On Platonism in Set Theory
Abstract
This article points at some (strictly) mathematical methods, which often tend to display not fully conscious treatment of mathematical reality as given, existing and already-present-there. This attitude is prequisite for mathematical research (including set theory), and not merely apsychological add-on, and the methods can be best described as „platonism as method ofenquiry in mathematics” (pl.Metod.) and „platonism as mode of existence of infinity” (pl.Niesk.). Thus, platonism becomes one of the problems internal to mathematics. Identifying pl.Metod. and pl.Niesk. as such, being described here with respect to set theory, is only astarting point in the process of grasping and explaining platonism. This requires phenomenological hermeneutics of mathematics to be conceived (cf. [Z. K.]).
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