Mathematical truths are often so compelling that some mathematicians, scientists, and philosophers posit a purely nonmaterial realm of eternal truths accessible to the mind alone. Mathematical physicist Simon Altmann carefully criticizes this revival of dualistic philosophy ß la Plato in this highly stimulating book. Has mathematics and physics discovered a new supernatural world, or is this mental cosmos simply an outgrowth of natural evolutionary processes? This is the crucial philosophical issue that Altmann elucidates. Altmann provides a thorough philosophical basis to understand the meaning of natural law, the scientific method, and causality in science. He reviews the classical approach to time, space, and the laws of mechanics, and discusses the implications of relativity theory. Key modern concepts, like randomness, probability, and time's arrow are explained, and the nature of mathematics and G÷del's theorems is discussed in depth. A mystery-free treatment of quantum mechanics, Schrödinger's cat, and the famous Bell inequalities follows. He also assesses the reactions of various philosophical schools to these developments - idealism, physicalism, cultural relativism and social constructivism. The book concludes with a fascinating dialogue on science and belief. Educated lay readers will welcome Altmann's engaging and lucid exposition.