Our Knowledge of the External World [NOOK Book]

Overview

The very relevance and legitimacy of philosophy is examined in this explosive and controversial work which investigates the relationship between ‘individual’ and ‘scientific’ knowledge, and questions the means by which we come to understand the physical world.

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Our Knowledge of the External World

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Overview

The very relevance and legitimacy of philosophy is examined in this explosive and controversial work which investigates the relationship between ‘individual’ and ‘scientific’ knowledge, and questions the means by which we come to understand the physical world.

Read More Show Less

Product Details

  • ISBN-13: 9781134026913
  • Publisher: Taylor & Francis
  • Publication date: 3/4/2009
  • Sold by: Barnes & Noble
  • Format: eBook
  • Pages: 232
  • File size: 262 KB

Meet the Author

Bertrand Russell (1872-1970). The leading British Philosopher of the twentieth century, who made major contributions to the area of logic and epistemology. Politically active and habitually outspoken, his ethical principles twice lead to imprisonment

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Read an Excerpt


LECTURE V THE THEORY OF CONTINUITY The theory of continuity, with which we shall be occupied in the present lecture, is, in most of its refinements and developments, a purely mathematical subject very beautiful, very important, and very delightful, but not, strictly speaking, a part of philosophy. The logical basis of the theory alone belongs to philosophy, and alone will occupy us to-night. The way the problem of continuity enters into philosophy is, broadly speaking, the following : Space and time are treated by mathematicians as consisting of points and instants, but they also have a property, easier to feel than to define, which is called continuity, and is thought by many philosophers to be destroyed when they are resolved into points and instants. Zeno, as we shall see, proved that analysis into points and instants was impossible if we adhered to the view that the number of points or instants in a finite space or time must be finite. Later philosophers, believing infinite number to be self-contradictory, have found here an antinomy : Spaces and times could not consist of a finite number of points and instants, for such reasons as Zeno's ; they could not consist of an infinite number of points and instants, because infinite numbers were supposed to be self-contradictory. Therefore spaces and times, if real at all, must not be regarded as composed of points and instants. But even when points and instants, as independent entities, are discarded, as they were by the theory advocated in our last lecture, the problems of continuity, as I shall try to show presently, remain, in a practically unchanged form. Let us therefore, to begin with, admit points and instants, andconsider the problems in connection with this simpler or at least more familiar hypothesis. The argu...
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Table of Contents

Introduction
Preface
I Current Tendencies 13
II Logic as the Essence of Philosophy 42
III On Our Knowledge of the External World 70
IV The World of Physics and the World of Sense 106
V The Theory of Continuity 135
VI The Problem of Infinity Considered Historically 159
VII The Positive Theory of Infinity 189
VIII On the Notion of Cause, with Applications to the Free-Will Problem 214
Index 247
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