[lit-ideas] Number: Logic and Grammar

From: Jlsperanza@xxxxxxx
To: lit-ideas@xxxxxxxxxxxxx
Date: Tue, 21 Sep 2004 21:39:58 EDT
 
 
In a message dated 9/21/2004 8:08:18 PM Eastern Standard Time,  
andreas@xxxxxxxxxxx writes:
A number  is a quantity, for example: X.  If you have 2 X (written out as 
XX), then  it's just 
two of the X. The concept of XX includes the concept of one X  and one X. The 
concept of one 
X includes the possiblity of multiple  X.

-----
 
Okay. Let's take apples
 
One apple. I have the concept of 'one' (adjective) and the concept of  
'apple' (noun). This does not always work ("one sugar" makes little sense, or  
"one 
water"). If we say "two apples", I need to have the concept of "apple" and  
the concept of "two" -- I don't think I need to have the concept of "one". It  
may be a 'form of life' -- to use Wittgenstein's term -- where things only 
_come  in pairs_. 
 
Actually a lot of our concepts work like that. At a seminar in linguistics  
attended by many including L. Horn, they discussed the implicatures of
 
        "My ball itches".
 
The sentence was dubbed 'ungrammatical' by many in that it's never  specified 
which (of the two balls) actually itches. (Some proposed that the  utterer is 
mono-testicular, to bestow the sentence with an otherwise dubious  
grammaticality).
 
Quine, in _Methods of Logic_, comments on the highly complex logical form  of 
something like,
 
         "The twelve apostles ate  bread".
 
For Quine, "twelve" works like "some" and "all" (and "many"), as a  
quantifier. He held that there is a iota-quantifier, "the apostle", (1x), and a 
 binary 
quantifier (2x), etc. He considered that these were really higher-order  
quantificational operators. George Boolos has developed some of Quine's views 
--  
in his posthumous _Logic, Logic, and Logic_ --, where again, the idea of 
number  is given some sort of 'truth-functional' approach _vis a vis_ Frege's 
ramblings  on the issue (as tr. by J. L. Austin -- R. Henninge knows about 
that).
 
I believe Kant was one of the first to approach the issues involved, and he  
certainly said that the concept of 12 is included in the concept of 5 and in 
the  concept of 7 _and_ in the concept of addition. So it's not just that 7 and 
5  make 12. It's a special 'and' ("7 and 5 make 2" if 'and' gets interpreted 
as  'minus' there). 
 
Cheers,
 
JL
 
 

 


------------------------------------------------------------------
To change your Lit-Ideas settings (subscribe/unsub, vacation on/off,
digest on/off), visit www.andreas.com/faq-lit-ideas.html
[lit-ideas] Number: Logic and Grammar

Other related posts:
