Introduction to Mathematical Philosophy by Bertrand Russell is a classic work that explores the philosophy of mathematics, drawing on Russell's knowledge of philosophy and mathematics. It introduces and explains key concepts such as numbers, finitude, correlation and relation, mathematical limits, infinity, propositional descriptions and classes, and the relationship between mathematics and logic. The Routledge Classics edition includes a new Foreword by Michael Potter.

Format: Hardback
Length: 202 pages
Publication date: 15 September 2022
Publisher: Taylor & Francis Ltd

The philosophy of mathematics is a field that deals with questions at the frontier of knowledge, where comparative certainty is not yet attained. However, to be fruitful, it is essential to have a solid understanding of the more scientific parts of mathematics. In his book Introduction to Mathematical Philosophy, published in 1919, Bertrand Russell draws on his extensive knowledge of philosophy and mathematics to provide a comprehensive introduction to the subject.

Introduction to Mathematical Philosophy

Russell's book is divided into two distinct directions: one that is driven by a mechanical kind of simplicity and builds towards complexity, and one that searches for abstractness and logical simplicity by asking what general principles underlie mathematics.

Definition of Numbers

Russell begins by defining numbers, which he describes as "the simplest and most fundamental concept in mathematics." He explains that numbers are used to count and measure physical objects, and that they can be represented in various ways, such as integers, fractions, and real numbers.

Finitude

Russell then discusses finitude, which is the idea that there are a finite number of things in the universe. He explains that this idea is based on the principle of induction, which states that if a set of objects has a certain property, then all objects in the set must have that property.

Correlation and Relation

Russell also discusses correlation and relation, which are two fundamental concepts in mathematics. He explains that correlation is the relationship between two variables, and that relation is the relationship between two sets of variables. He also discusses the concept of mathematical limits, which are the boundaries of mathematical objects.

Infinity

Russell then discusses infinity, which is the idea of a number that is greater than any finite number. He explains that infinity is a concept that is used in many different fields of mathematics, including geometry, calculus, and number theory.

Propositional Descriptions and Classes

Russell concludes with a fascinating summary of the relationship between mathematics and logic, of which he states logic is the youth of mathematics. He explains that logic is the study of the principles of reasoning, and that it is used to prove mathematical theorems.

Conclusion

In conclusion, Introduction to Mathematical Philosophy is a brilliant introduction to the subject of mathematics. Russell's clear and concise prose makes the book accessible to a wide range of readers, and his insights into the nature of mathematics and logic are invaluable. This Routledge Classics edition includes a new Foreword by Michael Potter, which provides a fresh perspective on the book's significance.

Weight: 580g
Dimension: 216 x 138 (mm)
ISBN-13: 9781032312675