The Mathematical Core of the External World Problem: Carnap's Construction of the External World and Karl Gerhards's 'Der mathematische Kern der Aussenweltshypothese'

Alan Richardson (UBC Vancouver) gives a talk at the MCMP workshop "Influences on the Aufbau" (1-3 July, 2013) titled "The Mathematical Core of the External World Problem: Carnap's Construction of the External World and Karl Gerhards's 'Der mathematische Kern der Aussenweltshypothese'". Abstract: Carnap, in his "Intellectual Autobiography," tells the story of reading in 1921 Bertrand Russell's book, Our Knowledge of the External World. In this anecdote he calls Russell "the strongest influence" on his "philosophical thinking in general" during the period of writing the Aufbau. But, while the meth- odological lessons of Russell loomed large in Carnap's mind, the actual techniques developed in the Auf- bau for constructing the external world differ considerably from Russell's own. Thus, noting Russell's influence does not take us very far in figuring out what the external world problem was for Carnap or what resources might be brought in to solve it. In this essay, I compare some of the constructive proce- dures of the Aufbau to procedures developed in Karl Gerhards's paper "Der mathematische Kern der Aussenweltshypothese" of 1922. Not only does Carnap refer to this paper in the crucial sections of the Aufbau where the construction of the external world is sketched, but this paper was precirculated and discussed at the 1923 Erlangen Conference at which Carnap and Reichenbach met and which Carnap subsequently called "the small but significant initial step in the movement of a scientific philosophy in Germany." Not only are some of Gerhards's constructive procedures and resources more closely related to Carnap's than are Russell's, but also Gerhards places his own work in a context created by the work of Helmholtz and Mach. The point of this endeavor is to enrich the resources we bring to bear in thinking about Carnap's philosophical project in the Aufbau.