### In the Footsteps of Rudolf Carnap I

#### Posted by David Corfield

Last week I gave a couple of talks in Germany. Thursday saw me in the town of Wuppertal, famous for its Schwebebahn, a railway built above the river Wupper, which snakes its way through the middle of the town. As you can see from the pictures, the trains hang underneath the rail. Wuppertal is also well-known for being home to the factories of Friedrich Engels’ family. Somewhat less known is that it was the birthplace of the philosopher Rudolf Carnap, a central figure in the Vienna Circle.

I’d gone to the town at the invitation of the IZWT, the university’s history and philosophy of science group. Now, one of the best things about giving a talk is, of course, the chance it offers to find weak points in your position, and to learn about related work. I wasn’t disappointed. At dinner afterwards, we discussed the Hungarian contribution to history and philosophy of mathematics. Imre Lakatos’s work I know well, and behind him there was the figure of Árpád Szabó, best known for his thesis that Greek mathematics arose hand-in-hand with the dialectical method of Eleatic philosophy. Szabo and Lakatos had planned to write a two volume work on the use of the dialectic method in mathematics, Szabo for the Greeks, Lakatos for modern mathematics.

What I learned at the meal, from Erhard Scholtz, was of the work of a third Hungarian, Imre Tóth, a Hungarian historian of mathematics, who has extensively studied the creation and reception of non-Euclidean Geometry. Toth believes there to have been a strong connection between Ancient Greek philosophical and mathematical work on the principles of geometry, and their philosophical work on ethics and politics, especially with regard to Aristotle.

This is certainly something I should follow up. One lead I have is this talk, “Noneuclidean Geometry before Euclid?” by Hardy Grant, York University:

ABSTRACT: That Aristotle adumbrated noneuclidean geometry has been urged for many years by Imre Toth, and has been denied just as repeatedly by G.E.R. Lloyd, our leading modern authority on Greek science. The question resurfaced last summer on one of the e-mail discussion groups on the history of mathematics. I shall try to sketch the competing positions and to set the debate amid wider issues of axiomatics and mathematical necessity in Aristotle and beyond.

## Re: In the Footsteps of Rudolf Carnap I

No story of Wuppertal can be complete without mentioning

Alice in Den Stadten(1974), Wim Wenders’ film which put Wuppertal on the world map.