Willard Van Orman Quine

Quine and Logical Positivism 229
that, if he wishes to discuss it, he must state his methods clearly, and give
syntactical rules instead of philosophical arguments. (1937, 51)
Note that Carnap’s notion of language is richer than the usual one
and includes both formation rules, which constitute the grammar of
the language, and transformation rules, the axioms of the system.
The only constraint is pragmatic, what advances the science carried
out in these languages.
On the account just given, Carnap was forced to his tolerant conventionalism
by the need to uphold a weaker form of analyticity than
that given by explicit definition. But there is overdetermination here,
and the principle of tolerance chimes well with the Vienna Circle’s
antimetaphysical rejection of pseudoproblems in philosophy. The
fruitless debates that had raged in the 1920s between Hilbert and
Brouwer and their followers could not be rejected out of hand, since
the leading protagonists were two of the greatest mathematicians of
their time. But here, it seemed, was a way of resolving, or better, dissolving,
the apparent issues between them. Whether tolerance does
or does not achieve this result has been disputed, but Carnap and his
followers were certainly convinced that it did and thus had a positive
reason for holding to it.
Espousing tolerance was not by itself enough to save analyticity
for mathematics in the face of Gödel’s first incompleteness theorem.
Carnap had also, in effect, to replace logical deduction by logical consequence.
Tarski is generally credited with discovering the correct
notion of logical consequence, but Carnap himself achieved that for
two particular languages he investigated in The Logical Syntax of
Language. What he did not achieve was a completely general account
of this key notion that could be applied uniformly to a wide
class of languages. Nonetheless, his accomplishment on this score
is considerable. By his notion of rules of consequence, as opposed
to rules of deduction, he arrived at truth definitions for his formal
languages I and II (for a detailed assessment of the semantic content
of The Logical Syntax of Language, see Coffa 1987, 285–326).
3. “rudolf carnap, teacher and friend”
In September 1932 Willard Van Orman Quine arrived in Vienna. Aged
24, he had completed his Ph.D. at Harvard the previous spring, in his
second year as a graduate student, and had been awarded a one-year
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