Tag Archives: Bertrand Russell
“Perhaps the most important advantage of ‘useless’ knowledge is that it promotes a contemplative habit of mind…[This] has advantages ranging from the most trivial to the most profound.…
Curious learning not only makes unpleasant things less unpleasant, but also makes pleasant things more pleasant. I have enjoyed peaches and apricots more since I have known that they were first cultivated in China in the early days of the Han dynasty; that Chinese hostages held by the great King Kaniska introduced them to India, when they spread to Persia, reaching the Roman Empire in the first century of our era; that the word ‘apricot’ is derived from the same Latin root as the word ‘precocious’ because the apricot ripens early; and the A at the beginning was added by mistake, owing to a false etymology. All this makes the fruit taste much sweeter.” – Bertrand Russell. In Praise of Idleness (1935)
“The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts.” – Bertrand Russell
In the foundations of mathematics, Russell’s paradox (also known as Russell’s antinomy), discovered by Bertrand Russell in 1901, showed that some attempted formalizations of the naive set theory created by Georg Cantor led to a contradiction. The same paradox had been discovered a year before by Ernst Zermelo but he did not publish the idea, which remained known only to Hilbert, Husserl, and other members of the University of Göttingen.
According to naive set theory, any definable collection is a set. Let R be the set of all sets that are not members of themselves. If R is not a member of itself, then its definition dictates that it must contain itself, and if it contains itself, then it contradicts its own definition as the set of all sets that are not members of themselves. This contradiction is Russell’s paradox.