ABSTRACT
After having passed in review in the last chapter the first two phases in the evolution of mathematics, those of direct and indirect symbolism as we have called them, we propose in the present chapter to sketch very rapidly the other two phases which we consider must still be examined. When this has been done a brief summary, in the chapter which follows this, of all that we have said concerning mathematical reasoning and the function which symbolism has performed in this kind of reasoning, will enable us, by way of conclusion, to make certain comparisons between mathematics and mathematical logic.
