[lit-ideas] Griceian Numbers
- From: Jlsperanza@xxxxxxx
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Fri, 15 Jun 2012 21:25:51 -0400 (EDT)
In a message dated 6/15/2012 12:08:47 P.M. UTC-02,
donalmcevoyuk@xxxxxxxxxxx quotes interestingly from Ayer,
"In the case of the numerals, he learns, say, the word ‘three’ by having
trios of bricks or slabs or whatever pointed out to him; or he may be taught
the difference between ‘three’ and ‘four’ by having them correlated
respectively with a triad or a quartet of bricks.”
“It would be wrong, however, to say that he was being shown numbers in the
way he was being shown specimens of building materials. The difference lies
not the different character of the ‘objects’, but in the different roles
that the two sorts of signs play in the language game.”
McEvoy:
"showing the sense of ‘slab’ is to show in a distinct way to showing the
sense of ‘brick’; or that showing the sense of ‘1’ is to show in a
distinct way to showing the sense of ‘10’."
In his second post, entitled, "Ayer on Wittgenstein II", McEvoy adds of
"Ayer’s interpretation [being] defective because Ayer does not grasp the
underlying ‘key tenet’" which is "also by Ayer’s account of the Tractatus
where Ayer also does not grasp the importance of the ‘key tenet’ to
understanding that work."
----
I don't see why numbers should play such an important rule in the tenets,
key or other.
Numbers are very difficult items in the philosopher's discourse, and I'm
not surprised that Witters was confused about them. But Ayer seems to make a
good point that:
"Pass me three apples"
is about apples and about three.
McEvoy, above, speaks of the _sense_ of "10".
Senses should not be multiplied beyond necessity -- Grice says. "Modified
Occam's Razor". He is against using 'sense' for things like 'to', 'of', or
'or', even.
So, while "apple" may have a _sense_, what would the sense be of sensing
that "10" also has a sense.
My knowledge of Griceian numbers is formed out of various sources: one is a
PhD dissertation by a "Nederlands" philosopher (written in English, th
ough). There is some further interesting material in Levinson's book on
"Implicature". Finally, I probably learnt most from Quine's "Methods of Logic".
Quine considers:
"And then Jesus fell asleep. The twelve apostles followed suit."
Quine wants to consider the logical form of:
"The twelve apostles wore hats."
and fails.
From what I recall, he proposes
(Ex)Ax -- there are apples.
This should be distinguished from:
(Ex1)Ax. There is one apple.
(Ex2)Ax. There are two apples.
...
(Exn)Ax. There are n apples.
Boolos, who learned from Quine (at Harvard -- recall that Grice's lectures
on implicature were given at Harvard) has dealed with this in terms of the
'plural' form. As Warnock notes, in "Metaphysics and Logic", there is no
sign of plurality in Logic. Logicians (and philosophers) are never interested
in plural.
Thus,
"My mother speaks French"
is not about _one_ mother. Although Russell speaks of 'uniqueness' in his
account of 'THE king of France', note that Grice uses the 'iota operator'
(ix)Kx
The king of France
If we want to say "he is bald"
(ix)Kx & Bx
and so on.
There was a symposium on this. The example provided by Joshi was (he is a
male linguist):
"My ball itches".
He was wondering whether the 'implicature' was that he only had one ball.
Unfortunately, native speaker intutions from the female members of the
audience were missing, and it was decided that while there may be an
implicature
to the effect that Joshi had only one ball (as he utterered the utterance)
it is in no way an entailment.
Similarly, to use Strawson's example in "Introduction to Logical Theory",
where he credits all he knows to Grice:
"All the books in the room are by French authors".
In a scenario where there are no books in the room, the above comes us
true.
Back to Warnock, Warnock considers:
Tigers exist.
as otiose. Note that the logical form does not specify the _number_.
I'm not surprised that speakers get confused about this. J. Krueger was
asking about 'vos' in the Romance Languages. Indeed, there is a T-V
distinction:
'thou' -- for example, is original SINGULAR.
Yet nobody says,
"thou art lovely"
The SINGULAR form has become obsolete, and English speakers say,
"You are lovely"
But YOU was originally a PLURAL form. The idea is that the plural is used
singularly.
----
It would be good to revise the logical forms proposed for basic utterances
of the type that McEvoy discusses in his exegesis of Ayer on Witters.
"Pass me three bricks"
is Witters's famous example -- used by Stoppard in one of his plays. Ayer
seems right that while we may speak of the sense of 'brick', it would be a
'different' language game to focus on 'three'.
'three' is an adjective, 'brick' is a noun. While 'sense' applies best to
nominal expressions (both nouns and adjectives) it is best to stick to the
_sense_ of a (common) noun. The 'sense' of an adjective can be defined
extensionally as the items following under it (the members of the class): thus,
the meaning of "Sweet" (the sense of 'sweet') may be given extensionally by
providing a list of all things which are sweet. Grice of course notes a
paradox of extensionalism when it comes to vacuous predicates.
But 'sweet' is still different from 'three':
"Pass me three red apples"
"red" can be defined extensionally as all things which are red, and
intensionally in terms of the physical properties of the continuum.
Ditto, "apple" which is defined in botany.
But what about 'three'? Who defines 'three'?
Russell was right in being a logicist, for he wanted (even if he failed) to
provide a logical background to mathematics (logicism). The first Witters
thought he understood Russelll; the second and third Witters show that this
was never the case.
And so on.
Of course, the famous paradox of Anti-Griceians concerns the disimplicature
of numerals (cardinals):
"She ate three apples".
---- (core included -- not just the edible part) -- vide Koch.
But she actually ate _five_, one finds out later.
In this scenario, where she ate five apples, 'she ate three apples'
FOLLOWS. The implicature pertaining to the maximal reading of numerals can be
explained Griceianly, but never Wittgensteinianly, for he never really cared
for the _sense_ of a number, whether showable by the sayable or not.
Or something.
Cheers,
Speranza
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