Friedman writes extensively on this topic in papers collected at the beginning of Logical Positivism Reconsidered.
Poincare and conventional choice. Arithmetic fixed, but conventional choice of geometry. Disc model shows this, so that Helmholtz-Lie theorem does not say which of 3 geometries can be empirically determined.
With Einstein and choice of Riemannian geometry, geometry now becomes empirical.
Carnap: moves from formal-intuitive-physical geometry of thesis to L rules and P rules.
Intuitive space is synthetic a priori in Kantian sense, but is topological of indefinite dimensions via Wesenserschauung on any, even imagined, object. (Friedman later says locally Euclidean, kind of agreeing with Husserl.) Intuitive geometry mediates between formal and physical. Gives spatial form to formal geometry. Free choice or convention as to metric.
Intuitive geometry seen as too quick by Weyl as a Wesenanalyse. His is a sophisticated result, relying on work of many people. More in Husserlian tradition, Becker and Geiger.
Early Weyl uses a priori thought to single out a subset of Finslerian metrics, those which allow a unique affine connection. Turns out to be . Thus, infinitesimally ‘Pythagorean’ with scale gauge theory. This was used in an attempt to wed electromagnetism to gravitation. Can be thought of as an infinitesimal Klein program. Motivation from Fichte.
Mutual orientation of metrics at different points is a posteriori.
Carnap, extra metric is conventional, for Weyl it is empirical, as captured by the field equations, rather as specific form of Newton’s Law of Gravitation is empirically discoverable.
Many objections came from physicists about scale gauge theory. If two paths with the same endpoints generated different scale changes, how could we have universal spectra?
Later Weyl: empiricist turn, spectroscopic data needs accommodating. Relates electromagnetism to matter, rather than space-time. Change of gauge group to U(1), so this concerns only interference effects, not spectra. Philosophical reflection tends to separate from maths and physics. Friedman says more like Cassirer.
Later Carnap, also like Cassirer, no room for intuition. Both have given up on search for a permanent a priori (is this true for Carnap and logic?) Why not then devote our energies to Weyl? He gives us a forerunner of gauge field theory, group representation theory for quantum mechanics, …
Other chapters on Schlick, and conventionalism.
Also, see Sholtz for work on Weyl, and on Cartan.
Created on November 9, 2012 at 18:27:24. See the history of this page for a list of all contributions to it.