Paradox

Originally uploaded by punyamishra

All Cretans are liars

said Epiminedes,

a Cretan,

a classic Paradox.

If Epiminedes tells the truth

then he must be lying.

And if he is lying,

he is telling the truth.

Sounds like a

contradiction,

doesn't it?

But a paradox is

different from

a contradiction.

Contradictions

are not allowed:

because

P and Not P

implies any Q.

In other words,

a contradiction

implies

any proposition.

"The Pope and I are two".

said Russell,

"If 2 = 1, then

the Pope and I are one."

Thus went Russell's proof

that he was the Pope.

But a paradox

is different,

its more valuable.

It increases

the size

of your universe.

Russell's paradox

showed the gaps

in set theory

and set the stage

for the next

leap forward.

Paradoxes

are the stuff

of which

giant leaps

are made.

GB #31

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