Logic as a Science and Logic as a Theory: Remarks on Frege, Russell and the Logocentric Predicament

Abstract

Since its publication in 1967, van Heijenoort’s paper, “Logic as Calculus and Logic as Language” has become a classic in the historiography of modern logic. According to van Heijenoort, the contrast between the two conceptions of logic provides the key to many philosophical issues underlying the entire classical period of modern logic, the period from Frege’s Begriffsschrift (1879) to the work of Herbrand, Gödel and Tarski in the late 1920s and early 1930s. The present paper is a critical reflection on some aspects of van Heijenoort’s thesis. I concentrate on the case of Frege and Russell and the claim that their philosophies of logic are marked through and through by acceptance of the universalist conception of logic, which is an integral part of the view of logic as language. Using the so-called “Logocentric Predicament” (Henry M. Sheffer) as an illustration, I shall argue that the universalist conception does not have the consequences drawn from it by the van Heijenoort tradition. The crucial element here is that we draw a distinction between logic as a universal science and logic as a theory. According to both Frege and Russell, logic is first and foremost a universal science, which is concerned with the principles governing inferential transitions between propositions; but this in no way excludes the possibility of studying logic also as a theory, i.e., as an explicit formulation of (some) of these principles. Some aspects of this distinction will be discussed.