The Principles of Mathematics - Couverture souple

Couverture souple

ISBN 10 : 1230430911 ISBN 13 : 9781230430911

A propos du livre

Présentation de l'éditeur

Principles of Mathematics was published in 1903, and most of JL it was written in 1900, In the subsequent years the subjects of which it treats have been widely discussed, and the technique of mathematical logic has been greatly improved ;while some new problems have arisen, some old ones have been solved, and others, though they remain in a controversial condition, have taken on completely new forms. In these circumstances, it seemed useless to attempt to amend this or that, in the book, which no longer expresses my present views. Such interest as the book now possesses is historical, and consists in the fact that it represents a certain stage in the development of its subject. I have therefore altered nothing, but shall endeavour, in this I ntroduction, to say in what respects I adhere to the opinions which it expresses, and in what other respects subsequent research seems to me to have shown them to be erroneous. The fundamental thesis of the following pages, that mathematics and logic are identical, is one which I have never since seen any reason to modify. This thesis was, at first, unpopular, because logic is traditionally associated with philosophy and A ristotle, so that mathematicians felt it to be none of their business, and those who considered themselves logicians resented being asked to master a new and rather difficult mathematical technique. But such feelings would have had no lasting influence if they had been unable to find support in more serious reasons for doubt. These reasons are, broadly speaking, of two opposite kinds :first, that there are certain unsolved difficulties in mathematical logic, which make it appear less certain than mathematics is believed to be ;and secondly that, if the logical basis of mathematics is accepted, it justifies, or tends to justify, much work, such as that of Georg Cantor, which is viewed with suspicion by
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Présentation de l'éditeur

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Détails de l'édition

• Date d'édition: 1738
• ISBN 10: 1230430911
• ISBN 13: 9781230430911
• Reliure: Broché
• Langue: anglais