[hist-analytic] Quine, Aune, Jones: on defining analyticity
Roger Bishop Jones
rbj at rbjones.com
Mon Mar 23 18:00:41 EDT 2009
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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