been not the end of the logicist movement but the beginning of its fame; Gödel’s
proof did not destroy but added heat to the fire. It was from this point that
Wittgenstein, whatever private misgivings he had held previously about the
consistency of his own approach in the Tractatus, moved increasingly into
public opposition to his old school—probably not least because his major rival
in the Circle, Carnap, was sticking to the logicist road.
Gödel’s proof did not derail latter-day logicists, but gave them new direc-
tions in which to work. Unlike Neo-Kantianism, Carnap’s program was not a
movement losing its position in attention space but an energetically expanding
one. New and fundamental obstacles could not defeat it, but became grist for
its mill.
Carnap’s 1928 Der Logische Aufbau der Welt constructed all meaningful
(i.e., empirically verifiable) statements out of a Russellian hierarchy: signs for
individuals, classes, classes of classes, supplemented by a sign for empirical
elements. Methodologically the system was solipsistic; it is my individual
experiences which are the foundation. By 1934, under the stimulus of Tarski
and Gödel, Carnap had shifted to the impersonal syntax of a universally valid
language; the basic elements were now the natural numbers (integers), from
which are successively constructed the real numbers and a four-dimensional
space-time, which is a set of all points with numbered coordinates. In this
language all statements of empirical science can be translated into something
like “red appears at point (x, y, z, t).” This translation game did not actually
go beyond sketching the form of descriptive statements, and took for granted
that mathematical laws existed or would be forthcoming which would explain
recurrent patterns in space-time; in short, it was a philosophical program
sailing under the rhetoric of the unification of science. In the 1940s Carnap
responded to criticisms by loosening the system still further, reintroducing
higher-order concepts which he had previously rejected as meaninglessly meta-
physical. By now he was dividing the language of science into an empirical
observational language plus a theoretical language or formal calculus for
deducing connections (Wedberg, 1984: 207–229). This formalism in turn
provided the target for radical revisions by Quine and others.
Carnap’s shift to the language of physics broke away from the older
phenomenalism supported by Schlick, toward Neurath’s rival camp. The Vi-
enna Circle was splitting in not just two but three main directions: Schlick’s
old program, now reduced to following the lead of Wittgenstein—what Neu-
rath called the “right wing”—plus Carnap’s continuing development of logi-
cism, and a “left wing” led by Neurath. Wittgenstein moved increasingly
toward becoming a rallying-point for outright opposition to logical positiv-
ism; abandoning his older logicism to Carnap, he shifted abruptly toward
Gödel’s position and even surpassed him in extending the radicalness of its
implications for philosophy. The action which kept the loyalists of the Vienna
The Post-revolutionary Condition^ •^729