Resumen

Bertrand Russell is an important and interesting figure, undoubtedly the most read, honored, and reviled English-speaking philosopher of the twentieth century. And his “Introduction to Mathematical Philosophy” is no less fascinating. Indeed, Russell's above-mentioned work, published in 1918, has sometimes rightly been called “an admirable exposition of che monumental work Principia Mathematica”. The main object of Russell’s book is number, and everything belonging to number, to arithmetic, and to the logic of arithmetic. The foundations of arithmetic always remained the focus of Russell's interest in logic and mathematics, and his views had a profound influence on the reform movement of mathematics education that began around 1960. Since che beginning of the 19" century, mathematics showed a strong tendency towards arithmetization, because space and the continuum seemed beset with seemingly intractable otherness. By the end of the 19‘ century, even number appeared not to be so transparent and so immediately given anymore and the question “what numbers are” arose to explain and co complete the foundations of arithmetic itself by means of logical analysis and set theoretical construction.