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The Perfect Paradox

Book By: essay fitzgerald
Riddles



The ultimate, hardest paradoxes
will be unleashed in this start
to the soon publishing book by
me and my best friends.


Submitted:Sep 23, 2010    Reads: 1,110    Comments: 1    Likes: 0   


Which came first: The Chicken or the Egg?

Crocodile Dilemma:

"I took your child, but I'll promise you this: I'll return your son,

if you can predict what I'll do next."

Unexpected Hanging Paradox:

A judge tells a condemned prisoner that he will be hanged at noon on

one weekday in the following week but that the execution will be a surprise

to the prisoner. He will not know the day of the hanging until the executioner

knocks on his cell door at noon that day.


Having reflected on his sentence, the prisoner draws the conclusion

that he will escape from the hanging. His reasoning is in several parts.

He begins by concluding that the "surprise hanging" can't be on a Friday,

as if he hasn't been hanged by Thursday, there is only one day left -

and so it won't be a surprise if he's hanged on a Friday.

Since the judge's sentence stipulated that the hanging would be a surprise

to him, he concludes it cannot occur on Friday.

He then reasons that the surprise hanging cannot be on Thursday either,

because Friday has already been eliminated and if he hasn't been hanged

by Wednesday night, the hanging must occur on Thursday, making a

Thursday hanging not a surprise either. By similar reasoning he concludes

that the hanging can also not occur on Wednesday, Tuesday or Monday.

Joyfully he retires to his cell confident that the hanging will not occur at all.


The next week, the executioner knocks on the prisoner's door at noon on

Wednesday - which, despite all the above, will still be an utter surprise to him.

Everything the judge said has come true.


Monty Hall Paradox: Suppose you're on a game show, and you're given the

choice of three doors: Behind one door is a car; behind the others, goats.

You pick a door, say No. 1, and the host, who knows what's behind the doors,

opens another door, say No. 3, which he knows has a goat. He then says to you,

"Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Sorities paradox (also known as the paradox of the heap):

One grain of sand is not a heap. If you don't have a heap, then adding

only one grain of sand won't give you a heap. Then no number of grains

of sand will make a heap. Similarly, one hair can't make the difference

between being bald and not being bald. But then if you remove one hair

at a time, you will never become bald. Also similar, one dollar will not

make you rich, so if you keep this up, one dollar at a time, you will never

become rich, no matter how much you obtain.

WARNING: MOST DIFFICULT Bernadete's Paradox: A man called Prometheus

angers Zeus, so Zeus gathers an infinite number of demons and issues them

with the following commands. Demon 1: if Prometheus is not dead in one hour

kill him, Demon 2: if Prometheus is not dead in half an hour kill him, Demon 3:

if Prometheus is not dead in quarter of an hour kill him, and so on. As it turns out

Prometheus was dead within the hour (as he didn't really have much chance).

The council of gods was not happy about this and pressed Zeus on the point.

But none of his demons could be found guilty, as, for each positive integer n,

it was not possible for the nth demon to have killed Prometheus because the (n + 1)th

demon should already have done so.

Exception paradox: if every rule has an exception (this is the false premise),

then there must be an exception to the rule that every rule has an exception.

1. Every rule has an exception. (Statement)
2. "Every rule has an exception" has an exception. (By 1)
3. There exists some rule R without exception. (By 2)
4. Since R is a rule, by the first statement it must have an exception.

But by 3, it does not have an exception - a contradiction.


Or, in another view:

1. Every rule has an exception. (Statement)
2. "Every rule has an exception" has an exception. (By 1)
3. There exists some rule R without exception. (By 2)
4. Since R is a rule, by the first statement it must have an exception.

Therefore, the statement should be the only rule that doesn't have an exception, what could be called a contradiction.
5. The rule itself represents its own exception, because

it should be the only rule without an exception.


Raven Paradox: 1) All ravens are black.

In strict logical terms, via the Law of Implication, this statement is equivalent to:

(2) Everything that is not black is not a raven.

It should be clear that in all circumstances where

(2) is true, (1) is also true; and likewise, in all circumstances where

(2) is false (i.e. if we imagine a world in which something that was

not black, yet was a raven, existed), (1) is also false.

This establishes logical equivalence.

Given a general statement such as all ravens are black, we would generally

consider a form of the same statement that refers to a specific observable

instance of the general class to constitute evidence for that general statement.

For example,

(3) Nevermore, my pet raven, is black.

is clearly evidence supporting the hypothesis that all ravens are black.

The paradox arises when this same process is applied to statement (2).

On sighting a green apple, we can observe:

(4) This green (and thus not black) thing is an apple (and thus not a raven).

By the same reasoning, this statement is evidence that

(2) everything that is not black is not a raven. But since (as above) this statement

is logically equivalent to (1) all ravens are black, it follows that the sight of a

green apple offers evidence that all ravens are black.

The Pinocchio paradox: What would happen if Pinocchio said

"My nose will be growing"?

Quine's Paradox: "Yields falsehood when preceded by its quotation"

yields falsehood when preceded by its quotation.

If the paradox is not clear, consider each part of the above description

of the paradox incrementally:

it = yields falsehood when preceded by its quotation
its quotation = "yields falsehood when preceded by its quotation"
it preceded by its quotation = "yields falsehood when preceded by its

quotation"

yields falsehood when preceded by its quotation.

With these tools, we may now reconsider the description of the paradox.

It can be seen to assert the following:

The statement "'yields falsehood when preceded by its quotation'

yields falsehood when preceded by its quotation" is false.

In other words, the sentence implies that it is false, which is paradoxical -

for if it is false, what it states is in fact true.





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