Dr. Jan-Willem Romeijn
(University of Groningen)

The Nature of Space

Imagine that at the Philosopher's Fancy Fair you wander into a tent named "Kant, Leibniz, and Möbius". Inside you are met with a rather puzzling show: a perfectly symmetric human being drops gloves, books, and other such asymmetric objects into a weirdly shaped tube. And at first glance the objects come out the same at the other end of the tube. But when you look closer, they are all miraculously turned into their mirror image! The left glove becomes a right one, the book shows mirrored writing. How can that be?

In this workshop we investigate a puzzle due to Kant concerning so-called enantiomorphs, objects of which the mirror image is genuinely different. For example, a left glove genuinely differs from its mirror image: no amount of twisting and turning will make the left glove fit in the place of a right one. Kant initially argued that only space itself can ground the intrinsic difference between these objects and that, following Newton, space must therefore exists as an independent reality. But a fifteen year older Kant returned to the puzzle to show that it leads us to the idea of space as a pure intuition, thus developing the views of Leibniz. However, as I will argue in the first part of the workshop, the puzzle is quite independent of this controversy over the ontology of space.

In the second part of the talk, we will all construct a two-dimensional variant of the aforementioned fancy fair attraction using paper and tape, and consider it in the light of the geometric view on space deriving from Riemann, Möbius and Einstein. We will find that assuming an intrinsic difference between left and right hands forces us to endow space with a number of specific properties. Moreover, I will argue that these properties are at variance with some compelling intuitions on the nature of space. We are thus led to believe that there is no intrinsic difference between a left and a right hand, and that the fancy fair attraction may very well exist.

Jan-Willem Romeyn (1975) studied at Utrecht University, where he graduated cum laude in physics and philosophy. Following these studies, he was employed as a statistician in financial consultancy. He received a doctorate cum laude in philosophy from the University of Groningen in 2005, after which he lectured in philosophy of science and statistics at the Psychology Department of the University of Amsterdam. As of January 2007, he works on a post-doc project concerning cognitive psychology and philosophy of science at the University of Groningen.