The Principles of Mathematics 1
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In our eReader you can find the full English version of the book. Read The Principles of Mathematics 1 Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book The Principles of Mathematics 1
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No mathematical subject has made, in recent years, greater advances than the theory of Arithmetic. The movement in favour of correctness in deduction, inaugurated by Weierstrass, has been brilliantly continued by Dedekind, Cantor, Frege, and Peano, and attains what sjem^ its final goal by means of the logic of relations. As the modern mathematical theory is but imperfectly known even by most matljiematicians, I shall begin this Part by four chapters setting forth its oti+lines in a non-symbolic... form. I shall then examine the process of deduction froii> a philosophical standpoint, in order to discover, if possible, whether any unperceived assumptions have covertly intruded themselves in the com'se of the arcrument.
I j 108. It is often held that both number and particular numbers am\ indefinable. No'.'. definability is a word which, in Mathematics-, lias a precise sense, though one which is relative to some given set of notions "f".
Given any set of notions, a term is definable by means of these notions when, and only when, it is thj only term having to certain of these notions a certain relation which itstlf is one of the said notions.
What to read after The Principles of Mathematics 1?
You can find similar books in the "Read Also" column, or choose other free books by Russell Bertrand to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
No mathematical subject has made, in recent years, greater advances than the theory of Arithmetic. The movement in favour of correctness in deduction, inaugurated by Weierstrass, has been brilliantly continued by Dedekind, Cantor, Frege, and Peano, and attains what sjem^ its final goal by means of the logic of relations. As the modern mathematical theory is but imperfectly known even by most matljiematicians, I shall begin this Part by four chapters setting forth its oti+lines in a non-symbolic... form. I shall then examine the process of deduction froii> a philosophical standpoint, in order to discover, if possible, whether any unperceived assumptions have covertly intruded themselves in the com'se of the arcrument.
I j 108. It is often held that both number and particular numbers am\ indefinable. No'.'. definability is a word which, in Mathematics-, lias a precise sense, though one which is relative to some given set of notions "f".
Given any set of notions, a term is definable by means of these notions when, and only when, it is thj only term having to certain of these notions a certain relation which itstlf is one of the said notions.
What to read after The Principles of Mathematics 1?
You can find similar books in the "Read Also" column, or choose other free books by Russell Bertrand to read onlineMoreLess
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