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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.
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".
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]
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.
B. Russell: The principles of mathematics I, Cambridge 1903. B. Russell: On some difficulties in the theory of transfinite numbers and order types, Proc. London Math. Soc. (2) 4 (1907) 29-53. P. J. Cohen: Set Theory and the Continuum Hypothesis, Benjamin, New York 1966. S. Wagon: The Banach–Tarski Paradox, Cambridge University Press ...
Topics about Paradoxes in general should be placed in relevant topic categories. Pages in this category should be moved to subcategories where applicable. This category may require frequent maintenance to avoid becoming too large.
In mathematics, ideas are supposedly not accepted as fact until they have been rigorously proved. However, there have been some ideas that were fairly accepted in the past but which were subsequently shown to be false. The following list is meant to serve as a repository for compiling a list of such ideas.
In logic, Richard's paradox is a semantical antinomy of set theory and natural language first described by the French mathematician Jules Richard in 1905. The paradox is ordinarily used to motivate the importance of distinguishing carefully between mathematics and metamathematics.