[hist-analytic] Frrom AUNE: Analytic and A Priori (7-11)

Roger Bishop Jones rbj at rbjones.com
Tue Apr 21 15:07:40 EDT 2009


This is the last installment in my response to Aune,
and is principally concerned with what he calls
the "truth-certifying property" of a definition
of analyticity.

On Monday 23 March 2009 20:32:52 Bruce Aune wrote:

>7.    The principal significance of the preceding paragraphs for my
>ongoing dispute with Roger is that the original notion of
>analyticity, Kant’s, was intimately connected with a way of
>ascertaining the truth of a special class of judgments, or
>statements.

I don't believe Kant supplied such a method.

>Kant’s conception of analyticity is now generally
>conceded to be inadequate because it applies, at best, to a narrow
>class of statements, UAJs of subject-predicate form or, expanded in a
>natural way, to a narrow class of universally quantified
>conditionals.

It is immediately apparent from a reading of Kant's definition
of analyticity that he does not himself regard his definition
as constrained to "UAJ"s.  He explicitly regards his definition
as also applicable to negations of subject predicate sentences,
and from this we can reasonably infer that by similar
unspecified means he would accept its extension to other
kinds of judgement (though possibly he thought there were
no other kinds apart from negations).

>Frege’s conception, which Frege explicitly advanced
>(in his “Foundations of Arithmetic”) as a means of accommodating the
>new logic that he had a large part in inventing, is also closely tied
>to a way of showing the truth of analytic statements:  S is
>analytically true iff is reducible to a truth of logic by a
>replacement of synonyms for synonyms.

I don't believe that this is Frege's view, it is rather,
a corruption of Frege's view which Quine found it convenient
to attack in "Two Dogmas".
Frege's position required only the elimination of definitions,
which is less problematic since it does not depend on a general
notion of synonymy, and cannot therefore be accused on this
count of circularity.

>In my book I argue that
>Frege’s conception is still unacceptably narrow, but my own
>conception, which is a modification of Carnap’s, retains the truth-
>certifying property.

I would be interested to know what weakness in Carnap's conception
of analyticity your own is intended to remedy.
As you know my own conception is easily seen to be
equivalent to Carnap's.

>8.    In a couple of his recent notes, Roger claims that the
>requirement that an adequate specification of analyticity should
>possess this last property “can and should be rejected.”

This is not correct.
I was quite careful in what I rejected, and what I rejected
was the existence of an effective decision procedure for
analytic truth.
If your notion "truth-certifying property" entails the
existence of a decision procedure then its non-existence
either for mine or for Kant's concept of analyticity
would follow from my denial.

>9.    He says, first, that “It is clear that to establish "truth" of
>a sentence must be in general no more difficult than establishing
>"analyticity", since every analytic sentence [according to his
>specification] is true.”

Should I read the parenthesised interjection as indicating that
you have a conception of analytic truth in which an analytic
truth need not actually be true?
This would be a radical departure from precedent, as well
as rather strange terminology.
Of course, sometimes the term "analytic" is used to encompass
both "analytic" and "contradicatory" but that was obviously
not the usage in my above argument (surely it is obvious that
what I there intended was the platitude that
"every analytically true sentence is true")?

>This remark does hold for Roger’s unusual
>and anomalous notion of analyticity, but it does not hold for
>traditional approaches to analyticity, which purport to make it clear
>just how analytic statements are to be identified and why they
>deserve to be considered true. Roger bypasses this concern entirely.

I have given a definition.
I certainly intend to make clear how analyticity can be established.
However, I will not be able to supply a decision procedure,
any more than Kant could for his conception of analyticity.

>10.  Roger also says, “It is also clear that even when the semantics
>of a language as a whole is as clear as it possibly could be, for
>example the semantics of first order arithmetic (which is as clear as
>any language of similar expressive power, and clearer than most) this
>does not mean that there is any reliable way of deciding whether
>sentences in the language are true.” But the truth of mathematical
>truths has always been considered philosophical problematic.

Well my definition of analyticity, just like Carnap's encompasses
all the truths of mathematics, so you will therefore understand
why I cannot supply a decision procedure.

>Mathematicians prove them (when they can) by deducing them from
>various axioms, but how do we know that standard axioms are, in fact,
>true?  To ask this question is not cast doubt on their truth; it is
>to ask what it rests on, what its basis is.  Gödel thought we can
>apprehend basic mathematical truths by some kind of direct intuition,
>which he considered analogous to vision; others, such as Carnap, who
>considered them analytic, thought they were reducible to logical
>truths.

I don't think this is a satisfactory account of Carnap's position.
He regarded mathematical truths as logical truths, not as reducible
to logical truths, and if an account were to be given of the
basis for belief in the truth of the axioms, this would be as
true by convention, and as constituting part of or the whole
of the definition of the terms they contain (i.e. as implicit
or explicit definitions).

>(When logicists claimed they were true because analytic,
>they were not even suggesting that they are true for the simple
>reason that they are necessary.)

Carnap defined necessity in terms of analyticity so that
course was not open to him.  But the end effect of my
position is the same as Carnap's.  Whichever is taken
as "primitive" is not important, because Carnap and
I, when called upon to explain the primitive concept
will give similar answers.
This is because Carnap and I see that when "true in
virtue of meaning" is explained as "tautologous" along
the lines of Wittgenstein's tractatus (which Carnap mentions
in this context) then the result is the same as the explanation
of necessity as "true in every possible world".
This is because "state of affairs", "possible world",
"state description", "model" all contain the same information.
(you have to drop Wittgenstein's insistence on the logical
independence of distinct atomic propositions to make
this work for Carnap's notion of analyticity).

>11. The current issue in philosophy about analyticity is partly
>directed to the task of finding an acceptable criterion for analytic
>truth, one satisfied by all and only uncontroversial examples, that
>shows how such truths “are possible” and can be known by human beings
>without requiring them to possess some supposed faculty of a priori
>intuition, of the sort rationalists suppose; and it is partly
>directed to the question of whether the objects of human
>understanding, as Hume described them, can in fact be divided into
>two discrete classes, one concerned with matters of fact and
>existence, and one concerned with matters that can be decided without
>reference to anything irreducibly empirical, except possibly for
>ideas we happen to have or what meaning we give to various words.  I
>can’t see that Roger’s conception of analytic truth applies to either
>of these matters.  It seems to bypass them entirely.  For that reason
>alone, I doubt that most philosophers will find it useful.

"The current issue in philosophy about analyticity"!

I just looked at a paper by Peacocke in which he begins by
listing five problems which any philosophical theory of the
a priori "must" address, not one of which I intend to consider
in my monograph.

Naturally I don't accept your attempt to set my agenda.
Whether my concerns are "current" is not of interest
to me, I am much more interested in fundamental problems
which are timeless.

I have given a *definition* of analyticity, which I intend
in my monograph to expand upon.
I will not be giving a "criterion" for analytic truth,
nor will I even mention that concept, but I do intend
to describe methods which may be used to establish analytic
truths (which come down to proof in some analytically sound
deductive system). 

I am puzzled that you should think a definition which is put
forward to make more precise Hume's fork is not applicable to
that purpose, especially when it is equivalent to the
definition most often cited by philosophers in the 20th
century.

Roger Jones




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