After a phase of radical mathematical innovations between 1918 and 1925, often with strong repercussions in physics (from foundations of analysis, via general relativity, differential geometry and unified field theory to the representation theory of Lie groups), Hermann Weyl turned toward writing his contribution Philosophie der Mathematik und Naturwissenschaft on the philosophy of mathematics and natural sciences, in the sequel abbreviated PMN [Weyl 1927, Weyl 1949], for the Handbuch der Philosophie [Baeumler/Schroeter 1927]. It was a time of reorientation for him with regard to foundations of mathematics and to the question of how mathematics may contribute to understanding of the external (natural) world. The phase of his most radical interventions into the foundations of mathematics in a constructivist perspective from 1916 to 1919 and an intuitionist one, 1919 to 1922, lay just behind him.