Furthermore, it should also be noted that every precise physical experiment that it has been possible to accomplish has verified the anticipations of the Lorentz-Einstein transformations; it is owing to this fact that the theory was not abandoned years ago. This in itself should warn us against asserting that the transformations possess no physical significance. Thus far we have been concerned with generalities and have merely attempted to show why Bergson’s solution of the problem must be discarded on first principles. Leaving aside this aspect of the question, it is instructive to consider the formal proof which he presents in support of his contentions. He appears to realise that the entire matter hinges on the measure of physical reality which should be credited to the Lorentz-Einstein transformations. Accordingly, he attempts to prove that these transformations do not represent reality, but possess a mere fictitious mathematical significance having nothing in common with the physical world. He calls them “phantasmatical,” contending that mathematicians, not being trained in philosophy, are severely handicapped when they attempt to interpret their equations, and are incapable of distinguishing mathematical fictions from physical reality. So Bergson proceeds to demonstrate the fictitious significance of the transformations. He first serves us with a series of arguments based on the principle of the relativity of motion itself. In the very first paragraph, however, he confuses the relativity of Galilean motion with the complete relativity of all motion, Newtonian and special relativity with visual relativity, velocity with acceleration. All these errors relate to classical science itself; and it is obviously quite impossible to discuss Einstein’s theory intelligently until we have acquired at least an elementary knowledge of classical mechanics. Following this philosophical demonstration, he goes on to give us a mathematical one; but all he succeeds in proving is that he has not the slightest conception of the most elementary properties of mathematical transformations.