Preproceedings 2006 - Austrian Ludwig Wittgenstein Society

The Analytic Theory of the A Priori: Ayer’s Argument
Tommaso Piazza, University of Salzburg, Austria
In Language, Truth and Logic Ayer offers systematic
presentation to the Viennese view that all a priori
knowledge is knowledge of analytic statements. Such
conception represents one of the most original
contributions proposed by the Wiener Kreis to defend the
empiricist epistemological principle that all knowledge of
reality stems and is justified by experience. The existence
of the statements of mathematic and logic has ever
represented a problem for the empiricist principle: on the
one hand, such statements seem to be known; on the
other hand such statements seem to express necessary
truths. Since experience can never justify knowledge of a
necessary statement, the admission of logical and
mathematical knowledge seems to entail the bankrupt of
the empiricist principle.
In response to this difficulty, Viennese logical
empiricists have maintained that logical and mathematical
statements, though necessary and known a priori, do not
violate the empiricist principle, because they are analytic
statements, that is to say, they are not statements about
reality.
Two main issues emerge from within this empiricist
solution: the first one concerns the very notion of
analyticity, the second one concerns the epistemological
role such notion has been taken to perform. In this paper I
shall not take issue with respect of the second issue. I
shall rather query one major presupposition in Ayer’s
conception of analyticity. I shall try to show that Ayer’s
notion of analyticity either entails counterintuitive
consequences, or that it is not sufficient to ground the
claim that all a priori knowledge is not knowledge about
reality.
The chapter The A Priori of Ayer’s Language, Truth,
and Logic presents an argument to defend the claim that
all statements known a priori are analytic statements,
together with a definition of analyticity (Ayer 1957, pp. 78-
79). Ayer’s argument can be systematized as follows:
A statement is analytic iff its truth is determined by
the meaning of its constituting expressions alone;
The truth of a statement is determined by the
meaning of its constituting expressions alone iff its truth
can be ascertained just by inspecting the meaning of its
constituting expressions;
The truth of the statement “either some ants are
parasitic or none are” can be ascertained by inspecting the
meaning of the constituting expressions;
The truth of “either some ants are parasitic or none
are” is determined by the meaning of its constituting
expressions;
“either some ants are parasitic or none are” is
analytic.
With the further principle
(CT) Statement “p” is analytic in the sense of (1) iff
“p” is not about reality,
the argument allows the derivation of the claim that
(AT) every statement that is known a priori is not
about reality.
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The argument, as it stands, is not sound. This can
be shown either by arguing against (1), or by questioning
one of its other premises. I begin by reviewing the second
strategy. The transition from (3) to (4) is valid, because it
appeals to (2). (2)’s left to right direction is unquestionable.
However, (2)’s right to left direction is much more
controversial. The rationalist Ayer opposes, for instance,
might deny it on the grounds that, on her intuitionistic
account of a priori knowledge, understanding certain
statements suffices to ascertain their truth without its being
the case that these statements’ truth is determined by the
meaning of their constituting expressions alone. More than
this, (2) could be questioned on broadly krepkean grounds.
For instance, it could be argued that the statement “stick S
is one meter long a t” is a statement whose truth can be
ascertained by considerations of meaning facts alone,
while it could be maintained at the same time that it is the
very length of S at t that makes the statement true (Kripke
1987, p. 153). However, these complaints raise delicate
issue in epistemology and semantics. So, for the sake of
argument, we can grant (2) to the empiricist, and proceed
to consider (1).
Few preliminary observations are in order. Ayer’s
original formulation is rather unfortunate: «a proposition is
analytic when its validity depends solely on the definitions
of the symbols it contains» (Ayer 1957, p. 78). Propositions
do not contain symbols, statements do. Accordingly, I have
interpreted Ayer as defining a sentential property, rather
than a property of propositions. It is an argument that can
be valid; statements, or propositions, can be true.
Accordingly, I have read “valid” as a misguiding variant for
“true”. Recent interpreters of Ayer’s argument have
proposed slightly different readings. Casullo has retained
talk of propositions, while reframing the definition in biconditional
terms, and in terms of truth. Swinburne has
offered the following reinterpretation:
A proposition is analytic if and only if any sentence
which expresses it expresses a true proposition and
does so solely because the words in the sentence mean
what they do (Swinburne 1987, p. 173).
I quote it at length because there is one feature of it
I shall retain in what follows, that is to say reference to the
property a sentence possesses when it expresses a truth
solely because the words in the sentence mean what they
do. This pretty vague interpretation of Ayer’s no less
ambiguous «depends solely» will prove of central
importance, in what follows, for assessing whether Ayer’s
argument actually succeeds in showing that all a priori
knowledge is not knowledge of reality.
The following argument is aimed at showing that (1)
is highly problematic, and so that despite (CT), no
statement can be analytic according to (1) and then via
(CT), not about reality. The argument proceeds by pointing
out that its acceptation entails the claim that the property
of being true on the sole basis of the meaning of its
constituting expressions is possibly instantiated, and by
showing that the latter claim entails counterintuitive
consequences.
Which counterintuitive consequences derive form
admitting the possible instantiation of the sentential