In these chapters, Carnap outlines the role of geometry in the general theory of relativity and addresses the status of geometrical knowledge in that context.

As in the preceding chapters, much of Carnap’s discussion is devoted to an introductory presentation of the physics and mathematics, so our discussion can be devoted in part to sorting that out, but there are also two groups of philosophical issues you should think about.

•  The first group concerns the status of geometry. First of all, is the geometry of physical space something that is open to empirical investigation or is it simply a matter of convention? This is one way of formulating the issue raised by Poincaré’s views. Formulate Carnap’s position for yourself and consider alternatives to it. One kind of alternative that has become more prominent since Carnap’s book was written sees physical space as having as determinate a reality as any other feature of physical theory. People holding this view might see Carnap or Reichenbach (on some ways of understanding his views) as excessively conventionalist. You might think about this issue in connection with Reichenbach’s “rule” concerning “universal effects” (pp. 169-171). Is this a conventional stipulation for the purpose of simplification or does it have a different significance?

•  The question of whether geometry needs to be visualizable leads Carnap to consider several issues regarding the uses of models in science (see pp. 173-176). We earlier discussed the question of whether laws on the one hand or models and analogies on the other were more central to scientific theories (see the reading guide for 9/26 on chs. 23-24 for some background). Although issue is probably in the back of Carnp’s mind here, he explicitly addresses some other issues. One of the things you should do in preparing this part of the assignment is to look issues that you think it would be worth discussing.