"The doctrine of universal flux is caricatured by Plato, and it is difficult to suppose that any one ever held it in the extreme form that he gives it. ....Logical oppositions have been invented for convenience, but continuous change requires a quantitative apparatus, the possibility of which Plato ignores. What he says on this subject, therefore, is largely beside the mark. At the same time it must be admitted that, unless words, to some extent, had fixed meanings, discourse would be impossible. Here again, however, it is easy to be too absolute. Words do change their meanings... It is necessary that the changes in the meanings of the words should be slower than the changes that the words describe; but it is not necessary that there be no changes in the meanings of words. Perhaps this does not apply to the abstract words of logic and mathematics, but these words, as we have seen, apply only to the form, not to the matter, of propositions. Here, again, we find that logic and mathematics are peculiar. Plato, under the influence of the Pythagoreans, assimilated other knowledge too much to mathematics. He shared this mistake with many of the greatest philosophers, but it was a mistake, none the less."