“Tertium Non Datur:” Husserl’s Conception of a Definite Multiplicity

Abstract

In his Logical Investigations ¹, Husserl proposed a harmonious division of labor between the mathematician and the philosopher in matters concerning logic. The mathematician was to continue doing what he was most competent at, namely, constructing deductive systems, without concern for the sense of such systems or for their critical status as contributions to a broader field of scientific knowledge. The philosopher’s task was to be different: to clarify what is involved in formal systems as contributions to the goal of genuine knowledge. Such a position makes certain basic assumptions. It assumes, for example, that mathematical construction can be effectively carried out without concern for its sense or applicability and yet yield results that, when applied to some domain, can contribute to knowledge. This position does not necessarily assume that subsequent reflection aimed at discerning the sense and epistemic contribution of such mathematical procedure can be accomplished without a background of technical competence in mathematics.