Dasein - Monoskop

22 PART II
speaks of number names and number signs as "symbolic constructions
for the species of the number concept which are not genuinely
accessible to us" 46 , and writes:
A number system, like for instance our decadic one, can thus
be regarded as a complete reflection of the realm of numbers as
such, that is, of the real numbers which are generally inaccessible
... We are thus fully entitled to regard the indirect constructions
of the system as symbolic surrogates for the numbers as such. 47
Several remarks are called for by these passages.
First of all, despite the strong platonistic flavour of the last
two quotations, it must be remembered that in the very same book
Husserl rejects the notion of the actual infinite as being of a "counterlogical
character". 48 This suggests that whereas we can perhaps
attribute to Husserl some form of realism with respect to concepts on
the basis of these sentences (the being of concepts is independent of
their being thought), we should nevertheless distinguish this position
from a fully-fledged Cantorian platonism. 49
Second, it is important to note, as has recently been persuasively
argued by J. Ph. Miller 50 , that the Philosophy of Arithmetic
is not a homogeneous book. For instance, as Miller has pointed out,
the book contains two different conceptions as to how the problem of
extending the psychological analysis of cardinal numbers to rational,
irrational and imaginary numbers is to be dealt with. Some parts of
the Philosophy of Arithmetic, and especially those dealing with the
psychological genesis of the number concepts, came from Husserl's
Habilitationsschrift of 1887. Other parts were written three or four
years later at a time when Husserl's position towards the problem of
extension had undergone severe changes and when he had also begun
to take a keen interest in Cantor's highly platonistic set theory. 51
Thus the possibility cannot be ruled out that different, perhaps even
conflicting, conceptions found their way into Husserl's book. Perhaps
Husserl had held a more strongly psychologistic-constructivistic
position in his Habilitationsschrift in 1887, but he had moved somewhat
away from this position towards platonism by 1891, when the
Philosophy of Arithmetic was published.
Third, it should be noted that the wording of the passages