[lit-ideas] Re: Griceian Numbers
- From: Jlsperanza@xxxxxxx
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Sun, 17 Jun 2012 10:33:17 -0400 (EDT)
In a message dated 6/16/2012 11:31:52 P.M. UTC-02,
RichardHenninge@xxxxxxxxxxx writes:
"it was at the great lecture given by Bultinek on Scalar Implicatures and
Their Use in the Edjukayshun of Childers."
Indeed.
There are various issues involved with D. McEvoy's use of the 'number'
example in Wittgenstein. In a previous post, McEvoy, quoting the link to the
Stanford Encyclopedia entry on Wittgenstein on mathematics, suggested that
perhaps this area would also shed light on the 'key tenet' (by which McEvoy
means the thesis that the show/say distinction applies to both the TLP and
the PI, as it is NOT commonly held; on the contrary, the tenet is regarded
as being basic for the exegesis of TLP, only).
To that effect, McEvoy quoted extensively and interestingly from a manual
of the history of philosophy ("a sequel to Russell", the author -- Ayer --
pretentiously called it), whose chapter V is all about the latter Witters.
This got me re-interested in such grand claims by Witters (or their negation
-- it is never clear if Witters is _joking_ when he presents "The
Philosopher" as providing such nonsensical claim for the only effect of him
(Witters, in the role of the Non-Philosopher) refuting him ("The Philosopher").
Ayer made a couple of informal remarks about the difference between 'being
shown numbers' and 'being shown building materials'. This is a bit vague,
and in McEvoy's paraphrase we have phrases like, "being shown "three"", I
think, versus "being shown "brick"". I refer to this:
"being shown "brick""
which I think is McEvoy's phrase, not Ayer. For Ayer speaks of being shown
building materials, whereas, in McEvoy's paraphrase, we are being shown the
"word" "brick". This may serve as evidence that sometimes the untechnical
uses of 'show' and 'say' are stretched by McEvoy to provide material for
his interpretation about the 'key' tenet. But he makes interesting commentary
on the need (or lack of it) for the provision of subscripts: in what way
would showing-1 "three" differ from showing-2 "brick", and so on?
Now, back to the Scalar Implicature, etc. As we know, Grice considers two
quantifiers in "Logic and Conversation" (and more):
(Ex) --- "some", "AT LEAST *ONE*.
(ix) ----- "the"
He is claiming that it is a commonplace in philosophical logic that there
may be divergences between the formal device and the natural language
counterpart -- and he intends to show the commonplace false -- resting on the
mistake of ignoring the 'implicature'. We also see how Grice applies this
notion for informal uses of "a" ("an"), which is an etymological variation of
"one".
From etymology online:
"a":
"indefinite article, mid-12c., a variation of O.E. "an" (see "an") in which
the "-n-" began to disappear before consonants, a process mostly complete
by mid-14c. The "-n-" also was retained before words beginning with a
sounded -h- until c.1600; it still is retained by many writers before
unaccented
syllables in h- or (e)u-, but is now no longer normally spoken as such.
The "-n-" also lingered (especially in southern England dialect) before -w-
and -y- through 15c."
"an"
"indefinite article before words beginning with vowels, 12c., from O.E.
"an" (with a long vowel) "ONE; lone," also used as a prefix "an-" "single,
lone;" see "one" for the divergence of that word from this. Also see "a", of
which this is the older, fuller form. In other European languages, identity
between indefinite article and the word for "one" remains explicit (e.g.
Fr. un, Ger. "ein", etc.) Old English got by without indefinite articles:
"He was a good man" in Old English was
"he wæs god man".
Circa 15c., "a" and "an" commonly were written as one word with the
following noun, which contributed to the confusion over how such words as
"newt"
and "umpire" ought to be divided (see N).
In Shakespeare, etc., "an" sometimes is a contraction of "as if" (a usage
first attested c.1300), especially before it.
"one"
"O.E. "an", from P.Gmc. *ainaz (cf. O.N. einn, Dan. een, O.Fris. an, Du.
een, Ger. ein, Goth. ains), from PIE *oinos (cf. Gk. oinos "ace (on dice),"
L. unus "one," O.Pers. aivam, O.C.S. -inu, ino-, Lith. vienas, O.Ir. oin,
Breton un "one")."
"Originally pronounced as it still is in "only", and in dial. "good 'un",
"young 'un", etc.; the now-standard pronunciation "wun" began c.14c. in
southwest and west England (Tyndale, a Gloucester man, spells it "won" in his
Bible translation), and it began to be general 18c."
"Use as indefinite pronoun influenced by unrelated Fr. on and L. homo.
Slang one-arm bandit "a type of slot machine" is recorded by 1938."
"One-night stand is 1880 in performance sense; 1963 in sexual sense."
"One of the boys "ordinary amiable fellow" is from 1893. One-track mind is
from 1927."
----
---- Grice applies this to "one dog", "one woman", "one tortoise". His
example:
"Jones went into a house yesterday and found a tortoise inside the front
door".
It would be ridiculous to utter the above if the utterer means to
communicate that Jones went to his OWN house, where he found, naturally, HIS
OWN
tortoise inside the front door.
Grice writes:
"I could produce similar linguistic phenomena involving the expressions "a
garden", "a car", "a college", and so on."
---- Grice notes that the correlation (Ex)=1 sometimes gets disimplicated.
"I broke a finger yesterday" (uttered by a nurse?) ("reverse implicature",
Grice calls it).
"I've been sitting in a car all morning" -- non-implicature.
--- In any case, Grice allows for (Ex)=1 as the LOGICAL form and explain
any divergence in terms of implicature. By doing this, he is allowing for a
UNIFIED logicist programme, where we don't need to multiply the 'senses' of
"(Ex)".
The remedy by Witters would rather be that since there are multifarious
uses of 'one', Frege's point about "(Ex)" is misguided and that we learn 'one'
by showing ones. Hardly illuminating.
Grice is not even considering Witters's criticism here, but one like Cohen,
who proposes that
'one'
has DIFFERENT senses:
Jones is meeting a-1 woman this evening.
Jones is meeting a-2 woman this evening.
Grice's gloss: "the implicature seems to be that the afore-mentioned woman
is NOT Jones's wife, mother, sister, or perhaps even close platonic friend"
(WoW:37).
Repugnance for rejection of the unified logicist programme has Grice
uttering such genialities like:
"I am inclined to think that ONE would NOT lend a sympathetic
ear to a PHILOSOPHER who suggested that there are
three SENSES of the exprssion "an x": ONE in which it means
roughly 'something that satisfies the conditions defining
the word x' [as in Witters, "Pass me one brick"], another in
which it means approximately "an X (in the FIRST sense) that
is ONLY REMOTELY related in a certain way to some
person [or central individual] indicated by the context", and
yet another in which it means "an X (in the FIRST sense) that is
CLOSELY related in a certain way to some person [or central
individual] indicated by the context." (WoW, 38)
--- (I'm happy that B. B. focused his thesis on 'two' rather than 'one'
(1,000 samples from the British National Corpus, for surely there is some
sense (albeit confused) in Aristotle when he says that '1' is NO number -- but
a monas, rather, an unity -- not an arithmos).
No. Indeed, one would not lend a sympathetic ear -- or if I did, I would
ask my sympathetic ear to be RETURNED --. Especially when the implicature
account -- explaining each breach of (Ex)=/=1 as a flouting of a
conversational maxim -- is so ready "at hand". And so on.
Finally, in any case, it may do to revise in what way the logicist
programme (McEvoy thinks Witters is opposing it, and Grice defending it)
brought
in by Frege, Russell, and alas, the early Witters wins the day.
One thing to consider is that 'x', 'y', 'z', etc. as used by Frege for
variables must then belong to what the linguists call countable or "non-mass"
nouns.
"Sugar is sweet"
then would imply some modification in terms of logical form
(x)S1x --> S2x
sounds a bit odd if we consider that the use of quantifiers must allow for
things like "a sugar". Surely, the statement to consider would be:
"Some sugar is black".
(Ex)Sx & Bx
If we use Grice's table above, we indeed have:
"At least one sugar is black".
----- Personally, I don't have a (one) problem with that, but my aunt may.
Philosophically more important, it may relate to Ayer's bricks and three.
For if we use Aristotle's, and indeed Strawson's, individuation principle
(Strawson in "Individuals: an essay in descriptive metaphysics" -- something
like Grice's bible) and Socrates is approaching, we may be able to say:
Three individuals are approaching.
What d'you mean?
Well: Socrates, Socrates's nose, and Socrates's left toe.
---
Indeed, if an individual (referent of a nonmass countable noun) is a
spatio-temporal continuant, such nonsense as "Three individuals are
approaching"
when Socrates is approaching should be licensed by logic.
So, it may seem that indeed Ayer is right and it's BRICKS that are basic,
qua building material, rather than 'three'. Ayer and Witters and Grice agree
that there is NO 'object' (to use Witters's vague notion) of a
mathematical kind that the number word "three" refers to (Witters uses the
neutral
Bedeutung here, which translates as "reference" rather than "Sense" (Sinn),
contra the Stanford Entry). But there is still a difference between the ROLE
of 'three' in "Three bricks" and the role of "yellow" in "three yellow
bricks".
For, again, 'yellow' shares some similarities with 'three', in that it can
confuse.
To use the example in the Stanford entry for Mathematics in Aristotle:
There are three black cows in the field.
No problem with 'cow' and its relevance to (Ex): "at least one cow?". "No,
not at least one cow; I said _three_."
I.e. the quantifier applies strictly to the predicate "C":
(Ex3)Cx & Bx
Note that we have done without the otiose 'three' qua adjective having
incorporated the numeral ONTO the quantifier. But we still have to deal with
the predicate "B" as opposed to "C" (black versus cow).
Now, in SECOND-ORDER predicate logic, indeed "black" may become a
COUNTABLE, non-mass noun. To consider Grice's example, in examining ties for a
possible purchase:
"Two people are considering the purchase of a tie which of them know to be
medium green; they look at it in different lights, and say such things as
"It is a light green now", or "It has a touch of blue in it in this light""
(He is considering the disimplicature of 'is'). (WoW 44).
But to reuse his example:
"a light green"
"a medium green"
are phrases which seem to allow for the formalisation
(Ex)Gx
i.e. while it is the TIE that is medium green or light green (as the case
may be), we have ways (in higher-orders of the predicate calculus) to turn
the utterance to be ABOUT the colour word itself, as when we say that
"Medium Green is Mary's favourite colour" -- The use of this type of statement
strictly requires a reduction in terms of first-order: for any x that May
happens to see, Mary would rather like to see x as Medium Green" (Cfr.
"Sincerity is a virtue").
---
So, I would think that, no, the philosophy of mathematics does not really
give much support to the key tenet, anyway, since any serious philosopher
bringing in number words would require an expansion as to the logical form.
And this is particularly evident in any discussion of the "KEY tenet", for
if the TLP is good about one thing is those statements as the ones I quoted
from:
_http://www.sparknotes.com/philosophy/wittgenstein/section1.rhtml_
(http://www.sparknotes.com/philosophy/wittgenstein/section1.rhtml)
"Wittgenstein draws an important distinction between saying and showing."
-- this distinction does not seem to have a base in Graeco-Roman philosophy.
The Latin concept of 'dictiveness', for the 'sayable' may apply. But it is
more controversial to look for a Graeco-Roman equivalent to 'show':
De-MONSTRATIO a good candidate, if not perfect.
"While a proposition *says* that
such-and-such fact is the case, it
*shows* the logical form by virtue of
which this fact is the case."
---
"The upshot of this distinction is that we can only say things about facts
in the world; logical form cannot be spoken about, only shown."
"Because logical form shows itself and cannot be spoken about, there is no
need for the so-called logical objects, the connecting glue between
different propositions that plays a central role in the logic of Frege and
Russell."
"Wittgenstein asserts that most philosophical confusion arises from trying
to speak about things that can only be shown."
----
NOTE that while 'show/say' were never technical words in the philosophical
lexicon (contra Witters), Witters is not just using these neologisms (in
the lexicon) in ANY way, but connecting them with technical notions in the
logicist programme, such as 'logical form'. What an expression SAYS, its
logical form, what it shows, and so on.
If Witters changed his mind completely and turned into a constructivist and
generally sceptical sort of fellow, and very "anti-philosophical" in his
views, it's Witters's loss. Those who still look for philosophy will know
that simplifications uttered by Witters with the only purpose of fascinate
his students (he was a tutor at heart) need not fascinate those who are not
(his students). Or something.
Cheers.
Speranza
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