11 Brain Twisting Paradoxes

Hi All
My first post on ATS
This came about after talking through the possible paradoxes of the Terminator films with my friend earlier this evening i.e Kyle Reese being John Connor's Father in the first Terminator.
And this led us to this link : 11 Paradoxes
My favourites are number 8 The arrow paradox & Number 2 The Paradox of the Court.
Hope you all enjoy.....

reply to post by BlackCommander


What was the Terminator paradox? Was it how John Conner was born to begin with the first time to make Kyle have to go back in time to save him?

After reading the first four "paradoxes", I have concluded that at least some of these paradoxes are only paradoxes in our perception, not in the action occurring. And, there are faulty assumptions being made. Therefor I wouldn't call any of numbers 11-8 a paradox. e.g. in #8, motion has nothing to do with an instant. Physics shows that everything can only approach an absolute, not attain it. And therefor there is no absolute instant, only a number set as it approaches zero or infinity, and such mathematical perception renders the assumption of the instant when regarding motion to be void.

In # 10 it sets the assumption that a heap of sand = 1,000,000 grains of sand and that a heap minus 1 grain is still a heap. It then goes on to contradict the assumption in order to set up the "paradox". That's not a paradox. It's faulty logic.

Interesting read still, even if the logic isn't quite there (in the first part that I've read).

reply to post by tinfoilman



This link shows the predestination paradox we were talking about if this helps.
I did not want my original post to be information overload so to speak, I am still scratching my head over a couple of paradoxes in the list.

Predestination Paradox

reply to post by pirhanna


Fully agree, start 4u. I lost interest in the first regarding omnipotence. I see no paradox at all there only that the writer discards upfront that an omnipotent being can will itself out of omnipotence and then starts to pile on conjectures...

reply to post by pirhanna

I completely agree some assumptions are circumspect on some of these paradoxes, I find the addition of time into these scenarios really affects the level of comprehension sometimes and complexity.

Originally posted by pirhanna
In # 10 it sets the assumption that a heap of sand = 1,000,000 grains of sand and that a heap minus 1 grain is still a heap. It then goes on to contradict the assumption in order to set up the "paradox". That's not a paradox. It's faulty logic.

It's not really faulty logic. It serves a purpose. These come from philosophy where arguments are "set up" on purpose so we can better reason about our world.

For example in real life a pile is subjective. What I think is a pile is different than what you think is a pile. If it gets small enough I might say, well it's no longer a pile, where it might have to get half that size before you agree.

But then the conversation is over and all we're left with is a subjective answer. However, one may not want a subjective answer. Perhaps there is a more definite answer if we just define our terms correctly and "set up" the argument.

So these arguments are purposely set up. And many times when you do this you will get definite answers and know more about the world. But sometimes setting up the argument leads to paradoxes like this because what you're talking about only has a subjective answer and not a definite one. But at least now we know that it only has a subjective answer.

But either way we know more about our world so it served its purpose.

Originally posted by BlackCommander
reply to post by tinfoilman

 

This link shows the predestination paradox we were talking about if this helps.
I did not want my original post to be information overload so to speak, I am still scratching my head over a couple of paradoxes in the list.

Predestination Paradox

Ah, well I believe time travel paradoxes usually aren't actually paradoxes. They only seem to be paradoxes because we're missing information. When dealing with time travel we're talking about multiple versions of a single event, but we usually only get to see ONE version of said event. Sometimes two or three if it's a movie.

However, when talking about a time travel loop, well it's a loop. And we don't know how long it's been looping. There may have been thousands of loops before we ever get to see one.

For example, how many times has Kyle Reese went back in time to save Sarah Connor? We have no idea, it' s a loop. But we only get to see one loop. We didn't see all the other versions that may explain how John Connor was originally born.

For example in Terminator 2, the machines were made by Cyberdyne Systems. But the only reason Cyberdyne Systems knew how to build the machines was because they had the neural net CPU from the first terminator.

How did Cyberdyne Systems figure out how to build the machines the first time in the first loop when they wouldn't of had access to the CPU because it hadn't been sent back in time yet? Well, we might have never known because Terminator 2 didn't show us that loop.

But, lucky for us, Terminator 3 DOES show us that loop. Since they destroyed Cyberdyne In Terminator 2 we get to see a different loop in Terminator 3. Perhaps similar to what the original loop would have looked like. IN T3 we find out that the military originally made the Skynet and the machines and Cyberdyne may of had nothing to do with it.

What we were actually seeing in T2 was an alternate loop where Cyberdyne got hold of the CPU before the military had a chance to make their own machines.

See, once we get to see all the loops, many times, if not every time the paradox goes away. For example Kyle was sent back to save John Connor, but was there an original loop where John Connor had a different father?

If so perhaps Kyle gets sent back to Sarah Connor and becomes John's father where originally he had a different father. Either way we still get a John Connor. But there's no paradox.

Just like if I invent a time machine and go back and kill my father before I'm born. So, now I'm never born. So, now I never invent time travel. However, since I never invented it, perhaps 10 years later someone else DOES. They use it go back in time and see me trying to kill my father and stop me. Since I get stopped, I'm still born, and now we're back to the original loop where I invent the time machine.

Except now my father tells me this story about the time someone tried to kill him and this time I don't back and try to kill him because now I know I'd get stopped and we're in a different loop.

Or maybe the other guy just kills my father too. So, no paradox. Either way father is dead.

See, that's why I don't believe in time travel paradoxes. I only believe it seems that way because we don't get to see all the loops that would explain the paradox away.

reply to post by BlackCommander

i like paradoxes, but most stem from the same problems: inserting an infinite quantity or poor definitions.

11. the problem here is not adequately defining "omnipotent" and not establishing a time frame. a being that can do anything COULD make a stone that it couldn't lift for a time, but then afterwards allow itself to lift the stone, fulfilling both requirements. it also could make two separate realities where it both could and couldn't.

10. poorly defined terms. the point where a heap of sand ceases to be a heap is arbitrary and relative, yet it is declared as an absolute. mathematically expressed, it would be something like x-1=x is true. x would have to be infinite.

9. another paradox existing due to definitions. what one considers "interesting" or "noteworthy" is subjective.

8. a quantized version of time solves this paradox. it is overtly simplistic in nature, as a moving arrow has a different value than a stationary one.

7. inserting an infinite value where there is actually a finite value. in this case it deals with space. theoretically you can divide by 2 forever, but not in reality.

6. this isn't a paradox at all. if the hay is perfectly equal, either pile would suffice, and which one the animal picked would be based on neurological inputs and habits. perhaps the animal prefers it's right side over the left.

5. this isn't a paradox either because thursday afternoon hasn't passed yet, so the prisoner can't know that he won't be executed friday.

4. this is in the same vein as "this sentence is false". it is created when no time frame is allotted.

3. same "this sentence is false" created by not adding a time frame, creating an infinite quantity.

2. protagorus is correct. there are two different contracts at work. protagorus was to be paid when euathlus won his first case. euathlus never had any cases, so protagorus sued him for the amount owed. the court's ruling wouldn't nullify the contract between euathlus and protagorus, but would be a second contract in and of itself.

1. an unmovable object couldn't exist in the same universe as an unstoppable object. that is the simple solution. the complex solution is to say that they could exist in the same universe, so long as they never met. the paradox only exists if the two meet, so if they are kept separate, they could exist at the same time.

0. a simple solution is that the universe isn't infinite, and that there are wavelengths of light that humans cannot see. the night sky isn't "dark" at all, actually.

reply to post by Bob Sholtz


I completely agree paradoxes are subjective and have preconditions I just went through the mental loops earlier with a friend of mine and came to similar conclusions but in the main I thought it would be a fun first post.

Very interesting stuff here, and some great displays of reasoning by all those who've posted. As far as Olber's paradox goes, wouldn't it be logical to say that even if there are an infinite number of stars (white trees), then there must also be an infinite number of planets (black trees); therefore, if one were viewing from a point, the color (or lack thereof) they would see would depend on whether they are nearest to a planet, or a star; if a planet is in front of a star, the light is blocked, and so they will see nothing (black), but if a star is nearest to them with no planet to obstruct it, then they would see light (white).

Essentially, the paradox seems flawed from my perspective because they are assuming that there are only stars, when we know that there are also planets which block the light of stars. So if you were to look at the picture shown in the article and replace some of the white points with black points which obstruct/absorb light from the white points, it would change the paradox entirely, and bring us closer to the reality that we currently experience.

Perhaps someone can point out if my logic is flawed, and/or provide a counter. Fascinating to ponder about nonetheless, particularly because I do indeed believe that the universe is infinite.

Other than that, because the thread brings up the Terminator movies, I'd like to add a bit of fluff on the side for the entertainment of everyone, particularly those of us who are big fans of T2. It was one of my favorite movies as a kid, I must have watched that movie about thirty times in half as many years.

So I'd like to share this brilliant low-budget remake of T2, which honestly has to be one of the most hilarious things I've ever seen on the Internet, and that's saying a lot, especially for a self-proclaimed comedy connoisseur such as myself. Fans of the movie will hopefully be very pleasantly surprised, enjoy!

Most of these paradoxes are just faulty assumptions and can easily be resolved. However mathematics almost collapsed when it ran into some paradoxes at the very heart of all mathematics, set theory. My favorite of this type is Russels paradox.

Consider the possible abomination of a set actually containing itself as a member. All the sets we are familiar with don't have this property and therefore call the set of all sets that do not have themselves as a member the set of all nice sets, or N for nice.

The paradox occurs when we ask this question, is N a nice set?

If N were a nice set then it must be a member of N, the set of all nice sets. But this implies it's not a nice set.

If N is not nice then N does not contain itself as a member and by definition it is therefore a nice set.

Thus N can neither be nice nor not nice. Doom quickly follows.

Reading those things are like trying to understand Gödel's incompleteness theorems---I've tried...I really have...but this must be beyond my comprehension I really...really want to understand and I am constantly reading and watching TED..but sometimes my brain just doesn't work like their brains...WHY????

reply to post by BlackCommander


11. "The paradox states that if the being can perform such actions, then it can limit its own ability to perform actions and hence it cannot perform all actions, yet...This seems to imply that an omnipotent being’s ability to limit itself necessarily means that it will, indeed, limit itself."

This isn't a paradox, the author is assuming that an Omnipotent being must exercise every potential action that is possible just because it can. This simply isn't true. Also, the fulcrum of logic in this word problem exists in the fact that an Omnipotent being should be able to outdue itself. This is impossible because the definition of omnipotence means that it cannot be challenged or outdone by anything, even itself. That's like saying, because an omnipotent being isn't more powerful than the definition of omnipotence, then he can't be omnipotent. That is obvious faulty logic.

10. "1,000,000 grains of sand is a heap of sand. (Premise 1)
A heap of sand minus one grain is still a heap. (Premise 2)
Repeated applications of Premise 2 (each time starting with one less grain), eventually forces one to accept the conclusion that a heap may be composed of just one grain of sand"

This is just outright stupidity. The definition of "heap" clearly means a group of something, aka plural amounts of something. There is no paradox, a single grain of sand can never be considered a heap, just like a shoe can never be considered to be a paperclip. Replace the word heap with its definition and this "paradox" simply becomes a child's word game. watch, "Or one may accept the conclusion by insisting that a (group of) sand can be composed of just one grain. yeah. Next.

9. Interesting Number Theory....is complete bullsh*t. If you take a bunch of uninteresting (pretty vague what makes a number interesting or uninteresting, you'd think these terms would need to be neatly defined if you're going to call it an official paradox) numbers, then that somehow makes the smallest uninteresting number interesting? What the f*** does that even mean? If it's a group of uninteresting numbers, being the smallest or highest in the group doesn't change the very quality that placed it in the group in the first place. This is another example of faulty logic, and frankly this whole list is starting to seem extremely unintelligent.

8. The arrow paradox. Another non-example of a paradox. This is similar to the saying that if you cut in half the distance it takes to move from point a to point b, and cut that distance in half over and over again, you will never get to a single unit of distance. So it must be impossible to move. But it's obviously not impossible to move so this is not a paradox since we prove it wrong constantly. Real paradox's can't be proven wrong or right in the physical world so easily.

too tired to even try the rest.

reply to post by pirhanna


I completely agree, if you set a standard then remove a grain you no longer meet that standard, in that example they keep changing the standard.

A few of these are just confusing because of what common perception was at the time it was created. Now the John Conner, Terminator paradox...I gave up on that when I was 10, it just didn't make sense unless we bring in some disinformation and self created history.

The person that made this list needs to realize there is a difference between a paradox and just not understanding something.

Originally posted by Bob Sholtz
11. the problem here is not adequately defining "omnipotent" and not establishing a time frame. a being that can do anything COULD make a stone that it couldn't lift for a time, but then afterwards allow itself to lift the stone, fulfilling both requirements. it also could make two separate realities where it both could and couldn't.

So this being just decided not to be able to do it for a while? Seems to me it was still able to do it. If I tie my hand to the ground I am still able to lift it, I just have to untie it first.

If the being creates two separate realities, then it is not impotent in one of them, true. But you can still say it was able to lift the stone. No one ever said it has to be lifting this stone at every single point in time and space, in every possible alternate reality.

So, let's assume that there is no arbitrary time frame. And i would define omnipotent as "able to do absolutely anything". Anything we can imagine, that is. The being might be both able and unable to lift the stone in some cosmic, mysterious way that we can't comprehend, but let's not go there now.

So:

1. There is no limit to how heavy a stone the being can create.

2. The beings ability to lift stones is limitless.

If this is true, it should be able to lift any stone it creates. But then it is unable to create a stone that is too heavy. Therefore it is not omnipotent.

Of course you could also say that if it can create a stone of infinite weight and it has infinite strength, then it is always able to lift exactly as big a stone as it is able to create. Because one infinity can't be bigger than the other (I guess, this might not be entirely true in higher maths?). Se maybe the concept of infinity is problematic here.

But I do not think this an excuse to dismiss the paradox. Both alternatives still seem impossible to me and that's the whole point of paradox, right?

More or less agree with you about the rest of them, I think.

reply to post by Subnatural

what does "all powerful" mean to you? the ability to do anything?

then it stands to reason the being could create a scenario where it willingly would allow itself to not do something. essentially, the ability to choose one thing over the other. OR, as i said, creating a reality where both are possible.

this allows it's all powerful attribute to exist at the same time as not being able to lift the stone.

did you consider that the all powerful being could create a reality where logic as we understand it doesn't function, and that it both could and couldn't lift the stone at the same time?

truthfully, i find this particular paradox to be so human. it is built only on human concepts of what all powerful would look like.

reply to post by BlackCommander

The good ol omni potence paradox-back in the 1970's we used to say"If GOD can do anything...can he create a rock so heavy that even he cannot lift"?