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

Baynesr at comcast.net Baynesr at comcast.net
Sun Mar 29 15:08:44 EDT 2009



I don't think Quine is "calling for a 
definition of a relational sense of of 
'analytic'. This conjures up the image 
of a guy looking for a lost dog he 
loves. This is not Quine's position. 
Let me use hyperbole in the opposite 
direction: Quine believes that 'analytic' 
is a worthless idea, whether you you 
view it as relational or as indexed to 
a language. This is in marked contrast 
to 'true' which is also indexed, but 
has a lot more going for it. I remain 
a little puzzled by your use of "general." 
What you seem to mean, following Quine 
(rightly enough) is 'analytic' where 
in 'analytic in L' 'L' is to be understood 
as a variable. But now if it is a variable 
it is either existential or universal. 
If existential, then the force of 'general' 
becomes an issue; if universal, then you 
may encounter problems related to the 
paradoxes since the universal quantifier 
will include the meta-language. A better 
sense of general is one, entirely, devoid 
of reference to language, such as we 
find in Kant. That in my opinion is what 
we need. In fact, I think it is an easier 
objective. Kant got it, basically, right! 

I follow Kant: 'analytic' characterizes 
judgments, not sentences (only derivatively 
sentences). I find judgments more credible 
than "worlds." I'm acquainted with my 
judgments but I've never been to another 
world. I'm not being as cynical as I know this 
must sound. I simply do not believe that 
there ARE other possible worlds, whereas 
I am convinced there are judgments belonging 
to "judgers." Nor do I believe that there 
are propositions, except in the sense of 
constructs, perhaps. Behind these expressions 
of skepticism is my radical nominalism. 
If Frege, for example, is a nominalist it is 
nothing that strikes me as obvious. 

There is one point of very strong agreement 
between us, I think. The place of 'necessity' 
in dealing with 'analytic' presents a challenge. 
If you go back to Kant, I think you will be 
surprised at how few instances there are where 
Kant mentions necessity in connection with 
analyticity. His thinking, I believe, is that 
as long as all analytic sentences are a priori 
then all analytic sentences are necessary. 
However, if you think of analyticity one way 
(roughly: "the concept of the predicate is 
contained in the concept of the subject," 
adjusting for 'predicate' in the domain of 
judgments: call predicates 'what is asserted 
in a judgmet of some subject') then there is 
very little reliance on the concept of 
'truth' and so little to do with necessity, 
per se. If a concept of necessity is possible 
outside of language, then a "general" definition, 
one not relative to ANY language, is in the offing. 

I'm skipping the next couple of points because 
I think both of us were unclear. I plead guilty 
since I started it. I'll return to the definability 
of concepts such as 'satisfaction' later. Here 
we encounter issues that are very similar. 
Satisfaction, at least in a Tarskian, sense is not 
to be seen as a substitute for reference. But this 
is complex. Quine it should be mentioned doesn't 
take 'satisfaction' as undefined; but the definition 
he gives relies on language specific definitions. 
I'll have to look at it more closely. It's in his 
"On an Application of Tarski's Theory of Truth." 
Again, I haven't looked at this in a while but 
you might want to take a peek. (Selected Logic 
Papers). 

I will explain my point about Carnap's view 
of analyticity and L-truth. He begins the tradition, 
more or less, of assuming logical truths are 
analytic. Restricting ourselves for purposes of 
illustration to Boolean logic of propositions, 
we say that a proposition of logic is analytic 
if it is true in all state descriptions - there 
are qualifications to this, such as the propositions 
have to be in normal form. But the point is that 
the whole idea of L-truth and, therefore, analyticity 
in Carnap relies on state descriptions, and 
being "true" in all state descriptions (this relates 
to but is not exactly the same as worlds). But 
now analyticity depends on truth in Carnap. 
Since all other analytical truths, 'analytic' 
in the broad sense, depend on L-truths it follows 
that Carnaps position on analyticity, generally, 
depends on the analyticity of L-Truths. 

"the domain is part of the interpretation, and 
therefore the sentence must be true in interpretations 
with any cardinality" 

If you interpret the sentence '(Ex)(Ey)(z)[f(x) & 
f(y) -> f(z)]' in a domain containing more than 
two individuals it is not true. Similarly, if you 
the sentence '(Ex)(Ey)(z)[z=x v z=y & ~(x=y)' in 
any domain greater than or less than 2 it, too, 
is false. This is pretty much standard stuff. Similarly, 
in order to do the semantics for any system capable 
of handling transfinite numbers your are going to 
need more than a countable domain. Anyway, the real 
philosophical point is that the individuals 
constituting the domain enter into any philosophical 
account of a rational reconstruction of cardinal 
arithmetic. Related to this is a point I believe 
Hintikka makes, but I'd have to check. He notes that 
the domain of individuals cannot contain members that 
are not compossible, although I don' think he uses 
this expression. As long as we talk about language 
we are never going to understand the world, and the 
world is the subject matter of philosophy if not 
logic and its constructions. I side step your other 
argument since I say one thing; you say another, without 
argument. 

With respect to your other comments, I take a Quinean 
position. I understand the concept 'true' (consider 
Tarski "reliance" on Aristotle); I don't understand 
'analytic' ab initio. So I don't see much value in 
trying to define it with all the "mumbo logics" etc. 
The term, unlike 'true', is a technical term. Tell me 
why I need it and I'll wade through more of Carnap's 
efforts to do whatever it was he was trying to do. 
But outside the notion of a "judgment" I see little 
use for it, unlike 'logically true'. A final point. 

It has been argued, vigorously, (and here I'd mention 
Marian David's paper "Analyticity, Carnap, and Truth" 
_Philosophical Perspectives_, 10, 1996) that Quine 
will have to reject 'true' for the same reasons he 
rejects 'analytic'. Otherwise, the entire enterprise 
initiated by the "linguistic turn" is in danger. 
I agree with this assessment, but I don't agree that 
Quine is wrong for the reasons he gives. The question 
we might pursue is this: can we do without 'true' as 
well as 'analytic'? I think not. The problem runs 
deeper than constructed languages can carry us. A 
general concept of truth is what we get when we use 
Tarski as providing a criterion but find the definition 
to be "value added." The same might be said of 'analytic'. 

Finally, I like Quine have a problem with meanings; no 
one has a convincing argument so far as I can tell 
that we need them. We may need essences, but that 
depends on how we reconcile them with nominalism 
in an empiricist epistemology. 


Regards 


----- Original Message ----- 
From: "Roger Bishop Jones" <rbj at rbjones.com> 
To: hist-analytic at simplelists.com 
Sent: Saturday, March 28, 2009 3:58:01 PM GMT -05:00 US/Canada Eastern 
Subject: General v. specific definitions of analyticity 

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 
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://rbjones.com/pipermail/hist-analytic_rbjones.com/attachments/20090329/22907986/attachment-0002.html>


More information about the hist-analytic mailing list