In connection with Lem’s three degrees classification of genies, I will offer a personal view of Vopěnka’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 phenomenologically-founded mathematics in general. Finally, I will try to grasp the philosophical message of Vopěnka’s phenomenological exposition of mathematical infinity which may permanently influence some branches of mathematics, beyond the scope of its foundations
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