[hist-analytic] Carnap and Grice on "meta-language"

[Jlsperanza at aol.com]

In a message dated 3/8/2010 7:13:26 P.M. rbj at rbjones.com writes  about OL 
and ML (object language and metalanguage) and whether NL or FL (natural  
language or formal language) are good for either. 

"I think it matters  what purpose you have in mind. His main interest... 
would have been in the  status of 
judgements in the formal object language"
 
"FOL"
 
complete with semantics. 
 
"Or else we would switch to a formal metalanguage."
 
"FML"
 
"The latter is certainly my preference."
 
"we side step as far as possible difficulties 
in the semantics of  natural languages by stipulative 
definition, either of concepts or  languages."
 
which is not, necessarily, to say, 'truth by convention'. I would need to  
know the etym. of stipulation. sounds like mani-PULATION, and I wouldn't be  
surprised if some think that stipulations should NOT be mismanipulated.


'Peano Arithmetic, but the "PA" usually refers 
specifically to  first-order arithmetic (Peano's original 
axioms were higher order).   ...
with "set theory all the time"
 
"There is a problem of regress in the foundations of abstract  
semantics, which corresponds to the problem of the infinite 
hierarchy of  metalanguages, and this is an interesting 
problem which I haven't actually  noticed anyone (apart from 
myself) taking much interest in.  But even  for me, its a bit 
academic.  The problem of regress is not practically  
significant."
 
--- Well, I suppose one would hope that the ML is final, if one is going to 
 pull yourself by your own bootstraps. It SEEMS an academic question how 
one is  going to pull one's pulling yourself by your own bootstraps. But there 
is charm  in the hierarchy.
 
For we can speak of L1, L2, L3, ... Ln -- and if we want, say, English, by  
definition to be our only source here, we are assuming a language to be 
able to  project an ifinite number of orders.
 
First-order:
 
Jenny is beautiful.
 
Second order (Strawson, Logic and Predicate in Logic and Language)
 
Beauty is in the eye of the beholder.
 
THIRD order? 
 
I would already at a loss to think of a third-order utterance in English.  
When presented with a simple SIMPLE second-order one, I cannot make sense of 
it  unless I translate it to first order, which IS a bother -- "Can't you 
SEE  beauty? That's lack of vision" -- as someone would say -- Grice contra 
"Q" in  the last two pages of WoW).
 
"Beauty is in the eye of the beholder" tr. to first-order.

Jenny is beautiful TO YOU but not to me, for 'to be beautiful' is not a  
monadic predicate but a dyadic one, etc.
 
But again, higher orders than the second escape me (on a Friday). 
 
J. L. Speranza