Dasein - Monoskop

HUSSERL'S PHENOMENOLOGY AND LANGUAGE AS CALCULUS 13
cific moments in this period?
The answer that will be outlined in this chapter can be put in the
following way. Initially Husserl's central concern was with formalism
in higher analysis, that is in (higher) mathematics, and in logic.
Between 1887 and 1890 Husserl sought to undermine the meaningneglecting
formalist threat posed foremost by von Helmholtz and
Kronecker. This Husserl did by applying the tools of descriptive
psychology. These tools Husserl had come to appreciate when studying
under Brentano in Vienna between 1884 and 1886. The project
that Husserl undertook during the late 1880s was to find a partly
philosophical, partly psychological foundation for higher analysis by
explaining the psychological genesis of cardinal numbers. Husserl's
ultimate hope was that such a foundation for elementary arithmetic
could then be extended to the whole of analysis. Around 1890, however,
Husserl came to realize that this hope was vain. He now saw
that his earlier psychological theory concerning the origin of our concept
of cardinal numbers could not be extended in a natural way to
cover rational, irrational and imaginary numbers. In order to explain
and justify operations with such numbers, psychology was of little
use, and formal logic had to be evoked instead. Husserl was subsequently
willing to accept formalism. This acceptance was, however,
subject to important qualifications. In the manuscripts written in
the early nineties, published recently under the fitting title "On the
Philosophy of the Calculus" 9 , Husserl analyzed the structure and
generation of algorithms, giving special emphasis to the observation
that algorithms can be interpreted and re-interpreted over different
domains. No surprise, therefore, that Husserl studied Boolean and
Schroderian algebra during the same time. Yet from his encounter
with Schroder's logical algebra 10 , Husserl took home much more than
just an additional appreciation for the re-interpretability of formal
systems. This additional lesson was a critical one: Husserl began
to see that he could challenge formalism—something he himself had
only recently been attracted by—in a new way. Schroder seemed
to Husserl to neglect the important question as to the relations between
his algebra of classes and what this algorithm was taken to
represent: judgments, deductions, or, more generally, logical operations.
In other words, Schroder's formalism neither answered nor