Author Description

In this work we expose in an easy and simple, but precise, way of understanding, to those who start university studies: the objectives, the fundamental concepts, the theories, the most important procedures and the metaphysical foundations, of mathematics and logic, both of the classical logic and the modern logic. We paid special attention to the theories and concepts necessary to understand language and the application of said sciences to the development of automatic control systems, computers and robots, all of which reproduce intellectual processes, and use artificial intelligence and artificial languages. In it, we also analyze the most important contributions to the historical development of the theories and concepts in question, and paid especial attention to the contributions of George Boole, George Cantor, Gottlob Frege, Charles Sanders Peirce, William James, David Hilbert, John Dewey, Bertrand Russell, Ludwig Wittgenstein and Rudolf Carnap.