On the traditional interpretation, Rudolf Carnap's classic Der logische Aufbau der Welt (The Logical Structure of the World) defends the following thesis: All scientific sentences can be translated (via definitions) to equivalent ones which consist solely of (i) logical signs and (ii) terms that refer to "the given". On a more recent interpretation, the Aufbau aims to show an even stronger claim: All scientific sentences can be translated (via definitions) to equivalent ones which are purely structural, i.e., which consist solely of logical signs. According to both interpretations, the Aufbau is a famous and perhaps notorious failure.
The question that I am going to deal with in my paper is: How much of the original Aufbau can actually be saved? I will argue in favour of a weakening of the original hypothesis: All scientific sentences can be translated to empirically equivalent ones which consist solely of (i) logico-mathematical signs and (ii) terms that refer to a subject's experiences, where the translations express subject-invariant constraints on experiences. If A is translated to tr(A), then tr(A) expresses the empirical content of A, but tr(A) is not claimed to be synonymous to A or to have same truth value as A. Furthermore, the translation mapping is not in each and every case set up on the basis of explicit definitions.
In order to defend this hypothesis one has to show how the new weakened
"Aufbau-like" programme solves or circumvents the problems that
affected the original Aufbau project. I will try to outline how a new
constitution system addresses the well-known difficulties concerning
(i) the basis of experience: phenomenalistic vs. physicalistic, (ii)
the method of abstraction in the old Aufbau does not yield the intended results, (iii) dimensionality: Carnap's original assignment of dimension numbers to quality spaces fails, (iv) holism and theoretical terms: theoretical terms cannot be introduced by explicit definition, (v) disposition terms: their analysis demands a theory of empirical content for modal conditional operators, (vi) structuralism: the final elimination of empirical predicates in the original Aufbau does not reduce descriptive sentences to purely logical ones. I will focus on problem sets (ii), (iii), and (iv), while only sketching the new accounts of how to cope with the other problems.