Critique of Reichenbach’s and Carnap’s Philosophy of Geometry

Abstract

In Der Raum,¹ Carnap begins his discussion of physical space by inquiring whether and how a line in this space can be identified as straight. Arguing from testability and not, as we did in Chapter One, from the continuity of that manifold, he answers this inquiry as follows: “It is impossible in principle to ascertain this, if one restricts oneself to the unambiguous deliverances of experience and does not introduce freely chosen conventions in regard to objects of experience.”² And he then points out that the most important convention relevant to whether certain physical lines are to be regarded as straights is the specification of the metric (“Mass-setzung”), which is conventional because it could “never be either confirmed or refuted by experience:” Its statement takes the following form: “A particular body and two fixed points on it are chosen, and it is then agreed what length is to be assigned to the interval between these points under various conditions (of temperature, position, orientation, pressure, electrical charge, etc.).