Recently, Hj. Mellin, in a lengthy examination, offered a critique of my Axiomatization of the Theory of Relativity. A discussion of the objections that Mellin raises to my axiomatization, and thereby to the theory of relativity, seem to me to serve the general interest because of their fundamental nature and his clear formulation of views which are most often only operative on a subconscious level, and I would therefore like to answer them here.

1. The most significant difference in our positions lies in our understandings of the relationship between the mathematical discipline of geometry and reality. Here, I adopt the perspective (which is often incorrectly termed conventionalism) that the geometrical axioms as mathematical propositions are not at all descriptive of reality; this only occurs when physical things are shown to be coordinated to the elements of geometry (coordinative definitions). If we take very small bits of mass to be points, light rays to be straight lines, and the length of a segment to be determined by the repeated placement of a rigid rod, then the statement that straight lines are the shortest becomes an (empirically proven) statement about real things. Without such coordinative definitions, these propositions say nothing about reality. Mellin's objections to this view rest on his stressing the so- called intuitive necessity of the geometric axioms.

2. […]