The Aufbau (The Logical Structure of the World) attempts to build a Konstitutionssystem — a rational reconstruction of all the concepts of empirical science from a minimal basis. The basis is phenomenalist: elementary experiences (Erlebnisse) and a single primitive relation of remembered similarity between them. From these materials, using only the resources of mathematical logic (specifically the Principia Mathematica of Russell and Whitehead), Carnap attempts to define — step by logical step — the concepts of quality classes, sense organs, the spatial order of the physical world, the mental states of other persons, and the cultural objects of the human sciences. Each concept is explicitly defined in terms of its predecessors in the construction; nothing is assumed that has not been logically derived.
The philosophical motivation behind the construction is the verificationist criterion of meaning: a statement is empirically meaningful if and only if it can be translated, without loss of cognitive content, into a statement about elementary experiences. The Aufbau attempts to show that all scientific concepts satisfy this criterion: they can all be explicitly defined in terms of the experiential basis. Conversely, concepts that resist such definition — traditional metaphysical concepts like "substance," "thing-in-itself," "absolute spirit" — are revealed as meaningless pseudo-concepts. The construction is both a positive programme (showing what is meaningful) and a critique (diagnosing what is not).
Carnap himself came to see the strict phenomenalist programme as untenable: the construction of the physical world from pure experiential data proved far more complex than anticipated, and by the 1930s he had shifted to physicalism (constructing everything from physical rather than phenomenal terms). Quine's "Two Dogmas of Empiricism" (1951) raised a deeper challenge: the programme assumes a sharp analytic-synthetic distinction and a reductivist account of meaning that Quine argued were both indefensible. Yet the Aufbau remains philosophically significant: it is the most rigorous realisation of the empiricist programme and the clearest demonstration of both its power and its limits.
The Logical Structure of the World was published in 1928 as Carnap's Habilitationsschrift. It was written during Carnap's years in Vienna, in close engagement with Schlick, Neurath, and the other members of the Vienna Circle. The English translation by Rolf George (1967) includes an important new preface by Carnap assessing the programme in retrospect.