Editing Rudolf Carnap (section)

=== ''Der Raum'' ===
From 1919 to 1921, Carnap worked on a doctoral thesis called ''Der Raum: Ein Beitrag zur Wissenschaftslehre'' (''Space: A Contribution to the Theory of Science'', 1922). In this dissertation on the [[Foundations of geometry|philosophical foundations of geometry]], Carnap tried to provide a logical basis for a [[Philosophy of space and time|theory of space and time in physics]]. Considering that Carnap was interested in [[pure mathematics]], [[natural sciences]] and philosophy, his dissertation can be seen as an attempt to build a bridge between the different disciplines that are geometry, physics, and philosophy. For Carnap thought that in many instances those disciplines use the same concepts, but with totally different meanings. The main objective of Carnap's dissertation was to show that the inconsistencies between theories concerning space only existed because philosophers, as well as mathematicians and scientists, were talking about different things while using the same "space" word. Hence, Carnap characteristically argued that there had to be three separate notions of space. "Formal" space is space in the sense of mathematics: it is an abstract system of relations. "Intuitive" space is made of certain contents of intuition independent of single experiences. "Physical" space is made of actual spatial facts given in experience. The upshot is that those three kinds of "space" imply three different kinds of knowledge and thus three different kinds of investigations. It is interesting to note that it is in this dissertation that the main themes of Carnap's philosophy appear, most importantly, the idea that many philosophical contradictions appear because of a misuse of language, and a stress on the importance of distinguishing formal and material modes of speech.