Carnap's central mission was inspired by Bertrand Russell's conception
of a scientific philosophy based on the advances in logic to
which Frege and Russell had made major contributions.
The idea was that philosophy could be made rigorous by adopting these new
methods and confining itself to logical analysis, so that the theorems of
philosophy became, like those of mathematics, theorems of applied logic.
As an essential preliminary to rendering philosophical reasoning rigorously
deductive it would be necessary to provide for precision in the articulation
of philosophical problems through aoption formal languages, in the process of
which many problems previously thought to be philosophical would be shown to
be either problems belonging to empirical science, or to be incapable of being
made definite.
The purpose of philosophy would be to aid and abet empirical science in ways
similar to those in which Principia Mathematica had provided a model
for the development of mathematics using the new methods, i.e. by developing
formal languages suitable for use in science, thus clarifying scientific
concepts and providing for rigorous reasoning in the context of scientific
theories.
Carnap's mission also embraced the use of inductive reasoning in science,
but we will not be concerned here with that side of Carnap's work,
the debate between him and Carnap can be understood pretty well if we
think of Carnap's work as having been concerned principally with the
application of the new deductive logic to philosophy and science.
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