Anonymous wrote: : I'm in grade 10 advanced and I'm doing : a project on Paradoxes and fallacies. : I'm having a hard time understanding most : of the solutions to the famous paradoxes.
Post some of them here and we can discuss them.
My favorite paradox is Russell's Paradox (due to Bertrand Russell in 1902): Construct a set S containing all sets which do not contain themselves. Does S contain itself? (If it does not, then it should. But if it does then it should not!)
People often restate this in terms of books (instead of sets) which refer to themselves. Can you create a book containing a list of all books which do not refer to themselves. Should your book be listed in itself? (Only if it is NOT listed in itself!)
Another variant is "the village barbar" who shaves those (and ONLY those) who do not shave themselves. Does the barbar shave himself?
This paradox forced mathematicians to very carefully reconstruct set theory (on which the rest of mathematics is founded). There is still no universally accepted approach to avoid this paradox. Most methods amount to setting out very careful rules about what you are allowed to do that prevent you from even asking the question! _ |/|\/| || N-k N N+k-1 |\| |orewood || 4 + 4 + 4 is always a perfect square! @south.sd41.bc.ca|| - Burnaby South Mathematics 10 Honours 1996/97
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