The aim of the second part of this philosophical diptych is an attempt at discussing the place of the meta-subject reflection concerning fractal structures in classical issues of the philosophy of mathematics. The authors show that fractal structures lead toward essential broadening of that issues beyond traditional frames of the questions about the nature of mathematical objects (ontology of mathematics) or the status of mathematical knowledge (epistemology of mathematics). Particularly, they are interested in two problems: (1) Does process of generating fractal structures prove that co-called new mathematics has quasi-empirical character and in what meaning of that? and (2) Can the philosophical idea of emergence be applied to characterise the features of that structures?
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