Poincaré argued that geometry, including the topology of continuous space, is chosen by convention relative to coordinated physical laws, making pure topological facts theory-laden.
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convention(Used to distinguish mere regularities from convention-governed regularities in the analysis of meaning.)
A regularity that obtains because there is something akin to an agreement among a group of people to keep the regularity in place.
geometry(Abstract view following the acceptance of non-Euclidean and Riemannian geometries)
Whatever can be described within the Riemannian formalism; an abstract structure defined by a consistent metric, not necessarily tied to physical or Euclidean space.