[hist-analytic] Frrom AUNE: Analytic and A Priori

[Bruce Aune]

This is my last attempt to deal with Roger’s proposals regarding  
analyticity.  I told Roger before that I saw little profit in  
continuing our discussion, but I now think that a few further remarks  
might possibly be worthwhile.  I will number my remarks so that  
distinct points can be considered separately.

1.    I continue to believe that Roger’s use of the expression  
“analytic” is idiosyncratic and misleading, but I think he is  
entitled to use it as he wants to, so long as he makes his meaning  
clear to others.  They may, or they may not (as I believe), find his  
usage useful.

2.    The standard philosophical use of the expression comes from  
Kant, who used it in raising a philosophical problem that has no  
connection that I can see with Roger’s concerns.  This philosophical  
problem persists, at least in a qualified way, and that is my  
principal reason for thinking that Roger’s use is less than useful.

3.    Kant explicitly applied the expression to universal affirmative  
judgments, leaving its application to other judgments essentially  
open. (This is one standard criticism with his procedure.) As Kant  
understood them (following the logicians of his day), universal  
affirmative judgments (or UAJs) contain two terms, a subject term and  
a predicate term.  Such judgments are true when their predicate term  
applies to whatever falls under their subject term.  Kant's  
definition of an analytic judgment is built upon this semantical rule  
and shows us why analytic judgments are bound to be true.  A UAJ is  
true, he said, when its predicate term is contained in the concept of  
its subject; it is contained in such a way that if the subject term  
applies to anything x, its predicate is guaranteed to apply to it as  
well.  If A&B is the subject term of a judgment J and B is its  
predicate term, we can see that a thing x is truly described by A&B,  
x is truly described by B as well.  There is no philosophical problem  
in seeing why such judgments are true, both universally (for every  
object x, as we should say today) and necessarily (there are no  
possible exceptions).

4.    UAJs that are not analytic are, Kant stipulated, synthetic:   
this is just what a synthetic UAJ is suppose to be.  Although we can  
see a priori that analytic UAJs are true, the universal and necessary  
truth of synthetic judgments is highly problematic.  There is no  
discernible connection between subject and predicate that guarantees  
their truth; this must be accomplished by some “third thing,”  
something additional to semantic inclusion. The question “How could  
judgments of this second kind possibly be known to be true a priori?"  
is the fundamental topic of Kant’s famous Critique of Pure Reason.

5.    In the new logic introduced by Frege, Kant’s UAJs were  
transformed into universally quantified hypotheticals, the subject  
and predicate terms of Kant’s judgments becoming predicates attached  
to common bound variables.  Although it is easy to see that anything  
falling under the predicate “an F that is a G” must equally fall  
under the predicate “a G,” so that “For all x, if x is an F that is a  
G then x is a G” is clearly universally and necessarily true, it is  
not easy to see how hypotheticals of other type are equally true  
universally and necessarily.

6.    Kant was convinced that representative examples of  
arithmetical, geometrical, and metaphysical judgments (or assertions)  
are true yet synthetic.  He tried to show in his first Critique that,  
in spite of being synthetic, such judgments are necessarily true.   
Few philosophers today think Kant efforts in his first Critique were  
successful; in the last 20 years of my professorial career I devoted  
more than 15 courses exclusively to Kant’s critique, and I am  
convinced that his efforts were uniformly unsuccessful.  The  
epistemological rationalists of the past twenty years—Chisholm,  
BonJour, and others—have written books and articles trying to show  
that their favorite examples of synthetic a priori statements are  
actually true, but they have plenty of contemporary critics, and the  
contemporary philosophical tide a pretty clearly turning against them.

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.  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.  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.  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.

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.”

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.”  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.

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.   
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.  (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.)

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.
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