Review represents a new edition of the Moscow seminar on philosophy of mathematics works. The book deals with two interrelated problems: the problem of “the incomprehensible effectiveness" of mathematics and the problem of the ontological status of mathematical objects. The conditions of applicability of mathematical theories in the natural, social and human sciences. Ideas and themes proposed by the authors of articles have goal to reveal perspective analysis of the subject, which allows detect its previously implicit sides. This approach makes possible to put different questions related to the foundations of mathematics and provide an additional impetus to research in this area.

The new book by Professor David J. Stump explores and develops the theories of the a priori, which are rarely considered in contemporary epistemology and philosophy of science: the theories of pragmatic and functional a priori, proposed in the early XX century by Clarence Irving Lewis and Arthur Pap. The author begins with the analysis of «constitutive elements of science» and Henri Poincare's conventionalism. He consistently and historically examines the approaches towards the theories of the a priori within the philosophy of science in the XX-XXI centuries, and also develops his own original approach to a priori based on the philosophy of science.