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

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, G¨odel 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.