Dasein - Monoskop

HUSSERL'S PHENOMENOLOGY AND LANGUAGE AS CALCULUS 27
mentary arithmetic is a limited algorithm whose extension is fully explained
and justified by the general principles concerning the extension
of any formal algorithm. Vis-à-vis the questions as to whether
cardinal numbers are the basis of extension and as to whether there
must always be a strict parallelism between sign and conceptual content,
Husserl's answer is now negative:.
The concept of cardinal number does not allow for extensions;
what is extended and what allows for extension is only the arithmetical
technique. The latter knows of and constructs negative,
imaginary, irrational and fractional numbers which serve the
purpose of making the calculus more complete, and which in
this respect have a great logical significance. But they lack all
conceptual content that goes beyond the algorithmical. 67
In his letter to Stumpf Husserl uses the picture of concentric
circles to explain his idea. The innermost circle consists of elementary
arithmetic, the next circle contains fractions, and so on. As we
go from the inside outwards, the numbers in each successive circle
are formally derived by way of generalized operations from numbers
in an earlier circle. The calculation rules are to be formulated in
such a way that each equation is valid in the circle whose numbers
the equation in question refers to, regardless of possible derivative
transitions through more outer circles. 68
The lesson Husserl takes home from these considerations is that
mathematics, more specifically, analysis or arithmetica universalis,
is a part of formal logic where formal logic is understood as "the
art of signs". 69 Husserl's capitulation in the face of his own by now
rather non-psychological and formalistic solution to the problem of
extension is even so radical as to deny analysis the status of a science:
"Based on all this I may say: The arithmetica universalis is
no science, but a part of formal logic, which in turn I would define
as the art of signs (etc. etc.) and [which I would] call one of the
most important chapters of logic as the technology [Kunstlehre] of
knowledge." 70 This remark is highly interesting since, for once, it
reveals that in the early 1890s Husserl was holding a view of logic
as Kunstlehre that in 1896, when he wrote the Prolegomena of the
Logical Investigations, he would renounce as being insufficient and