Reduction and Elimination in Philosophy and the Sciences

Quine on the Reduction of Meanings
Lieven Decock, Amsterdam, The Netherlands
Quine’s semantic nihilism is well-known. From his earliest
work onwards, he expelled meanings from his ontology.
One of the important innovations in his doctoral thesis, The
Logic of Sequences, which is a reworked version of
Whitehead and Russell’s Principia Mathematica, was
extensionalism. Quine replaced the intensional
propositional functions by extensional classes. During his
trip to Europe in 1933, he discovered that this had become
standard practice in Europe, and has defended
extensionalism ever since, even in his latest writings. The
only universals one should accept are classes. He
regarded classes or sets as bona fide objects, because
there is a clear criterion of identity, viz. classes can be
identified through their members. For intensions no such
criterion is available, so they cannot be hypostasised
(1960:244). For some years, Quine also tried to get rid of
classes (Quine 1936; Goodman & Quine 1947), but he
came to recognize the necessity of positing sets, thus
giving up strict nominalism.
Quine’s extensionalism has determined his views on
meaning and semantics. Attributes or meanings, the
intensional components of universals, are only acceptable
if they can be given a clear criterion of identity. In practice,
this meant that meanings are only acceptable insofar they
can be reduced to clearly identifiable objects, i.e. classes
of classes, … , of physical objects. In Quine’s work, one
can find two concrete proposals for such a reduction. In
the first proposal empirical meanings are characterised as
stimulus meanings, i.e. classes of physical stimuli, in the
second they are classes of linguistic expressions. Quine
judges both proposals unsuccessful.
Quine defines a stimulus meaning as the ordered
pair of the affirmative stimulus meaning and the negative
stimulus meaning (1960:31-35). The affirmative stimulus
meaning is the class of all stimulations to which a given
speaker at a date would assent; the negative stimulus
meaning the class of stimulation to which she would
dissent. The proposal can be sharpened by using reaction
time to measure doubt, or by introducing a modulus, i.e. a
maximum time duration for stimulations. So far, stimulus
meaning is reduced to an ordered pair of classes of
stimulations. An ordered pair can be reduced by means of
Kuratowski’s or Wiener’s reduction method to sets (1960
§53). Hence, a stimulus meaning is clearly identifiable if
stimulations can be reduced to simpler entities. The
stimulations can be ocular irradiation patterns together with
“the various barrages of other senses, separately and in all
synchronous combinations” (1960:33). Ocular irradiation
patterns are types of evolving chromatic irradiation
patterns of all durations up to some modulus. An
alternative is defining an external momentary stimulation
as “the set of [a person’s] triggered receptors.” (1981:50)
Quine’s notion of stimulus meaning is unproblematic from
a reductionist point of view. Empirical meanings are
reduced by means of reduction strategies that are
acceptable for Quine to entities that Quine finds
unproblematic, namely physical objects and classes.
The reduction strategy is clearly inspired by
Carnap’s reduction programme in Der logische Aufbau der
Welt. Quine’s worries concerning stimulus meaning accord
with his objections to Carnap’s early reduction programme
and his later verification theory of meaning (Carnap 1936).
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Quine believes that stimulus meaning is restricted to
observation sentences, whereas most sentences are not
immediately linked to sensory stimulations. Only sentences
at the boundary of the web of belief have stimulus
meaning, but this is only a small fraction of all sentences.
Hence, stimulus meaning is not a viable basis for
semantics, because the meaning of most sentences
cannot be explained as stimulus meaning. In brief, Quine
has given an impeccable reduction strategy, and at the
same time pointed out its severe limitations.
In Quine’s second reduction strategy, “we could
define the meaning of an expression as the class of all
expressions like it in meaning.” (1992:52; see also
1960:201; 1979:140; 1981:46). The reduction of
expressions is unproblematic, either to classes (via Gödel
numbering and the reduction of numbers to sets) or to
classes of physical objects (inscriptions). More noteworthy,
the class of meaningful expressions can be precisely
delineated in grammar (see Decock 2002:86). For the
reduction strategy to work, the only further requirement is
that a precise characterisation of the dyadic predicate “x is
alike in meaning with y” or “x is synonymous with y” is
elaborated. In his early work, Quine is extremely sceptical
about this notion of synonymy, especially for standing
sentences (1960:201). Of course, one can use stimulus
meaning to define synonymy, and even with the help of
first order logic extend this notion to ‘cognitive synonymy’
(1979), but this will not help for standing sentences. The
only alternative is to characterise synonymy by means of
the notion of analyticity: “Once we have analyticity,
cognitive equivalence is forthcoming; for two sentences
are cognitive equivalent if and only if their truth-functional
biconditional is analytic.” (1992:54f) In view of Quine’s
well-known demise of the analytic-synthetic distinction, this
looks like a dead end.
However, in an interview on the occasion of the Rolf
Schock prize in November 1993, Quine said:
Yes so, on this score I think of the truths of logic as
analytic in the traditional sense of the word, that is
to say true by virtue of the meanings of the words.
Or as I would prefer to put it: they are learned or can
be learned in the process of learning to use the
words themselves, and involve nothing more. They
are analytic in the same sense in which the standard
example such as “No bachelor is married”, is
analytic: something that’s learned in the process of
learning to use the word “bachelor” itself.
(Bergström & Føllesdal 1994, 199f)
This passage and other more covert passages (1974:79;
1992:55) look like a recantation of one of Quine’s most
famous claims. Quine admits that theorems of first order
logic can be analytic, and that sentences such as “No
bachelor is married” can be analytic. It is arguable that
Quine has regarded first order logic as analytic since the
end of the 1940s, or even propositional logic as analytic
since ‘Truth by convention’ (1936). Nevertheless, the claim
that “No bachelor is married” can be analytic, is a radical
departure from earlier claims. Quine here offers a clear
behaviouristic characterisation of analyticity. This further
implies that synonymy and meaning become unproblematic,
at least for expressions that are analytically equiva-