Poincaré's conventionalism holds that the topology and continuity of space underdetermine geometry, but this underdetermination shows geometry is conventional, not that it requires independent grounding.
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Underdetermine(in epistemology (theory of knowledge))
When something doesn't give you enough information to figure out the complete answer—it leaves multiple possibilities still open.
conventionalism(Philosophy of language debate in Plato's Cratylus)
The view that the correctness of names is determined by social consent and agreement rather than by natural resemblance or description
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.