Bertrand Arthur William Russell, a British philosopher, and logician are known for his work on mathematical logic and analytic philosophy. His most important contributions were:
1. He thought that mathematics can be reduced to logic.
2. He refined Gottlob Frege’s predicate calculus.
3. He strongly defended neutral monism.
4. He gave the theories of definite descriptions, logical atomism, and logical types.
Beside George Edward Moore, Bertrand Russell also has been recognized as one of the founders of modern analytic philosophy.
He recreated the study of logic by his work on Principia Mathematica with A.N. Whitehead.
In his career, he contributed to many other fields, for instance, ethics, politics, education, history of ideas, popular sciences and religious studies. He was awarded Order of Merit and Nobel Prize in Literature in 1949 and in 1950, respectively.
His view on Logic:
His main contributions includes the paradox which has his name which he discovered in 1901 also known as Russell’s antinomy or Russell-Zermelo paradox, his work on the theory of types and his work on logic. The paradox comes up in connection with the set of all sets that are not members of themselves. Such a type of set, if in any way exist, will be a member of itself if and only if it’s not a member of itself. Russell’s work and his discovery amounted large work in logic, set theory and the philosophy and foundations of mathematics. His own response to his paradox came when he developed the theory of types. His basic idea was that the Russell set can be ignored or avoided by arranging all the sentences in some hierarchy, for instance, beginning with sentences about the individuals at the first lowest level, then the sentences about the sets of individuals at the second lowest level, and so on and so forth.
He developed his theory of types in 1908 in the article “Mathematical Logic as Based on the Theory of Types’’ and the work “Principia Mathematica’’ which he co-authored with Prof. A.N. Whitehead. There were two versions, “simple theory’’ in 1903 and “ramified theory’’ in 1908. But both the versions were criticized at that time. For some people, the important solution was that solution which can resolve all the known paradoxes at once. Russell noted that it’s very unlikely to find some solution which can resolve all the known paradoxes.
Russell’s idea of the theory that mathematics is in some important sense reducible to logic is of great significance. His logicism contains two main ideas:
1. All the mathematical truth or knowledge can be translated into logical truths.
2. All the mathematical proofs can be reinterpreted as logical proofs.
In summary, Bertrand Russell says that “ The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists in the analysis of Symbolic Logic itself’’.
Russell’s Work in Analytic Philosophy:
Bertrand Russell tried to clarify some issues in philosophy by using his idea of logicism. He made contributions to the areas like “metaphysics’’, “epistemology’’, “ethics’’ and “political theory’’. He writes “Ordinary language is totally unsuited for expressing what physics really asserts since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say’’.
Also, he says, “None of our beliefs are quite true; all have at least a penumbra of vagueness and error. Every man of science whose outlook is truly scientific is ready to admit that what passes for scientific knowledge at the moment is sure to require correction with the progress of discovery; nevertheless, it is near enough to the truth to serve for most practical purposes, though not for all. In science, where alone something approximating to genuine knowledge is to be found, men’s attitude is tentative and full of doubt.’’
To get to the highest form of truth and knowledge, we should get all the perspectives in the account, then think on all the relevant facts with all the people even when they have opposite bias than us. These methods and way of thinking will be built out of scientific knowledge.
Rajeev Singh is a 1st-year Ph.D. Research Fellow at Institute of Nuclear Physics Polish Academy of Sciences, Krakow Poland.
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