Gruenbaum on Eddington's Criticism of Poincare
Sir Arthur Stanley Eddington (1882-1944)
Gruenbaum on Eddington's Criticism of Poincare
Sklar, after presenting Poincare's view of conventionalism with respect to geometry, proceeds to "The Empiricist Reply to Poincare" (Sklar 1974, 94). Here, Arthur Eddington's view in his Space, Time, and Gravitation (1953) is quoted, and Eddington's view is summarized by Sklar as follows:
Poincare has apparently shown us that we can construct alternative, incompatible geometries of space (or spacetime) which are equally compatible with the same observational data, no matter how much data we accumulate. The two thoeries he constructs each have a geometric part and an additional "physical" part; so, by making suitable modifications in the physical part of the total theory, we can "save" any geometric hypothesis we like from refutation by any amount of experimental data. Now Poincare thinks that this forces us to the conclusion that we must simply choose one alternative theory or the other by making a "conventional" choice. In a sense this is correct, but in a trivial and not particularly interesting sense. The conventional choice we must make is neither more nor less than a conventional choice of using a certain verbal sound or written symbol with a certain meaning. Properly speaking there is only one theory, although it is written in two different ways. The confusion comes about because, in the two expressions of the same theory, words are being used with different meanings. (Sklar 1974, 96-97)
And Sklar adds that "Reichenbach presents us with a similar reply to the conventionalist thesis. It does not, I believe, differ significantly in fundamentals from Eddington's briefly-related account" (Sklar 1974, 97).
Well, I am not sure whether Sklar's interpretation is correct, or whether it does justice to Reichenbach's view. Actually, Gruenbaum (quoting another passage from Eddington) argued forcibly that Eddington's view misses the whole point of "conventionalism", by trivializing it as a semantical thesis that we can freely choose to give any meaning to any word. We have to remember that Gruembaum's book appeared about ten years before Sklar's book.
Gruenbaum's main contention is that we have to distinguish the thesis of conventionality of congruence from the trivial semantical conventionalism (TSC). The former
is, in the first instance, a claim concerning structural properties of physical space and time; only the semantical corollary of that thesis concerns the language of the geo-chronometric description of the physical world. (Gruenbaum 1963, 26)
Referring to Riemann and Poincare, Gruenbaum continues:
For what these mathematicians are advocating is not a doctrine about the semantical freedom we have in the use of the uncommitted sign "congruent". Instead, they are putting forward the initially non-semantical claim that the continue of physical space and time each lack an intrinsic metric. And the metric amorphousness of these continua then serves to explain that even after the word "congruent" has been pre-empted semantically as a spatial or temporal equality predicate by the axioms of congruence, congruence remains ambiguous in the sense that these axioms still allow an infinitude of mutually exclusive congruence classes of intervals. ... In short, the conventionality of congruence is a claim not about the noise "congruent" but about the character of the conditions relevant to the obtaining of the kind of equality relation denoted by the term "congruent". (Gruenbaum 1963, 27)
Now, we have to point out this difference between Sklar's and Gruenbaum's view: While Gruenbaum is talking about the conventionality of "congruence", Sklar is assuming that "we have two expressions of the same theory" and talking about the meaning of each word in each expression of the whole theory. Gruenbaum tries to concentrate on the notion of congruence (geometric notion), whereas Sklar first invokes the whole theory and then divides it into geometric and physical parts.
I myself find Gruenbaum's approach more persuasive, because it seems to me that "the whole theory" is out of reach, unless we start from its parts, geometry and physics; and conventionality is needed in the geometric part, the whole unattainable without it. Thus, even though it may be admissible to talk about linguistic conventionality in the whole theory, it is a mere corollary, as Gruenbaum says, when non-linguistic conventionality is already assumed. But for more on this, see pp. 24-44 of Gruenbaum's book.
Eddington's book is still available in paperback, as one of the Cambridge Science Classics (1987). Eddington's own work (1919) for experimental confirmation of one of Einstein's predictions is also discussed in chapter 7. Since Eddington was a fine writer, it is quite worthwhile to go through this book.
Last modified March 30, 2003. (c) Soshichi Uchii