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Introduction to Mathematical Philosophy

Autor Bertrand Russell
en Limba Engleză Paperback – 14 mar 2020
"The philosophy of mathematics will naturally be expected to deal with questions at the frontier of knowledge, as to which comparative certainty is not yet attained. But separation of such questions is hardly likely to be fruitful unless the more scientific parts of mathematics are known. A book dealing with those parts may, therefore, claim to be an introduction to mathematical philosophy..." - Bertrand Russell, from the Preface
First published in 1919, Introduction to Mathematical Philosophy shows Russell drawing on his formidable knowledge of philosophy and mathematics to write a brilliant introduction to the subject. Russell explains that mathematics can be approached in two distinct directions: one that is driven by a mechanical kind of simplicity and builds towards complexity, from integers to fractions and real numbers to complex ones; and one that searches for abstractness and logical simplicity by asking what general principles underlie mathematics.
From here Russell introduces and explains, in his customary pellucid prose, the definition of numbers, finitude, correlation and relation, mathematical limits, infinity, 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."
This Routledge Classics edition includes a new Foreword by Michael Potter.
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Specificații

ISBN-13: 9781420968118
ISBN-10: 1420968114
Pagini: 148
Dimensiuni: 141 x 215 x 12 mm
Greutate: 0.2 kg
Editura: Neeland Media

Descriere

Descriere de la o altă ediție sau format:
First published in 1919, Introduction to Mathematical Philosophy shows Russell drawing on his formidable knowledge of philosophy and mathematics to write a brilliant introduction to the subject. This Routledge Classics edition includes a new Foreword by Michael Potter.

Cuprins

Foreword to the Routledge Classics Edition Michael Potter  Preface  1. The Series of Natural Numbers  2. Definition of Number  3. Finitude and Mathematical Induction  4. The Definition of Order  5. Kinds of Relations  6. Similarity of Relations  7. Rational, Real, and Complex Numbers  8. Infinite Cardinal Numbers  9. Infinite Series and Ordinals  10. Limits and Continuity  11. Limits and Continuity of Functions  12. Selections and the Multiplicative Axiom  13. The Axiom of Infinity and Logical Types  14. Incompatibility and the Theory of Deduction  15. Propositional Functions  16. Descriptions  17. Classes  18. Mathematics and Logic.  Index

Notă biografică

Bertrand Russell, (18 May 1872 - 2 February 1970) was a British philosopher, logician, mathematician, historian, writer, essayist, social critic, political activist, and Nobel laureate. At various points in his life, Russell considered himself a liberal, a socialist and a pacifist, although he also confessed that his sceptical nature had led him to feel that he had "never been any of these things, in any profound sense. Russell was born in Monmouthshire into one of the most prominent aristocratic families in the United Kingdom In the early 20th century, Russell led the British "revolt against idealism" He is considered one of the founders of analytic philosophy along with his predecessor Gottlob Frege, colleague G. E. Moore and protégé Ludwig Wittgenstein. He is widely held to be one of the 20th century's premier logicians.[67] With A. N. Whitehead he wrote Principia Mathematica, an attempt to create a logical basis for mathematics, the quintessential work of classical logic. His philosophical essay "On Denoting" has been considered a "paradigm of philosophy".[71] His work has had a considerable influence on mathematics, logic, set theory, linguistics, artificial intelligence, cognitive science, computer science (see type theory and type system) and philosophy, especially the philosophy of language, epistemology and metaphysics. Russell was a prominent anti-war activist and he championed anti-imperialism. Occasionally, he advocated preventive nuclear war, before the opportunity provided by the atomic monopoly had passed and he decided he would "welcome with enthusiasm" world government.[74] He went to prison for his pacifism during World War I. Later, Russell concluded that war against Adolf Hitler's Nazi Germany was a necessary "lesser of two evils" and criticised Stalinist totalitarianism, attacked the involvement of the United States in the Vietnam War and was an outspoken proponent of nuclear disarmament. In 1950, Russell was awarded the Nobel Prize in Literature "in recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thought"