## Paradoxes and Fallacies(Alex and Charlie were walking when they met their friend Simon) Alex: Hi, Simon!Simon: Hi, Alex! I have recently disproved the big bang theory.Charlie: How did you manage that?Simon: It means that the universe is finite at all times. But then you can
reach the edge! What happens once you reach the edge? You can’t just
“fall off”.Charlie: Hang on! The Earth is finite. If you walk on it for as long as
you want, you will never reach the edge because there isn’t one!Alex: That’s mostly correct but some cosmologists believe that the
universe is connected like a giant dodecahedron. If you go through one face
you come out of the opposite one. But you wouldn’t even notice. There
is another answer. If the universe expands faster than the speed of light,
you can never reach the edge because it is expanding faster than you can
travel.Charlie: Here’s another one. Mrs Jones once tells you that she has
two children. At least one is a girl. What is the chance that they are both
girls?Simon: ½. The other one is either a boy or a girl.Alex: No. That is a common fallacy. The answer is one third. Consider the elder
child. The elder child could be a boy or a girl. The younger child could
also be a boy or a girl. There are four combinations. Rule out the one where
both are boys and that leaves three equally likely cases. In one of them
both children are girls.Simon: There is one that I can’t understand. There is a barber who
shaves inhabitants of a certain village. He shaves everyone who does not
shave themselves but does not shave anyone who does. It seems like a perfectly
natural case but who shaves the barber?Charlie: If the barber shaves himself then he is shaved by the barber so
he doesn’t. If he doesn’t then he is shaved by the barber so
he does. Uh oh. We have a paradox.Alex: This is Bertrand Russell’s barber paradox. The only solution
I can think of is that the barber is not an inhabitant of the village. Russell
originally explained it in terms of sets. His barber was the set of all
sets which do not contain themselves as members. My solution means that
that is not a set.Simon: Let x^{2} = x + x + x + x... with x xs. Taking the derivative, 2x =
1 + 1+ 1+ 1... with x 1s so 2x = x and 2 = 1.Alex: That one is easy. You forgot to account for the change in the number
of xs. Accounting for this is enough to make it 2x.Charlie: There are probably many more paradoxes and fallacies but I have
to go. Bye!## Related entries• Coming soon | ||

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