Title: Mathematical Knowledge and the Role of an Observer: Ontological and epistemological aspects,
Abstract: As David Berlinski writes (1997), the existence and nature of mathematics is
a more compelling and far deeper problem than any of the problems raised by
mathematics itself. Here we analyze the essence of mathematics making the main
emphasis on mathematics as an advanced system of knowledge. This knowledge
consists of structures and represents structures, existence of which depends on
observers in a nonstandard way. Structural nature of mathematics explains its
reasonable effectiveness.