Ernst Mach and Eric Voegelin's Solution

[The reformulation of the Newtonian definitions and of the first law of motion] did not get under way for more than a century. The principal cause of the stagnation was the fact that the deficiencies in the theoretical structure did not impair the advancement of science. . . .[Resistance to revision was typified by Carl Neumann's 1870 treatise in which he argued that acceptance of relativity would produce the intolerable result that a rotating star, in the absence of other bodies in the universe, would have to be at rest, and therefore could not flatten at its poles. In 1901 Ernst Mach replied, finally, that] there is no profit in making a senseless assumption for the purpose of avoiding a contradiction. Moreover, in a mental experiment only nonessential circumstances may be modified. That the existence of the surrounding material world is without influence, however, must not be assumed a priori. . . .

The answer is excellent in its firmness and intention but is lacking somewhat in theoretical precision. . . . Relativity is not an appurtenance of objects that exist in themselves but is part of the logical structure of a science of phenomena. Hence it is impermissible to isolate a phenomenon and ask what properties, for instance, a rotating star would have—in itself—after the relational field in which it is a phenomenon is abolished. An experiment can and must abstract from concrete, physical circumstances in order to isolate that part of the total phenomenon that can be mathematized and expressed in a law of science. It cannot, however, abstract from the logic of science and still remain scientific. The argument from the body that rotates in absolute motion makes precisely this epistemological mistake. With the clarification of the mistake the problem of absolute motion disappears.

Chapter 4, The English Quest for the Concrete
§ 3, Absolute Space and Relativity, pp 204-205.