Dasein - Monoskop

2 PART II
directly. For instance, we shall have occasion to observe fundamental
differences between Husserl's and FYege's respective conceptions of
logic, and far-reaching parallels between Heidegger's and Wittgenstein's
views of language.
2. THE INTERPRETATIONAL FRAMEWORK
The interpretational framework referred to above is Jaakko Hintikka's
distinction between two types of theories of language, namely,
views of "language as the universal medium" vs. views of "language
as calculus". This distinction is a generalization of a contrast between
two ways of looking at logic suggested earlier by the late
Jean van Heijenoort. In his paper "Logic as Calculus and Logic
as Language" 2 , van Heijenoort contrasts two strands in the recent
history of logic. The first takes logic to be a universal language,
the second conceives of logic as a calculus, in the sense of being
re-interpretable in a large scale like a calculus. The universalist tradition
is represented among others by Frege and Russell, the calculus
tradition among others by Boole, Schroder and Löwenheim.
In defending himself against Schroder's criticism of his Begriffsschrift,
Frege stressed that he had not only developed a logic in
the sense of a calculus ratiocinator, but also, and primarily, a logic
in the sense of a lingua characteri(sti)ca. 3 According to van Heijenoort,
Frege's emphasis on lingua as opposed to calculus is mainly
based on two points. On the one hand, Frege goes beyond the propositional
calculus in analyzing propositions into predicates, names,
variables, and quantifiers. This allows, for the first time, an actual
translation of mathematical and scientific propositions into the logical
notation. On the other hand, Ftege's approach does not allow
for any changes of the universe of discourse, as did Boole's, De Morgan's
and Schroder's. For iYege, the universe of discourse is fixed
not only in the sense that "he restricts himself to one universe",
but also in the sense that "his universe is the universe". 4 This second
point has several important consequences, three of which van
Heijenoort spells out. First, functions must be defined for all their
possible arguments, i.e., for Frege, defined for all objects. Second,