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Principia Mathematica by Alfred North Whitehead, Bertrand Russel
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**About this book :- **

**Principia Mathematica ** written by
** Alfred Whitehead, Bertrand Russel **.

The mathematical treatment of the principles of mathematics, which is the subject of the present work, has arisen from the conjection of two different studies, both in the main very modern. On the one hand we have the work of analysts and geometres, in the way of formulating and systematising their axioms and the work of analysts and geometers, the way of formulating and systematising their axioms and the work of Cantor and other such matters as the theory of aggregates. On the other hand we have symbolic logic, which after a necessory period of growth, has now thanks to Peano and his followers acquired the technical adaptability and the logical comprehensiveness that are essential the technical adaptability and the logical comprehensiveness that are essential to a mathematical instruments for dealing with that have hitherto been the beginnings of mathemtics.

From the combination of these two studies two results emerge, namely 1) that was were formely taken tacity or explicity as axioms are either unnecessary or demonstarable 2) that the same methods by which supposed axioms, which has formerly been regarded as inaccessible to human knowledge.

**Book Detail :- **
** Title: ** Principia Mathematica I
** Edition: ** 2nd
** Author(s): ** Alfred Whitehead, Bertrand Russel
** Publisher: ** Cambridge University Press
** Series: **
** Year: ** 1963
** Pages: ** 719
** Type: ** PDF
** Language: ** English
** ISBN: **
** Country: ** US

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**About Author :- **

The author **Alfred North Whitehead **, OM FRS FBA (1861–1947) was an English mathematician and philosopher. He is best known as the defining figure of the philosophical school known as process philosophy, which today has found application to a wide variety of disciplines, including ecology, theology, education, physics, biology, economics, and psychology, among other areas. Whitehead would teach and write on mathematics and physics at the college until 1910, spending the 1890s writing his Treatise on Universal Algebra (1898), and the 1900s collaborating with his former pupil, Bertrand Russell, on the first edition of Principia Mathematica. He was a Cambridge Apostle.

In 1910, Whitehead resigned his senior lectureship in mathematics at Trinity and moved to London without first obtaining another job. After being unemployed for a year, he accepted a position as lecturer in applied mathematics and mechanics at University College London, but was passed over a year later for the Goldsmid Chair of Applied Mathematics and Mechanics, a position for which he had hoped to be seriously considered. In 1914, Whitehead accepted a position as professor of applied mathematics at the newly chartered Imperial College London, where his old friend Andrew Forsyth had recently been appointed chief professor of mathematics. In 1924, Henry Osborn Taylor invited the 63-year-old Whitehead to join the faculty at Harvard University as a professor of philosophy. The Whiteheads would spend the rest of their lives in the United States.

The author ** Bertrand Russel ** began his published work in 1896 with German Social Democracy, a study in politics that was an early indication of a lifelong interest in political and social theory. In 1896 he taught German social democracy at the London School of Economics. He was a member of the Coefficients dining club of social reformers set up in 1902 by the Fabian campaigners Sidney and Beatrice Webb.

In 1897 he wrote An Essay on the Foundations of Geometry (submitted at the Fellowship Examination of Trinity College) which discussed the Cayley–Klein metrics used for non-Euclidean geometry. He attended the First International Congress of Philosophy in Paris in 1900 where he met Giuseppe Peano and Alessandro Padoa. The Italians had responded to Georg Cantor, making a science of set theory; they gave Russell their literature including the Formulario mathematico. In 1903 he published The Principles of Mathematics, a work on foundations of mathematics. It advanced a thesis of logicism, that mathematics and logic are one and the same.

In 1905 he wrote the essay "On Denoting", which was published in the philosophical journal Mind. Russell was elected a Fellow of the Royal Society (FRS) in 1908. The three-volume Principia Mathematica, written with Whitehead, was published between 1910 and 1913. This, along with the earlier The Principles of Mathematics, soon made Russell world-famous in his field. In 1910 he became a University of Cambridge lecturer at Trinity College, where he had studied.

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**Book Contents :- **
**Principia Mathematica ** written by
** Alfred Whitehead, Bertrand Russel **
cover the following topics.
**Introduction**

1. Preliminary Explanations of Ideas and Notations

2. The Theory of Logical Types

3. Imcomplete Symbols
**Part-1 Mathematical Logic**

A. The Theory of Deduction

B. Theory of Apparent Variables

C. Classes and Relations

D. Logic of Relations

E. Products and Sums of Classes
**Part-2 Prolegomena to Cardinal Arithmetic**

A. Unit Classes and Couples

B. Sub Classes, Sub Relations and Relative Types

C. One Many, Many-One and One-One Relations

D. Selections

E. Inductive Relations

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