This is a well known paradox written by the great stoical logician Chrysippos. The poet, grammarian and critic Philetus of Cos was said to have died of exhaustion attempting to resolve it.

**1st problem:**

A Cretan sails to Greece and says to some Greek men who are standing upon the shore:

"All Cretans are liars."

Is he lying or telling the truth?

**2nd problem:**

Read after resolving the first as this contains a massive hint.

2. Now assume that either all Cretans are liars or all Cretans tell the truth.

A Cretan states "All Cretans are liars and all I say is the truth."

Is he lying or telling the truth?

If someone says "I always lie", are they telling the truth? Or are they lying?

**Rational assumptions:**

A liar always tells lies, and a truth-teller always tells the truth.

If a person is not a liar, then they are a truth-teller, and vice versa.

This Cretan is not the only Cretan.

The two problems are of disjoint cases.

**Resolution**

1. His statement is false (and he is a liar) if there is at least one Cretan who is not a liar.

2. His statement is false (and all Cretans are liars); the "all I say is the truth" part is false.

http://en.wikipedia.org/wiki/Square_of_opposition

**Examples of incorrect interpretations from replying posts**

He means that everyonehaslied, but is not necessarily aliar.This is an attempt to find a loophole in the wording, which is not an objective response to a

logic problem. If you're going to make a semantic argument, you might as well state that words are not universally meaningful. You could be right, but this is no fun and detracts from the idea of a paradox (or really, anything...).

This is not a paradox.

It IS a paradox (the word is just a descriptive label), even if it is not 'truly paradoxical'.

**Note that this thread is closed since there have been hundreds of posts and resolution is summarized in this very first post.**

Analogue paradox to the paradox of liar formulated English logician, philosopher and mathematician Bertrand Russell.

There was a barber in a village, who promised to shave everybody, who does not shave himself (or herself).

Can the barber shave himself and keep the mentioned promise?

Edited (better wording?):

In a village, the barber shaves everyone who does not shave himself/herself, but no one else.

Who shaves the barber?

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1. Let's say (hypothetically) there is a bullet, which can shoot through any barrier. Let's say there is also an absolutely bullet-proof armour, and nothing gets through it. What will happen, if such bullet hits such armour?

2. Can a man drown in the fountain of eternal life?

3. Your mission is to not accept the mission. Do you accept?

4. This girl goes into the past and kills her Grandmother. Since her Grandmother is dead the girl was never born, if she was never born she never killed her grandmother and she was born.

5. If the temperature this morning is 0 degrees and the Weather Channel says, "it will be twice as cold tomorrow,".... What will the temperature be?

6. Answer truthfully (yes or no) to the following question: Will the next word you say be no?

7. What happens if you are in a car going the speed of light and you turn your headlights on?

8. I conclude with this challenge:

Let the God Almighty create a stone, which he can not pick up (is not capable of lifting)!

]]>"Two guys kill themselves by jumping out of the roof."

Who kills them, the roof, or each other?

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A slim crocodile living in Nile took a child. Mother begged to give him back. The crocodile could not only talk, he was also a great sophist, and so he stated: "If you guess (Edited: predict the fate = guess correctly), what I will do with him, I will return him. However, if you don't guess his fate I'll eat him." What statement shall the mother make to save her child (what about a vicious circle ...)?

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If destiny designed a master plan, which defines everything that is to happen, isn't it useless to for example go to a doctor? If I am ill and it is my destiny to regain health, than I will regain health whether I visit a doctor or I don't. And if I shall not be healthy again, than I will not with or without help.

If I am ill and destiny has a definite plan for me, than it is useless to go anywhere.

How could you question the presented opinion?

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This version of the famous paradox was presented by an English mathematician P. E. B. Jourdain in 1913.

The following inscriptions are on a paper:

*Back side*

Inscription on the other side is true

*Face side*

Inscription on the other side is not true

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What is better than eternal bliss? Nothing. But a slice of bread is better than nothing. So slice of bread is more than eternal bliss.

]]>In the Theory of Relativity it states that objects age slower the faster their velocity, and that light always travels at C...no matter your velocity, you can never catch up to a receding light.

If light can never be caught up to, then it can not be used to measure speed.

Then how, can an Earth age more than an astronaut...since neither knows which one is truly the faster velocity.

This...is Paradox #1, of Relativity. There are more to come...

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**What Happens?**

You can have the fraction 1/2. There is also 1/3. And 1/4, 1/5, 1/6, 1/7, etc. The fractions go on to 1/infinity. Isn't it odd to think that an uncountable number can be only a little more than zero?

]]>Say someone goes to the grocery store and buys 100 identical cans of cat food. They are in a hurry, so they attempt to go through the express lane, claiming that they really only got 1 item: cat food. But the cashier does not agree, saying they actually have 100 items. Who is correct?

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Sophist: "Yes. Greedy man gives his cash with sorrow. However, he doesn't have the cash with sorrow, so he gives what he doesn't have."

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Because if mass and energy can't be created,

then you and me should not exist.

But in the world of science, isn't faith required to discover whether or not something is worthy of being deemed fact or fiction? With all the insistent studies to cure diseases, researches on what might be out there in space, and even simple things like what might happen if two chemicals are mixed... isn't there a level of faith there to give the drive to discover in the first place?

And to look at the situation in vice versa, isn't all religion and faith based on some sort of fact to begin with? If you say no, then are you calling history a sham?

]]>1. This is a true paradox, and thus unsolvable.

2. Perhaps the unstoppable force was diverted from its course. The immovable object would not have moved, and the force would not have ceased.

3. The unstoppable force passes through the immovable object, not colliding with any of its atoms as it does so.

Please let me know if my reasoning is faulty or if there are other solutions to this paradox.

]]>Then at t=2, my balance is £1,010. So if I ask to withdraw all my money, so I now have £1,010 in my wallet.

Then I use my time machine to travel to the day after I deposited the original £1,000, call this t=1,and deposit half the money in my wallet, that is, £505.

I then go back to t=3, where I still have the other £505 in my wallet.

BUT... If I deposited the money, then at t=1 I had £1,505, instead of £1,000. So at t=2, adding 1% interest gives me £1,520.05, so THAT'S actually how much I withdraw. So I deposited half of that = £560.02 and kept £560.02 for myself at t=3 (I'll give the extra penny to charity)

But that's more money, which means it actually become more, and more, and more.

Does it converge, or do I have a truly infinite supply? Can we increase our final outcome if the initial parameters change?

Let's go to the maths!

Let M be the amount of money I have (since all my money at any given point is either in the bank or in my wallet, I only need one letter to denote this. M_{0 }is my starting money at t=0, M_{1 }is money at t=1, and so on. M_{0 }= £1000

Let I be the interest rate, aka 0.01.

Let P be the proportion of my money I deposit at t=1 (the rest I keep at t=3, giving the remainder to charity), this = 0.5.

Equations:

A. M_{1 }= M_{0}+P*M2

B. M_{2 }= M_{1}* 1 + I)

C. M_{3 }= (1-P)*M_{2}

Substituting A into B gives

M_{2 }= (M_{0}+P*M_{2})*(1+I)

M_{2}/(1+I) = M_{0}+P*M_{2}

M_{2}/(1+I)-P*M_{2 }= M_{0}

M_{2}*(1/(1+I)) - M_{2}*P = M_{0}

M_{2} * (1/(1+I)-P) = M_{0}

M_{2} = M_{0 }/ (1/(1+I) - P)

So the amount we end up with at then end (M_{3}) is

1-P

------------- * M_{0}

1/(1+I) - P

If 1-P > 1/(1+I)-P, we made a profit.

1 + I > 1

-> 1 / (1+I) < 1

-> 1 / (1+I) - P < 1-P

We made a profit.

How much profit? If it's more than I, this was worth it.

Let's plug in our values:

(1 - 0.5) / (1/1.01 - 0.5)

= 1.0202020202...

We (slightly more than) doubled the interest rate.

In fact, changing the interest rate with P = 0.5 doubles the interest rate

What about different values of P (putting depositing more at t=1)?

Lower values of P end up giving results close to 1.01, but higher values give more profit: for example, (1 - 0.9) / (1 / 1.01 - 0.9) 1.11, effectively bumping up the interest rate to 11%.

However, going too high gives negatives, so what's the highest point we can go to?

Answer: P = 1/1.01 = 100/101. Then our money goes to infinity. (as we divide by 0)

So for interest rate I, depositing (1/(1+I)) of the money at t=1 when in the past means you end up with an infinite amount.

Of course, due to rounding, you can't deposit exactly this amount, but you get more money each "iteration" so you can round it more accurately each time. And if you give the remainder of division after rounding to charity, you'd be helping infinitely too. (in most cases)

The only limit is the amount of money your wallet can carry at once as you travel through time.

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