Gruenbaum on the Duhemian Thesis and Einstein's Philosophy of Geometry
Gruenbaum on the Duhemian Thesis and Einstein's Philosophy of Geometry
Einstein, in several places, propounded his view on the nature of geometry (Einstein 1921, 1949). He endorses the view which is normally attributed to Pierre Duhem and Quine that any physical hypothesis is subject to empirical test only together with many auxiliary hypotheses, so that there can be no decisive refutation of that hypothesis. This Duhemian Thesis implies that only the whole theoretical system can be compared to experience, not any particular hypothesis taken in itself. Applying similar considerations to the question of physical geometry, Einstein expressed his sympathy with (not exactly accepting it) the following view:
Geometry (G) predicates nothing about the relations of real things, but only geometry together with the purport (P) of physical laws can do so. Using symbols, we may say that only the sum of (G) + (P) is subject to the control of experience. Thus (G) may be chosen arbitrarily, and also parts of (P); all these laws are conventions. All that is necessary to avoid contradictions is to choose the remainder of (P) so that (G) and the whole of (P) are together in accord with experience. (Einstein 1921, in Sidelights on Relativity, 35)
Thus, Einstein comes very close to what he takes as Poincare's position (Einstein said, "Sub specie aeterni Poincare, in my opinion, is right") that our choice of geometry is "conventional", not determined by empirical evidence alone, even if we are talking about physical geometry, not mathematical or pure geometry (but he added an important qualification, as you can easily confirm by reading the whole text; see Einstein on Geometry).
Gruenbaum's critique is directed to this view of Einstein (Gruenbaum 1963, 106-151). His argument has three parts.
(1) Gruenbaum points out the distinction between Trivial and Nontrivial versions of the Duhemian Thesis; Trivial version allows one to change the meaning of words, in order to save a hypothesis from falsification, and Nontrivial version prohibits this. Gruenbaum claims that Nontrivial version must be adopted for Einstein's argument. However, he argues that Nontrivial version is logically non-sequitur, and it is actually false (110).
...a necessary condition for the non-triviality of Duhem's Thesis is that the theoretical language be semantically stable in the relevant respects. (111)
(2) According to Gruenbaum, Poincare's view is often misunderstood, and Einstein's reading is no exception. According to Gruenbaum's reading, Poincare, in his "conventionalism", elaborated the thesis of alternative metrizability, due to Riemann. And as Gruenbaum sees, Poincare was not an opponent of qualified empiricist (as regards physical geometry) such as Reichenbach and Carnap. (Qualified empiricist admits a sort of convention, such as Reichenbach's "coordinative definitions"; but he asserts that, given such conventions, physical geometry can be determined empirically.)
From the standpoint of synthetic geometry, the latter choice effects a renaming of optical and other paths and thus is merely a recasting of the same factual content in Euclidean language rather than a revision of the extra-linguistic content of optical and other laws. The retainability of Euclideanism by remetrization, which is affirmed by Poincare, therefore involves a merely linguistic interdependence of the geometric theory of rigid solids and the optical theory of light rays. (119)
(3) Finally, Gruenbaum propounds his main contention: Geometry as a physical hypothesis can be separately testable, contrary to the Duhemian Thesis. Since the argument in this part is rather complicated, I will not try to summarize.
Although Gruenbaum's view is criticized by a number of people (see Gruenbaum 1974, part iv), and revised in several places, it is a valuable contribution to the philosophy of (physical or synthetic) geometry, and deserves close studies.
References
Einstein, A. (1983) Sidelights on Relativity, Dover (this includes "Ether and the Theory of Relativity", 1920, and "Geometry and Experience", 1921).
Einstein, A. (1949) "Reply to Criticisms" in Albert Einstein: Philosopher-Scientist (ed. by P.A. Schilpp).
Gruenbaum, A. (1963) Philosophical Problems of Space and Time, Alfred A. Knopf.
Gruenbaum, A. (1974) Philosophical Problems of Space and Time, 2nd ed. (1st edition is reprinted, with extensive supplementary materials), Reidel.
Last modified March 30, 2003. (c) Soshichi Uchii