Let it be said at once that our investigations will lead to the unveiling of certain illusions which the spectator-consciousness has woven round these two gifts of Galileo. This does not mean that their significance as fundamentals of science will be questioned. Nor will the practical uses to which they have been put with so much success be criticized in any way. But there are certain deceptive ideas which became connected with them, and the result is that to-day, when man is in need of finding new epistemological ground under his feet, he is entangled in a network of conceptual illusions which prevent him from using his reason with the required freedom.