At various times in his long and distinguished life, Bertrand Russell – born on May 18, 1872, at Trelleck in Monmouthshire, Wales –was described as a philosopher, logician, mathematician, historian, writer, social critic, and political activist.
The Stanford Encyclopedia of Philosophy says Russell’s “most influential contributions include his championing of logicism (the view that mathematics is in some important sense reducible to logic), his refining of Gottlob Frege’s predicate calculus (which still forms the basis of most contemporary systems of logic), his defense of neutral monism (the view that the world consists of just one type of substance which is neither exclusively mental nor exclusively physical), and his theories of definite descriptions, logical atomism and logical types.”
It goes to on to say that “Russell is generally recognised as one of the main founders of modern analytic philosophy. His famous paradox, theory of types, and work with A.N. Whitehead on Principia Mathematica reinvigorated the study of logic throughout the 20th century.”
He also made significant contributions to a range of other subjects, including educational theory, the history of ideas and religious studies.
In full, his name was Bertrand Arthur William Russell, Third Earl Russell of Kingston Russell, Viscount Amberley of Amberley and of Ardsalla. Among his many achievements, he won the Nobel Prize for literature in 1950.
Russell formulated what became known as Russell’s Paradox, which he published in his book Principles of Mathematics in 1903.
In an article for Scientific American magazine, John T. Baldwin and Olivier Lessmann from the University of Illinois at Chicago explained it thus: Consider a group of barbers who shave only those men who do not shave themselves. Suppose there is a barber in this collection who does not shave himself; then by the definition of the collection, he must shave himself. But no barber in the collection can shave himself. (If so, he would be a man who does shave men who shave themselves.)
“Russell’s own answer to the puzzle came in the form of a ‘theory of types’,” the writers explained.
“The problem in the paradox, he reasoned, is that we are confusing a description of sets of numbers with a description of sets of sets of numbers. So Russell introduced a hierarchy of objects: numbers, sets of numbers, sets of sets of numbers, etc. This system served as vehicle for the first formalisations of the foundations of mathematics; it is still used in some philosophical investigations and in branches of computer science.”
Russell was also a staunch defender of logicism, the theory that mathematics is in some important sense reducible to logic. As he summarises, “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”.