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

Roger Bishop Jones rbj at rbjones.com
Fri Mar 20 17:12:59 EDT 2009


On Thursday 19 March 2009 11:34:38 steve bayne wrote:
...
>In order to assess your theory of analyticity,
>we need to know what "objects" can be said to
>be analytic on your account.

I didn't really put forward a "theory",
I put forward a definition, which was intended
to be read as a proposal for usage, not a
description or explication of previous usage
(though it is arguably consistent with much
prior usage).

>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'.

The two are not incompatible.
He says that before we can understand rules
for specific languages we "must" understand
the general notion.
He is calling for the general notion to be
explained, and denying that it can be.

Prior to Carnap, so far as I am aware,
no-one discussed anything but the general
notion (though not explicitly talking in
terms of variable L).
I believe it to be a mistake ever to
consider language specific definitions
of analyticity.

>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).

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.

I would not look back to Frege for help
in dealing with semantics these days, though
no doubt his work has contributed in important
ways to modern methods in this area.

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.

>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.

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.

(i.e. they would not accept a proof of some
result as of any value if they were not
satisfied that the deductive system was sound)

>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.

I'm afraid I don't understand your point here.

>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.

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".

>Now a lot of people will take exception to this
>but I've never had a satisfactory answer.

If I understood the question I would have a
shot at giving you satisfaction.

>By the way, I can't find your remark on Kripke
>on the underdermination of truth.

Doesn't ring any bells for me, are you sure
it was my remark?

Roger




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