[hist-analytic] Quine, Aune, Jones: on defining analyticity

steve bayne baynesrb at yahoo.com
Tue Mar 24 07:44:47 EDT 2009


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 witha grain of
salt. 

First, even though you have an attempt at a general 
definition, it is still a definition of analyticity
in terms of language. There is relativity to an
unspecified language but language nonetheless; so
the notion of necessity remains semantic. 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. So what
you have is a trade off: involving analyticity in *some* language,
but your "admissible" models are quite specific. He
tries to dodge this a bit in his remarks on designation,
but they are still a dodge. 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 Carnaps orbit will maintain that three things are
involved here.

The first thing is language specific analyticity; then
there is analyticity for *some* language; 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. 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).
Now I ask: What makes THESE truths analytic? Validity in
all admissible models? This does not seem like what you are
after. 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.

On '(Ex)(Ey)(z)[f(x) & f(y) -> f(z)]' my point is that
logical truth is relative to the cardinality of the domain.
Logical truth in first order logic is relative to the
cardinality of the domain of the language. You are right that
it is not perfect; quantification over the predicate would
be necessary. This is one of those things we could get hung
up on. I think it is important but it raises issues that 
may get us off track. Not sure. Let me say something related,
not the same, but more interesting philosophically.
Once you assign values to the individual constants in any
interpretation then a sentence like '~(a = b)' becomes
"analytic," or necessary. That is if 'a' and 'b' are 
logically proper names etc. But here analyticity has nothing
to do with Carnap's "admissible" models, but with any
model! 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. Further, what is a sentence that is not a
sentence of a language? 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. Ontological relativity is 
what results when you deny analyticity in the way Quine
has done it. Carnap wants to resist this, partly because his
attachment to science is deeper than Quine's, philosophically.
But that is a long story. My position is that there are
necessities that do not depend on models. 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?
 

STeve



________________________________
From: Roger Bishop Jones <rbj at rbjones.com>
To: hist-analytic at simplelists.com
Sent: Monday, March 23, 2009 6:00:41 PM
Subject: Re: Quine, Aune, Jones: on defining analyticity

I'm afraid there is some repetition in the following
response to Steve.  Hope it isn't too tedious.

On Saturday 21 March 2009 17:42:20 Baynesr at comcast.net wrote:

>On analyticity, post Kant, prior to
>Carnap, the idea is kicked around
>in terms of validity, in particular
>proof theory. I know of no definition
>of 'analytic' which is not language
>specific, post Tarski. Can you cite
>one?

Depends what you count as "post Tarski".
Taking this as after his paper on the
definition of truth we have, Ayer, Carnap,
Quine, Kripke.  All of whom took analytic
to mean "True in Virtue of Meaning".
Admittedly, Quine didn't think the definition
worked but all the others seemed to find
it useful.

Of course it depends what you mean by
"language specific".  (and I see now from
comments below that at least some of the time
you are using this in a sense distinct from
that which I have been employing)
What I meant by that was a definition of
analyticity for some specific language.
In another sense even the generic
definitions of analyticity are language
specific, in the sense that a sentence
can only be said to be analytic in some
particular language, given the semantics
for that language.  If you spell out the
generic definitions, then analyticity will
be a relation between sentences and languages,
or between sentences and the truth conditions
of the relevant language, or else a property
of a pair consisting of a sentence and a language.
But then you need some context too.

>If this is
>your view, and you may be right, I think
>what we need is something to justify this,
>beginning with what you take 'analytic'
>to mean. Indeed, my reason for having
>some sympathy for what I take to be
>your program is that neither truth
>nor validity captures analyticity.
>There is this business about "essence"
>that will not go away, unless we make
>the Quinean (Carnapian) "semantic
>ascent."

Well you have my proposed definition,
in terms of necessity.
By saying "expresses a necessary proposition"
the semantics of the language is made
central, since the semantics tells us what
proposition is expressed by each sentence.
(a proposition is the meaning of a sentence,
in some given context)
However, "true in virtue of meaning" would
do almost as well if that is any easier
for you to understand.

These definitions are "generic" in the sense
that they define analyticity for a broad range
of languages, but they do define it in terms
of the semantics of the language, so the concept
of analyticity thus defined is not a property of
sentences, it is a property of sentences in some
given language (ordered pairs perhaps), or a
parameterised property of languages.

The important part is that the definition of
analyticity and the definition of the semantics are
separated out, whereas in language specific
definitions of analyticity, the definition
of analyticity is in effect a (partial) definition
of the semantics of the language.

>>I do of course accept that when analyticity
>>is defined explicitly in terms of meanings,
>>or when that it done indirectly as in my
>>proposed definition, then to apply the notion
>>to specific languages you need to have some
>>information about the semantics of the
>>languages in question.
>
>Yes. However, meaning is language specific,
>like 'analytic' in my opinion. A set of
>morphemes may have one meaning in one language
>and another in another language.

Yes I don't deny that.
I advocate a single generic definition of analyticity
in terms of semantics (or truth conditions)
and my definition in terms of necessity is such
a definition since necessity is semantic
(a property of propositions), together with
definitions of semantics which are specific
to each language.

>>So far as Kant is concerned, my proposal is
>>intentionally divergent from Kant.
>>My monograph is to make a feature of
>>Hume's fork, which Kant was inspired to reject.
>
>Since I'm, more or less, a Kantian, it is
>essential to any comment on my part that you
>flesh this out or be more specific.

Isn't identifying analyticity and necessity
specific enough to set me apart from Kant?
(counting the whole of mathematics as analytic)
I don't know much about Kant's philosophy but
my understanding was that he was aroused from
his dogmatic slumbers by Hume's fork and he
differed from Hume in regarding mathematics
as synthetic.
(though Hume didn't have the words)
The important thing is that Hume trashed
metaphysics and Kant revived it.

>>Well they don't use the terminology, but one
>>can see in mathematical practice that
>>mathematicians take great pains to ensure
>>that mathematics is analytic.
>
>There are mathematicians of great talent
>who affirm the Kantian position, e.g.
>Poincare.

I am talking about contemporary mathematicians.
Poincare was active at the time of flux
in the foundations of mathematics, and therefore
pre-dates the standard practice to which I
was alluding.
For that matter there may well still be
Kantian's about, and I think there are very
large numbers of mathematicians who don't
have a clue what the word "analytic" means.
But you would have to look very hard to
find mathematicians who do not think that all
their results are proven by sound deductive
methods, and that suffices to ensure that the
results are analytic (by "my" definition)
even if they don't know it.

>>I'm afraid I don't understand your point here.
>
>The example I've seen most often is:
>
>(Ex)(Ey)(z)[f(x) & f(y) -> f(z)].
>
>In a universe where the domain is 2 or
>less, it is logical truth. But in a
>universe of 3 individuals it is not.

The example isn't quite right, (you need
to insist on x and y being distinct) but
in any case you can't constrain the
domain and still talk about it being
a logical truth.
You can say "true in every interpretation
whose domain is no larger than 2 elements",
but "logical truth" in this context
would normally be taken to mean
"first order valid"
(supposing your formula to be in first
order logic)
which means true in every interpretation
(whatever the size of the domain).
However, I still don't understand the point
you are trying to make.

If your problem is with my claim to
analyticity of mathematics, then you
have to get the semantics straight.
If we take mathematics to be done in
set theory, then the relevant language
is first order set theory and the semantics
must include stiplulation of the intended
interpretation, i.e. the cumulative heirarchy
or some sufficiently large initial segment of it)
In that case "true in virtue of meaning"
means "true in the cumulative heirarchy"
which all the theorems of set theory most
probably are.  If mathematicians did not
believe that then they would abandon set theory
(or find some other theory/interpretation
combination such that they theorems are true
in the interpretation(s)).
Mathematicians really do believe that their
theorems are true, and since the domain of
discourse is abstract, truth and analyticity
will coincide (existence of abstract objects
is not contingent).

>>All theorems of sound deductive systems
>>are analytic in the sense in which Carnap
>>and I use the term, and in the sense
>>"true in virtue of meaning".
>
>Well, I'm still not sure, since Carnap
>offers several definitions of 'analytic'.
>Do you have one in mind in particular?
>Which?

Although Carnap had several different approaches
to "defining analtyicity" for specific languages,
(which wass really his way of defining the semantics
of a language, but not later - see below) he did
nevertheless always have an overall generic concept
of analyticity and I am not aware of any significant
change to this (though doubtless he put it
in more than one way).
The best place to find this is in the Schilpp volume
(see below).

I looked back at my very concise notes on Carnap's
philosophy

http://www.rbjones.com/rbjpub/philos/history/rcp000.htm

and found some interesting stuff.
In the section on semantics, paragraph headed
"semantics and modality".
When Carnap came to considering modal logic, he decided
to define logical necessity in terms of logical truth
(which for him was the same as analyticity).
This is the opposite of my proposed definition of
analyticity, so in effect he is agreeing with me
that the two concepts are interdefinable, but chosing
to do it the other way round.
("a proposition is logically necessary iff a sentence
expressing it is logically true")
This is in the biographical part of the Carnap Schilpp
volume.

Elsewhere in that volume there is a paper by Bohnert
on "Carnaps Theory of Definition and Analyticity"
in which there is some discussion of the distinction
raised by Quine between definitions of analyticity
for specific languages, and the of "the general
relative term 'analytic'" for variable S and L.
Bohnert thinks this latter will be something like
a family resemblance concept for which no definition
will be feasible.
In Carnap's response however, which is very short and
approving, he contradicts this particular point, saying:

  "it is possible to give general exact definitions
   both for A-truth (analyticity) and for truth
   provided that other suitable concepts occurring
   in these general definitions are introduced by
   recipe definitions"

(here "general" is my "generic" and "recipe" is my "specific")
Carnap refers to an earlier response in which he
gives he then position on semantics and which contains
general definitions for truth and analyticity (pp900-905)
I'm please to say that in this (possibly his last
account of his position on these methods) he is doing
broadly what I have been suggesting is desirable.
i.e. that there should be no language specific
definition of analyticity, only a general one, which
defines analyticity for an arbitrary language in terms
of the semantics of that language (not in terms of a
definition of analyticity for that language).
The definition of semantics is in this proposal given
as rules of designation, not as a language specific
definition of truth or analyticity.

Hope this is not just adding to the confusion!

Roger Jones
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