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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 ]
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 ]
The Bertrand paradox is a problem within the classical interpretation of probability theory. Joseph Bertrand introduced it in his work Calcul des probabilités (1889) [1] as an example to show that the principle of indifference may not produce definite, well-defined results for probabilities if it is applied uncritically when the domain of possibilities is infinite.
These paradoxes have stirred extensive philosophical and mathematical discussion throughout history, [1] [2] particularly regarding the nature of infinity and the continuity of space and time. Initially, Aristotle 's interpretation, suggesting a potential rather than actual infinity, was widely accepted. [ 1 ]
A falsidical paradox establishes a result that appears false and actually is false, due to a fallacy in the demonstration. Therefore, falsidical paradoxes can be classified as fallacious arguments: The various invalid mathematical proofs (e.g., that 1 = 2) are classic examples of this, often relying on a hidden division by zero.
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.