[hist-analytic] Tarski, Carnap and Grice on "snow is white"

Roger Bishop Jones rbj at rbjones.com
Sun Mar 7 17:36:39 EST 2010


On Friday 05 Mar 2010 17:59, Jlsperanza at aol.com wrote:
> In a message dated 3/5/2010 9:29:36 A.M. Eastern Standard
>  Time, rbj at rbjones.com writes:
> and my example was offered as an analytic
> proposition in the metalanguage,
> 
> ---
> 
> Oops, thanks for that.
> 
> So if I'm following. Since English can be the
>  Meta-language, we don't really need a formal proof, as
>  it were that something is analytic _in_ the
>  meta-language. But I guess the idea is to proceed,
>  _informally_, as we have proceeded, _formally_, in the
>  construction of the object-language. I suppose the  mere
>  _examination_ of a claim (in the meta-language) would be
>  enough for the  analyst to judge whether it is analytic
>  or not. My procedure would be to refer  to something
>  like the corresponding object-language tautology, i.e.
>  the  meta-language analytic sentence _sans_ quotation
>  marks, as it were. But there  may be more complications.
>  Where would philosophy be without them?!

If you are trying to decide the status of a claim in the 
metalanguage about the status of a claim in the object 
language (as to whether it is analytic) then the key 
consideration is whether your knowledge of the meaning of 
the claim in the object language comes from your knowledge 
of the meaning of the metalanguage or not.

When your metalanguage is informal that may be hard to 
determine, even if the object language is formal.
For example, if I said

	"0=0" is analytic in the language PA

you have a problem in settling what the scope of the 
definition of PA is.
If the meaning of PA (not the meaning of "PA") is part of 
its definition (i.e. of the definition of "PA") then that 
statement is analytic.  But is it?  If you look for 
definitions of PA, you will get some precise definitions of 
the formal system, and its not hard to figure out from the 
associated narrative what is the intended semantics,
But as to whether the semantics part of the definition, I 
don't know how you could decide that, I don't think the 
literature would be sufficiently explicit.  Some of the time 
it would be clear that PA is just a formal system and 
encompasses only the syntax. (in which case the claim would 
be synthetic, possibly, or possibly would fall down a 
crack).

If you set out to use your informal language more precisely, 
and in it you actually do offer a definition of PA and include 
in it the definition the semantics, then you would be able to 
assert that the above claim is analytic.
But I have never seen that done.

The whole area, using natural languages as metalanguages for 
formal systems, is a case of pushing natural languages into 
new territories, and when you do this you are likely to find 
that unless you make the meanings definite by careful 
stipulation, they will not be sufficiently definite for 
judgements to be possible about this kind of issue.

RBJ



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