[hist-analytic] Carnap, Grice, and the Infinity
Jlsperanza at aol.com
Jlsperanza at aol.com
Sat Mar 6 17:25:19 EST 2010
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
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
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
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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