Date of Award
Master of Arts (MA)
Professor M. Radner
The aim of this paper is to deal with one aspect of an exchange in the journals between Bertrand Russell and Henri Poincaré from 1896 to 1900, namely the question of "What, if anything, is the empirical content of Geometry?", as well as the question of "What the answer to this will shed upon the nature of Space?"
This exchange, hereafter referred to as the "Russell-Poincaré Debate", finds its root in Russell's first major philosophical work, his Cambridge dissertation, An Essay On The Foundations of Geometry. Here Russell first proposes that there is an empirical content to Geometry. An overly flattering review of this Essay by L. Couturat, as well as Bertrand Russell's article "Are the Axioms of Euclid Empirical?", prompted Poincaré to publish a critical reply, "Des Fondements de la Géométrie, a propos d'un livre de M. Russell." To this Russell replied in an article entitled "Sur Les Axiomes de la Géométrie", to which Poincaré wrote "Sur Les Principes de la Géométrie, réponse a M. Russell". Finally, Poincaré included a chapter on "Space" in his Science and Hypothesis. Poincaré's position remains consistent throughout this exchange that the axioms of geometry are conventionally, but not empirically, chosen.
The various arguments which Russell and Poincare advanced on behalf of their respective "empiricist" and "conventionalist" these are set forth at length in the first chapter of my thesis. Russell's early work on projective geometry is noted, and his views concerning the possibility of empirically investigating the nature of space are pulled out of various reviews written by him at this time. The interchange between Russell and Poincaré next presented has (to the best of my knowledge) never before been translated, nor has its import for the conventionalist thesis hitherto been analyzed.
The second chapter of my essay consists of a discussion of various philosophical problems concerning space, time, and geometry, which grow out of the Russell-Poincaré exchange. The philosophical consequences of the conventionalist viewpoint is assessed; here it is argued that Poincaré's conventionalism was more than merely "trivially linguistic". Discussion of this question is focused upon the role of co-ordinative definitions in certain astronomical experiments. Various objections to conventionalism are also discussed.
In the third and final chapter the validity of the conclusions contained within Russell's dissertation is examined in light of contemporary developments in mathematics and the physical sciences.
Gross, Timothy John, "The Russell-Poincaré Debate Concerning the Foundations of Geometry and the Nature of Space" (1974). Open Access Dissertations and Theses. Paper 537.