The Paradox of the Stone

God is all-powerful, or as theologians put it, “omnipotent”; there is nothing that he cannot do. This is part of the definition of “God”.

Can God create a stone that is so heavy that he cannot lift it? Either he can or he can’t.

If God can’t, then he isn’t all-powerful. If God can’t create a stone that he can’t lift, then there is something that he can’t do. Since God is all-powerful, though, he can do everything; there’s nothing that he can’t do. That includes creating a stone that he can’t lift. Since God is omnipotent, then, he must be able to create a stone that is so heavy that he can’t lift it.

If God can create a stone that is so heavy that he can’t lift it, though, then he also isn’t all-powerful. If God can create a stone that is so heavy that he can’t lift it, then there’s something that he can’t do: lift that stone. Since God is omnipotent, then, he must be unable to create a stone that is so heavy that he can’t lift it.

God’s omnipotence, then, means that he is both able and unable to create a stone that is so heavy that he can’t lift it. He can’t be both able and unable to do this, though; either he can or he can’t. So which is it to be?

Theseus’ Ship

Theseus is remembered in Greek mythology as the slayer of the Minotaur. For years, the Athenians had been sending sacrifices to be given to the Minotaur, a half-man, half-bull beast who inhabited the labyrinth of Knossos. One year, Theseus braved the labyrinth, and killed the Minotaur.

The ship in which he returned was long preserved. As parts of the ship needed repair, it was rebuilt plank by plank. Suppose that, eventually, every plank was replaced; would it still have been the same ship?

A strong case can be made for saying that it would have been: When the first plank was replaced, the ship would still have been Theseus\' ship. When the second was replaced, the ship would still have been Theseus\' ship. Changing a single plank can never turn one ship into another. Even when every plank had been replaced, then, and no part of the original ship remained, it would still have been Theseus\' ship.

Suppose, though, that each of the planks removed from Theseus\' ship was restored, and that these planks were then recombined to once again form a ship. Would this have been Theseus\' ship? Again, a strong case can be made for saying that it would have been: this ship would have had precisely the same parts as Theseus\' ship, arranged in precisely the same way.

If this happened, then, then it would seem that Theseus had returned from Knossos in two ships. First, there would have been Theseus\' ship that has had each of its parts replaced one by one. Second, there would have been Theseus\' ship that had been dismantled, restored, and then reassembled. Each of them would have been Theseus\' ship.

Theseus, though, sailed in only one ship. Which one?

The Tristram Shandy Paradox

Tristram Shandy is a novelist writing an auto-biography. Unfortunately, he writes very slowly; each day of his life takes him a year to write about.

The Tristram Shandy paradox asks: If Shandy continues at this rate for eternity then will his book ever be finished?

Russell, who invented this paradox, suggested that the book would be finished. Given an infinite amount of time, for every day in Shandy’s life there is a year to spend writing about it; there are, after all, an infinite number of years in which to write the autobiography. The autobiography therefore can be completed.

This doesn’t seem right though. With each passing year, Shandy completes his writing about one day, but leaves another three hundred and sixty-four days undocumented. Every year, then, there are three hundred and sixty-four days more for Shandy to write about; the more time passess, the further behind he falls.

How can it be that Shandy ever falls further behind, and yet that given an eternity he will complete his work?

The Two Envelope Paradox

You’re on a game show. You’re given a choice between two envelopes containing money, knowing that one of the envelopes contains twice as much as the other. You get to keep the contents of whichever envelope you choose.

Having chosen the envelope, you open it, and find that it contains $1000. Before the game ends, though, you get one chance to change your mind, to exchange your envelope for the other one. The two envelope paradox arises because no matter which envelope you chose in the first place, it always seems that swapping is the rational thing to do.

Suppose that you chose the envelope containing the least money. If you swap for the other envelope, then you’ll double your money to $2000. You could gain $1000 by swapping.

Suppose that you chose the envelope containing the most money. If you swap for the other envelope, then you’ll halve your money to $500. You could lose $500 by swapping.

If you decide to exchange envelopes, then, then you could gain twice as much as you could lose. Your chances of gaining are equal to your chances of losing. Exchanging envelopes is therefore the rational thing to do.

Had you chosen the other envelope, though, then you could have reasoned in precisely the same way. Whatever amount of money you had taken from the other envelope, you could have reasoned that by exchanging you had twice as much to gain as to lose, and that your chances of gaining and losing were equal, and so that you should choose to swap.

Whichever envelope you choose in the first place, then, you’re better off swapping it for the other one when you get the chance.

The Unexpected Hanging

A murderer had been found guilty of a particularly heinous crime. The judge sentencing the murderer decides that death is too good for him; he wants to make him suffer. He passes his sentence, \"You will be taken from this place, and hanged from the neck until you are dead. Before that, though, you will suffer anguish, waiting, never knowing whether this will be the day that you will die. One morning, sometime in the next week, it will happen, but until it does you will live in fear.\"

The murderer leaves the courtroom with a light heart, knowing that the sentence handed down to him cannot be carried out.

He reasons like this:

Suppose that on the seventh morning I am alive. I will know that that is the day that I am to die. But the judge said that I would not know the day that I am to die. Therefore I will not be hanged on the seventh day. The sixth day is the last day that it could be.

But in that case, if I am alive on the sixth morning then I will know that it is the sixth day on which I am to be hanged. But the judge said that I would not know the day that I am to die. Therefore I will not be hanged on the sixth day.

He continues, applying the same reasoning to the fifth day, and then to the fourth, and so on, concluding that he cannot be hanged on any day according to the judge’s instructions. The sentence handed down to him cannot be carried out.

The Parodox of the Stone is very intriguing to me! I have to remember to ask a priest about that before I die. =P

Of course, the other ones are quite interesting as well. Nice job scrounging these up!

I think I know a way that the Paradox of Stone can be solved. If God can do anything, he could make himself physically weaker, but still able to create a stone too heavy for himself to lift. However, he could also increase his physical strength so that he could now lift the stone he was previously incapable of lifting.

The Shandy one is simple. He will never finish even with infinate time he would be so far behind and still have so much work to do. It would take him 365 days for one day. That leaves those days left for him to still do which will take him 365 days each. That\'s another 133,225+ days for all those. And even with unlimited time that will only give him more days to right about and to procrastinate on.

That aside, was it said that he was alive for this eternity? How do we know that he didn\'t keep writing in the netherworld? =P

The one about the man sentenced to hanging is pretty funny. About Theseus\'s ship: it is my belief that the newly re-boarded one is Theseus\'s ship. If the first ship was taken apart board by board, this means it resembles a ship in no way. Since the past is technically only an idea, as far as I know, and there is no way to reclaim it, these boards have lost all semblances of being the ship. The original components, excluding the planks, of the other ship must belong to the newly boarded one, seeing as it was never replaced. Therefore, Ship A is basically still the same ship isn\'t it? It just has new boards.

I\'m not saying God will ever lose his omnipotence (He would probably never do anything as useless as creating an immovable rock), but if he were to create this rock unmovable by even God, I think that not only would he no longer be omnipotent, but he\'d have discovored he was never omnipotent to begin with. Therefore, because he is omnipotent, his omnipotence gives him the good sense to know not to create such a rock, as he would lose his powers of omnipotence. really, it makes no sense, as facts would have to be terribly alterable for such knowledge to exist. Really, I guess such a thing may come down to the ability to choose one\'s own destiny. Please remember, I\'m not denouncing God, I\'m speaking theoretically.

In the case of the envelope, I think it has a lot to do with the financial status of the person recieving the money, and also common sense. For instance, if I were to open one with $1000 dollars, I\'d take it because I\'d be extremely happy to have it even if I also stood to win $2000. A better example is that if I opened one and it contained $2000, I\'d take it, as $2000 is a very strange base. It is highly unlikely that the deviator of the scenario would have included $2000 as a base and $4000 as the greater. Therefore, I would realize that the $2000 envelope was probably the larger.

Ah well. That\'s all I can figure out.

Stone: What if God doesn\'t have a physical body?

I was thinking the same thing last night. The only solution to the Paradox is if God\'s physical manifestation (If there is one) were limited on worldy strength. That way, he could create a stone heavier than he could lift, but only in a physical manifestation. =P

I find Theseus\' ship to be the easiest one to solve, next to the Tristler Shandy one.

Theseus\' ship: the solution lies in ownership. So long as Theseus owns the ship that he sails home in, it doesn\'t matter which ship it is. If you take apart your car, piece by piece, replacing each piece with a new one as you go, when you\'re done it\'s still your car because you own it, no matter where the parts came from. If you take out and repair each piece, it\'s still your car, since the pieces you removed and cleaned are yours and you paid for them in one way or another, it\'s still your car. So, if Theseus\' ship was dismantled and replaced board by board in order of need of repair, and then later had all the parts removed, restored, and reassembled, and then had the whole thing burnt in a huge bonfire and somebody replaced it with another ship that looked identical and he took it and sailed away with it, so long as nobody disputes the ownership of the boat, he still sailed his own, one and only boat home.

Shandy Paradox: Tristler Shandy can\'t finish the book so long as he\'s alive. While he may have an eternity to finish the book, he doesn\'t have an eternity to live. So, if you allow him to, through the hands of someone else or in the next life he would complete his book. If you don\'t believe in that sort of thing, then no, he wouldn\'t finish the book. That simple.

Immovable Stone: As for the Stone theory... I cite AimMan. If God\'s as smart as everyone says he is, he wouldn\'t make a stone that proves otherwise. Besides, God moves the planet, suns, stars, etc. right? If the rock were that heavy, it\'s density would probably create some sort of gravitational pull that would suck the Earth into a collision with it, wouldn\'t it? We\'d just revolve around the rock for eternity. Seriously not cool.

The Unexpected Hanging: Why not just hang the man in his sleep at 12:01? He wouldn\'t expect it then, and he can\'t go a week without sleep. So, if you hung him at the first possible time in the \"morning\", he would have no idea when he\'d be hanged, and he\'d suffer not knowing that he was going to be hanged then.

That\'s not a proven fact, and is thusly worthless in proving anything.

Let\'s see. God posts \"God does not exist\"

Please, does anybody else see the irony?

This one makes a lot of sence. No matter hpw heavy he makes the stone, he will always be able to lift it, if he is truely omnipotent.



It is not the same ship. If I buy a computer, and it breakes so I get it replaced part for part, it is still my computer, but it is not the same computer. The same goes here.

That was also on an episode of Only Fools and Horses. Trigger says that he has used to same broom for 20 years (I think. It\'s a long time since I last saw this). \"It\'s has 17 new handles and 21 new heads\". So Dansel askes how is it the same broom? It isn\'t, just as this isn\'t the same ship.




He will never finish his autobiography. He\'ll die before he\'s anywhere near finished.



Ah, money. The source of all modern-day evils. I say, that as long as you have as much money in your envelope, be happy. If you want more through greed, or need, swap. It may pay off, it may not. If you have the $1000, but the other envelope has $2000, but you have no real desire for any more money, then be content.



If you live to the seventh day, then you know when it will be. If you live untill the sixth day, then you don\'t know whether you\'ll die today or tomorrow. if you live to the fifth day, then it could be any of three days. Useing your logic, then if you are on Monday, then you can be sure that it would happen on either Monday, Tuesday, Wednesday, Thursday, Friday, Saturday or Sunday. Yes, that narrows it down a whole lot.

woah. paradox-es are offically pwnage material. Since my thoughts are alot like other thoughts posted, i\'ll just say \"What they said.\"

I\'ve got another one, there\'s a lot of speculation on this one but I thought it had to be here:

The Paradox of Time: The Time Machine

If, and I say IF, somebody would ever invent a time machine, and that person would go back in time, even him/her being there would alter the history of his/her present. Therefore, that persons future world would be destroyed and replaced by the Altered Fututre World, or there would be created another Dimension.

Now, let\'s call this person Bill.
Bill just made a time travelling machine, in the year XXXX(X?), he pulls the lever, the machine activates, and WHOOSH! Bill vanishes into thin air...
Or does he? If the past exist, somewhere and somehow, and IF he somehow got there IF his machine worked,
But... could he actually go back? Isn\'t there an alarm system that makes sure you can\'t travel back in time?
Well, anyway, Bill got there, now what?
Just his presence there could change things through time, Bill might never ever even invent a time machine in his present! So he couldn\'t have travelled back in time, so he couldn\'t have made a time machine, so he couldn\'t have travelled back in time, so so he coudn\'t have made a time machine, so
Etcetera, etcetera, etcetera...
You could go on forever...
Maybe the world would stop existing? Maybe Bills future world would be destroyed and replaced by a new one, one in which there aren\'t any time machines?
Maybe Bills future world will go on existing, but the \'other\' world would have another future? The world would have split into two dimension at the exact time when Bill got into the \'present of history\'.

Who knows? Can you solve the problem?
;D

He doesn\'t control us, He gave us free will, choice-to be in our own existnace with or without him. Name all these so-called paradoxes.

[Edited on 5-8-2005 by Sephiroth XX]

About the God-thing, maybe God doesn\'t exist as a being itself, but that everything living has something in it, a part of \'God\', God then is actually a huge puzzle, which only will be solved once all living can accept each other and live together in a peaceful way,
thereby \'God\' cannot create a stone he cannot lift himself, since he doesn\'t exist yet,



BTW, Mega X, could you put all your other Paradoxes in here, too?
I saw about 4(!!!) other topics of yours, all about just 1 paradox.
Since this topic seems to be the longest lasting one, why don\'t you put the others in here too? Unless they aren\'t real paradoxes or aren\'t \'fun\' enough to discuss about...

:cool:

[Edited on 6-8-2005 by Morphman]

I\'m pretty certain this doesn\'t void his control of everything. He could still take back control at any time (in fact, by the Bible, supposedly He plans to influence the world of His own accord when He reclaims his remaining believers to Heaven), and therefore is technicly still in control, even if he isn\'t moving us like puppets. He could if he wanted to, but he\'s granted us the ability to conciousness. Really, that is what makes us human.

Argh. Must. Avoid. Discussing. Religion.

Ha, the Sun and stars don\'t move. =D