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

Roger Bishop Jones rbj at rbjones.com
Mon Mar 8 16:21:34 EST 2010

On Monday 08 Mar 2010 00:53, Jlsperanza at aol.com wrote:
> In a message dated 3/7/2010 5:36:47 P.M. Eastern 
>  Standard Time, rbj at rbjones.com writes:
> The whole area, using natural  languages as metalanguages
>  for formal systems, is a case of pushing natural 
>  languages into new territories
> It was my understanding that Carnap was pretty happy with
>  English (or German) as the metalanguage. Seeing that he
>  was a student of Esperanto, I wouldn't be surprised if
>  he thought the latter too would do.

I think it matters what purpose you have in mind.
His main interests would have been in the status of 
judgements in the object language, rather than the status of 
judgements in the metalanguage, i.e. the status of 
judgements in a formal language rather than an informal 
language.  However, he did want all his philosophical 
judgements to be analytic, so there is a presumption that 
that would be the case.

In relation to my expressed reservations on this, arising 
from doubt about the meaning of names of object languages, I 
think one can possibly get out of this by invoking context.
Even if the meaning of the name of a language did not 
encompass the semantics of the language, one would expect 
that when judgements about analyticity of judgements in the 
object language are involved the context would suffice for us 
to know what semantics is at stake.

But I do think we are outside Carnap's sphere of interest 
(and mine really).  I think if these issues became 
significant we would either be more explicit in making sure 
that our notion of language, and the definitions of specific 
languages we offered did include the semantics.
Or else we would switch to a formal metalanguage.
The latter is certainly my preference, I would normally want 
to formalise a definition of a language and its semantics so 
that these fine points about the semantics of natural 
languages are not significant.

There is a general strategem here, which Carnap and I adopt, 
which is, because our subject matter almost never is a 
natural language, we side step as far as possible difficulties 
in the semantics of natural languages by stipulative 
definition, either of concepts or languages.

> So let's assume that we have FL (formal language) and MFL
> (meta-formal-language). Incidentally when you say 0=0 in
>  PA I understand A to  stand for arithmetic, right? And
>  the P for pure, perhaps, I assume. So we have  FL,
>  formal language and a meta-language for FL which is also
>  formal. So rather  than just "MLF" we may use "FMLF",
>  right?

Sorry, that's Peano Arithmetic, but the "PA" usually refers 
specifically to first-order arithmetic (Peano's original 
axioms were higher order).  But I don't think it matters, 
any arithmetic will give you "0=0".

> Finally, the incissive, I hope not, since it's silly:
>  regressus ad infinitum. Do we need a FMLFMLF, or is the
>  Bootrap to be of some use. Would a formal melanguage
>  just do for our decision to deem this 'analytic' or not,
>  or are we relying or trusting that our meta-language is
>  self-entrenched, as it were?

In his syntactic phase Carnap thought he could get away 
using the same language for object and metalanguage (because 
that's what Goedel did).
Even if you are doing semantics (or at least abstract 
semantics) you can use set theory all the time, because its 
easy to find for any set theory as object language a slightly 
stronger one which will do for a metalanguage.

There is a problem of regress in the foundations of abstract 
semantics, which corresponds to the problem of the infinite 
heirarchy of metalanguages, and this is an interesting 
problem which I havn'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 


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