Geometry and Physical Space

Abstract

What is the status of geometry as a theory of physical space? Traditionally it was assumed that the axioms of Euclidean geometry were known a priori to be true of physical points and straight lines.  With the development of non-Euclidean geometries the conceivability of the falsehood of the parallel axiom was conceded, but it was still widely held that physical space was Euclidean. Contemporary physics offers a non-Euclidean account of the geometry of physical space, and in light of this it may be thought that the question of the correct geometry of physical space is an empirical one. However, an alternative approach was prominent in the early twentieth century, according to which the question concerning which is the ‘correct’ geometry of physical space is a matter of conventional choice rather than objective fact. This chapter examines the view that the status of geometry is conventional.