Essay on Bertrand Russell

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Bertrand Russell

Introduction

Bertrand Russell was one of the preeminent thinkers of the 20th century. His work on mathematical logic laid the basis for a good portion of modern mathematics; his political thought was influential both in his time and after; and his philosophical thought is both complicated and highly intelligent. He is considered one of the two or three most important logicians of the 20th century. During his lifetime he was a high profile figure and grew to have a high degree of respectability -- in fact, he died at age 97, in 1970, so during his own lifetime he saw his own fame grow to immense proportions. He also fits Howard Gardner's ideas on genius in many ways, although not all of them, as we shall see.

But
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It was a huge, daunting undertaking; along the way, Russell enlisted the help of his friend, Alfred North Whitehead, and the task of writing the book took over ten years.

The book is complicated; exceedingly complicated, in fact. Russell biographer Ray Monk calls it almost totally incomprehensible, and Russell himself recognized that he had written a work that few in the world would ever read and fewer would understand. The three volume work, which is filled with symbols that Russell and Whitehead devised for the specific purpose of writing the book, doesn't even reach the "occasionally useful" proof of 1 + 1 = 2 until almost halfway through.

On top of this, Russell ran into a paradox while writing the book. This paradox, called Russell's Paradox, deals with the set of all sets that are not members of themselves. Attempting to construct such a set leads to an unavoidable paradox. It is analogous to the thought problem: If the barber is defined as someone who cuts the hair of those people who do not cut their own hair, who cuts the barber's hair? This logical problem dogged Russell incessantly and was a flaw in the architecture of Principia Mathematica. In fact, later in the century, the logician Kurt Godel proved that, as Monk puts it: "there can . . . be no logical theory within which all truths about numbers can be derived as theorems; all logical
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