Similarity Assessments, Spacetime, and the Gravitational Field: What Does the Metric Tensor Represent in General Relativity?
In this paper I explore the dialectics underlying the choice between a geometrical and a field interpretation of the metric tensor gab in general relativity. My aim is to examine the role of a specific type of reasoning process (which I call ‘similarity-based reasoning’) in interpreting gab. In recent years, philosophers of physics have claimed that the problem of choosing between the two interpretations in question is somehow insubstantial. This appearance of insubstantiality, I contend, stems from a basic form of underdetermination that affects the concepts of spacetime and physical field in the context of general relativity.