[hist-analytic] Carnap, Grice, and the Infinity

[Jlsperanza at aol.com]

In discussing ways to narrow down the use of "language" in both Carnap  (R. 
B. Jones's task) and Grice, I quoted from Gr89:296 -- to the effect of  
'infinite'.
 
I am reminded that mention of infinity may do, too, with Davidson's  
arguments against 'learnability'. I would address the Gricea point from yet a  
different perspective. This is aleph-numerable infinite, so pretty learnable 
(to  me, I hope). But is such a notion necessary for Grice's big target, 
utterer's  meaning, or should we just agree with S. Yablo, that, "implicature  
happens"?
 
Grice writes: "In some cases ["Logiclandian" as it were, I owe the  term to 
L. J. Kramer. Elsewhere. JLS] -- "the _ARTIFICIAL_ [emphasis mine. JLS]  
communication devices _MIGHT_ [emphasis mine. JLS] have  certain _other_ 
[emphasis mine. JLS] features too, over and above the  one of being artificial: 
they might, for example, involve a FINITE number of  fundamental, focal, 
elementary, root devices [vocabulary, lexicon, including  constants and other. I 
am reminded of MacFarlane -- student with Grice at  UC/Berkeley -- and his 
excellent entry on l. constants in the Stanford Ency.  JLS], and a FINITE 
set of modes or forms of combination (combinatory  operations, if you like 
[syntactics. JLS] which are capable of being used over  and over again. In 
these cases, the creatures will have, or be near to having,  what some people 
[Carnap? R. M. Martin? Chomsky  surely. Davidson -- vis a  vis his 
learnability constraint. JLS] thought to be characteristic of a  _language_ [emphasis 
mine. JLS]: namely: a communication system with a FINITE  SET of initial 
devices [constant, but not variable, for those would be  'infinite'?. JLS], 
together with SEMANTIC provisions for them, and a FINITE set  of different 
syntactic operations or combinations, and an understanding of what  the functions 
of those modes of combination are."
 
The grasp with the infinity, which perhaps did trouble Carnap too, cames  
in the next passage:
 
"As a result," Grice writes, "they [the pirots. JLS] 
*can* [empahsis mine, for no one _will_ under their finite  circumstances. 
JLS] generate an INFINITE number
of sentences or complex  communication devices, together with a 
correspondingly infinite set of  things
to be communicated, as it were"


-----
 
When Grice delineates the six stages of his programme or grand plan or  
grand project (WoW:vi -- first two pages) he starts, logically -- but cfr.  
compositionalists -- with utterer's meaning and proceeds to expression meaning. 
 In principle it is VERY possible to attain the level of the 'implicature' 
or at  least utterer's meaning, _sans_ recourse to this denumerable infinity 
that a  'language' involves -- formal or not --. It's only stages 4 or 5, 
as I recall,  which deal with a specification of what it means for an item 
_in_ the system to  mean this or that.
 
It would seem that if pirots are language-destitute, but can still _mean_  
this or that, they may not and perhaps should NOT have recourse to such a  
(pretty unintuitionistic) infinite. For they will rely on procedures in each  
other pirot's (including themselves') repertoires. 
 
In any case, I thought the credit to Davidson and his stress on these  
issues was pretty relevant to bring to the forum, even in a discussion of Carnap 
 and Grice.
 
A final point by now: the entry for 'constants' by MacFarlane,  
incidentally, referred to above, includes gems like this (He regularly  teaches "Grice" 
at Berkeley and I met him at Yale -- _very_ clever philosopher  -- he likes 
Greek philosophy, too).
 
"While it is generally agreed that signs for negation, conjunction,  
disjunction, conditionality, and the first-order quantifiers should count as  
logical constants, and that words like "red", "boy", "taller", and  "Clinton" 
should not, there is a vast disputed middle ground. Is the sign for  identity 
a logical constant? Are tense and 
modal operators logical  constants? What about "true", the epsilon of 
set-theoretic membership, the sign  for mereological parthood, the second-order 
quantifiers, or the quantifier  "there are infinitely many"? Is there a 
distinctive logic of agency, or of  knowledge? In these border areas our 
intuitions from paradigm cases fail us; we  need something more principled."
 
This actually should lead us to the other bit of that pair: the  
Yablo-Haslanger, for I'd need to revise what Haslanger let me have re: Myro's  System 
G -- for it includes, I think, pretty detailed things on 'chronometrics'  -- 
to formalise the Grice-Myro theory of time-relative identity. But if  
MacFarlane is right, as I think he is, the System G would not be just formal  
under that guise, and we may need to specify the introduction of the  
chronological modality in terms which does not clash with a more regimented  
first-order predicate calculus, the Canon. If only to play with it, and perhaps,  
flout it? -- Cheers,

J. L. Speranza
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