Formal Logic

Topics: Logic, Philosophy, Gottlob Frege Pages: 5 (1685 words) Published: December 19, 2008
Bertrand Russell's Contribution to the Development of Formal Logic


Since the beginning of time, man has been in search of answers. These philosophical enquiries are what gave birth to everything we know, such as science, law, and religion. It has laid the foundation to which all theories and discoveries have come from, and it is the soil from which the fruits of life have grown. The formal definition of philosophy is that it 'is the study of general and fundamental problems concerning matters such as existence, knowledge, truth, justice, beauty, validity, mind and language.'[1] Based on this definition, we conclude that philosophy encompasses and addresses everything in life and beyond.

The history of philosophy dates back to approximately the sixth century B.C which proves that man has been born with the curiosity and hunger for knowledge, and that they have been in search for true meaning since the beginning of time. The timeline of philosophy is divided into three periods with a fourth period currently being established. These periods are called ancient philosophy, medieval philosophy, and early modern philosophy. The fourth and recent period is known as contemporary philosophy and it started in 1900. Many of contemporary philosophers have altered the way we view philosophy. They have introduced a new area of philosophy called analytic philosophy, and Bertrand Russell is one of the founders. In addition, he is known to be one of the two most influential and important logicians of the twenty first century. These contemporary philosophers have also narrowed the gap between philosophy and science. This is essential for the progression of philosophy due to the fact that it proves that everything is relative. It also introduces the idea that there is a link between religion and science, and that link is philosophy.

Bertrand Russell was a philosopher who was originally from Wales. His contributions were not restricted exclusively to philosophy; they extended into politics, history and mathematics among other fields. He was born in 1872 which was when the British Empire was at its peak of domination and strength. During this period his grandfather Lord Russell, was the Prime Minister; therefore making his involvement in politics inevitable. He was a liberal thinker and he did not believe in the conventional political views of people. On the contrary, his beliefs promoted peace as opposed to war, and at a time of such economic and political instability, his opinions were controversial and they eventually lead him to prison. [2]

He started writing his book, Principles of Mathematics, in 1898 and completed it in 1903. The main thesis is that mathematics and logic are identical and that mathematics is deduced from logic itself. This thesis revolutionized the way people viewed mathematics as well as logic till this very day. During the time he was writing his book, he discovered one of the most famous paradox's of the twentieth century which was named Russell's Paradox and is also known as Russell's Antinomy. This paradox states that 'the paradox arises within naive set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of itself, hence the paradox.' [3]

He made this discovery during the spring of 1901, and although there were previous philosophers who touched upon similar antinomies, none of them were able to achieve such precision in their paradoxes as Russell had done. Neither did they anticipate the precipitation of knowledge that would follow. The impact of this paradox was profound due to the fact that it became the foundation in which people analyzed logic and mathematics. It caused great ramifications to the theory of a universal class, which is what was widely believed and followed. It affected many philosophers in general, as well as individually. An example of this is Gottlob Frege, another...
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