Dasein - Monoskop

16 PART II
fact is important from the standpoint of our study, since Husserl
sees in von Helmholtz's and Kronecker's stance a purely formalistic
position that seeks to exclude questions of meaning from the realm
of mathematics. As Husserl sees it, for von Helmholtz and Kronecker,
cardinal numbers are mere signs and arithmetic is a game
with 'meaningless' signs. 16
How crucial his opposition to formalism is for Husserl is clear
from the fact that as earlv as in the "Introduction" to his Habilitationsschrift
Husserl singles out formalism for special criticism.
Husserl writes that "one will never succeed in charming away material
difficulties by means of verbal or formalistic tricks" 17 and he goes
on to criticize the Riemann-IIelmhoItzian theory of space, claiming
that analytical geometry is not really without reliance upon intuition
(Anschauung): analytical geometry relies centrally on the idea
that each point in space can be characterized by giving its distance
from three "fixed 'co-ordinate axes'". According to Husserl, this
assumption is not intelligible without our intuition of space as threedimrnsional.
18
As is clear from the context in which he presents this criticism
during the late 1880s, Husserl regards descriptive psychology as the
most important weapon against meaning-denying formalism. It is
true that he also speaks of the important achievements of "modern
logic" 19 and stresses the crucial role of "scientific psychology and
logic" 20 in clarifying the foundations of mathematics. Yet in his actual
treatment of the number concept Husserl relies on psychology
alone arid regards logical definitions of number (for instance, the one
suggested by Frege) as insufficient. Husserl also states quite explicitly
that psychology is not only involved in the clarification of the idea
of number but is the only forum on which such a clarification can
take place: "In truth, not only is psychology indispensable for the
analysis of the concept of number, but rather this analysis even belongs
within psychology." 21 This smacks of psychologism, to be sure,
even though it is quite certain that Husserl by no means held that
mathematics was nothing but "'parts or branches' of psychology".
In the logical Investigations he explicitly states that "no one" could
hold such a view, which makes it very unlikely that he should have
done so himself only a decade earlier. 22 That Husserl could write