Theories of Order in Carnap's Aufbau

Paul Ziche (Utrecht) gives a talk at the MCMP workshop "Influences on the Aufbau" (1-3 July, 2013) titled "Theories of Order in Carnap's Aufbau". Abstract: "Order" is a key term in debates in, and between, fields such as logic, philosophy of mathemat- ics, theoretical biology and philosophy of science around 1900. In § 3 of the "Aufbau", Carnap refers af- firmatively to a number of relevant authors: Whitehead and Russell, Driesch, Ostwald, Husserl, and many more. This list already indicates how broad and, from today's point of view, internally heterogeneous the discourse on order has been in this period. This paper will motivate why the notion of "order" played such a crucial role around 1900, and what its strategic position in those debates has been: "order" was conceived of as an ultimately abstract and general concept that could, nevertheless, be given content via, among others, mathematical and logical methods, or within fields such as biology. On the other hand, these diverse lines of influence also shaped the status of the field of logic itself. In a second step, it will be asked how Carnap views this discourse on order, and how he reacts to it, and to the broader ideas that form the strategic background of the notion of "order".