[hist-analytic] General v. specific definitions of analyticity

Roger Bishop Jones rbj at rbjones.com
Sat Mar 28 15:58:01 EDT 2009


Steve,

I think I've already said this but I'll say it
again.  We are at odds on the meaning of "general"
or "generic" in relation to definitions of 
analyticity.

Quine calls for a definition of analyticity
for variable S and L, not for one independent
of language.  This is to be contrasted with
a definition for some specific language.
This is what I also have advocated, it is what
is normally supplied as a definitions of analyticity
(though the reference to L may be implicit) and
this is what Carnap supplies in his general 
semantics in the Schilpp volume.

If analyticity is to be a characteristic of sentences
then it must be relative either to a language
or to a semantics.  If you want something which
is independent of language then it would have
to be a characteristic of propositions rather
than statements, and in my proposal that would
be the property of necessity, which is of course
normally defined as "true in every possible world"
and can in principle be ascertained for propositions
without knowing the language of any statement
expressing the proposition.

On Tuesday 24 March 2009 11:44:47 Steve bayne wrote:
>I'm going to reply "out of order." Hopefully, this will
>become self-explanatory. In Carnap's conception of
>analyticity in the Schilpp volume his views had changed
>considerably; just as they had changed from the
>Introduction to Semantics to Logical Syntax of Language.
>Carnap, as I said, offered a number of accounts of
>analyticity. This last one doesn't possess the generality
>I think you need to affect agreement. So when you speak of
>unspecified languages this must be taken with a grain of
>salt.

Its just as general as it can hope to be!

>First, even though you have an attempt at a general
>definition, it is still a definition of analyticity
>in terms of language.

Yes.

>There is relativity to an
>unspecified language but language nonetheless; so
>the notion of necessity remains semantic.

I don't know how necessity got in here, but I agree
that it is semantic (which doesn't exclude its being
metaphysical, since a metaphysic may be embedded in
the semantics of a language).

>Secondly,
>while the language at issue may be unspecified the
>fact is that unlike his earlier attempts at codifying
>a definition, such as in Foundations of Mathematics,
>this one is straightforwardly model theoretic.

This is however the definition of the semantics of
a language, not the definition of the concept of
analyticity.

>So what
>you have is a trade off: involving analyticity in *some* language,
>but your "admissible" models are quite specific.

The models are part of the semantics of the language,
which I agree will be specific to the language.

>He tries to dodge this a bit in his remarks on designation,
>but they are still a dodge.

There is no need, in my opinion, to dodge it.
He does not claim that definitions of semantics are
general, he claims this only for the definitions of
"truth" and "analyticity".

>There remains specificity
>as long as the lexicon belongs to the language rules.
>Further, in earlier accounts "semantical rules" don't
>enter. Now you may codify a general definition of
>"semantical rule" but whenever you use a language then
>you are stuck with some one list of rules. The philosopher
>outside Carnap's orbit will maintain that three things are
>involved here.
>
>The first thing is language specific analyticity;

But what you mean by that is different to what Quine,
Carnap and myself mean by it.

>then there is analyticity for *some* language;

Not clear what you mean by this.

>but, then, there
>is analyticity that is "free" of language, entirely. This
>I'll call the "ontological" view, where necessity reflects
>on the world rather than "today's" admissible model
>or the latest "mumbo logic" in the journals.

Well, this can only be for propositions, and still
depends upon a concept of possible world which may
be language specific (though we may expect this to 
be part of the proposition).

>The happy fact, from my point of view is that what
>ALL of Carnap's definitions of 'analyticity' presuppose
>is the analyticity of logical truths
>(truths derivable from null set of premises).

I don't understand why you say they "presuppose" this.
For Carnap logical truth and necessity both mean the same
thing as analyticity.

>Now I ask: What makes THESE truths analytic? Validity in
>all admissible models?

Whether you call these possible worlds or admissible
models is unimportant, the end effect is the same.
We are talking here about the domain of the truth
conditions, the conditions under which the truth conditions
must supply truth values, and for analyticity or necessity
the truth value must be true under all such conditions.

>This does not seem like what you are after.

I think it is. I think Carnap thinks it is too.

>I suspect that in any of Carnap's definitions of
>'analytic' you will find that the tie to a particular language,
>even when we speak of 'some' language, is the concept of
>truth. The machinery in the Schillp volume in my opinion is
>cumbersome, unintuitive, and philosophically dubious IF you
>think of analytic truths as independent of language in the
>usual and "acceptable" sense.

I don't. And I don't understand why you want to do that.
The canonical informal account of analyticity in
the twentieth century was "true in virtue of meaning",
and the meaning of a sentence clearly depends upon the
language in which it is interpreted.

>On '(Ex)(Ey)(z)[f(x) & f(y) -> f(z)]' my point is that
>logical truth is relative to the cardinality of the domain.

And my response was, that in the usual definition
this is not the case, because the usual definition is
"true in all interpretations", the domain is part
of the interpretation, and therefore the sentence must
be true in interpretations with any cardinality.
(unless you are talking of a Carnapian notion of logical
truth, i.e. analyticity, in which case the semantics
may constrain the admissible interpretations).

>Logical truth in first order logic is relative to the
>cardinality of the domain of the language.

No it isn't. (not at any rate if you mean by "logical truth",
as most people dealing with first order logic do,
"first order validity".  If you are speaking of
"truth in an interpretation", which is not the same as
logical truth, that depends on all features
of the interpretation, including its domain) 

In first order logic the language does not constrain
the cardinality of the domain (except to require it
to be non-empty).
Not as usually understood at least.
Of course, you could give a more specific semantics
to a first order language is you like.

>But more important, perhaps, and probably more
>productive for discussion is when you say:
>"so the concept of analyticity thus defined is not a property of
>sentences, it is a property of sentences in some
>given language"
>
>I don't see the difference, yet, clearly. The operant difference
>seems to be that analyticity is a property of "sentences in
>some given language." But how can it be a property of a sentence
>in some language and not be a property of sentences?
>I'm a bit mystified.

There are several ways of doing this which is one of the
problems, too many choices.
Some of them are shown in my mathematical model.

You can treat analyticity as a property of ordered
pairs, of which the first element is a sentence in context,
and the second is the language, (or just the semantics
of the language).
This isn't a property of sentences because in order
to get a truth value you have to have not only the
sentence but also the language, and the same sentence
may be analytic in one language, but not in another.
To get a property of sentences you have to fix
the language say to L, then you get the property
of sentences which might be called "analyticity in L".

Alternatively you might make analyticity into a
parameterised or higher order property, a function
which takes a language and yields a property.
i.e. analyticity is a function which given some
language "L" returns the property "analytic in L".

>Further, what is a sentence that is not a
>sentence of a language?

"P \/ -P" is often cited as if we know what it
means, but this sentence belongs to many formal
languages and you do not know what it means until
you know what language it is supposed to be in.
A string of characters, or even an abstract syntactic
structure, is a concrete or abstract sentence which
has no language unless one is supplied separately.

For natural languages overlap is rare, so its not
always necessary to specify the language, we can
guess what the language is.

>I think the key thing in all this
>is 'true'. Correspondence is to 'true' as necessity is to
>'analytic'. Finally, you seem to accept meanings (to get
>Carnap's extended sense of analyticity etc), but Quine's
>objections here stand, I think.

I am not a nominalist (at least not in the sense in
which Quine is sometimes tempted to be).
I have no problem with meanings.

>My position is that there are
>necessities that do not depend on models.

How do they fail to depend upon the notion of possible world
(which is what a model becomes when we deal with languages
for describing the real world).

>The idea in
>philosophy ought to be: "Let's get one good "model" of the
>world; the model is not the guide; the world is the guide
>to the model and that model is not a matter of choice. True
>this is almost Thomistic, but so what?

You are welcome to try.
But in practice we need several.

In science, we really do need both the Newtonian and the
relativistic models of the universe.

There are lots of problems with terminology here,
because philosophers and logicians don't use the
same terminology, and nor for that matter do
all logicians use all the same terminology much
less all philosophers.
So a lot of our disagreements here are probably
cause by diverse terminology.
This could take a long time to work through!



regards,
Roger




More information about the hist-analytic mailing list