Fundamental physics asks philosophers new questions

Modern fundamental physics poses new questions for philosophy, which, as it seems to us, have not yet received appropriate attention from philosophers of science. This paper formulates a number of such questions in order to present them to the attention, first of all, of professional philosophers. A rough list of the main themes is as follows: 1) Cosmic variance problem and the meaning of theoretical cosmology; 2) Epistemological status of the concept of Multiverse in cosmology; 3) The operational status of quantum macrostates and the relation of this problem to cosmology; 4) The meaning of the physical reality in the ``final theory''; 5) Criticism of the string theory in the relation with the item 4 above.