Bolzano and the Traditions of Analysis

Abstract

Russell’s discussion of analytic philosophy in his popularHistory begins on a surprising note: the first analytic philosopher he mentions is . . .Weierstrass. His further remarks—in which he discusses Cantor and Frege, singling out their work in the foundations of mathematics—indicate that he thought that the origin of modern philosophical analysis lay in the elaboration of modern mathematical analysis in the nineteenth century [13, 829-30]. Given the markedly different meanings attached to the word “analysis” in these two contexts, this juxtaposition might be dismissed as merely an odd coincidence. As it turns out, however, modern philosophical and mathematical analysis are rather closely linked. They have, for one thing, a common root, albeit one long since buried and forgotten. More important still, and apparently unknown to Russell, is the circumstance that one individual was instrumental in the creation of both: Bolzano. Russell’s account could easily leave one with the impression that analytic philosophy had no deep roots in philosophical tradition; that, instead, it emerged when methods and principles used more or less tacitly in mathematics were, after long use, finally articulated and brought to the attention of the philosophical public. A most misleading impression this would be. For right at the beginning of the reconstruction of the calculus which Russell attributed to Weierstrass we find Bolzano setting out with great clarity the methodology guiding these developments in mathematics—a methodology which, far from being rootless, was developed in close conjunction with Bolzano’s usual critical survey of the relevant philosophical literature. But not merely that: for Bolzano also put this methodology to work with considerable skill and precision, developing many of the central