[hist-analytic] Quine, Aune, Jones: on defining analyticity
baynesrb at yahoo.com
Thu Mar 19 07:34:38 EDT 2009
On Wednesday 18 March 2009 00:59:43 steve bayne wrote:
>>All the action is 'analytic-for L_0'. The reasons
>>one might give vary; some depending on what approach
>>you take to philosophical problems more generally.
>>'Analytic' as a semantical notion, like 'true', is
>>understandably restricted to a particular language.
>Surely that's not the case.
I meant, here, 'analytic' in 'analytic-for L_0'
or where we speak of sentences as analytic.
Sure for Kant this is not the case, but mainly
because for Kant judgments are analytic, not
sentences in any underived sense.
So as long as you are speaking of sentences
then to describe a sentence as analytic is a
meta-linguistic statement. Frege's accepts
thoughts or propositions and, so, here there is
no idea of 'analytic' as a meta-linguistic
predicate. This sort of thing begins with
people like Hilbert and Lowenheim, which
you probably know already.
In order to assess your theory of analyticity,
we need to know what "objects" can be said to
be analytic on your account.
On Quine, you are incorrect, in my opinion.
Quine is not calling for a general notion to
be explained; he is denying the existence of
any general notion. I doubt that the idea
of such a general notion would make sense to
him. Same with 'true'.
Now if you take analyticity as truth based
on meaning, then you have 'meaning' to
contend with; you need to establish what
meaning is and, especially, if you are
asserting a connection between meanings etc.
Keep in mind that 'meanings', even, if you
accept translation are creatures or language;
so if you want to arrive at, say, a Kantian
idea of analyticity you need to link meanings
and concepts. Fregean functions are
sometimes thought to serve this purpose; then
there is the notion of meanings as captured
in "worlds"; that is, senses, intensions
etc. become expressed in terms of extensions
over worlds (essentially Carnap, Montague).
As for your last points: I believe necessity
is generic; that there are different ideas
of necessity. Part of the issue historically
is that before DeCartes the importance of
necessary truths is not to guarantee certainty,
at least in any obvious sense; it is to enable
truths, such as Anselm's argument and the
difference between sophistry and philosophy,
although this latter has an epistemical
"spin"; it is not in any case Cartesian
doubt that is involved.
The issue of analyticity has a couple of
extremes that need to be avoided. Spelling this
out is a long story I just can't enter into; but
here are a couple of thoughts.
One, among several, complications related to
analyticity is related to mathematical foundations.
This is not an epistemological area of investigations.
Validity theory is not designed to solve the
problem of skepticism in mathematics. Recall my
question about whether truths of logic, even
of the Boolean sort, are analytic? Quine and
others take this as given. I don't. At the level
of functional logic we find ourselves in
deeper waters - confusion over problems of
infinite cardinals, for example. But what is
very puzzling is the role of domain size in
axiomatic treatments of foundations. whether
a truth in functional logic (first order) is
a tautology or simply false depends on the
size of the universe. The old Axiom of Infinity
was indicative of this problem. If the size of
a domain is contingent then it is arguable that
no truth of logic is analytic in a certain sense.
Now a lot of people will take exception to this
but I've never had a satisfactory answer.
By the way, I can't find your remark on Kripke
on the underdermination of truth. He has some
completeness theorems and others have them.
(they come cheaper by the dozen) but I found this
an interesting point.
From: Roger Bishop Jones <rbj at rbjones.com>
To: hist-analytic at simplelists.com
Sent: Wednesday, March 18, 2009 3:28:35 PM
Subject: Re: Quine, Aune, Jones: on defining analyticity
On Wednesday 18 March 2009 00:59:43 steve bayne wrote:
>All the action is 'analytic-for L_0'. The reasons
>one might give vary; some depending on what approach
>you take to philosophical problems more generally.
>'Analytic' as a semantical notion, like 'true', is
>understandably restricted to a particular language.
Surely that's not the case.
Is Kant's definition of "analytic" specific to some
language? Is Frege's? Is Ayer's?
We know Carnap, at least in his syntactic phase
advocated defining "Analyticity-in-L", but I
consider that to have been a grave mistake which
has lead to many problems (and invited "Two Dogmas").
In the passage you cite Quine is complaining that
by defining analytic in L_0 for various languages:
> We do not begin to explain
> the idiom 'S is analytic for L' with variable
> 'S' and 'L' even if we restrict the range of 'L'
> to the realm of artificial languages".
And he evidently (and in this I agree with him)
is calling for the general notion to be explained.
(though he finds it easier to criticism his own
generic accounts of language specific definitions)
This is what the phrase:
"true in virtue of meaning"
does, and it is also what I do in my mathematical model.
It is also what I do in the definition which
I proposed to use in my monograph.
>If you don't do this, you invite paradoxes etc, and
>probably abandoned that way of doing philosophy where
>the objective is to construct languages based on what,
>in fact, turn out to be one's philosophical positions.
>Not just "languages" but a language that captures
>all "analytic" sentences in the way that isn't much
>different from capturing all and only sentences that
>are 'grammatical' in a single generative theory of
>syntax. There are parallels.
A general account of analyticity of the kind
which Quine speaks of does not presume that
all analytic sentences are expressible in a single
The definition of analyticity is much much less
problematic than the definition of the semantics
of a language.can be, which is why a clear
distinction should be drawn between defining
the concept of analyticity and defining the
semantics of a language, and why a specific
definition of analyticity for some language
>Up to this point, we don't appear to disagree.
If the "we" you speak of is you and I, I am
startled to see you write this.
The two principle points you have discussed
so far are:
1. Whether analyticity should be defined
generically or separately for each language.
2 Whether analyticity is or is not the same
To which my answers are "generically" and "yes",
and if I have understood you correctly yours
are "separately" and "no".
I hope I have misunderstood you.
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