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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".
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.
Paradoxes of the Infinite (German title: Paradoxien des Unendlichen) is a mathematical work by Bernard Bolzano on the theory of sets. It was published by a friend and student, František Přihonský, in 1851, three years after Bolzano's death. The work contained many interesting results in set theory.
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.
In philosophy and mathematics, Newcomb's paradox, also known as Newcomb's problem, is a thought experiment involving a game between two players, one of whom is able to predict the future. Newcomb's paradox was created by William Newcomb of the University of California 's Lawrence Livermore Laboratory .
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 ...
As Stewart Shapiro explains in his Thinking About Mathematics, Russell's attempts to solve the paradoxes led to the ramified theory of types, which, though it is highly complex and relies on the doubtful axiom of reducibility, actually manages to solve both syntactic and semantic paradoxes at the expense of rendering the logicist project ...