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Bertrand's box paradox: A paradox of conditional probability closely related to the Boy or Girl paradox. Bertrand's paradox: Different common-sense definitions of randomness give quite different results. Birthday paradox: In a random group of only 23 people, there is a better than 50/50 chance two of them have the same birthday.
With the epsilon-delta definition of limit, Weierstrass and Cauchy developed a rigorous formulation of the logic and calculus involved. These works resolved the mathematics involving infinite processes. [35] [36] Some philosophers, however, say that Zeno's paradoxes and their variations (see Thomson's lamp) remain relevant metaphysical problems.
In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published by the British philosopher and mathematician Bertrand Russell in 1901. [ 1 ] [ 2 ] Russell's paradox shows that every set theory that contains an unrestricted comprehension principle leads to contradictions. [ 3 ]
This category contains paradoxes in mathematics, but excluding those concerning informal logic. "Paradox" here has the sense of "unintuitive result", rather than "apparent contradiction". "Paradox" here has the sense of "unintuitive result", rather than "apparent contradiction".
The Principles of Mathematics (PoM) is a 1903 book by Bertrand Russell, in which the author presented his famous paradox and argued his thesis that mathematics and logic are identical. [1] The book presents a view of the foundations of mathematics and Meinongianism and has become a classic reference.
Newcomb's paradox was created by William Newcomb of the University of California's Lawrence Livermore Laboratory. However, it was first analyzed in a philosophy paper by Robert Nozick in 1969 [1] and appeared in the March 1973 issue of Scientific American, in Martin Gardner's "Mathematical Games". [2]
Russell was impressed by the precision of Peano's arguments at the Congress, read the literature upon returning to England, and came upon Russell's paradox. In 1903 he published The Principles of Mathematics, a work on the foundations of mathematics. It advanced a thesis of logicism, that mathematics and logic are one and the same. [49]
In one of the most important compendia of mathematical logic, compiled by Jean van Heijenoort, Richard's article is translated into English. The paradox can be interpreted as an application of Cantor's diagonal argument. It inspired Kurt Gödel and Alan Turing to their famous works.