Principia Mathematica is a math book written by two writers. The book is present in three volumes and was written by Alfred North and Bertrand Russell. The volumes were published in 1910, 1912 and 1913 respectively. The book deals with the foundation of math and the topics that are compulsory to understand the basics of math.
Principia Mathematica Pdf Review:
This book was written by the authors in an attempt to come up with a set of rules based on the logic that could explain all mathematical problems. With this theme, the book became one of the most influential books of the era because the idea that a common axiom could explain all mathematical truths was very intriguing and interesting to people. However, 20 years after the publishing of the book, Gödel came up with his theory which said that for such a common set of rules to exist, there were two things to be considered. First, not all principles should be explainable by these inference rules. Secondly, the set of rules was to be inconsistent to make it functional.
Principia Mathematica Pdf Features:
- The authors try to look for common inference rules by talking of the relations that exist between cardinal arithmetic.
- Each volume has different sections dealing with different topics of math and how they could be related due to the common aspects that they have.
Table of Contents:
- Title page of the first edition of Principia Mathematica, Volume 1 (1910)
- Cover of the first paperback issue of Principia Mathematica to *56 (1962).
- “Preliminary Explanations of Ideas and Notations,”
- “The Theory of Logical Types,” and
- “Incomplete Symbols.”
- “The Theory of Deduction,”
- “Theory of Apparent Variables,”
- “Classes and Relations,”
- “Logic of Relations,” and
- “Products and Sums of Classes”,
- “Prolegomena to Cardinal Arithmetic”,
- “Unit Classes and Couples,”
- “Sub-Classes, Sub-Relations, and Relative Types,”
- “One-Many, Many-One and One-One Relations,”
- “Inductive Relations
- “Definition and Logical Properties of Cardinal Numbers,”
- “Addition, Multiplication and Exponentiation,” and
- “Finite and Infinite”.
- Part IV, “Relation-Arithmetic”,
- “Ordinal Similarity and Relation-Numbers,”
- “Addition of Relations, and the Product of Two Relations,”
- “The Principle of First Differences, and the Multiplication and Exponentiation of Relations,” and
- “Arithmetic of Relation-Numbers”;
- Part V, “Series”,
- “General Theory of Series,”
- “On Sections, Segments, Stretches, and Derivatives,” and
- “On Convergence, and the Limits of Functions.”
- Volume 3 : Part V,
- “Well-Ordered Series,”
- “Finite and Infinite Series and Ordinals,” and
- “Compact Series, Rational Series, and Continuous Series.”
- Part VI, “Quantity”,
- “Generalization of Number,”
- “Measurement,” and
- “Cyclic Families.”
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