In 1928, armed with the new logic of Principia Mathematica, the philosopher Rudolf Carnap built the world. In his work Der logische Aufbau der Welt, Carnap sketched a general theory of constitution systems of concepts for science. For this, he developed the method of quasi-analysis, which constitutes new concepts starting from similarity relations. I have applied these ideas in the context of conceptual spaces.
I just started working alongside Alan Richardson and Christopher Pincock as a scientific co-editor of the Aufbau volume of the Collected Works of Rudolf Carnap (general editor André Carus). We work alongside Christian Damböck and Caterina del Sordo, who are developing the Meiner critical edition, and also the members of the Rudolf Carnap Digital project. Stay tuned!
Some of my publications in this area are:
- Belastegui, J. (2026): Chapter 72: New Developments of Carnap’s Aufbau: Quasi- Analysis, Abstraction and Representation. In Christian Damböck and Georg Schiemer (eds.) Carnap-Handbuch. Leben-Werk-Wirkung, J.B. Metzler Verlag (Springer, Open Access). 10.1007/978-3-662- 72937-3, ISBN: 978-3-662-72936-6.
In his Aufbau and in previous work, Rudolf Carnap introduced a new method that he called quasi-analysis. One aim of quasi-analysis was to provide a reconstruction of properties as sets of similar objects by assuming as primitive only similarity relations. This is what I call the step of abstraction of quasi-analysis, and was explained in detail by Hannes Leitgeb. Based on Goodman’s objections to the method, Leitgeb singled out the conditions under which such reconstruction works given certain natural assumptions.
Another aim of quasi-analysis was to transform a description of objects based on their similarity relations into a property-based description of objects. This is what I call the step of representation of quasi-analysis, and was worked out in full detail by Thomas Mormann. Mormann showed how one can conceive of quasi-analysis as a representation of each object as a bundle of properties (those properties being the ones constructed in the previous step). In this chapter I compare both approaches to give a full description of the quasi-analytic method.