Leibniz Equivalence. On Leibniz's (Bad) Influence on the Logical Empiricist Interpretation of General Relativity

Einstein’s “point-coincidence argument'” as a response to the “hole argument” is usually considered as an expression of “Leibniz equivalence,” a restatement of indiscernibility in the sense of Leibniz. Through a historical-critical analysis of Logical Empiricists' interpretation of General Relativity, the paper attempts to show that this labeling is misleading. Logical Empiricists tried explicitly to understand the point-coincidence argument as an indiscernibility argument of the Leibnizian kind, such as those formulated in the 19th century debate about geometry, by authors such as Poincaré, Helmholtz or Hausdorff. However, they clearly failed to give a plausible account of General Relativity. Thus the point-coincidence/hole argument cannot be interpreted as Leibnizian indiscernibility argument, but must be considered as an indiscernibility argument of a new kind. Weyl's analysis of Leibniz's and Einstein's indiscernibility arguments is used to support this claim

Is Wave Mechanics consistent with Classical Logic?

Contrary to a wide-spread commonplace, an exact, ray-based treatment holding for any kind of monochromatic wave-like features (such as diffraction and interference) is provided by the structure itself of the Helmholtz equation. This observation allows to dispel - in apparent violation of the Uncertainty Principle - another commonplace, forbidding an exact, trajectory-based approach to Wave Mechanics.Comment: 13 pages, 4 figure