Philosophy of Physics and Mathematics - Concept and Reality

We try to analyze some logical and philosophical aspects of the quantum theory and G\"{o}del's theorem on incompleteness in this article. It is shown, that logic must develop concepts of relativity (up to the introduction of logical "reference systems", similar to the physical reference systems) and nonpredicative notions must become foundation of the logical constructions. Model theory must more flexibly individualize elements of sets and their features. Relation between modern mathematics and philosophical concepts of Hegel and Berkley is shown.\newline We didn't discuss some generally known aspects of G\"{o}del's theorem, quantum phenomena. Philosophical themes are given very briefly. The theory of category is briefly touched upon too. It is desirable (but not necessary) that, despite our century of narrow specialization, the reader get to know all these subjects. It is described in details only that, in what we managed (or it seemed to manage) to tell something new in the above mentioned questions. Philosophy of Physics and Mathematics - Concept and Reality, 2026, ORCID https://orcid.org/0009-0002-3637-9000 Volodymyr. M. Zhuravlov msc: 03A05 03H99, udc: 510.2