Where modern formulations of relatively theory use differentiable manifolds to space-time, Einstein simply used open sets of R 4 , following the then current methods of differential geometry. This fact aids resolution of a number of outstanding puzzles concerning Einstein's use of coordinate systems and covariance principles, including the claimed physical significance of covariance principles, their connection to relativity principles, Einstein's apparent confusion of coordinate systems and frames of reference, and his failure to distinguish active and passive transformations, especially in (...) the context of his hole and point-coincidence arguments. (shrink)

In this critical notice we argue against William Craig's recent attempt to reconcile presentism (roughly, the view that only the present is real) with relativity theory. Craig's defense of his position boils down to endorsing a ‘neo-Lorentzian interpretation’ of special relativity. We contend that his reconstruction of Lorentz's theory and its historical development is fatally flawed and that his arguments for reviving this theory fail on many counts. 1 Rival theories of time 2 Relativity and the present 3 Special relativity: (...) one theory, three interpretations 4 Theories of principle and constructive theories 5 The relativity interpretation: explanatorily deficient? 6 The relativity interpretation: ontologically fragmented? 7 The space-time interpretation: does God need a preferred frame of reference? 8 The neo-Lorentzian interpretation: at what price? 9 The neo-Lorentzian interpretation: with what payoff? 10 Why we should prefer the space-time interpretation over the neo-Lorentzian interpretation 11 What about general relativity? 12 Squaring the tenseless space-time interpretation with our tensed experience. (shrink)

Moritz Pasch (1843ber neuere Geometrie (1882), in which he also clearly formulated the view that deductions must be independent from the meanings of the nonlogical terms involved. Pasch also presented in these lectures the main tenets of his philosophy of mathematics, which he continued to elaborate on throughout the rest of his life. This philosophy is quite unique in combining a deductivist methodology with a radically empiricist epistemology for mathematics. By taking into consideration publications from the entire span of Paschs (...) highly original, but virtually unknown, philosophy of mathematics is presented. (shrink)

Translator's summary The translated paper is an extract, published in 1945, of an unpublished thesis, of both historical and technical import, dealing with notions of definability and their relation to invariance under automorphisms. The author develops a metamathematical Galois theory, and discusses and anticipates some aspects of higher-order model theory in an informal but conceptually rich manner.