by J. L. Speranza
---- for the Grice Club

J was hyperlinking, "Owen Barfield", comments, this blog -- to his interesting post on "Descriptions" elsewhere -- his blog on Contingencies. It's all about uniqueness, and more. So, here some copying and pasting from Grice on what he calls the "Russellian expansion".

--- I have discussed elsewhere -- in a couple of threads elsewhere which I entitled, Shuga-free -- Grice's indebtedness to Hans Sluga for having pointed to him how to deal with (ix) --. Grice's discussions with Sluga postdated his locus classicus on implicature, so beware.

In any case, here is Grice on uniqueness:

A Russellian expansion of 'the' involves three clauses:

CLAUSE 1:
"There is at least one king of France"

CLAUSE 2:
"There is at MOST one king of France"

CLAUSE 3:
"Whatever is king of France is bald"

------ Grice, WoW: 273 -- Studies in the Way of Words.

I was so fascinated by this that I wrote, elsewhere, on the decalogue, because it was this phenomenon that led Grice to add a maxim to the nine maxims mentioned in the locus classicus to yield a 'conversational immanuel' or 'decalogue'.

Grice goes on. His point is with "~". As he notes, the three clauses "cannot all be denied together. If it is false that there exists at least one king of France, it is vacuously true that whatever is king of France is bald (that nothing is both king of France and not bald)."

The implicatum concerns some clarification on what we mean by clause III.

As Grice notes,

"the third clause is general in form. And we can think of a general
statement -- "Whatever is king of France is bald" -- as being
either something the establishment of which depends on the
complete enumeration of a set of instances, or as soemthing to
be an inductive step."

--- Approaching the third clause. Via complete enumeration.

"Let us suppose it is enumertatively based. That is, we are
to think that "Nothing that is [king of France] is not [bald]" as
to be reached by finding the isntances of '[king of France]'
and seeing that none of them fail to be '[bald].'

Disregarding, to echo Russell, those scenarios where the King of France wears a wig.

Grice continues:

"For it to be possible to establish this
enumeratively if the whose sentence, "The king of
France is bald" is true, it must be that there
exists JUST ONE [king of France] which is the
basis of the enumeration. And so we have, in effect,
a conjunctive statement that tells us there are a
certain number of cases (just one) that would
test a certain generalisation, and then gives us
the generalisation."

There is a caveat here. Grice notes: "It would seem to
be very peculiar to imagine that anybody could be in
the situation in which he was prepaed to speak of
'[Whatever is king of France is bald]' but not as being
common ground, because he woud have to be put in the
position of saying something like, 'I can accept
that nothing is king of France but not bald, what
'what is [king of France] is [bald]' is true, and si aso to
be established by a commplete enumeration, but what I
am uncertain about is whether you are right about
whether there are any instances of 'king of France' or, if
so, how many.'"

--- Surely that's not very natural. Grice comments:
"It is not necessary that it should be IMPOSSIBLE for
somebody to be in that position, but that it is certaintly
not to be expected."

---

ii. Second approach to "Whatever is king of France is bald" via mathematical induction.

"Now, suppose we take "Whatever is king of France is bald", not
as an enumerative generalisation, but as an open one."

The same caveat occurs: "It is prima facie not to be
expected that you would find somebody in the position
of being prepared to concede the generalisation, 'Whatever
is king of France is bald', but being concerned about
whether and how often that generalisation is
instantiated."

Hardly what Grice calls the 'natural' situation ("and the implicature depends on what is to be expected").

This allows Grice to argue that:

"we could perhaps explain why it is that
somebody who says it is NOT the case
that the present king of France is bald
... would also be implicating, though
not explicitly STATING [or displaying. JLS]
that there is a UNIQUE king of France."

(WoW: 275).

I once played with Quine's example of the twelve apostles in "Methods of Logic", since I was considering how 'the' relates or fails to relate to the unary quantifier.

Ten green bottles sitting on the wall,
Ten green bottles sitting on the wall,
And if one green bottle should accidentally fall,
There'll be nine green bottles sitting on the wall.

"the bottle" -- vs. 'one bottle'.
"the ten green bottles -- vs. 'ten green bottles'.

-- In any case, it amuses me how people can be confused about uniqueness meaning 'unus' when in fact, 'the ten green bottles' is still a unique definite descriptor which is best symbolised by what Quine has as a 10-ary quantifier

(Ex10) x is Green and sitting on the wall.

(Ex9) x is green and sitting on the wall.

and so on till you get to

"the one green bottle"

(Ex1) x is green and sitting on the wall.

Boolos -- whom Grice quotes in "Vacuous Names" -- related this to the point about plural, and I learned much about this via discussion, public too, with Randall Helzerman.

For recall that for a logician (Ex) reads as -- to echo Grice in WoW:ii -- first paragraph -- 'some' AND 'at least one'.

"Some kings of France are bald" is, logically, true, even if ONE king of France is bald.

(Warnock had to swallow this Griceian point in his fascinating, but seldom quoted, "Metaphysics in Logic", repr. in Flew, Essays in Conceptual Analysis -- an early piece written for the Revue of Philosophy in the 1950s.).