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Principia Mathematica (3 Volumes) by Alfred North Whitehead (Author), Bertrand Russell (Author)

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Principia Mathematica (3 Volumes) by Alfred North Whitehead  (Author), Bertrand Russell  (Author)
   
  
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'Principia Mathematica: Volume 1'
By Alfred North Whitehead  (Author), Bertrand Russell  (Author)

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'Principia Mathematica: Volume 2'
By Alfred North Whitehead  (Author), Bertrand Russell  (Author)

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'Principia Mathematica: Volume 3'

By Alfred North Whitehead  (Author), Bertrand Russell  (Author)

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Description:


The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. It was an attempt to describe a set of axioms and inference rules in symbolic logic from which all mathematical truths could in principle be proven. As such, this ambitious project is of great importance in the history of mathematics and philosophy, being one of the foremost products of the belief that such an undertaking may be achievable. Principia Mathematica is considered one of the twentieth century's most important works in mathematical logic, and placed 23rd in a list of the top 100 English-language nonfiction books of the twentieth century by Modern Library.

Volume I: Part I - MATHEMATICAL LOGIC - The Theory Of Deduction - Theory Of Apparent Variables - Classes And Relations - Logic And Relations - Products And Sums Of Classes - Part II - PROLEGOMENA TO CARDINAL ARITHMETIC - Unit Classes And Couples - Sub-Classes, Sub-Relations, And Relative Types - One-Many, Many-One, And One-One Relations - Selections - Inductive Relations


Volume II With Additional Errata To Volume I: Part III - CARDINAL ARITHMETIC - Definition And Logical Properties Of Cardinal Numbers - Addition, Multiplication And Exponentiation - 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 - Arithmetic And Relation-Numbers - Part V -SERIES - General Theory Of Series - On Sections, Segments, Stretches, And Derivatives - On Convergence, And The Limits Of Functions

Volume III With Additional Errata To Volumes I And II: Part V - SERIES (Continued) - Well Ordered Series - Finite And Infinite Series And Ordinals - Compact Series, Rational Series, And Continuous Series - Part VI - QUANTITY - Generalization Of Number - Vector-Families - Measurement - Cyclic Families

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One of the most significant philosophers of this century especially in America, Alfred North Whitehead, was of English origin and spent the first part of his life in England where he studied mathematics and philosophy. Later he taught in both Cambridge and London before migrating to America where he was to spend the last part of his life at Harvard University. Whitehead was first attracted to the Catholic Church which, however, he did not enter. In fact, while remaining very much interested in questions of religion throughout his life, he refused to join any organized religious institution. His early works were mostly on mathematics, and it was as a mathematician that he met his student Bertrand Russell and together they wrote the Principia Mathematica which took them until 1910. This major work of logic remains one of the basic texts of this century on the philosophy of mathematics and the relationship between mathematical and formal logic. Whitehead was also very much interested in the foundations of physics and wrote Enquiry Concerning the Principles of Natural Knowledge to that end followed by the non- mathematical treatment of physics in The Concept of Nature.

While in America, Whitehead wrote most of his metaphysical works beginning with Science and the Modern World in which he criticized scientific materialism and it was also there that he wrote his Process and Reality which is perhaps his most important work in which he developed the idea of process philosophy, a philosophy which sees the whole of reality as a series of becomings. His last major work Adventures of Ideas summarizes his views on God, humanity and the universe. Whitehead is known not only as the founder of process philosophy but also process theology, and these ideas have had notable influence in America mostly as a result of his famous student Charles Hartshorne, the American philosopher, who propagated Whitehead's teachings after the latter's death. 

(Seyyed Hossein Nasr)
 
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Bertrand Russell, an early student of Whitehead, is one of the most well-known of the British philosophers and logicians of this century. At once an accomplished mathematician and philosopher, he was also an activist in the political realm especially during his later days. Much.of his later fame in fact rests upon his political and social activities rather than the purely philosophical works for which he became known in his earlier years.

Early in life, Russell became a religious skeptic and remained so until his death. It was at Cambridge that, while studying philosophy, he became interested in the foundations of knowledge. Influenced first by idealists such as G.E. Moore, he turned more and more towards empiricism, positivism and materialism and remained a positivist the rest of his life. In An Enquiry into the Meaning of Truth and Human Knowledge/ Its Scope and Limits, he sought to pare down and reduce to the simplest expression, the claims of human knowledge. In The Principle of Mathematics, he investigated the relation between philosophy and mathematics which culminated in the joint work, Principia Mathematica/ with Whitehead. He exerted altogether an immense influence upon the analytical movement as well as on the study of logic in general in the fourteenth/twentieth century. 

Russell also wrote a number of more popular works, such as A History of Western Philosophy/ Why I am not a Christian and Autobiography which made him more influential and famous than other philosophers in non-philosophical circles. He epitomizes the domination of positivistic philosophy which refuses to deal with any subject that cannot be logically, and for some operationally, defined and has a strong anti-metaphysical bias and opposition to religious and spiritual matters which have concerned so many philosophers over the ages. This type of philosophy has been dominant in most British and American universities during the past few decades. As a result, Russell has also influenced a number of Muslim writers and philosophers who have studied in England and America in contrast to the European continent, where existentialism and phenomenology have been more prevalent to this day. 

(Seyyed Hossein Nasr)
 
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