The author’s attitude to foundations of mathematics, which he describes as commonsensical, assumes a permanent interaction between the foundations and the current mathematical practice (“applications”). It is opposed in this sense to the “Bolzano-Frege-Peano-Russell tradition” (making part of today’s Analytic philosophy), which attempts to provide Formal Axiomatic Method with a philosophical underpinning disregarding its problematic status in the context of the current mathematical research.