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Introduction to Mathematical Philosophy [Englisch] [Taschenbuch]

III Russell Bertrand
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Kurzbeschreibung

30. April 2014
An unabridged, unaltered printing of the Second Edition (1920), with original format, all footnotes and index: The Series of Natural Numbers - Definition of Number - Finitude and Mathematical Induction - The Definition of Order - Kinds of Relations - Similarity of Relations - Rational, Real, and Complex Numbers - Infinite Cardinal Numbers - Infinite Series and Ordinals - Limits and Continuity - Limits and Continuity of Functions - Selections and the Multiplicative Axiom - The Axiom of Infinity and Logical Types - Incompatibility and the Theory of Deductions - Propositional Functions - Descriptions - Classes - Mathematics and Logic - Index

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Introduction to Mathematical Philosophy + The Problems of Philosophy + A History of Western Philosophy (Routledge Classics)
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Produktinformation

  • Taschenbuch: 216 Seiten
  • Verlag: Merchant Books (30. April 2014)
  • Sprache: Englisch
  • ISBN-10: 1603866485
  • ISBN-13: 978-1603866484
  • Größe und/oder Gewicht: 1,2 x 15 x 22,6 cm
  • Durchschnittliche Kundenbewertung: 4.0 von 5 Sternen  Alle Rezensionen anzeigen (3 Kundenrezensionen)
  • Amazon Bestseller-Rang: Nr. 579.494 in Fremdsprachige Bücher (Siehe Top 100 in Fremdsprachige Bücher)

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Synopsis

1919. Russell was a prolific writer of many books on a variety of subjects including mysticism, mathematical philosophy and Bolshevism. Contents: The Series of Natural Numbers; Definition of Number; Finitude and Mathematical Induction; The Definition of Order; Kinds of Relations; Similarity of Relations; Rational, Real, and Complex Numbers; Infinite Cardinal Numbers; Infinite Series and Ordinals; Limits and Continuity; Limits and Continuity of Functions; Selections and the Multiplicative Axiom; The Axiom of Infinity and Logical Types; Incompatibility and the Theory of Deduction; Propositional Functions; Descriptions; Classes; and Mathematics and Logic. See other titles by this author available from Kessinger Publishing. -- Dieser Text bezieht sich auf eine vergriffene oder nicht verfügbare Ausgabe dieses Titels.

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4.0 von 5 Sternen
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4 von 4 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen A very accessible mathematical classic 30. September 1998
Von Ein Kunde
Format:Taschenbuch
An excellent and lucid exposition of what we really mean when we talk about 2 houses, or 1/2 an hour, or square root of 2 meters, or that the counting numbers are infinite. It does not require any prior mathematical knowledge beyond the basics, although it probably will be of interest only to those that care about math at its most abstract. It is fascinating to realize how much we take for granted when we do math and how much ingenuity it takes to pin down the concept of number. Highly recommended.
War diese Rezension für Sie hilfreich?
7 von 11 Kunden fanden die folgende Rezension hilfreich
Von Ein Kunde
Format:Taschenbuch
This book is important for revealing Russell's views, at a certain point in his career, on the philosphies of mathematics and logic. But it says little on other philosophical viewpoints (even if only to criticise them). It might be better titled now 'Introduction to a Mathematical Philosophy (Called Logicism)'. We can hardly blame Russell for not knowing about the later developments of the subject (especially Godel), but it is worth bearing in mind that the book was written before some very important discoveries.
Like anything Russell wrote, it is a pleasure to read - his writing style is wonderful, and quite extraordinary when one realises how quickly he wrote this book (in prison, too!), but I suspect that for many readers the mathematical content will prove a little tricky to grasp.
As a historical document, it is fascinating; as an introduction to mathematical philosophy it is too narrow-minded for 1999.
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4.0 von 5 Sternen Russel in senem Element 19. Dezember 2012
Von Mike
Format:Taschenbuch|Verifizierter Kauf
Es ist zwar eine Introduction (Einführung), aber eine gewisse mathematische Vorbildung wäre enpfellungswert. Aber für den Preis kann man kein Fehler machen.
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133 von 135 Kunden fanden die folgende Rezension hilfreich
3.0 von 5 Sternen Substantial effort required. Careful reading necessary. 2. Oktober 2003
Von Michael Wischmeyer - Veröffentlicht auf Amazon.com
Format:Taschenbuch
Bertrand Russell and Alfred North Whitehead created the monumental work Principia Mathematica (1910-1913), the ambitious and comprehensive effort to provide a detailed reduction of the whole of mathematics to logic. In 1919 Russell was jailed for antiwar protests and while in prison he wrote Introduction to Mathematical Philosophy, a seminal work in the field for more than 70 years.
I have devoted substantial time and effort to this 200 page book. Unless you are a student of logic, this book may not be for you. I suggest alternatives below.
I stayed the course and worked my way through each chapter, sometimes backing up, and often repeating several chapters before advancing again. Bertrand Russell is admired for his eloquence and style. Nonetheless, I can assure you that a methodical reading will require much effort.
I was forewarned. At one point a friend and colleague, a previous professor of mathematics at Texas A&M, expressed surprise that I was tackling this particular book. He considered Russell's work to be dated and not particularly easy going. I continued plodding along.
Russell begins with familiar ground, Peano's effort to derive the entire theory of natural numbers from five premises and three undefined terms (primitives). Russell demonstrates why Peano's approach fails to serve as an adequate basis for arithmetic.
In chapter 2 Russell introduces the work of Frege, who first succeeded in logicising arithmetic. We are led to a definition of number: the number of a class is the class of all those classes that are similar to it, or more simply, a number is anything which is the number of some class.
The third chapter introduces properties termed hereditary, posterity, and inductive. After some effort, we define the natural numbers as those to which proofs by mathematical induction can be applied. We also learn that mathematical induction is not valid for infinite numbers.
Russell now addresses the serial character of natural numbers, a characteristic involving finding or construction of an asymmetrical transitive connected relation.
In Chapters 5 and 6 Russell distinguished between cardinal numbers (the earlier definition of number) and relation numbers (also called ordinal numbers). I had difficulty with the interplay between the relations aliorelative, transitive, asymmetrical, square, and connected. For example, an asymmetrical relation is the same thing as a relation whose square is an aliorelative.
In chapter 7 I was initially surprised by Russell's assertion that the common belief that the complex numbers include the real numbers, the real numbers include the rational numbers, and the rational numbers include the natural numbers is erroneous and must be discarded.
The next thee chapters - infinite cardinal numbers, infinite series and ordinals, and limits and continuity - were more difficult. Eight more chapters follow.
Introduction to Mathematical Philosophy is philosophy, logic, and mathematics. It investigates the logical foundations of mathematics. It requires very careful reading.
I can suggest alternatives. Howard Eves in his delightful Foundations and Fundamental Concepts of Mathematics offers an excellent chapter titled Logic and Philosophy that compares three approaches - Logicism (Russell and Whitehead), Intuitionism (Brouwer and Heyting), and Formalism (Hilbert's Grundlagen der Geometrie). He also provides in an appendix a short overview of Godel's theorems (1931) which demonstrated that no complete or consistent axiomatic development of mathematics is attainable.
I also highly recommend Godel's Proof, a short book by Ernest Nagel and James R. Newman. Godel's Proof demonstrates that Russell and Whitehead's Principia Mathematica must necessarily be incomplete and inconsistent.
37 von 38 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen A very accessible mathematical classic 30. September 1998
Von Ein Kunde - Veröffentlicht auf Amazon.com
Format:Taschenbuch
An excellent and lucid exposition of what we really mean when we talk about 2 houses, or 1/2 an hour, or square root of 2 meters, or that the counting numbers are infinite. It does not require any prior mathematical knowledge beyond the basics, although it probably will be of interest only to those that care about math at its most abstract. It is fascinating to realize how much we take for granted when we do math and how much ingenuity it takes to pin down the concept of number. Highly recommended.
72 von 79 Kunden fanden die folgende Rezension hilfreich
3.0 von 5 Sternen A very dated and one-sided introduction to the subject 12. Juli 1999
Von Ein Kunde - Veröffentlicht auf Amazon.com
Format:Taschenbuch
This book is important for revealing Russell's views, at a certain point in his career, on the philosphies of mathematics and logic. But it says little on other philosophical viewpoints (even if only to criticise them). It might be better titled now 'Introduction to a Mathematical Philosophy (Called Logicism)'. We can hardly blame Russell for not knowing about the later developments of the subject (especially Godel), but it is worth bearing in mind that the book was written before some very important discoveries.
Like anything Russell wrote, it is a pleasure to read - his writing style is wonderful, and quite extraordinary when one realises how quickly he wrote this book (in prison, too!), but I suspect that for many readers the mathematical content will prove a little tricky to grasp.
As a historical document, it is fascinating; as an introduction to mathematical philosophy it is too narrow-minded for 1999.
13 von 13 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen Good introduction To Mathematical Logic 8. Juli 2005
Von Robert E. Murena Jr. - Veröffentlicht auf Amazon.com
Format:Taschenbuch
Bertand Russell's "Introduction to Mathematical Philosophy" provides the reader with a great understanding of mathematical philosophy in a very simple and straightforward manner. Though this is an introductory work it may not be casual reading to all who endeavor to read it. Beginning with definition of numbers and sets it expands to provide definitions of simple and complex and builds to provide a good understanding of the logic behind mathematics. While much of what is spoken about may seem very elementary the logic behind certainly is not. While the book is not nearly as expansive ad "Principia Mathematica" it is a good distillation of the bigger work and provides a great introduction to anyone wishing to explore that work. I recommend this book to anyone interested in formal logic and believe that it should be in the required reading for any formal logic introductory class. Further anyone interested in reading Goedel's work's which expand on Russell's work needs at least to read this work prior to Goedel. I find this book to be very succinct and readable and ultimately very worthy of the effort it takes to read.

-- Ted Murena
27 von 34 Kunden fanden die folgende Rezension hilfreich
3.0 von 5 Sternen A postcard from the past 12. April 2002
Von A. Fischer - Veröffentlicht auf Amazon.com
Format:Taschenbuch
Once upon a time, long long ago there was a group of people that believed that mathematics could be completely reduced to just a study of logic. One of the principal members of this group was Bertrand Russell (who along with Alfred North Whitehead wrote the almost incomprehendable Principia Mathematica). Jump ahead 20 years when there entered men like Godel who showed that the entire endevour was doomed for failure.
This is a text written before that fateful discovery, and as such does not have the benefit of the Incompleteness Theorem to flesh out the ideas. As such, most of the material is wanting, at best, to the contemporary reader of mathematics. Adding to this the fact that the communication of mathematical ideas has tremendously changed in the intervening years, and the result is a text that, though one day had great significance, today seems like a much faded phtotgraph from a by-gone era.
Maybe this makes the text interesting in itself. However, those readers that wish for a current look at mathematical thought, and an introduction to the philosophy of mathematics may be best served by looking elsewhere.
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