In connection with Lem’s three degree classification of genies
I will offer a personal view of Vop`inka’s alternative set theory and of its relation
to Cantor’s set theory and Robinson’s nonstandard analysis. I will sketch some
reasons which, in my opinion, restrict the potential of the Alternative Set Theory
in particular, as well as of the phenomenologically founded mathematics
in general. Finally, I will try to grasp the philosophical message of Vop`inka’s
phenomenological approach to mathematical infinity which may permanently
influence also some branches of mathematics, beyond the scope of its foundations.