Geometry and Convention: A Critical Discussion

Abstract

GEOMETRY AND CONVENTION: A CRITICAL DISCUSSION A COLLECTION of essays/ together with the essays of George Schlesinger and the essay of Hilary Putman, replies to which are contained in this collection, provide contemporary philosophers of nature with a twentieth-century counterpart of the famous Leibniz-Clarke correspondence. Griinbaum levels an all-out attack on that form of spatial and temporal absolutism which holds that distances and durations are intrinsic features of space and time. He upholds a form of relativism according to which space and time have distances and durations only relative to physical devices such as rods and clocks and according to which a significant conventional element is involved in specifying how such devices determine distances and durations. Schlesinger claims that hypothetical empirical facts-the lengthening of the day as measured by a pendulum, the increase of the velocity of light as measured by rods and pendulum clocks-could force us to accept the view that everything has doubled in size overnight. But how can one be forced to accept nocturnal doubling if one is free to account for the hypothetical facts by supposing that the laws of nature have changed their dependence on lengths and hence that things have not doubled in size at all? By rejecting this alternative Schlesinger is made by Griinbaum to appear as a spatial absolutist who holds that space has an intrinsic metric and that this metric can change. Putnam's long criticism of the first essay in Griinbaum's collection is an attempt to show that Griinbaum has exaggerated the role of convention in regard to spatial and temporal measures. One should consider geometrical and chronological matters in the context of an 1 Adolf Griinbaum, Geometry and Ch1·onometry in Philosophical Perspective, University of Minnesota Press, Minneapolis, 1968. Pp. 386. $3.45. 343 344 MILTON FISK entire physical theory, and then, according to Putnam, it will be apparent there is little room left for convention. From this point of view, one can say that intervals in space and time have, in an objective way, magnitudes. In his 175 page reply to Putnam, Griinbaum denies he has been unaware of important theoretical and empirical constraints in the choice of a metric. But, granting the constraints, there is still an important element of convention since, he points out, space and time as mere sets of points and instants lack metrical properties. Such, then, in barest outline are the issues in this lengthy debate over the status of spatial and temporal magnitudes. It is with considerable misgivings that I add to this already voluminous discussion. Griinbaum's 196~ essay in the third volume of Minnesota Studies in the Philosophy of Sciencethe substance of which appears again as Chapters 1-4 of his Philosophical Problems of Space and Time and is Chapter 1 of the present collection-sparked the discussion. This essay developed Reichenbach's emphasis, particularly in The Philosophy of Space and Time, on definitional or conventional elements in geometry and chronometry. Griinbaum finds the justification for the conventionalism Reichenbach advocates in the idea of Riemann that continuous manifolds have no intrinsic metric. In Chapter~. Griinbaum joins together replies to two of Schlesinger's papers, the first of Schlesinger's papers appearing in Philosophical Studies (15, 1964) and the second in The Australasian Journal of Philosophy (.~5, 1967). Griinbaum 's replies originally appeared along with these papers. The third and final chapter, published in the fifth volume of Boston Studies in Philosophy of Science, is the reply to Putnam's critique in the second volume of The Delaware Seminar. The thoroughness of Griinbaum's exposition and of his replies is accompanied by an undesirable amount of repetitiveness . And the polemical bombast, especially of the reply to Putnam, has interferred with the possibility of a clear statement of the fundamental issue between the two. The elaborate attempts to show how " Putnam flies in the face of my writings, is unmindful of an important caveat of mme, GEOMETRY AND CONVENTION 345 and saddles me with" so-and-so's error could, without loss, have been saved for private correspondence with Putnam. Despite such attempts, the reply contains many valuable elaborations of points Griinbaurn made in the 1962...