Introduction to Mathematical Philosophy

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Overview

2014 Reprint of 1919 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. "Introduction to Mathematical Philosophy" was written in part to express in a less technical way the main ideas of his and Whitehead's "Principia." According to Russell, "Mathematics and logic, historically speaking, have been entirely distinct studies. Mathematics has been connected with science, logic with Greek. But both have developed in modern times: logic has become more mathematical and ...
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Introduction to Mathematical Philosophy (Barnes & Noble Library of Essential Reading)

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Overview

2014 Reprint of 1919 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. "Introduction to Mathematical Philosophy" was written in part to express in a less technical way the main ideas of his and Whitehead's "Principia." According to Russell, "Mathematics and logic, historically speaking, have been entirely distinct studies. Mathematics has been connected with science, logic with Greek. But both have developed in modern times: logic has become more mathematical and mathematics has become more logical. The consequence is that it has now become wholly impossible to draw a line between the two; in fact, the two are one. They differ as boy and man: logic is the youth of mathematics and mathematics is the manhood of logic. This view is resented by logicians who, having spent their time in the study of classical texts, are incapable of following a piece of symbolic reasoning, and by mathematicians who have learnt a technique without troubling to inquire into its meaning or justification. Both types are now fortunately growing rarer. So much of modern mathematical work is obviously on the border-line of logic, so much of modern logic is symbolic and formal, that the very close relationship of logic and mathematics has become obvious to every instructed student. The proof of their identity is, of course, a matter of detail: starting with premises which would be universally admitted to belong to logic, and arriving by deduction at results which as obviously belong to mathematics, we find that there is no point at which a sharp line can be drawn, with logic to the left and mathematics to the right. If there are still those who do not admit the identity of logic and mathematics, we may challenge them to indicate at what point, in the successive definitions and deductions of "Principia Mathematica," they consider that logic ends and mathematics begins. It will then be obvious that any answer must be quite arbitrary."
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Product Details

  • ISBN-13: 9781614276302
  • Publisher: Martino Fine Books
  • Publication date: 5/6/2014
  • Pages: 218
  • Product dimensions: 6.00 (w) x 9.00 (h) x 0.50 (d)

Table of Contents

Introduction
Preface
Editor's Note
1 The Series of Natural Numbers 1
2 Definition of Number 11
3 Finitude and Mathematical Induction 20
4 The Definition of Order 29
5 Kinds of Relations 52
6 Similarity of Relations 52
7 Rational, Real, and Complex Numbers 63
8 Infinite Cardinal Numbers 77
9 Infinite Series and Ordinals 89
10 Limits and Continuity 97
11 Limits and Continuity of Functions 107
12 Selections and Multiplicative Axiom 117
13 The Axiom of Infinity and Logical Types 131
14 Incompatibility and the Theory of Deduction 144
15 Propositional Functions 155
16 Descriptions 167
17 Classes 181
18 Mathematics and Logic 194
Index 207
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Customer Reviews

Average Rating 3.5
( 22 )
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See All Sort by: Showing 1 – 20 of 22 Customer Reviews
  • Anonymous

    Posted December 20, 2006

    Good introduction to an overlooked but important part of philosophy

    The book explores a much neglected area of philosophy. The Nature of Mathematics and mathematical truth. It also touches briefly on the Ontology of mathematical concepts. Do mathematical concepts exist independently of mathematicians or instead are they invented by them. This is an obscure question to many but could be seen to be as important as asking 'do entities such as numbers and concepts exist independently of the material world. The answer to this question would have very important consequences for materialism as a reigning philosophy. Russell's book is a great intro to this neglected subject.

    7 out of 7 people found this review helpful.

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  • Anonymous

    Posted August 12, 2009

    Why pay for what you can get for free?

    Minus the editor's introduction, you can get this book free in several different formats elsewhere...
    http://people.umass.edu/klement/russell-imp.html

    2 out of 4 people found this review helpful.

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  • Anonymous

    Posted January 9, 2007

    First Class

    The only thing which could possibly make this book better would be if it were written after Godel's work.

    2 out of 2 people found this review helpful.

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