Å·±¦ÓéÀÖ

In Bertrand Russell's Introduction to Mathematical Philosophy, we are presented with a work of philosophical inquiry that explores the fundamental nature of mathematics and its relationship to the broader realm of human knowledge. At the heart of Russell's inquiry is the concept of the transfinite, which he defines as "the infinite which is reached by successive additions." This notion, which owes a great debt to the pioneering work of the German mathematician Georg Cantor, is explored in great depth throughout the book. For Russell, the study of the transfinite is not simply a matter of mathematical curiosity, but rather represents a fundamental challenge to our understanding of the nature of reality itself. As he notes early on in the book, "the infinite is in some sense the key to the whole of mathematics."
Throughout the book, Russell engages with a wide range of philosophical and mathematical thinkers, including Cantor himself, as well as a host of other luminaries such as Leibniz, Frege, and Dedekind. While he is deeply respectful of their contributions to the field, he is also unafraid to criticize their ideas when he feels that they have gone astray. Russell is realist, he believes that "The number is not a mere abstraction, it is something concrete and objective, existing in the same sense as any other physical object."