By Paul Arthur Schilpp
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Additional resources for Albert Einstein: Philosopher-scientist
To take the scenario of the ‘‘hole argument’’, assume that S contains a ‘‘matter hole’’ H inside of which, by deﬁnition, 8x 2 H, Tmn ¼ 0. Then the values of the metric ﬁeld gmn within H are determined, according to the Einstein ﬁeld equations, by the matter-energy ﬁelds Tmn ð 6¼ 0Þ outside and on the boundaries of H. Assume the solution set S assigns the distinct points P and P 0 within H the 0 , functions of the respective coordinates (in the values of the metric ﬁeld, gmn and gmn 0 same chart) of P and P .
The physical equivalence of these models expresses the principle of general covariance, understood actively as diffeomorphism invariance. Having now recognized his mistake, Einstein in 1916 sought to underscore this new understanding by adopting a programmatic characterization of what is physically observable as, in principle, reducible to the broad category of ‘‘pointcoincidences’’ (or intersections of world lines). 32 For according to this criterion there is truly no ‘‘empty space’’, no space-time points bereft of at least the metric ﬁeld and so no (merely) ‘‘topological space’’.
Kuhnian historiography of science will object that this is not at all a plausible description of the actual mode of conceptual change in science. But the metatheorem also presents something of an internal consistency problem in view of Reichenbach’s claim to have purged Kantian epistemology of its absolute elements. For how can an assertion that ‘‘there are no most general (coordinating) principles’’ and ‘‘no most general concepts’’, indeed, that even the concept of ‘‘coordination’’ itself may prove to be too narrow a deﬁnition of cognition,96 mesh with a meta-theorem asserting that modiﬁcation of coordinating principles (hence, change in the object of scientiﬁc knowledge) always proceeds in the determinate direction of successive approximation?
Albert Einstein: Philosopher-scientist by Paul Arthur Schilpp