XKCD brings up an interesting point.
If you start with any set of contradictory axioms (ie p and not p are both true for some p), you can "prove" the truth of just any statement you wish.
For example, given 4 = 3, can you prove that you are the Pope?
Alfred Whitehead, logician of Russell and Whitehead fame, was once asked this very question. His answer:
4=3 (by axiom)
2=1 (Subtract two from both sides)
It is well known that the Pope and I are two people.
Therefore, the Pope and I are One.
There are, of course, many ways of obtaining credit card numbers through false premises, though none of the famous ones involve logical deduction.
2 comments:
but wch axiom says 4=3 and why do we assume that..
@Maverick's Musings
The problem was posed as "given 4=3, prove that you're the pope". See above.
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