Abstract

The present article first places Mach’s consideration about space and geometry into the context of the discussion of these issues in the nineteenth and early twentieth century and then proposes three interpretations of Mach’s thesis, put forward in chapter XXI of his Knowledge and Error, that the problem of measuring the volumes of material bodies is the origin of geometry. According to the first of these interpretations, Mach’s thesis is an assertion about the historical origin of the science of geometry. Alternatively, one may understand Mach as suggesting that our geometric theorizing is best understood by relating it to our handling of material bodies and our interest in their volumes. Finally, Mach’s thesis may be conceived as asserting that the most appropriate form of geometry would be a metric geometry of the volumes of solids. The article concludes with a discussion of objections raised by Brentano against both Mach’s thesis of the priority of the measurement of volumes and his conception of bodies as complexes as sensations.