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HUSSERL'S PHENOMENOLOGY AND LANGUAGE AS CALCULUS 31
sential difference between language and calculus, and acknowledges
that Frege had done this even prior to his, i.e., Husserl's, review of
Schroder. However, after this reminder of their agreement, Husserl
goes on: "To be sure, it appears to me that the Begriffsschrift, since
it is meant to be a 'lingua characteristica,' should not be called 'a
formal language constructed after the arithmetical.' For it should be
certain that arithmetic is a 'calculus ratiocinator' and not a 'lingua
characteristica'." 84
In the same letter to Frege Husserl also notes that he finds himself
in agreement with Frege's opposition to formalism, or rather
"formal arithmetic", once formalism proclaims itself to be a "theory"
and not just a "technique" of arithmetic. And indeed, in an
unpublished manuscript of approximately the same time, Husserl relies
on Frege's arguments to refute one brand of formalism according
to which arithmetic operates with empty signs. "Against this theory
Frege was right in objecting ... that an empty sign does not
solve a [mathematical] problem; without content it is mere ink and
printing-ink on the paper having as such merely physiological attributes,
.. ," 85
However, in the light of his other writings from this period,
Husserl's agreement with Frege did not go very deep. Indeed, Husserl
noticed this himself. Earlier in the letter he mentions that his own
ideas with respect to the problem of extension are incompatible with
Frege's views as presented in "On Formal Theories of Arithmetic". 86
In this paper Frege in fact criticizes precisely the position that
Husserl was developing in his unpublished writing. Whereas—as
we have seen above—in 1890 Husserl accepts the view that only positive
cardinal numbers are grounded in concepts, and that signs like
1/2,1/3, and are therefore empty of conceptual content, Frege
explicitly rejects this view: "Despite the emphatic assertion that the
signs are empty and that it is they themselves that are the numbers,
in the background there always hovers the thought that they do signify
something and that it is these contents of signs that really are
the numbers." 87
Actually Husserl did not quite hold the position that FYege describes
and rejects. Husserl thought, not that the arithmetical signs
within the calculating process are simply void of meaning, but that