Contents: The philosophy of science: The faith of a logician The conception of philosophy in recent discussion. Philosophy and scientific methods thedistinction between the mental and the physical, Bacon and the inductive method- Philosophical refiections: The new realism. The new realism and the philosophy of Royce. Some difficulties in John Dewey`s anthropocentric naturalism. Hegel`s rationelism Belief. Croce and vico- Scientific casays: Einstein`s theory of relativity Roads to Einstein. A philosophy of mathematics. The logical foundations of the exact sciences. The origins of modern science