By the late 19th century several consistent non-Euclidean geometries, mathematically distinct from Euclidean geometry, had been developed. Euclidean geometry has a unique parallels axiom and angle sum of triangles equals 180º, whereas, for example, spherical geometry has a zero-parallel axiom and angle sum of triangles greater than or equal to 180º. These geometries raise the possibility that physical space could be non-Euclidean. Empiricists think we can determine whether physical space is Euclidean through experiments. For example, Gauss allegedly attempted to measure the angles of a triangle between three mountaintops to test whether physical space is Euclidean. Realists think physical space has some determinate geometrical character even if we cannot discover what character it has. Kantians think that physical space must be Euclidean because only Euclidean geometry is consistent with the form of our sensibility. Poincaré (1913) argued that empiricists, realists, and Kantians are wrong: the geometry of physical space is not empirically determinable, factual, or synthetic a priori. Suppose Gauss’s experiment gave the angle-sum of a triangle as 180º. This would support the hypothesis that physical space is Euclidean only under certain presuppositions about the coordination of optics with geometry: that the shortest path of an undisturbed light ray is a Euclidean straight line. Instead, for example, the 180º measurement could also be accommodated by presupposing that light rays traverse shortest paths in spherical space but are disturbed by a force, so that physical space is “really” non-Euclidean: the true angle-sum of the triangle is greater than 180º, but the disturbing force makes it “appear” that space is Euclidean and the angle-sum of the triangle is 180º. Arguing that there is no fact of the matter about the geometry of physical space. Poincaré proposed conventionalism: we decide conventionally that geometry is Euclidean, forces are Newtonian, light travels in Euclidean straight lines, and we see if experimental results will fit those conventions. Conventionalism is not an “anything-goes” doctrine—not all stipulations will accommodate the evidence—it is the claim that the physical meaning of measurements and evidence is determined by conventionally adopted frameworks. Measurements of lines and angles typically rely on the hypothesis that light travels shortest paths. But this lacks physical meaning unless we decide whether shortest paths are Euclidean or non-Euclidean. These conventions cannot be experimentally refuted or confirmed since experiments only have physical meaning relative to them. Which group of conventions we adopt depends on pragmatic factors: other things being equal, we choose conventions that make physics simpler, more tractable, more familiar, and so forth. Poincaré, for example, held that, because of its simplicity, we would never give up Euclidean geometry.