Richard Baker wrote:
>
>> Your "Paradox" is really a play on words, or an ill-defined question.
>
>Does anyone else have similar problems that may be true paradoxes?
>
Paradoxes _are_ play on words, on play on a badly defined set
of axioms. Most of them come with the careless use of words such
as "all", "none", etc.
One classical one, the barber paradox, is:
There is a city, this city has one (male) barber, and every man in this
city has his beard done, either by himself, or by the barber, but
never by both of them. Question: who cuts the barber's beard?
Another one (classical too) is the King's paradox:
A thief was captured, and the King decides to grant this thief a
grace: if he tells a lie, he will be crucified, if he tells a truth, he will
be burned to death in oil. The thief says: "I will be crucified"
Of course these paradoxes are equivalent to Russel's set-theory
paradox:
R = { X | X is not a member of X }
Is R a member of R?
Or on the blonde-girl paradox. Give her a piece of paper with
"READ WHAT IS IN THE OTHER SIDE" on both sides, and she
will never leave the loop.
OTOH, a vast set of paradoxes come out of a loosy handling of infinity.
Things like "take a random natural (or real) number..." are meaningless,
because there's no way to define _uniquely_ what is a random natural
or real number.
Alberto Monteiro
