Paradoxes and Paradoxial statements

[MyaMouse]

I looked through the first 15 pages and I didn't see a thread for this... So if there is one I didn't see it or it hasn't been posted in since October 2014.

 

 

So...

Paradoxes. There's a Wikipedia article on them that I read in class sometimes. I love the confusion, I love making them into unsolvable riddles, I just love them in general. I'd love to hear yours.

 

I've got a few...

 

• • This sentence is false

 

• The following statement is false

 

The preceeding statement is true

Which is true?

 

• A barber shaves all and only who do not shave themselves. Does he shave himself?

 

• A law student says he will pay his teacher when he wins his first case. The teacher then sues him for that amount of money. Will the student still have to pay?

 

•If Pinocchio says his nose is growing, what is happening to his nose?

 

Besides, I need some more to confuddle Alex and Esko

[Esko]

...and yet I find this thread

 

Yeah, you probably confuddled Alex both in Uniques AND in RL

 

anyways, to people who post after this, god help you with Mousie's paradoxes

[NatPur]

I think everyone comes to this thread, gets brain-busted, then leaves without adding anything because of the busted brain.

 

Well, one of the most obvious ones is: I'm a liar.

[georgexu94]

All Dragon Cave players in the forum are liars! I'm telling you the truth.

[Valvatorez]

Rule#23: Rule#63 is false.

 

Rule#63: Rule#23 is true.

[CursedFlames]

If there is a boat with a hundred pieces, and every year a different piece is replaced, after a hundred years is it the same boat?

 

 

Even more confusing:

 

All the old pieces were put in a shed, and after a hundred years another boat was built using those same pieces. Which one is the original?

 

 

Can (a) god create a rock that they can't lift?

In other words, can a person who can do anything create a rock that they can't lift?

Edited April 17, 2015 by BananaGummyBear64

[Naraku]

If you like Greek mythology, I have one. Hope you don't mind if I share a short-ish paradox story here. source I know it's not a statement, but it's worth reading.

 

Teumessian fox was a gigantic fox that was destined never to be caught. It was said that it had been sent by the gods (perhaps Dionysus) to prey upon the children of Thebes as a punishment for a national crime. Creon, the then Regent of Thebes, set Amphitryon the impossible task of destroying this beast. He discovered an apparently perfect solution to the problem by fetching the magical dog Laelaps, who was destined to catch everything it chased, to catch the Teumessian fox. Zeus, faced with an inevitable contradiction due to the paradoxical nature of their mutually excluding abilities, turned the two beasts into stone. The pair were cast into the stars, and remain as Canis Major (Laelaps) and Canis Minor (Teumessian Fox).

Edited April 17, 2015 by JolteonTails

[Rachel72]

I don't understand any of this.....

[Sundew]

If there is a boat with a hundred pieces, and every year a different piece is replaced, after a hundred years is it the same boat?

 

Even more confusing:

 

All the old pieces were put in a shed, and after a hundred years another boat was built using those same pieces. Which one is the original?

 

Can (a) god create a rock that they can't lift?

In other words, can a person who can do anything create a rock that they can't lift?

I've never found that one confusing, oddly enough. There's some ambiguity there, I understand that, but I only see it the one way: Yes, it's the same boat, and the original is the one with newer, replaced wood.

 

I'm going to try to explain my logic the best way I can, which is with a technology analogy. I'm not very good at explanations.

If you buy a smart camera phone (the replaced-piece ship), you'll start out with 0 photos. Get to 100 photos, and you've built your ship.

Maybe you've got limited storage and can't keep more than 100 photos on the phone at a time. Upload your existing photos to the Cloud and keep taking more. Eventually you've taken 200 photos on that phone, but only your 100 most recent ones are stored.

So you've got phone A, with 200 taken photos and 100 stored. This is ship A, the ship that continuously replaces its pieces.

Buy a new phone and download onto it your old software. You've got your 100 photos, the exact functionality that you first had with phone A, but on a technically different phone. This is phone B, equivalent to ship B, which was made using the stored original pieces of wood.

So while phone/ship B has the same appearance and use as phone/ship A did at first, it is technically still a new ship.

You can buy an iPhone 6 and download iOS 4.2.1 (okay, I don't actually know if you can, but this is just hypothetical), but that doesn't mean you've got an iPhone 4. You have a 6 with old software.

You can buy an iPhone 4 and update the software to iOS 8. You still won't have a new phone.

 

I don't know if I explained that well at all and I think I probably made it too complicated, so let me know and I'll try to word it better if I can. This is a stance I'm pretty sure on so I'm more than willing to defend/discuss it with anyone. ^^

 

Now the omnipotent deity being able to create a stone no one can lift--that's a paradox! It's been on the back burner (where they say thoughts cook best, right?) for a few months now and I can't come up with a solution, which is what makes it such a great paradox. <3

 

JolteonTails, that's also a good one. Since it's a paradox there's no solution, but if that were to play out, I'd guess that it'd be an infinite chase. The Teumessian fox would never escape and would always be chased, and Laelaps would never lose the fox, but would always be on its tail. That way the chase was never ended, and neither destiny is contradicted as long as they're both running.

Zeus made a much simpler resolution, though.

 

I think a paradox is something that is both true and false at the same time--a complicated question such as the ship one is not a paradox (in my definition), because it can be debated, and because people are capable of reading it as absolutely one way or the other. Unless that's just me.

 

A lot of the famous ones, like the apple and the raven (which I haven't really given a lot of thought, but I think is fairly simple when thought out logically) and the sand heap paradox (I absolutely despise that one, obviously heap ≥ x), aren't technically paradoxes IMO but riddles. Riddles have a clear solution, an either/or, while paradoxes are simultaneously true and false. Riddles make the world think, paradoxes make the world explode.

 

All those listed in the OP are paradoxes, by my definition.

Edited April 17, 2015 by ab613

[octopi]

...is it that hard to comprehend that some statements may be neither true nor false? Binary logic is an entirely human construct and isn't going to apply to everything. Also a lot of these resolve to true or false if we assume human beings aren't restricted to only lying or never lying.

 

That said, here's a fun puzzle:

1. Statements 1 and 2 have the same truth value - that is, either both are true or both are false.

2. I am a purple moose.

[orrrangeee]

Lol. We were discussing these in chess club. (No, not all chess clubbers are weirdos, contrary to on TV. I'm also an 100m sprint runner. Yes, you can be a nerd and still be able to run. )

 

A Cretan says: "All Cretans are liars".

If there is an exception to every rule, then every rule must have at least one exception; the exception to this one being that it has no exception." "There's always an exception to the rule, except to the exception of the rule—which is, in of itself, an accepted exception of the rule." "In a world with no rules, there should be at least one rule - a rule against rules."

[georgexu94]

If there is a boat with a hundred pieces, and every year a different piece is replaced, after a hundred years is it the same boat?

 

 

Even more confusing:

 

All the old pieces were put in a shed, and after a hundred years another boat was built using those same pieces. Which one is the original?

Well, simple. My body is comprised of different cells than from those when I was younger. Surely, I am still myself even with all my cells replaced, right? Assume we can revive those dead cells I lose and make a new human, then that would create a different human.

 

So, the boat with new parts after a hundred years is the original boat.

Edited April 18, 2015 by georgexu94

[dragongrrl]

Moderation in all things. That includes moderation, doesn't it?

[Coryn02]

Humility is about avoiding pride. But to what point can you be humble until you are now being proud? Or do you end up in a superposition of pride and humility?

Edited April 18, 2015 by Coryn02

[CursedFlames]

Can a set that contains all sets that don't contain themselves contain itself?

 

How can you open a box that is only openable when nothing's trying to open it?

 

Can a man who has never lied and never will lie say "I lied once"?

 

 

Also, that boat one is considered a paradox according to wikipedia. And wikipedia is always right.

[georgexu94]

How can you open a box that is only openable when nothing's trying to open it?

Do nothing. It will open itself.

[CursedFlames]

Do nothing. It will open itself.

I said "openable", not "open".

[georgexu94]

I said "openable", not "open".

Once it is openable, it will open itself. By some magical method.

[Wookieinmashoo]

I've never found that one confusing, oddly enough. There's some ambiguity there, I understand that, but I only see it the one way: Yes, it's the same boat, and the original is the one with newer, replaced wood.

 

I'm going to try to explain my logic the best way I can, which is with a technology analogy. I'm not very good at explanations.

If you buy a smart camera phone (the replaced-piece ship), you'll start out with 0 photos. Get to 100 photos, and you've built your ship.

Maybe you've got limited storage and can't keep more than 100 photos on the phone at a time. Upload your existing photos to the Cloud and keep taking more. Eventually you've taken 200 photos on that phone, but only your 100 most recent ones are stored.

So you've got phone A, with 200 taken photos and 100 stored. This is ship A, the ship that continuously replaces its pieces.

Buy a new phone and download onto it your old software. You've got your 100 photos, the exact functionality that you first had with phone A, but on a technically different phone. This is phone B, equivalent to ship B, which was made using the stored original pieces of wood.

So while phone/ship B has the same appearance and use as phone/ship A did at first, it is technically still a new ship.

You can buy an iPhone 6 and download iOS 4.2.1 (okay, I don't actually know if you can, but this is just hypothetical), but that doesn't mean you've got an iPhone 4. You have a 6 with old software.

You can buy an iPhone 4 and update the software to iOS 8. You still won't have a new phone.

 

I don't know if I explained that well at all and I think I probably made it too complicated, so let me know and I'll try to word it better if I can. This is a stance I'm pretty sure on so I'm more than willing to defend/discuss it with anyone. ^^

If I read this right, the two actual physical phones have not changed, only the software and the photos. In the case of the boats they were completely taken apart over time, so it's not quit the same as the cell phones. Unless I'm not reading it right?

 

@georgexu94: This one is pretty good, but this doesn't take into account the entire human being, particularly the conscious mind. It's still a part of you and the fact you can say " I have changed over many years, but I am still me" (and confirm it through IDs, that you are in fact the same person, even though changed) makes it not work as well. If boats had a consciousness there would be the same problem.

Edited April 18, 2015 by Wookieinmashoo

[georgexu94]

Once it is openable, it will open itself. By some magical method.

Of course, when I mentioned magic, I am referring to some outside force like the wind blowing the box and opening it in the process. The wind did not try to open the box. Oh, that wasn't the wind's purpose but it just happened to blow the box anyway. Let's then say the box toppled over and the lid fell over, thus opening it.

[MyaMouse]

The phone explanation just made my head hurt more.

 

[MyaMouse]

...is it that hard to comprehend that some statements may be neither true nor false? Binary logic is an entirely human construct and isn't going to apply to everything. Also a lot of these resolve to true or false if we assume human beings aren't restricted to only lying or never lying.

 

That said, here's a fun puzzle:

1. Statements 1 and 2 have the same truth value - that is, either both are true or both are false.

2. I am a purple moose.

Well, we're pretty sure you aren't a purple moose (could be wrong), which means both statements are false. But that means that the two statements do NOT have the same truth value, making the first true. And by the first being true, that also makes you a purple moose.

 

HEY WAIT

 

PI IS A PURPLE MOOSE

 

I HAVE TO TELL EVERYBODY

 

*runs off to find Mage*

[Fuzzbucket]

It is impossible to go anywhere, because before you can go anywhere you have to go halfway there, and before you can get halfway there, you have to get a quarter of the way there and before you can go a quarter of the way, you have to go one-eighth of the way; before an eighth, a sixteenth, before......

 

Zeno.

 

Same kind of thing with the hare and the tortoise - the hare will always win because (from wiki)

 

In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. – as recounted by Aristotle, Physics VI:9, 239b15

 

Also nothing actually moves because at any second in time, whatever it is we think is moving is actually stationary, because it is frozen in motion... It cannot move to somewhere it isn’t because there isn’t time for it to do so. And it can’t move to where it is now, because it’s already there. So, for that instant in time, it must be stationary. But because all time is comprised entirely of instants—in every one of which it must also be stationary—then it must in fact be stationary the entire time.

 

Yeah ?

 

And don't forget Catch-22:

 

 

    "You mean there's a catch?"

 

    "Sure there's a catch", Doc Daneeka replied. "Catch-22. Anyone who wants to get out of combat duty isn't really crazy."

 

    There was only one catch and that was Catch-22, which specified that a concern for one's own safety in the face of dangers that were real and immediate was the process of a rational mind. Orr was crazy and could be grounded. All he had to do was ask; and as soon as he did, he would no longer be crazy and would have to fly more missions. Orr would be crazy to fly more missions and sane if he didn't, but if he was sane, he had to fly them. If he flew them, he was crazy and didn't have to; but if he didn't want to, he was sane and had to. Yossarian was moved very deeply by the absolute simplicity of this clause of Catch-22 and let out a respectful whistle.

 

Then there's the crocodile one:

 

A crocodile snatches a young boy from a riverbank. His mother pleads with the crocodile to return him, to which the crocodile replies that he will only return the boy safely if the mother can guess correctly whether or not he will indeed return the boy. There is no problem if the mother guesses that the crocodile will return him—if she is right, he is returned; if she is wrong, the crocodile keeps him. If she answers that the crocodile will not return him, however, we end up with a paradox: if she is right and the crocodile never intended to return her child, then the crocodile has to return him, but in doing so breaks his word and contradicts the mother’s answer. On the other hand, if she is wrong and the crocodile actually did intend to return the boy, the crocodile must then keep him even though he intended not to, thereby also breaking his word.

Edited April 20, 2015 by fuzzbucket

[DigitalGarden]

• A law student says he will pay his teacher when he wins his first case. The teacher then sues him for that amount of money. Will the student still have to pay?

Yes; the student wins the case by rejecting the sue. Therefore the teacher gets paid basing on a different contract. If the student loses - the yes answer still stands, again, basing on different set of documents.

Edited April 20, 2015 by Light Concorde

[MyaMouse]

Yes; the student wins the case by rejecting the sue. Therefore the teacher gets paid basing on a different contract. If the student loses - the yes answer still stands, again, basing on different set of documents.

According to Wikipedia, it's a paradox but not really