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11 Brain-Twisting Paradoxes

7Raul7 . . . Comments

Paradoxes have been around since the time of Ancient Greeks & the credit of popularizing them goes to recent logicians. Using logic you can usually find a fatal flaw in the paradox which shows why the seemingly impossible is either possible or the entire paradox is built on flawed thinking. Can you all work out the problems in each of the 11 paradoxes shown here? If you do, post your solutions or the fallacies in the comments.

11

The Omnipotence Paradox

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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, on the other hand, if it cannot limit its own actions, then that is—straight off—something it cannot do. This seems to imply that an omnipotent being’s ability to limit itself necessarily means that it will, indeed, limit itself. This paradox is often formulated in terms of the God of the Abrahamic religions, though this is not a requirement. One version of the omnipotence paradox is the so-called paradox of the stone: “Could an omnipotent being create a stone so heavy that even that being could not lift it?” If so, then it seems that the being could cease to be omnipotent; if not, it seems that the being was not omnipotent to begin with. An answer to the paradox is that having a weakness, such as a stone he cannot lift, does not fall under omnipotence, since the definition of omnipotence implies having no weaknesses.

For more brain-twisting paradoxes, check out Paradoxes at Amazon.com!

10

The Sorites’ Paradox

A1 Sand Pile1

The paradox goes as follows: consider a heap of sand from which grains are individually removed. One might construct the argument, using premises, as follows:

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.

On the face of it, there are some ways to avoid this conclusion. One may object to the first premise by denying 1,000,000 grains of sand makes a heap. But 1,000,000 is just an arbitrarily large number, and the argument will go through with any such number. So the response must deny outright that there are such things as heaps. Peter Unger defends this solution. Alternatively, one may object to the second premise by stating that it is not true for all collections of grains that removing one grain from it still makes a heap. Or one may accept the conclusion by insisting that a heap of sand can be composed of just one grain.

9

The Interesting number paradox

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Claim: There is no such thing as an uninteresting natural number.

Proof by Contradiction: Assume that you have a non-empty set of natural numbers that are not interesting. Due to the well-ordered property of the natural numbers, there must be some smallest number in the set of not interesting numbers. Being the smallest number of a set one might consider not interesting makes that number interesting. Since the numbers in this set were defined as not interesting, we have reached a contradiction because this smallest number cannot be both interesting and uninteresting. Therefore the set of uninteresting numbers must be empty, proving there is no such thing as an uninteresting number.


8

The arrow paradox

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In the arrow paradox, Zeno states that for motion to be occurring, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one instant of time, for the arrow to be moving it must either move to where it is, or it must move to where it is not. It cannot move to where it is not, because this is a single instant, and it cannot move to where it is because it is already there. In other words, in any instant of time there is no motion occurring, because an instant is a snapshot. Therefore, if it cannot move in a single instant it cannot move in any instant, making any motion impossible. This paradox is also known as the fletcher’s paradox—a fletcher being a maker of arrows.
Whereas the first two paradoxes presented divide space, this paradox starts by dividing time – and not into segments, but into points.

7

Achilles & the tortoise paradox

Achilles Tortoise

In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 feet. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 feet, bringing him to the tortoise’s starting point. During this time, the tortoise has run a much shorter distance, say, 10 feet. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise. Of course, simple experience tells us that Achilles will be able to overtake the tortoise, which is why this is a paradox.

[JFrater: I will point out the problem with this paradox to give you all an idea of how the others might be wrong: in physical reality it is impossible to transverse the infinite – how can you get from one point in infinity to another without crossing an infinity of points? You can’t – thus it is impossible. But in mathematics it is not. This paradox shows us how mathematics may appear to prove something – but in reality, it fails. So the problem with this paradox is that it is applying mathematical rules to a non-mathematical situation. This makes it invalid.]


6

The Buridan’s ass paradox

Usa Deliberations Of Congress

This is a figurative description of a man of indecision. It refers to a paradoxical situation wherein an ass, placed exactly in the middle between two stacks of hay of equal size and quality, will starve to death since it cannot make any rational decision to start eating one rather than the other. The paradox is named after the 14th century French philosopher Jean Buridan. The paradox was not originated by Buridan himself. It is first found in Aristotle’s De Caelo, where Aristotle mentions an example of a man who remains unmoved because he is as hungry as he is thirsty and is positioned exactly between food and drink. Later writers satirised this view in terms of an ass who, confronted by two equally desirable and accessible bales of hay, must necessarily starve while pondering a decision.

5

The unexpected hanging paradox

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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.


4

The barber’s Paradox

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Suppose there is a town with just one male barber; and that every man in the town keeps himself clean-shaven: some by shaving themselves, some by attending the barber. It seems reasonable to imagine that the barber obeys the following rule: He shaves all and only those men in town who do not shave themselves.

Under this scenario, we can ask the following question: Does the barber shave himself?
Asking this, however, we discover that the situation presented is in fact impossible:

– If the barber does not shave himself, he must abide by the rule and shave himself.
– If he does shave himself, according to the rule he will not shave himself

Try some paradoxes with a mathematical twist! Buy Paradoxes in Mathematics at Amazon.com!

3

Epimenides’ Paradox

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This paradox arises from the statement in which Epimenides, against the general sentiment of Crete, proposed that Zeus was immortal, as in the following poem:

They fashioned a tomb for thee, O holy and high one
The Cretans, always liars, evil beasts, idle bellies!
But thou art not dead: thou livest and abidest forever,
For in thee we live and move and have our being.

He was, however, unaware that, by calling all Cretens liars, he had, unintentionally, called himself one, even though what he ‘meant’ was all Cretens except himself. Thus arises the paradox that if all Cretens are liars, he is also one, & if he is a liar, then all Cretens are truthful. So, if all Cretens are truthful, then he himself is speaking the truth & if he is speaking the truth, all Cretens are liars. Thus continues the infinite regression.


2

The paradox of the court

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The Paradox of the Court is a very old problem in logic stemming from ancient Greece. It is said that the famous sophist Protagoras took on a pupil, Euathlus, on the understanding that the student pay Protagoras for his instruction after he had won his first case (in some versions: if and only if Euathlus wins his first court case). Some accounts claim that Protagoras demanded his money as soon as Euathlus completed his education; others say that Protagoras waited until it was obvious that Euathlus was making no effort to take on clients and still others assert that Euathlus made a genuine attempt but that no clients ever came. In any case, Protagoras decided to sue Euathlus for the amount owed.
Protagoras argued that if he won the case he would be paid his money. If Euathlus won the case, Protagoras would still be paid according to the original contract, because Euathlus would have won his first case.

Euathlus, however, claimed that if he won then by the court’s decision he would not have to pay Protagoras. If on the other hand Protagoras won then Euathlus would still not have won a case and therefore not be obliged to pay. The question is: which of the two men is in the right?

1

The unstoppable force paradox

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The Irresistible force paradox, also the unstoppable force paradox, is a classic paradox formulated as “What happens when an irresistible force meets an immovable object?” The paradox should be understood as an exercise in logic, not as the postulation of a possible reality. According to modern scientific understanding, no force is completely irresistible, and there are no immovable objects and cannot be any, as even a minuscule force will cause a slight acceleration on an object of any mass. An immovable object would have to have an inertia that was infinite and therefore infinite mass. Such an object would collapse under its own gravity and create a singularity. An unstoppable force would require infinite energy, which does not exist in a finite universe.

Bonus

Olbers’ Paradox

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In astrophysics and physical cosmology, Olbers’ paradox is the argument that the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe. It is one of the pieces of evidence for a non-static universe such as the current Big Bang model. The argument is also referred to as the “dark night sky paradox” The paradox states that at any angle from the earth the sight line will end at the surface of a star. To understand this we compare it to standing in a forest of white trees. If at any point the vision of the observer ended at the surface of a tree, wouldn’t the observer only see white? This contradicts the darkness of the night sky and leads many to wonder why we do not see only light from stars in the night sky.

Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. Text is derived from Wikipedia.



  • oliveralbq

    i love this list, *except* for the entrys that are semantically misleading — those few that just seem to be written in an arguminative manner to throw us off — i hate those.

    • Which ones did you find semantically misleading? Just wanted to read them and see exactly what you mean.

      • oliveralbq

        its all of them — but each in their own unique way — so where some appear to be clever, some appear smart-assy, and some confusing — will be different for different interpretations

        im not sure that youll see exactly what i mean, because the nature of what i said requires some amount of personal interpretation. even as i wrote that comment, i imagined other people would relate, but perhaps would have different interpretations

        start with 11, 10, 8, and 5
        this intensedebate software is still chopping some of my comments up, so for the sake of continuity, ill give you a few examples, as you are reading……….check back

        • just for the record — good job raul — youve already got people thinking ;) — nice list

          ok—-let me start with the sand one–
          raul lays out a fine set of deductive logic premeses — a million grains of sand is a heap. great. now, take one away 999,999 grains of sand is a heap. fine. keep going with this and 1 grain of sand will be a heap. no nonono.
          semantical ambiguity here — we havnt defined heap.

          this works with other ambiguous units of measurments — if i have a carton of cigarettes, i have 200……if i have 171, i have 8 packs, and 11 looseys. if i have a pile of cigarettes, and i smoke one, i still have a pile.

          a pile is like a heap
          only semantically misleading is you take it to the point of raul's example, because if you have one grain of sand, you have a grain of sand, not a heap. hell 19 grains of sand isnt really a heap either, based on the connotation of the word heap — but where does it change to being an acceptable representation of the word?

          • I thought that was exactly the point of the paradox. There is no one point that a heap becomes less than a heap- i.e there is no amount at which a heap becomes a pile or a pile becomes a mound. Obviously one grain of sand is not a heap, but when taking away one grain of sand at a time you cannot decide a specific point at which it changed from a heap to not a heap.

            I hope that makes sense.

          • Spiderbait

            I would define a heap as too many to count at a glance. If you could count it at a glance then you wouldn't call it a heap, you would simply say how many there are. By that logic it would cease to be a heap at the moment you could tell how many there are by simply looking at them. It could also mean that when you know the number it ceases to be a heap meaning that it ceases to be a heap when you know there are a million grains of sand.

          • oliveralbq

            im not totally sure i could look at 23 grains of sand, and count them at a glance. i do believe i could look at 23 dead bodies, and count them at a glance. this is a whole different can of worms, because now, 23 is a heap *of some things*, but not others. in addition to that, even though i couldnt count 23 grains of sand, i wouldnt consider it a heap — 23 bodies, on the other hand, just may be a heap. now it starts to become individualistic as to what gets characterized as what, and why.

            thats actually why these paradoxes are so thought provoking.

          • The reasoning is great, keep it up guys and Raul achieved his goal with the list. But why did you use dead bodies as an example?!?
            Lol, very interesting…

          • oliveralbq

            way ahead of ya ;)
            and yep — love it love it
            so many different reasons different people like different lists…….

            and the dead body comment?
            i had been watching snatch, and that scene was on when brick top was talking to turkish in the pig sty — as i was writing the message, the monologue about removing the teeth and hair from a dead body before disposing of it by feeding it to the pigs, who can devour an entire body quick — telling statham that teeth and hair or nails (or whatever it was) are undigestable
            "of course you dont have to remove them, but you don't wanna go sifting through pig shit, now do ya?"

            and i thought — great example

            either that or a fascination with working dead bodies into an analogy at least once a week

            take your pick

          • i sent 2 or 3 examples….i think the other/s is/are held up in moderation…..as for this one, im looking at it backwards from the way you are. the paradox seems to preassume that a heap is a definable measure. where you say there is no amount at which a heap becomes a pile, then my question to you is: why are we trying to quantify these abstract measurments?
            what you said makes perfect sense. but so does this: i have ten amounts of sand on my porch, the smallest consists of 1 grain, the largest consists of 999,999 of them. how many piles do i have?

            cont'd……………………….

          • ……………………cont'd

            the paradox is mostly in semantics itself. i think i have 7 heaps, and you say i have 5. why are we of differing opinions, and what causes me to see 1000 grains as a heap, but disallows you to see that as anything other than a mound. some of these paradoxes cease to occur if you quantify the measurments — which is why, when i take you to the back porch, and i have ten different amounts of eggs, you can readily identify them as a pair, a dozen, a baker's dozen, and a gross of eggs etc., the thing is, out of the 11 examples, some are explained succintly, whereas others are shrouded in undefinable and abstract semantic terms.

          • Dana

            I took the the meaning the same way that trinity did. But here was what what I was wondering. If you accept that the grains of sand will eventually end at one and you haven't at any point stopped calling the heap, a heap, then would each little grain removed be considered a heap?

          • being a heap or not has more to do with it’s apparent structure , i.e how to grains of sand are group together to form a mound than anything else. you wouldn’t call a million grain of sand laid out flat on a surface a heap would you, like in the case of a beach? The definining point at which it cease to be a heap would be when the amount of sand is reduced tp a point that it could no longer form a triangular structure and this point differs between the type of sands and is dependent on various factors like humidity.

      • Tim

        JFrater's comments on Achilles and Tortoise were utterly misleading because they were completely wrong and demonstrated a complete lack of comprehension regarding the paradox. It is a mathematical problem. It makes perfect sense when formulated mathematically. I just doesn't make sense if you are duped into thinking about it non-mathematically. The problem is the ridiculous assumption that in the time it takes for achilles to reach the point where the tortoise was, the tortoise would still be ahead of him! This algorithm would find the point at which they cross, and has nothing to do with finding the relative distances they have travelled in a given time frame.

    • avedon

      If you say or even think you're an open minded person, you create a prejudice of your own freedom of though, which is a paradox.

      That's dope.

      • right — of course, if you think youre closeminded, you create an antiprejudice of your own lack of freedom of thought,

        it is here, where we have entered the realm of loophole jumping, where it becomes possible to justify almost anything — to the limits of mediocraty — sufficiently, but impossible to delve to depths of certain capacities due to inherent esotericism surrounding deeper analysis and idea construction.

        that's dope as shit, true dat

    • Tim

      also, the grain of sand heap thing is a load of crap. It obviously just depends on what your definition of a 'heap' is. For example, my definition of a heap is the shape. If it is no 'heaped' (e.g. was flat) it would not be a heap. The number of grains is fairly irrelevant. In my definition the miniumum to be a heap would be the minimum you can stack to still make a heap shape. What's your definition of a heap? As soon as you know what it is, there is no paradox. rubbish.

    • Tim

      5 (hanging) is also rubbish because obviously his logic only applied to the Friday yet he tried to apply it to all the other days … this isn't a paradox, this is a standard format for jokes. This is a joke not a paradox (literally).

    • Tim

      Olber's paradox … has paradox in the name because historically it was believed that the universe is infinite. So the resolution is: the universe isn't infinite … well, there's a surprise for everyone born in this century!!

  • TheFlu

    MY BRAAAAIN!!

  • VMP

    I thought I would be the first to post a comment, but then I thought that even if I dont, this still would be me first post for this list. And then, the second one posting after me would feel the same, extending to infinity. The truth may however be, that _)(#)([email protected]#*(!()@_#()[email protected]#()[email protected](#_)!(CJLKJ

  • krayz-yama

    oh what a nice list. It hurts my brain.

  • I think I just had a subdural hematoma. O_O

    Very interesting list though.

  • Fantastic list. As to number 6, I have a mental fix since we do encounter this paradox in everyday life.

    Do I go right, left or straight ahead?

    Many of us can't decide and resort to flipping a coin or something to force an action.

    I encountered it young while playing videogames.

    You're running through caves in a game and they fork. which way do you go?
    My answer is left. Always go left first, explore what is to be found then turn around and take the next left, thereby going everywhere.

    • Actually it's more like "follow the left wall."

      that will also get you out of a maze.

    • Spiderbait

      I always go the way I think will end in a dead end. There is usually something to signal this near the beginning of the tunnel but if there isn't any in the first tunnel then I head down the second one given that when I travel down the second one I either see something that implies it's a dead end or it doesn't and then I can't be bothered to try the second one again.

    • kristian kiel

      except if you find the end of the cave before having seen all of the cave, so if there is another way out from the cave, then it is locically impossible for you to have seen all of the cave…;-)

  • xristaravas

    Very interesting and confusing at the same list! Good job 7raul7.

  • Alot of think thinking involved in this list well done . Only ever heard of the bonus in a physics book once . However not my cup of tea . Find the subject boring ( i'm probly just too dumb and lazy though) Think this is definatly up JFraters alley .

  • KarlR

    Oh cool list…
    nice one again!:)
    One of the best.haha

  • intercosterclavical

    Nie list! I suppose you could also say for the unstoppable force paradox that if the universe contains an unstoppable force then by definition it cannot also contain an immovable object or else the force could not be defined as unstoppable. The two terms are mutually exclusive. Just saying.

  • Really interesting. Took me a couple of seconds and maybe a re-read to get some of them, but I liked it- tax my brain more please!

  • For the Buridan’s ass paradox, if the two piles are the same then just start with any pile, or each one bite from one then from another. Why would you starve to death thinking about which one to eat? I mean if you are starving, presumably your aim would be to feed yourself, and not think about "how best" to feed yourself (that's only something you think about when you are not that hungry, and hence is able to think about other things), so it wouldn't matter which pile you eat from, whether they're bigger or smaller etc. as long as it can fill you right? Or maybe I think in too simplistic a manner.

    Ouch, I think I just sprained my brain. Nice list though

    • Spiderbait

      I agree with you. This paradox seems to only work for completely logical beings and no living being is completely logical. If a computer faced this problem however (and didn't have a failsafe built into it to circumvent such a dilemma) then I'm pretty sure it would be stuck like that forever. I'm guessing this paradox was popularized by those that favored the idea that the man worked like a machine circa 1748.

      • I read an account once of a man who was "too logical". This was real, he was in an accident or had a brain tumor. Anyway, it actually look him ages to make simple decisions, like picking a breakfast cereal. There is a podcast that has a section about him at Radiolab NYC.

        • isnt there an iphone app for that?

          the decision between coco pebbles and count chocula shouldnt ever be that hard.

          do i want marshmelllows or no marshmellows? where the hell is my fone?!?

      • The second paradox is that a completely logical being would think "hmm, probably best I don't starve to death here" and start munching on either pile.

        The logical thing is to stop thinking about logic :D

    • kristian

      think of the piles as a kind of sweet that you can only eat one of , when you have eaten that sweet then you are full. if you equally want both sweets and can't save the other one, then you wouldn't be able to chose wich one to eat because you want them equally much.

    • It’s an interesting argument, but I think Aristotle’s paradox about the man who is as hungry as he is thirsty explains it better. If we imagine he has an ‘equal’ desire for both the food and the drink. The drink is exactly 20 miles away to his left and the food is exactly 20 miles away to his right, then he will spend a lot of time debating with himself which way he will go… until he takes a coin from his pocket and debates which way is heads and which way is tails.

  • liam

    in my opinion paradox's are things men have thought up in order to complicate things despite the fact that even with a simple bit of logic they could have an answer. for example The Buridan’s ass paradox. if both bales are identical the donkey would likely eat both bales.

    • Spiderbait

      But if we were to add that once the donkey has chosen a bale the other is taken away?

      • franruilob

        the question is rather, what pile would he eat FIRST?

        • The flaw in the paradox is the implication that one of the two choices is wrong and would have negative consequences. Since neither of them are wrong, then either pile can be chosen at random. If you can’t make a random choice on your own, then simply use a device (such as a coin flip) to do it for you.

          • what

            but what coin do i use??

        • max r

          while some of the other one are very intersting- the donkey one is pointless because- if a donkey was hungery obviously it wouldn’t think- oh these too hay bales are both equally appatizing i will wait to ponder that- no- its an animal it would just eat whatever. also, the tortoise race is interesting to think about but obviously if your going faster than someone you will pass them. and for the sand pile one- a heap is a heap- that one is just based on the fact that the actual word ‘heap’ has a very loose defanition.

          ….
          besides that – I found them extremly intersting and my brain kinda hurts to think about some of these things. but that’s the point of a paradox right? haha cool list

  • i'm keeping a copy of this somewhere i can find it later, because if i ever decide to go the route of professor, rather than researcher, these are about the best damn examples of busy work i think ive ever seen

    fuck off in my class?
    fine
    write a 25 page paper on the smallest possible heap of sand

    • Jen

      Love that idea.

  • Fayekename

    If I assume space is infinate then there are infinate possibilities. If there are infiniate possibilities then it is possible for something to be impossible. If something is impossible there are not infinate possiblitites.

    • Westley

      I don't think that having infinite possibilities makes the impossible possible. But in any case, having something that is impossible doesn't make the possibilities finite, just infinity minus one, which is still infinity.

  • Wuff

    @Fayekename
    What you're saying is that "EVERYTHING is possible" (infinite possibilities) also means that the impossible is included in that everything.
    If you think about it, you realize that the impossible is simply NOTHING. It's just not possible, therefore it doesn't exist, it's nothing. Everything for sure doesn't include "nothing" because in the range of "everything" (means all that does/will exist, all that is possible) there's no space for nothing (impossible). Nothing simply doesn't exist in everything. Nothing impossible exists. Not even in a space where everything is possible.

    The point is that were talking about possibilities here. A possibility is something that can actually exist and happen. Impossibilities can't be included in "possibilities", not even in endless possibilities. You then only had a huge load of possibilities, including everything ever possible, but not the impossible. Even if you somehow managed to add an impossibility to that many possibilities, you couldn't notice it, it wouldn't affect anything, it would just do nothing, it wouldn't even create a paradox, simply because it is not possible.

    PS: You will also never see something impossible being actually created. Else it would be possible, rite? And only then it would count into "infinite possibilities".

    • Spiderbait

      I love it when people refer to real things as impossible or supernatural given the implications.

    • Wuff, your argument sounds logical. Imposible is not in the range of possibilities. But if everything is possible, will these never clash ? Indeed they will therefore ''I am black'' and ''I am white'' are both possible? If I am black it is impossible for me to be white? Everithing hase it's oposition. So only 50% of thing will be posible. Also the existence of possibility creates imposibility which it has to relate to it order to exist. Is it therefore possible for the impossible to be possible ? If possibility exist in the way you say it does there's no impossible at all, so it is impossible for something to be impossible ??? Here we goo again… can't get to an end of all this argumentation. Why? because is IMPOSSIBLE :))

      • Wuff

        I actually had the same thoughts running through my mind for a while: Do endless possibilities include impossibilities? But it's still very hard to argue that infinite possibilities include impossibilities, because you're talking about an endless amount of things that CAN happen/exist. And impossible things just don't happen and exist :D

        "So only 50% of thing will be posible." Actually, in a space with infinite possibilities, everything that can somehow be, will be. If you say that 50% of all things will be possible because their oppositions will automatically impossible, I'd say that you could have one thing on one side of the space and their oppositions on the other side. Why not? As long as they don't cancel themselves out like an immovable object and an irresistible force do ^^

      • Jack Arthur

        You're thinking kind of backwards. You're starting from concepts and trying to 'get at' reality and this is backwards: in reality, reality informs concepts.

        IOW concepts – such as 'possible' – are simply descriptive elements. They are essentially temporal, impotent, malleable.

        The 'possibility' of you being either black or white is not a function of reality – in reality, only one of these "possibilities" is "possible" and the other is strictly "impossible" – but rather a function of my ignorance.

        In reality there is simply "what is"… and what is not, is impossible. We could entertain the "possibility" of the impossible being possible… but we'd simply be wrong.

        It means that 'possibility' and 'impossibility' do not *exist*; they are crude attempts at describing that which exists.

        The realization that all of language and conception is only a remembered impression of a perception of reality – rather than being prescriptive of it in any way or 'real itself' – is the solution to most of these paradoxes.

        • DanielXA

          Wait…what?

        • Mickey

          Both possible and impossible can exist..just not together. Its like yodas saying “do or do not there is no try” so its either possible (do) or its impossible (do not)..never both (there is no try).

      • Bob

        If the universe is infinitely large then there will be a solar system exactly like ours, with an earth exactly like ours, with a you exactly like you. Only black. Then you’re black and white at the same time.

  • yoyoy

    nice…

  • Arsnl

    Good list. i knew it was in the waiting for quite a while (since the beginning of listverse)
    Kind of amazing to see how many paradoxes can appear from not knowing the physical reality or a proper mathematical definition.
    Physically it is impossible to divide time/space into infinitely small parts. After a certain division of space we get Heisenberg's uncertainty principle. If you know the precision you dont know the momentum and vice versa. So the rules that define the "world of the large" brake down when we reach quantum levels. The math used isnt the same. You start using probabilities, and you begin to discover that the "world of the small" isnt deterministic.
    But a more serious statement i guess is jfrater's :"So the problem with this paradox is that it is applying mathematical rules to a non-mathematical situation." I dont understand it. Does it mean there are physical situations that can be resolved without using math? Doesnt this statement seem dangerous to you? Zeno just used the wrong math (he didnt know the modern definition of a limit -cauchy's definition-) and the wrong physics. One CANNOT learn/do physics without math. It cannot be done.
    The surprise hanging: the judge meant that all days had an equal probability not that the day would actually be unknown to the prisoner (also some knowledge of conditional probability is needed).
    Olber's paradox: well physics can explain that i imagine: absorption, diffraction etc.
    PS: i am aware that the purpose is not to solve the paradoxes but once you started to apply rigour you can drax some conclusions.
    another much more fun paradox would be the monty hall one- it deals with conditional probabilities.

    • Spiderbait

      Yeah the one about Achilles and the rabbit is more about strange logic. I even remember learning a mathematical equation dealing directly with one moving object catching up to a slower moving object and how to calculate that.

    • vince

      Actually the answer is that Achilles&Tortise Paradox and Arrow Paradoxes are not paradoxes, because they are wrong in their assumptions. They define a 'point'. In truth, in either Space OR Time, there is no such thing as a single 'point'. We use the word 'point' as being defined by "the smallest unit of measure we can comprehend"- be it space OR time. Reality does not have a smallest unit of measure- not a mathematical one.

      As soon as you can accept the fact that a single point can not exist- you can realize that they are not paradoxes, but incorrect logic puzzles. Example: which is faster- a bullet or a wuzzit? Well, a wuzzit doesn't actually exist- there is no such thing, so there is no answer- not even 'bullet' because it is asking for a comparison, and you can not compare a single object.

  • Arnaud

    The #8 paradox is base on the false asumption that Time is composed of instants… It is not… there is no such thing as an instant.
    A duration is not composed of instants. It's composed by smaller durations…
    The idea of a succession of instants is false because by definition, between two instants there is an infinity of instants. So the idea of a "next" instant doesn't make sense.
    It is the same for a line. A line is not composed of a succession of points. The notion of "next" point is false because between two points there is always an infinity of points. Therefore a line is composed of line segments… not of points.

    • Arsnl

      That depens actually. If you say line and you mean the actual line drawn by a pencil: then a line is a succesion of graphite atoms on a celulose fibers.
      If you mean the mathematical model: then a line is a succesion of points only it depends on what type of topology you use on that line. You can say its made up of points (and segments and any reunuion of segments and whatever you want) or you can say a line us just that the line its self and also nothing at all. You need to make a distinction between succesion: the fact that we can say that for example 1<2(here you are wrong) and succesion as in next- here you are right there is no next thats why in analysis we use the notion of neighborhood.
      But a line is made up of points since you can extract on point and look at it and put it back :-)
      ps: when talking about infinity you should be careful and check exactly what type of infinity you are refering. Check Cantor to see what i mean.

      • Arnaud

        I disagree… It's kinda OK to say that a line is made of points, but a line is not a "succession" of points. Because succession means that if you choose a point, there is a "next" point, and then another "next" point, etc…
        But that's not true, mathematically speaking.
        That's the flaw in Zeno's "theory"… He assumes that the arrow exist in an "instant" of time, that can be followed by the "next" instant. Actually the arrow can only exist in a duration, inside which there can be motion…

        • I see the flaw in it, definitely. But I like the idea it creates in my head. A 2-dimensional model of time, which is itself a dimension – now that's something I find hard to get my head around. What makes time a dimension anyway?

          • Guest

            Time is theorised to be in the 4th dimension, as explained in this theoretical video: http://www.youtube.com/watch?v=JkxieS-6WuA. As i believe we all agree there are at least 4 dimensions, as there exists four dimensional objects, the theory explained in this video seems very plausible

        • Jack Arthur

          Right. Conception is descriptive, not prescriptive. The action of the arrow precedes our conception of it.

      • Arsnl

        Well nobody defined a line as a succession of points in the sense point 1, point 2 so on and so forth. That is impossible because like Cantor said there are an infinitely types of infinity. I can count all the rationals in a given segment and i CAN point to you what that number is. Lets say you pick numer 1,37953 i can tell you whats the next rational number but i cant tell you whats the next real number.
        There isnt a bijection between the natural and real set.
        But mathematically when i say succesion of points i think of an ordered set. Mathematically its all straight forward. Ive checked merrian webster for a propee definition of succession and it said to follow in order. Well the line is ordered so for me its a succesion of points. You want to count them. Well its uncountable.
        You use a definition of segments that ISNT correct because even those segments are uncountable :-). You cant say what segment is segment number 2 and what segment is segment 3. Check some math books on set theory and a curious example would be the cantor set and fractals in general.
        About time well if you define it like a line its the same as any other line. If you are searching for a physical definition, i think its descrete but i dont know exactly. Just a guess here.

      • xdr

        Actually…. That is the reason why we have differential calculus. Infinite amounts of nothing equals something.

    • mick.G

      adding to that, motion is a function of both distance and time, to break it down further is just instantaneous displacement and time elapsed, basically, the person who made that paradox didn't know anything about elementary physics

  • emmy

    Traversing the infinite is possible, it's only a matter of how your increments are sized. There is no contradiction with the tortoise example. And there is no need to make conclusions on the nature of mathematical proof.

    • In fact it isn't in physical reality – if it were possible – the paradox would prove that one would never move. But in reality, Achilles does pass the tortoise. Maths describes many things that are impossible in reality and this is a case of that. Here is another example: -2. Show me an example of -2 in physical reality. You can't.

      • Arsnl

        -2 coulombs (as a charge), -2 can be a spin. You have to see the integers and the operation plus as a group so in this light -2 is the opposite of two. I remember you taking physics at a course. You have to be open to understand group theory and many more abstract notions. To do physics you have to do math there is no other way around it. And arguing about it is dangerous and refusing to do it will get you nowhere. Behind a mathematical equation there is a physical reality and that physical reality has to be understood.

      • emmy

        Your argument seems to be that since Achilles passes the tortoise, and you cannot pass an infinite set of points, it means that he must have traversed a finite set of points. Your second premise is untrue. Even if the points are infinite, they can still converge to a finite distance. It's simply a matter of taking smaller and smaller increments. In the example, Achilles does in fact cross an infinite number of points, which converge as he passes the tortoise.

        To be honest, I don't see the paradox at all, mostly because it's simply an illustration of a geometric series. Now if Achilles were to cross an infinite number of fixed lengths, say cms, then I'd be impressed.

      • Show me an example of -2 in physical reality. You can't.

        I wish I could use that logic to explain to my bank why my credit card bill doesn’t exist. Seriously, can “debt” be considered a physical manifestation of a negative number? Perhaps the counter-argument is that “debt” is a concept, and is not physical. I dunno man, whenever I tally up my debts, I become physically ill…

        • oliveralbq

          i actually saw this from the opposite standpoint.
          i will admit, when i read jamie's comment i tried to think of a way to refute it, just for the sake of argument.
          however, as for debt if — you owe the bank 5$ you said that you have -5 dollars in the account.
          im more inclined to believe that its more logical to look at it like this:

          if you have 25$in the bank, you have 25$
          if youre overdrawn by 5$, you do not have -5$ — you have 5$, albeit , in debt — or *they* have 5 of your dollars lent out in an unwritten iou, or however you want to rationalize that

          its the description of the noun to which you are assigning a number
          and i think jamie has a point there.
          if you are in the black, you have money in the bank.
          if youre in the red, i dont see where you have negative money, cause that doesnt make any damn sense — the integer is positive, its just attributed to something that justifies its absence, instead of something that justifies its presence.

          but if you have any luck with your creditors, wirte a list…."the top 1 thing you can tell your credit card company that will come across as 'piss off — not paying shit' "

          • If you dig a 2 ft deep hole, you can both trip over the “+2” ft high pile of dirt removed from the hole and you can also fall into the “-2” ft deep hole. Both the dirt pile and the hole exist in physical reality.

          • emmy

            I agree with Maggot here. -2 can describe anything opposing that which we set to be our route by 2 units. For example, going from A to B and ending up farther from B than A, we have arrived at a negative point in our system. Mathematics is inherently abstract, that is it's purpose. But it's abstractions are that of the real world, and represent the symmetries and patterns we see everyday. Again, there is no need to question the validity of maths from such a trivial example.

          • I don’t think maths is being questioned – it has its place for sure. But, not all of maths represents reality – and your example still doesn’t. Hand me -2 marbles. By your reasoning, giving me two when I ask for four is showing -2 – but that is not at all true. You can’t physically have -2 because “minus” is privation. In the same way that a doughnut hole doesn’t exist – yes, a doughnut exists and it is shaped in such a way that it has a “hole” in the middle, but you can’t actually give me the hole from the doughnut. “Hole” is a sign that describes the absence of something – and if it is absent you can’t give it. The age old axiom still remains true: you can’t give what you don’t have.

          • yeah…that ^^^^

            what he said.

          • emmy

            I cannot give you a minus just as I cannot give you a plus. Nor can I give you a doughnut, through that logic. The word "doughnut" is just as much convention as a minus or a plus, it's just a language. Giving you "2" marbles is just a representation of what I'm doing. In reality of course, I am giving you something, but the expressions I can use to communicate this exchange remains in my discretion, and are all equally valid as long as the maths is accurate. Just as you say that it doesn't make sense to have negative quantity because it's just a positive quantity backwards, I can say that it doesn't make sense to have a positive quantity, because it's just a negative quantity backwards.

          • Arsnl

            -2 isnt a privation, -2 is the opposite of something. its like you are saying that the charge of a body composed of 4 electrons and 2 protons is +6 cuz you 'always' have to add.
            of course its a model and of course some things dont make sense like infinity (when you have to eliminate it from equations) but your example is wrong. i would have chosen other examples: show me something that has the lenght PI or show me a fractal.
            freema dyson is a great scientist that pointed the faults of the model.

          • i know i know……..math is abstract —- and im not trying to get you to realize something you dont already know. its just wording.

            things extend (positively) in one direction or another — according to an old prof..

            the example in my class was that if you are at the equator, if you go 3 miles north, you are at +3(north) — if you go three miles south, you arent at -3 miles north, you are at +3 miles south.
            so if the level ground is the planar equivalent of the equator, +3 foot pile, +3ft hole.

            the point was further justified by pointing out that if the ground is 100 ft above sea level, your 3 ft hole is 97 ft above sea level.
            and…
            thats as far as i can take it, because tthen i asked him about new orleans lying below sea level……and i stumped him for a little while — he came back with some nonsense about
            +3 above and +3 below
            had this been today after reading this list, i would have pushed, but it was a few years back…..and i didnt care *that* much

          • emmy

            Haha, no no… My post referred to the tortoise example and Jamie's reply. Your right, anything that can be expressed as a negative integer can be expressed as a positive, it's just a matter of setting your conventions. but assigning negative values makes just as much sense as setting positive values. We're just not used to counting backwards, that's all.

          • true that

      • Arsnl

        @maggot: well you are right. In the physical world you have things that move in one direction and other things that move in the opposite direction. Things that turn in one direction and things that turn in another. To establish this correctly you need a coordinate system. Whats a coordinate system basically a line and an origin. In your case the origin is the state of your bank account when you open it. Then you add money to it, or you substract money(debt). Also another example would be the wheel of fortune. Lets say it all starts at your birth. Well for you the wheel of furtune is turning in a negative way. Thats what people would call “tough luck”

      • Arsnl

        Maggot what if you spread the dirt accros the surface of the earth (or send it in space). Will it still be a heap. Or will it transform in a black whole that absorbs turtles?

  • Arnaud

    The #3 paradox is much simpler…
    By saying "every creten is a liar", Epimenides only proves that there is at least one creten (not him) who is not a liar.
    That's because the opposite of "everyone is a liar" is not "everyone is truthful". The opposite actually is: "not everyone is a liar", that is "there is at least one who is not"…

    • Wuff

      For some reason my mind refuses to accept such a simple answer, but maybe you're right… There's no real flaw in your argumentation.

      This is a lie: All Cretans are liars.
      Then this is the truth: Not every Cretan is a liar.
      If not every Cretan is a liar, the first statement actually was a lie. No more paradox :D

    • Gav

      Although a classic tale, the more accurate paradox would be "I am lying", used by Mr Spock in the episode "I. Mudd" .

    • Spiderbait

      Totally agree. If I were to say that everyone on the Titanic was left-handed it would obviously be a lie (what conspiracy theorist would let that slip by him) but it wouldn't mean that everyone on the Titanic was right-handed either.

    • Mr.Europe

      There is more than one opposite in this sentence "every creten is a liar".
      One opposite is – None of cretens is a liar A.K.A Every creten is truthful.
      The other opposite is – Not all cretens are a liars.
      You see, we can choose, to what word we want the opposite to be. The first opposite was chosen to the word "liar". And the other opposite ( your opposite ) was chosen to the word "every".

      In my conclusion the two opposites are equal, so I dont know which one of them is true. Thats my idea…

  • GKLIYFL

    Great list, the best for a while!

  • Swark

    this is probably my favourite list on Listverse yet.
    i love paradoxes! yet if i start a paradoxical discussion with my friends, they usually disses me off for 'thinking too much' and just 'do what's easy and simple to understand'.
    especially those related to theology. they even say it's dangerous.
    for me, it is not about finding a definite answer. i am not seeking to be right.
    it is about thinking.

    • Spiderbait

      I think that if you don't think regularly you start to lose your ability to do so. That might sound stupid but think of all those that you hear about that seem to be incapable of simple logic, I think they simply do not bother to employ it.

  • enemy

    this is just mind boggling than what i use to believe. Empirically we are subject to unseen laws like laws of nature that we are still being awed by the mystery behind it. i think we should respect this laws because we are just speck in this universe.

  • sega

    The Buridan’s ass paradox, why not just combine the two stacks? problem solved.
    great thought provoking list. keep more lists like this and blogball's coming.

    • dammit, that was my solution, I was just checking if someone hadn't mentioned it yet…
      Good job..

    • Confused

      True but you cant exactly combine anthing. what if it was two roads or two houses

      • it becomes a different paradox, with different factors and different logical solutions

        anything that donkeys would eat, can be combined

        unless they eat water and oil —

  • enter

    the universe isnt infinite.

    • Gav

      mathematically or physically?

    • and how do you know it isn't infinite? have you been to the boundaries?

      • Ananda

        But it is proven that the universe is finite!!

  • Sarah

    I may just be being stupid, but I would have thought a lot of these paradoxes are obviously flawed.Number 3 as Arnaud has described – just because one man is incorrect in saying all Cretens are liars, does not therefore mean all Cretens have to be liars or truthful people; it is possible for some to be liars and some be truthful. Number 1 – logic would imply there cannot be both an immovable and unstoppable force on a collision course. Their unstoppability/immovability would become altered as soon as they meet and one would have to give way. For the hanging paradox (5), all that did was prove the judge was right in there was no way the prisoner could anticipate what day he would be hung – it was out of his power. He could only use his own logic but as soon as he had eliminated one day from possibility, it would always be a surprise to be hung on that day. For number 10, you could argue that a heap of sand needs to have so many grains in it before it is defined as a heap – it's just no one has specified what that number. If they did though, it would easily solve the problem.

    • Am not fully understanding all of the paradoxes but in answer to you response to no 5- its not so much about proving the judge right as it is that he had a logical solution to deciding which days he would not be executed on but in creating the solution he allowed the ability to be surprised to exist- as soon as he decided there was no day he could be executed, a hangman arriving would surprise him and therein lies the paradox.

      The grain of sand one works precisely on the fact that there is no number for a heap it is an abstract idea really. If you removed sand grain by grain there is no point at which it stops being a heap and therefore you have to continue until there is one grain of sand there as the term heap is not definitive.

      The liars one really does just depend upon your interpretation of it.

      I realy don't know enough about physic to comment on the collision one.

      • Sarah

        I see how the hangman story is a paradox, and it is clever, however it isn't an impossible dilemma – a prisoner could wake up every day expecting to be executed and not be surprised on the day he is, or like the one in the story, have his own system of logic and then be surprised when it does not follow his system. The story is just an example, not an impossible dilemma.

        With number 10, I don't think think it is a paradox. 'Heap' is defined as 'a group of things placed one on top of the other'. A group is defined as 'any number of entities consisting as a unit'. So a heap would be 'any number of entities consisting as a unit placed one on top of the other', which would require a minimum of two. So by definition, a heap could be classified as two items, so technically anything more than one grain of sand could be classified as a heap.

        I stand by the other two, they appear (to me at least) to be flawed.

        • It depends on your perspective as even if you class a heap as two things on top of one another, I wouldn't class two grains of sand as a heap.

          The Cretians really is just a case of opposites and is one that comes up time and again in different contexts the simplest versions I've just stolen from Thomjah's comment a couple below

          "This statement is not true."

          Or the two sentence version:
          A: "Sentence B is true."
          B: "Sentence A is false."

          • Sarah

            Surely the examples are slightly different.

            If a Creten says, "All Cretens are liars", is he lying? He has to be, because in order for his statement to be true, he would have to be a liar, which doesn't work. He could be lying of course, and every other Creten in Crete could be honest and that would work.

            The statement, "This statement is not true" is much more of a brain twister. Is it true or false? It doesn't appear to be either.

            I think the heap of sand puzzle does depend on your perspective, but if it's a subjective matter, can't the individual decide for themselves at what point the sand ceases to be a heap? I also wouldn't call 2 grains of sand a heap, but looking at exact definitions, it could technically be defined as that.

            Interesting list though, it does set the mind working!

          • Maggot

            It depends on your perspective as even if you class a heap as two things on top of one another, I wouldn't class two grains of sand as a heap.

            It doesn’t depend on your perspective. Just because you reject the known definition of “heap” by not classing two grains of sand piled one on top of the other as fitting the definition, doesn’t mean it is not a heap. By definition, it is, like it or not. The flaw in this paradox is in assuming that “heap” equates to quantity (or size), which it does not. Consider those same 1,000,000 grains of sand as instead being spread out over the entire surface of the earth. They are no longer in a heap, and yet you haven't removed any. A “heap” clearly means “position of an item in relation to the other(s) in the group”. It is not simply just the quantity of said item.

          • oliveralbq

            ladies and gentlemen, may i please have your attention.
            for today's performance, the role of "random contrarian" will be played by k.w.oliver
            –house lights go down–

            ok–from collins unabridged dictionary:
            "a collection of articles or mass of material gathered together in one place"

            from the dictionary of nouns:
            a pile or mass; a collection of things thrown together; a crowd; a large number.

            sarah's was from american heratige

            anyway, the known definition has changed, and you are now at the mercy of contradictary 'known' definitions, and we are back to 'heap' equating to quantity once again.
            you still cannot have them spread out arbitrarily across the earth, but you really cant have 3 stacked on top of each other either
            –unless youre cool with a mass or pile or collection consisting of 3
            collection i can see……
            3 pennies on top of each other isnt a heap or a pile — its a stack

          • You’re reaching, man. First, I am hard-pressed to find a dictionary definition of “heap” that does not include a reference to “one on top of another” or “pile”. That includes Collins (online), though I cannot find this so-called dictionary of nouns that you refer to, but even in your reference, it says “pile”.

            Second, in your stack of pennies example – “heap”,”pile”, and “stack” are all synonyms. http://thesaurus.com/browse/stack

            So no, the known definition has not changed and we are not back at equating “heap” with quantity, other than it having to comprise of “more than one” to be considered a heap, pile, or stack. Stack two grains of sand one on top of the other, and by definition, it’s a heap.

          • oliveralbq

            of course im reaching — stating concrete info isnt any fun…….sometimes.

            first — i did a poor job of referencing…..they were both direct quotes, but i fucked up both names.
            –collins english dictionary – complete and unabridged — "a collection of articles or mass of material gathered together in one place" is the direct quote — and by that definition, three grains sitting side by side is a heap.

            the other one is called:
            Dictionary of Collective Nouns and Group Terms. Copyright 2008 The Gale Group, Inc. All rights reserved. — that direct quote is the one about a collection or mass….etc. http://www.thefreedictionary.com/heap
            sarah's def from american heratige is there too.

            at any rate — i think this is the point where i tell you i dont necessarily think youre wrong — i was just pointing out another way of looking at it that i hadnt seen in the comments yet. now dr. pound would think you are wrong, but he's rapidly approaching senility anyway

          • now dr. pound would think you are wrong

            I would tell him to pound sand. A great big heap of it.

      • Gav

        #5 – The judge could have also done it on Saturday. Surprise! Really though, reverse logic doesn't always apply when moving forward.

        Grains of sand: when you remove a grain, place it in pile #2. Once pile #2 becomes a heap, you have, by your own definition, the number at which pile #1 ceases to become a heap.

        All Cretens ARE liars. About what, I have no idea.

  • Now concentrate……boobs……SH*T!

    Pa…ra…dox…para…dox…p…a…r…a…d…o…x……. Nevermind, where’s the list about bad popes.

  • Wuff

    Am I the only one caring about #2? ^^

    • no
      its actually one of the more interesting ones

      but i have to goto work in 5 min., and intensedebate, my motorola, and sprint are in a paradoxical love triangle, where — when one works, another always does, but not always the same one, and the third never does, but never for the same reason.

      see ya in 11 hours……..

  • thomjah

    Number 3 can be summed up in one single sentence:
    "This statement is not true."

    Or the two sentence version:
    A: "Sentence B is true."
    B: "Sentence A is false."

  • Bethany

    For #4: What if the barber were a woman?

    • Then she has hormonal issues and grows a tash.

    • Trish

      Hey Bethany: You just got the answer to an old riddle based on this paradox.

      It goes something like: There is a small where there is only one barber in the whole town. Furthmore there is a rule where all men must be clean shaven and no man can shave himself : only the barber can perform shaving duties. So if no one can shave himself and only the barber can perform shaves and yet the is clean shaven, who shaves the barber?

      The answer: No one, because the barber is a woman.

      Also, the way the paradox in worded in the post above makes it so that it is not a paradox anymore. It says that it "seems reasonable to imagine that the barber obeys the following rule: He shaves all and only those men in town who do not shave themselves." The paradox is phrased to say that men have a choice to either shave themselves or go to the barber: therefore the barber can simply shave himself and therefore avoid the paradox. the Paradox only comes into play the way I have phrased it.

  • I don't think number one IS a paradox at all.
    We know it cannot exist in reality but I also think it cannot exist hypothetically.

    Reason being is that it's nonsense, which isn't the same as a paradox.
    Consider these simultaneous equations:

    A + B = X
    A = 2B
    B = 2A

    It's nonsense.
    In the same way, the unmovable-object/unstoppable-force paradox is nonsense. The hypothetical existence of an unmovable object requires the non-existence of an unstoppable force. The reverse is also true. This make the two premises of the so-called paradox nonsense.
    Premise 1: The existence of an unmovable object (non-existence of an unstoppable force) .

    Premise one requires that there is no unstoppable force, but that happens to be premise two. Logically you get
    Premise 1 = Premise 1 + -Premise 2.
    Premise 2 = -Premise 1 + Premise 2.

    It's like trying to define a word by using the word you are defining in the definition itself. But times two for two premises.

    • Niek

      Actually your equations do have a solution. A = 0, B = 0. Therefor X = 0

  • Once again, Mathematicians take all the fun out of paradoxes. Great list, really, but number 6 was dumb. It wasn't a paradox, just a stupid, indecisive person (or ass). It didn't have any implicit contradictions or anything. But still, great list. I love paradoxes.

  • Louis

    I would have thought the Grandfather Paradox would have been on this list.
    If a man builds a time machine and goes back in time to kill his grandfather before he ever met his grandmother, what would happen? The grandparents would have never met, thus one of the man's parents is never born, thus he is never born. But if he is never born then he can never go back in time to kill his grandfather which means that one of his parents WILL be born, thus he will ALSO be born, which means he can go back in time and kill his grandfather.
    It just goes on and on forever.

    Another alternative is if the man goes back in time and prevents (through murder or any other way really) his past self to invent the time machine… What the actual hell happens? you figure it out.

    • Gav

      It creates a parallel timeline. Star Trek already said so, thus it must be fact.

      Really, if I go back and kill my grandfather, then that act MUST happen, regardless of what happens next. The only problem I have is when, in this new timeline, grandpa's grandson (not me) goes back in time and stops me from killing my/his grandfather. Would HE cease to exist?

    • Well, that's only if you believe that time exist as, essentially, one line. By that logic you would also be saying that there is no such thing as free will. Because the grandfather paradox is essentially saying that you can't change history because if you did go back in history and changed something, that change would have happened as part of history, so in which case you did not change history (there, another paradox).
      But if you think of time as a plane (or maybe as possibility tree-ish thing, where each node is your decision), then you could easily solve that paradox. You could logically go back in time to kill your grandfather and still exist, but the "grandfather" you killed wouldn't be your grandfather anymore, since for you to exist you would have been born to someone else.
      Of course, then there is the question of whether you are still "you" if you're not really "you" anymore, since you are technically not the same person as you were. Then you could go on to question what makes "you" "you", but then that would be a philosophical question of identity, which I don' t think anyone has an answer to, and is not really that relevant to the paradox.

    • The Grandfather Paradox actually PROVES that time travel is impossible. So if you rightfully remove this impossible premise from consideration, then you have no paradox.

      • Not quite, but that's only if you buy into the 'multiple timeline' theory.

        • 'multiple timeline' theory

          No such animal. You’ve been watching too many episodes of “Lost”.

    • Marvin

      The Grandfather Paradox isn't a paradox, really. Neither are most Time Travel paradoxes. The simple answer is all things that have happened will ALWAYS happen, even if one were to travel back in time. If they did travel back and try to change the past (unknowingly or not) then they will have just played their part in history as we know it. The other states that the moment any change in time occurs, it negates the future events causing that change. Thus, it is IMPOSSIBLE to change the past in anyway. The moment the grandson tries to kill the garndfather, he negates the events that lead up to it, and thus, it is an impossibility.

    • Marvin

      There is also the Time Loop Paradox. The example is, you lock yourself out of your house. Five minutes later, you are given a spare set of keys by yourself. You use them to open the door, where you see the original keys on your counter top and a time machine. You use the time machine to go back in time and give your past self the spare keys you just got, thus ending the loop. The Time Loop fails because it destroys the origin of the spare set of keys. Where did they come from? Out of thin air? Since it is a time loop, even IF you went back ten minutes and got the spare set made, you've destoryed that possibility with the time loop. And since there is no origin for the spare keys, the loop collapses on itself, thus failing. There is also the possibility that after a finite amount of times, the keys would wear down, through infinite trips. Once this happens, the loop is also destroyed.

      This is also known as the Time Machine (novel) Paradox. If the protagonist build a time machine to go back to save his dead wife and succeeded, then he would have no need to invent the time machine in the new reality. And thus, would have never gone back to save his wife from death.

    • Marvin

      Another less-popular theory states that since everything that was meant to happen has and will happen and that there are no such things as "alternate realities," that no matter what action you do, the timeline will find a way to fuix/heal itself back to the one known. Like, if you went back to kill baby Hitler, another person would become Hitler, regardless, because it is meant to happen. Or rather, if you DID manage to kill baby Hitler, you would have erased him from history and made him not exist. If he never existed, no one would ever have gone back to kill him (or had any memories of him to do such a thing). The fact that does exist states that it, in that sense, thereby cannot not exist. In fact, this destroys the entire premise of the movie Terminator. The fact that the Terminators exist in the future only proves that it is IMPOSSIBLE (as anyone in their existence knows) to kill them in the past or change past events.

      There is no such thing as a paradox that can't be solved. Most of it just involves a non-solution. Or rather, one part has to be wrong. Or even, the answer is simplier than the paradox implies.

      • Hrmmm

        id rather the split timeline/parellel universe theory
        cause it works for me

        because there fore if you did kill baby hitler
        then tht is changing the past therefore someone esle would become the baby you killed. but that person would suposedly become erased/someone else
        but who would that person there now be?
        that theory creats a paradox

  • Karl

    You forgot the Grandather Paradox and several other Time Travel Paradoxes….

  • joe r

    Number 10 – the heap of sand – is similar to a logic problem posed to us in Catholic high school, i.e., the Fallacy of the Beard.

    We all (presumably) can agree that one facial hair does not make up a beard. We all can agree that 10, 000 hairs do. At what point along the continuum bewtween 1 and 10,000 does it cease being a beard?

    To me the point of the exercise is simply that there are some things which do not lend themselves to numerical quantification.

    • Saki

      I'd rather say that the idea of a heap is a spacial idea, that is, defined by dimensions and not a quantifiable amount. If you say, for instance, that a 'heap' is at least 3 feet tall, than that is easily definable, and there is a limit to the definition.

    • John Herling

      It all depends on your definition of a heap. If even one grain of sand can rest on top of another, that can be defined as a heap. Only one grain of sand cannot be defined as a heap.

  • Nicole

    The 'interesting numbers' one made absolutely no sense to me – I've never heard of interesting or uninteresting numbers!

    • Arsnl

      Well i think it means interesting positive integers. Take 0 its interesting cuz if u add any number to 0 u get that number. 1 is interesting cuz if u multiply any number by 1 u get the same number. 2 is interesting cuz its the first prime number. 3 is interesting cuz the couple 2,3 is the only couple of prime numbers that are immediatly one after the other. 4 is interestin cuz you can write it as 2 2 and as 2*2. 5 is interesting cuz you can write it as a sum of all the primes before of it.
      Its a mathematical game. Ofcourse by the time you get to 1729 it gets a bit difficult to see why a number is special.
      For anyone interested id suggest the wikipedia article of Rahmanujan. He had quite a skill with these things.

  • Anti Emo

    This is your line of business isn’t it JFrater?

    Somebody please….please….explain in layman terms what is going on in no 8 and 7.

    And to the author how do you rate the paradox to give them a top 10? Cuz i dont think the unstoppable force paradox deserves number one.

    • frogmanster

      The Xeno's arrow is basically about breaking down time into fractions. Imagine that you fire an arrow while suspending an stationary arrow in the air. Now you imagine that you freeze time. Both arrows would remain perfectly still. But if the moving arrow is still in an instance of time, how can it be moving when time is flowly normally? And how would you tell the difference between the moving and non-moving arrow?

  • Beon

    I dont like this list because these arent really paradoxes, they are just word games constructed to fool the reader. Real paradoxes are for example The Monty Hall problem, where the scenario can be precisely defined, and the outcome is counter intuitive.

    11. Omnipotence doesnt exist in reality, its just a mental idea. It is easy to come up with similar silly ideas, but this doesnt make them paradoxes or interesting. It just proves that we have an imagination that goes beyond reality. “A white dot that turns black when you look at it. Which color is it?”, etc.

    10. The premise is wrong. Not all heaps of sand minus one grain is a heap of sand. Isnt this very easy to see?

    9. This is just a word game / poorly defined set of numbers. Define exactly what an interesting / non interesting number is first, and this paradox will not exist.

    8. Nothing is moving in an instant of time, so the premise is wrong.

    7. Easily proven using elementary Calculus. There is no paradox involved here, its just a word game.

    6. Must be the sillies word game Ive ever heard.

    5. At the time of sentence the day of hanging is unknown, not later as time passes. The prisoner misrepresents what the judge said.

    4. A simple word game, many similar can be constructed. This is just due to imprecise language, there is no paradox involved.

    3. Same as number 4.

    2. Same as number 4.

    1. Same as 11.

    • Harsha

      When unsure or unable to comprehend, just call it a silly word game!

    • Wow, you sure are smarter than 3000 years of philosophers. Congratulations.

      • alvhin

        hahaha

  • 7raul7

    7raul7 … ? isnt that me ? Yet I havent submitted this. Hey Jamie, help me out.

    • the plot thickens….

    • Dun DUN DUUUUUUNNNNN!!!! (sung to the tune of the "Dramatic Chipmunk" meme)

    • Team BANANA

      There are only two explanations to this :
      1) You were sleep-submitting this list
      OR
      2)This was submitted by your time-traveling future self

    • A new kind of trolling. List submission trolling. Instead of posting comments under the name JFrater that say "I'm a stinky ass wiener" followed by something anti-Semitic, the trolls now submit lists about paradox's under 7raul7's name… They are evolving.

      • I'm quite serious & I don't find anything funny with this shit. Either I know how my name got up there or they tell me that I submitted theis a long time ago & it wasn't published at that time.

    • classic.

      and on the list of paradoxes no less……

  • I think I should've waited till I'd been awake longer to read this list lol, my brain is all wonky now hehe.

  • stevezio

    My head hurts…thanks

  • Dan

    Wow my brain just exploded when I reading these Lol Awesome list

  • Spiderbait

    I applaud your reasoning and I hope that you will have a great feeling of superiority for the rest of the day.

  • Ricky

    Omnipotent being paradox.
    If you were to say that the o.b. can create an object so heavy they themselves cannot lift it, then you are stating that this action does not negate the fact that the o.b. is all-powerful.
    Let me rephrase this.
    If I can grow a hair that cannot be cut, can I no longer cut a hair?

  • frogmanster

    Xeno's arrow paradox is solved by Einstein's theory of relativity; where speed changes the colour and slowsdown time, warping the space around the arrow. Effectively, the solution to the problem lies not from viewing the arrow externally but from the arrow's viewpoint.

  • Anti Emo

    To people who keep saying their brain hurts or was injured in the process of reading this list please stop it. It has been done a lot of time and is no longer funny and it is very annoying.

  • Gav

    What if the stacks (or the food -vs-water) are 10 miles apart? With all things being equal, does it really matter?
    We endure this everyday in business; do we piss off and lose the customer in order to follow the boss' orders, thereby making our boss happy…but will it make our boss unhappy to lose that customer by following the boss' orders?

    • If the stacks are 10 miles apart the donkey doesn't see them and eats its owner instead.

  • i suppose — its semantically confusing which is all i meant in the first place, but i suppose you could argue it around to that conclusion

    • I like it when we have lists that we can discuss or even argue about without it becoming personal etc- its far more civilised.

      Did you decide the others you mentioned weren't as bad? I think sometimes with things like this you do just have to try and look at the from a different perspective to understand them.

      Now if anyone would care to explain the one with numbers I'd be most grateful- are natural numbers any tyoe of numbers in particular?

      • lists like this are fantastic.
        tyb's animal lists are fantastic, and blogball's ….well, shit…..all of his are fantastic.
        and people compliment jafe too….sometimes its more warranted than otther times, but in this case, having a list we can discuss is great……and a nice contrast to the previous lists — blogball's from yesterday, that is so rooted in facts and history, debating it isnt really an option — and the one before that, (apologies) where damn near everything can spark a high level discussion rooted in ethics and p.r.

        as for your other question — i just got home from work, and i dont want to be redundant and say somehting that someone said 7 hours ago, that i have not seen — let me catch up………………………………….

  • For the Omnipotence one, say the Omnipotent Being (OB) could not create a stone that it couldn't lift, because it could lift anything. How do you disprove that? I read that somewhere and I'm too tired and sick to think properly. Someone please disprove that.

  • Wait don't worry. Because if it can't create a stone that it can't lift it isn't omnipotent and yadda yadda yadda. Man. That was dumb of me.

  • Russ

    Euthalus could still not pay if he hired another lawyer to represent him in the lawsuit and the judge found the agreement to be legit. Since he still hasn't taken on a client (himself) and won (his lawyer won for him), he still wouldn't have to pay.

  • The Sanity Inspector

    "Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation.

  • Nikki

    Best list ever!

    Truly fascinating.

  • What about the Pinocchio paradox, wherein Pinocchio says, "My nose will grow now."
    His nose will only grow if he's lying, but if his nose grows, that means he was telling the truth, but if he tells the truth, his nose will not grow, and if his nose doesn't grow then that means he's lying etc.

    • Dang!

    • rumah makan padang

      Maybe, "the nose" take a while to think if this pino is lying or not,.and then the nose start growing (because he's lying),.and then the nose suddenly stops because he's telling the truth!

      yeah!(excuse my english)

      • Okay, this is how it ends:

        Pinocchio’s nose has a mind of its own, which is only capable of telling a lie from the truth. Pinocchio has no way to control his nose’s growth through his own mind, so his nose controls itself. But when Pinocchio said that his nose will grow, his nose will constantly think whether that statement was a lie or the truth. So, through repeated thinking without rest,

        Pinocchio’s nose will explode.(Or whatever happens to our brains when we think a lot without rest, to the point where it goes beyond the worst headache possible.)

        yeah!

    • Marvin

      Saying "My nose will grow now" is an assumption. And if he ever does eventually lie at least once in his lfie afterwards, then it will have turned out to be a truth, regardless of how he meant it. (But your definition of how soon "Now" is my change that.)

      And if he meant it as a lie, it doesn't matter because the real answer is that if it then DOES grow, it is the factual truth. Just not HIS truth. In other words, he was lying but just didn't know that that would happen, anyway, because he meant it as a lie. And if he meant it as a lie, he would only HAVE to assume it would not happen, otherwise he would know himself that he is telling the truth, and thus, negate it from growing. That doesn't make him a liar, it just makes him incorrect in that scenario. The results do not change his motives.

      And if he said it as a blank statement, not knowing either way, it would not grow, as a statement is not a lie. (Nor is it really a truth, but his nose only grows when he is lying.)

  • Wow fantastic stuff! Best work of 7Raul7 till now..

  • Love the list. A great way to get my brain thinking (and give it a headache j/k). I love to ponder stuff like this so I'm going to work on these for a while.
    Good work.

  • FlockO'Seagulls

    "This paradox seems to only work for completely logical beings and no living being is completely logical."

    Exactly! This is how the crew of the Enterprise was able to defeat Harry Mudd's androids.

  • Confused

    You forgot the 'Chicken or the egg' paradox

    Awesome list by the way

    • the mick

      i was thinking the same thing. one of the simplest paradoxes we are told about as kids.
      but what seems to be a paradox actually has a logical answer.

      • Confused

        i know, this should have been the bonus

        the world is simple, it's just people who complicate it.

        • the mick

          and of course, you do know the answer don't you?

          • Ken

            In case anybody is still wondering:
            http://newsfeed.time.com/2010/07/14/the-chicken-a

          • Harmony

            That works, I was just going to say that as stated it would be the egg because a chicken evolved from an egg-laying non-chicken at some point (wherever one decides to draw the chicken/non-chicken divide) but if you want to know if the chicken or the chicken's egg (as in "created by a chicken" ) came first, then obviously it would have to be the chicken, it's really just down to which question is being asked.

    • Not a paradox, and even as a child I knew this was a truly dumb question.

    • Marvin

      That's the easiest one of all! The egg was first laid by a non-chicken species, thus giving birth to the first chicken. The egg came first, in any scenario.

      • Hrmm

        but what if the species evovled via body changes and not reproducing
        therefore the chicken would be first
        so really there is no awnser

  • Bzzzzzztttt!!! My brain just short circuited…

    Love the heap of sand (The Sorites’) paradox…

    Btw, is "paradoxes" really a word? I'm conflicted.

    • Hmm. Thinking about it, I reckon the plural should be paradoces, which sounds like an ancient Greek warrior.

  • Also, Zeno was a goon. All of his paradoxes are just silly.

  • Also, most entertaining list, 7raul7!

  • I love the Achilles and the Tortoise Paradox. Broken down into points, it seems like Achilles could never feasibly reach the tortoise. I believe size plays a major part into this paradox. The strides of a larger "thing" would make up for the distance made by the smaller "thing", thus making the tortoise catchable. If you factor in speed, this will change everything. If I were a Struthiomimus, being sized up for Tyrannosaurus' lunch, the time it takes the big guy to get to where I just was, would give me ample enough time to make the same distance between two of us, that we originally had. Either way, this is a very perplexing thought. When I read the header, the first thing that popped into my brain, was the paradox that was provided in the Terminator movies. The machines simply would have had to been created in the future first. Here's one for you, which came first, the chicken or the egg?

    • the mick

      the chicken or the egg? dont you know the answer to this one?

    • the mick

      you know the answer to this one, don't you?

      • If the "egg or the chicken" paradox is SO simple to you "the mick", then please explain it to me in detail, because I'd love to hear it. Just remember, before you reply, that you're going to TRY and explain to me where a CIRCLE actually begins.

        • the mick

          NO CMC, the answer is simple and defined by MENSA. It goes like this:
          You have a chicken. Before this it was an egg. And it was a previous chicken that laid that egg. And that chicken was an egg before this. And so on. And so on. And you keep going back in time. hundreds of years. Thousands of years. MILLIONS of years. (fossils have been found and documented). At some point in history, the chicken we know today was something else. Related, sure, but something else nevertheless, just like we can trace the modern elephant to the prehistoric wooley mammoth. But we call it the wooley mammoth, not an elephant, although that is what it evolved to become. Just like the Sabre-toothed tiger has a modern decendant etc etc etc.. Back to the chicken. at some point in time it was not called a chicken, but what it LAID was still called an egg. So the answer is that the EGG came before the chicken.

    • Marvin

      If they were created in the future first (say, for example 2020), they kill the original origin by leaving the destroyed T-800 in the 80's, which inspires the creation of Skynet to create the Terminators back in the 80's now, instead of whatever original year they were originally created prior to the time travel, thus creating a time loop paradox of the Terminators creating themselves. And time loops fail most of the time due to the loss of the true origin (meaning the machines that were in 2020 first, built BEFORE they traveled through time. If you create a new origin for them in the 80's, you destroy the true origin, and thus, everything that preceeds it, even if that involves time travel.)

      In other words, nothing can create itself (without assistance from an original source). This only falls apart if you believe in alternate realities, which inself, has been proven to not be possible.

  • MHogan

    For the Omnipotence one, it is a matter of definition a rational. Asking an omnipitant being to make an object he can not move is no different then asking him to make a circle with corners. It's not that he is not powerful enough to make a circle with corners, it just doesn't make sense. It goes against tautology and isn't logical.

    • rumah makan padang

      nice one!
      i'm almost became atheist because of this one,..

  • I just read about the omnipotence paradox. Here's what I understand for the argument: since the being (say God) is omnipotent, then he has the ability to make himself unable to do something. So yes, he would be able to create a stone that he cannot lift because he makes himself unable to lift it. I guess the idea here is that when normally, we consider the idea of being "unable to do something", it is a passive state that we cannot control, whereas here, inability is an active state, so God actively makes himself unable to life the stone. I guess that sort of makes sense, once you wrap your mind around it.

    And I agree with Beon (not completely though) that a lot these paradoxes are just playing on the vagueness of words. For example, "heap" is a subjective idea. If I want to, I can define heap to be "comprising of more than 1 component", and you won't be able to logically argue that I am wrong since there is no definite definition for "heap". Then in this case, 2 grains of sand make a heap, but not 1 grain of sand, and that's when a heap turn into a "non-heap", paradox solved.

  • liim

    the answer to olber's paradox – if you extend an infinite line, it will eventually reach a star that may or may not be strong enough to be seen with the naked eye.

    Xeno's paradox – if we draw a difference between conscious and atomic motion, then we can divide it to a point in which your vibrating atoms already move the distance, and the constant halves are swiftly filled in with motion as the previous inertia travels through the systems.

    This could be proof for those guys OF molecular motion. like, it must exist or we couldn't move.

    • David Hopkins

      Assuming all lines of vision would be blocked by a star, even a star that couldn't be seen by the naked eye would still be surrounded by other stars everywhere we look.
      Imagine, hypothetically, ALL lines of sight are blocked by a star that, alone, is invisible to the naked eye. We still would not be able to see ANY night sky past the ongoing cover of stars. Therefore, we should still only see starlight.
      It's like why we can't see through a wall, even though every line of vision would be blocked by one molecule (which is, of course, invisible to the naked eye), or why we can't see any blue sky on a day where the sky is completely cloudy, yet we can't see an individual droplet of the cloud.

  • MHogan

    "Contradictions do not exist. Whenever you think you are facing a contradiction, check your premises. You will find that one of them is wrong."

    • T.J.

      thanks Ayn Rand, too bad your philosophy is so full of self righteousness it doesn't work in a fully global world

  • Gav

    11 (omnipotence-vs-stone) logic dictates since the premise of a stone is provable, the flaw lies in omnipotence which we can conclude does not exist. For its very existence contradicts itself.

    10 (heap) When pile #2 becomes a heap, then you have your answer.

    9 (uninteresting numbers) Purely subjective. We are led to believe that any singularity is 'interesting"? No two flecks of paint are the same so every fleck of drying paint is interesting?

    8 (arrow) Hullo?!!!! An "instant" does not exist. That's why when you blow up a picture to 4000x its original size (resolution constraints aside), it's all blurry.

    7 (Achilles & Tortoise) Step on the tortoise. You have to be somewhere where the tortoise's front feet have been. So step on the back and move on, Achilles.

    6 (dumb ass) With all things being equal, the choices become irrelevant. The only decision left is to decide or not decide.

    5 (Hangman) Reverse logic doesn't always work in forward motion.

    4 (Barber) This is not a physical limitation. I don't see a personal "rule" as a paradox. This one is just a plain dumb error in personal limitation. As a rule, I don't jump out of airplanes. But like shaving a beard, if circumstances demand it, I will.

    3 (Lying Cretens) Already solved by so many. The better one is "I am lying", to which I respond, "you are mistaken"

    2 (the court) The court would decide in favor of Euathlus because the terms of winning the first case had not been met. Now, if Euathlus learned well, he would hire a lawyer to represent him (or else he'd have a fool for a client). Thus, Euathlus still would not have won his first case and would still not have to pay.

    1 (unstoppable force) OK, this one fried my brain.

    Bonus (Olbers) We DO only see light in the night sky. It varies in shade, but it is still light. As the light from various sources continues to reach us, it will probably get brighter. Astrophysicists and Cosmologists have a problem with this?

    • skimitar

      On Olber's: you're partly right in that light from distance sources is stretched out due to redshift caused by the (accelerating) expansion of the Universe so that it is no longer visible to the eye.

      The other part of the solution is that the Universe is of finite age – stars didn't form until after the Big Bang and because space is big, there's lots of gaps through which we can see past stars to the moment when the Big Bang became transparent to electromagnetic radiation (which we see as the cosmic background microwave radiation – stretched to that wavelength by redshift).

      As well, the initial light from distant sources has not had time to reach us. And because the fabric of space expands at a speed faster than light (this does not contradict relativity, which talks of the speed of light as being a speed limit moving *within* space), light from some distant objects will never reach us.

      If anything, the Universe in billions of years will be a dimmer place as things move out of sight due to the expansion.

    • John Herling

      1 (unstoppable force) – The molecules of the irresistible force pass in between those of the immovable object.

    • Mark

      The mathematical concept of interesting and uninteresting numbers has nothing to do with subjectivity.

    • this is me

      11,9,4 Were talking theoretically here, not logically.
      3 Lying cretens – This isnt an answer, by saing that he`s wrong.
      1 Olbers – We DONT see light in the skyes. The light reaches our eyes, but we dont see it. Our eyes dont react to so weak light, or to light what varies in shade.

  • Foster

    As for number 5…I would chalk that up to bad logic rather then a paradox.

  • crazybandit

    The Achilles & Tortoise Paradox is so ridiculous.

    "Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise."

    Even if the tortoise did not have a headstart, the same could be argued. If Achilles passes through the same ground that the tortoise passes, then you can break that area into an infinite amount of points at which Achilles reaches "where the tortoise has already been." The problem is you can't break something down into infinite entities in a realistic situation. It is that simple.

    And mathematics does NOT contradict this paradox at all. You can solve it with algebra, geometry, calculus, and just about every other general field of mathematics.

    Just about every paradox is ridiculous. The paradox about the heap is not interesting at all. Of course it isn't defined by number. Words are born from abstract meanings, not mathematical meanings. One could argue that it is basically semantically ambiguous, but that is not the most accurate way of putting it.

    • T.J.

      in what way can you not break a distance into a infinite number of spaces in a real world situation? Even if you get down to half an atom there is still a 4th of an atom, or half an electron and so on. The mathematics represents the reality.

    • Beastly

      Terms like "heap" are considered in philosophy to be vague terms, such as short/tall, fat/thin hot/cold or even bald. They cannot be measured. They define a property of a relationship. Tall to an ant may be small to a human. Tall to a human may be small to a mountain – you get the idea. Thus the argument fails as there hasn't been made any specific definition of the term "heap". Even if there was, then another could be defined for another telling of the argument and so on, leading to an infinite number of definitions for the term heap, with a single grain of sand being just one of them.

  • Of course, all of these paradoxes make assumptions that may or may not be correct. Let us examine Buridan's Ass by way of example. In all likelihood, the ass will not, in fact, starve, but rather will eat from one or both stacks.

    Could an omnipotent being create an object so heavy that he could not move it? Of course, but the being is omnipotent and chooses not to do so, knowing that to do this is to bring his omnipotence into question.

    As for interesting numbers, what makes a number (an abstraction representing quantity) interesting? Are seven apples inherently more interesting than five apples? Are nine grains of sand less interesting than four grains of sand?

  • The barber has a beard. :P

    • John Herling

      Not unless he lives somewhere other than in the town, where all the men are clean-shaven.

  • Finnish man

    Well think about this:
    If 1/3 = 0,333333333…, then 3/3 = 3 x 0.333333333… = 0,999999999999… That means 1 and 0.999999999999… are the same number! :o

    • T.J.

      I love this, the difference is .000000….1 an impossible number since the zeros are infinite but the 1 completes it and makes it finite.

    • Brian

      Actually, they are. You can prove it to yourself by doing long division of, say, 3 divided by 3.

    • Mark

      Now that's just bad rounding…

  • billybob

    What exactly does Domo-kun have to do with #1?

  • Jake

    Oh, forgot the omnipotence one:

    11. Technically, the paradox is true. However, if the being can't lift the stone (which he can blame on the lack of exercise :-), he can still make it disappear, so he's still very powerful. I think the being should've dropped the stone on the person who thought of this paradox, or erase the whole planet, then bring it back just to make these people stop asking stupid questions :-).

    • dandan

      I think the being should've dropped the stone on the person who thought of this paradox, or erase the whole planet, then bring it back just to make these people stop asking stupid questions :-).

      hhahahha

  • Twisted_Love

    Oh I love this list, it's epic. I adore these brain-straining list, they're a real treat to my mind.

  • phynx

    I love this list.

  • Mikaela

    This list is fantastic!
    My linear algebra professor pulled out the Sorites' Paradox on us…
    It wasn't a very nice thing to do amongst the rest of the jibber-jabber he was throwing at us.
    He cackled.

  • The God paradox:

    Omnipotence is the power to do anything logically possible. Therefore God cannot create a stone that no one can left (assuming an omnipotent being exists) because it is logically impossible for that stone to exist.

    Just like God can't make a square-circle, or make two things occupy the same spatio-temporal place at the same time.

    Just because we can read the words of a sentence doesn't mean the sentence reflects possibility.

    Consider this: This sentence was not typed. > Obviously false, but you still read it.

    • You

      > This sentence was not typed
      Copy+Paste?
      Onscreen Keyboard?

    • Hassaan

      Nice one !

  • MouseintheHouseMI

    Getting from Point A to Point B requires you to cross an infinite number of mid-points.

    I always figured your speed can be measured in increments that are also infinite. Feet per second, inches per second, nanometers per second, micro-nanometers per second, and smaller and smaller to infinity.

    So, the # of mid-points to cross are infinte, but your speed is calculated infinitely, they balance each other out or cancle eachother out.

  • guinness13494

    I think if you acknowledge there's an Omnipotence being then you also acknowledge that he's evil. Most religions have a version of hell or some evil being that opposes the god. But if the god can do anything then why doesn't he kill the evil guy right now? Basically you have to acknowledge that the god is keeping the devil alive because he wants him alive to taunt and trick us for all our lives, and If god wants someone to taunt and trick us our entire lives then isn't he himself the "devil or evil entity?" That's the Logan Lyke paradox, if their exists any omnipotence being then he's the devil.

    • dope

      but if they devil is the ommipotence being than why doesnt he just turn the planet into hell??? because there is no devil and if an ommipotence being does exist than its in the form of no religion humans created. and why would an ommipotence being need a random animal(humans) on a random planet in the universe to worship itself? that would mean he needs a simple mortal being to survive making him not an ommipotence being.

    • lsuttercane

      The reason that God or o.b. would not kill the devil or whatnot, is because wihout his existence there would be no “free will”. God needs the devil, so people will have a choice….I think the term “sentient being” explains everything. We have to have free will, its the way we were designed, without free will we are no better than beasts, which have decision making capacities but are ruled by instinct, NOT free will.

  • Cant tell if I like it or hate it

  • For me, this is the heavy 12-grain bread of lists. I like 12-grain bread, but it's hard to eat a lot of it at once.

  • nimbus

    Obviously, the barber's wife shaves him. He may be the only male barber, but it doesn't say he's the only barber. It's only a paradox to men who only think with their testicles.

    • Perfect answer!

    • angry man

      Boo whoo!!!!!!!

  • Corey

    The only real paradox here is the omnipotence paradox, and that's only in philosophical debate about the existence of God. The rest of these are utterly stupid.

  • Surya

    Achilles and the tortoise paradox is no paradox at all. Here is how:

    To understand traveling through an infinite number of points let us consider the example of the motion of the minute hand of a clock. The minute hand, in order to reach the number 4 from the number 3 on the face of a clock, has to travel through an infinite number of points between those two numbers. But the minute hand has a finite speed (to be precise 360 degrees an hour). Now, how does an object with a finite speed travel past an infinite number of points? (I think this is the question of the Achilles paradox).
    The answer is simple. Although the minute hand of the clock has a finite speed in terms of "degrees per hour", it has an infinite speed in terms of "number of points per hour". The minute hand actually travels through infinite number of points per unit time. So it will have no problem passing through infinite number of points with an "infinite speed".
    So Achilles will have no problem catching up with the tortoise with an "infinite speed".

    • seb

      God one . .

    • T.J.

      you've kind of worked yourself into a corner. Does the clock hand have 2 speeds then? You are stating that a single object is traveling at 2 different speeds, or even that all things are traveling at infinite speed, regardless of the fact it is very clear that not all things travel at the same speed. Calling a set number of points doesn't change what they are, a sequence of points or locations, saying it is finite in on instance contradicts an infinite of the other. The are related, saying somehting is going 60 miles per hour is the same as that same distance in feet, and in inches, in fractions of an inch, and in infinitely smaller fractions of an inch, but everything clearly does not travel at infinite speed.

  • Ok A holes check this shit out. If I count by 1s forever that is infinity. If I count by 2s forever that is also infinity. Is one infinity bigger than the other? I'm sorry, I did not mean to blow your mind.

    • Arsnl

      There is no paradox at all. Mathematically two sets A&B have the same number of points if for every point in A you can find one and only point in B. So theres isnt anything magical about your statement. 100 years ago, Poincaré would have said you are a mad man.
      Ps: check out the infinite rooms hotel paradox. Its basically this: you have a hitel with infinetly many rooms 1,2,3…and they are all occupied. A new guest arrives. What do you do. Simple: you move guest 1 from room 1 to room 2, guest 2 from room 2 to room 3 and so on and so forth. And the one that just arrived you put him in room one. So for Infinity Hotel all rooms full doesnt mean you cant accept another visitor. German mathematician Hilbert came up with this example.

      • Ok I never said my thing was a paradox, it just blows minds. Also for every point in the one set there isn't one and only one point in the other. As for the hotel room your solution is dumb. I would just put the new guy in room infinity and one. Simple as hell.

      • Arsnl

        But yes you are. You are proving that the set 1,2,3,4… has the same number of elements as the set 2,4,6,8….
        And my solution isnt dumb. Those turists i can bet you are american. And as americans they are fat. So all the packing and moving to the next room will make the lose some fat.
        Ps: terribly sorry im replying to myself but im not at a computer right now.

        • Naw dude Maggot is right. Counting by 2s gets you there faster. As for the fat Americans comment, I am by far the sexiest one on this site. I am an American. Thus Americans are the sexiest people on earth. Pow blew your mind twice!

          • Idk I turn gay men straight… Er, wait…

    • If I count by 1s forever that is infinity. If I count by 2s forever that is also infinity. Is one infinity bigger than the other?

      No, but if you count by 2’s, you’ll get to infinity twice as fast.

      • Arsnl

        Infinity isnt a point so you cant “get there”.

        • No no no think about it… Maggot's right

          • the mick

            no, maggot is wrong. you have to study what infinity is to be able to draw a logical conclusion.
            you wont necessarily get to infinity any quicker.
            Think of this also: there are infinite numbers netween 1 and 2.
            start with 1. Then count by decimal points to 2. E.g. 1.000000000001, 1.00000000002 etc.
            the point being is that the decimal point, in terms of infinite numbers, can go to inifinity.

          • no, maggot is wrong. you have to study what infinity is to be able to draw a logical conclusion. you wont necessarily get to infinity any quicker.

            I’m never wrong. I’m right x infinity. Infinity + 1, even.

      • Arsnl

        Im sorry tits. I dont get these types of math jokes. You blew my mind with the sexiest american in a heap. But this i dont get :-(

  • William

    11) The Abrahamic God also had no beginning and no end. Logic alone can never explain that which requires faith.
    10) Oxford's dictionary:
    Heap: a mound or pile of a particular substance
    Mound: a raised mass of earth, stones , or other compacted material, sometimes created artificially for purposes of defense or burial
    Pile: a heap of things laid or lying one on top of another
    Conclusion: A heap of sand has nothing to do with how many grains there are but rather whether or not the collection of grains are noticeably higher than the surrounding material. Technically a kilogram of sand placed on a table would constitute a heap.

  • Moonbean

    So I've been fighting this headache all day… no joke…I know let me take a break and check out Listverse. Maybe they'll have The Top Ten Most Beautiful Beaches…or TyB will have the Ten Animals so Cute You Need Insulin to Look at Them… or Ten of the Most Soothing Lullabies…

    Ow…ouch…oooh…

    7Raul7, I. Hate. You. The. Most. My brain really does hurt, so I'll have to check back tomorrow. Great list though! (I think).

    • Moonbeam

      See I even spelled my name wrong. Sheesh… M O O N B E A M not B E A N!

  • William

    9) The set is uninteresting, by creating a subset of the lowest number it becomes interesting. That doesn't change the fact that the original set was uninteresting.
    8) Heisenberg's uncertainty principle: You cannot accurately measure both the speed and location of the arrow at the same time. If a camera takes a picture of the moving arrow at 1000 fps and the arrow is traveling 10m/sec then the arrow will still travel 1mm before the picture will be taken. Even stop motion cameras technically never actually record the specific position of the object but rather approximate the position at the point of capture unless they are moving slowly enough to capture the exact moment of potential energy.

  • William

    7) JFrater
    6) Philosophers are asses.
    5) Criminals are idiots, that's why their criminals. His logic was flawed.
    4) False premise. Also if you ran a lawn mowing business would you pay someone to mow your lawn?
    3) See 6.
    2) Anyone who represents himself has a fool for a client. No lawyer in his right mind would represent himself. Euathlus would have hired an attorney. If he lost, the payments would have to be made, if not it was his lawyer who lost the case not him.
    1) Exercises in logic involving impossible realities are unsolvable and usually don't pay very well either.
    0) The theory of an infinite and eternal static universe has been successfully disproven so the paradox no longer exists.

  • Spencer

    i think if an unstoppable force met an immovable object they'd go steady.

    • dandan

      so the "immovable object" win then?

  • Shade_2011

    Ah, this is like the first semester of law school all over again! Many of these are, as oliveralbq correctly pointed out, semantically misleading and drawing on logical faults. Something Socrates would have done! For example, the arrow paradox seems to me to be a falsehood. If one component of speed is time (and if I remember correctly, speed = distance/time?), then by forcing an inquiry based on "any one instant" or a "snapshot," then 'time' is artificially reduced to zero. No matter what algebra is used, a zero in this equation will make the answer also zero. Of course, I could have some flaws in my reasoning, as well- if so, anyone, please feel free to correct them!

  • This list is awesome. And did anyone besides me think for #1 "what if the force passed through the object?" like light through glass or water through a filter?

    • Swineflu

      you are supposed to assume that they are both solid objects, so for one to go through the other, there would have to be motion of the immovable object.

  • Colin

    That's Numberwang – Number 9 ;-)

  • Enjoyed the list very much will go over it again tommorrow, the brain is a wee bit slow right now, just had my nightcap and its off to bed

  • reefer

    wow man..that just blew my f-ing mind away

  • Since the Omnipotence paradox made it on here, why not also the Omniscient vs freewill paradox. The one where an all-knowing being – knowing the future as it knows the past – cannot exist alongside freewill and infact cannot have freewill itself.

    That is to say if you know the outcome of something you cannot change it – if you tried, you'd know ahead of time how you'd change it and how that change would affect the future – which you'd also know.

    Of just take the angle of the biblical god being described as omniscient and allegedly giving humans the gift of freewill.

    Although I'd hope you could put that paradox more succinctly

    • Ripzone777

      With freewill, humans are capable of setting thier lives onto many different pathways, which then lead onto many other pathways, like branches stemming from a tree. An Omniscient God knows the possibility and future of every path we could possibly take, therefore knowing the entire future, but giving us freewill in choosing our path.

      That's my interpretation of how this paradox is in fact possible :)

  • Boredsexratary

    My brain hurts :(

  • Dan

    Mathematics and logic are models, not concrete reality. In other words, paradoxes only exist because of faults in the model, not faults in reality. Though really, most of these are based on either impossibilities (the existence of things that do not exist, such as a perfectly rational being with no method for resolving competing equal priorities, or an unstoppable force) or on subtle flaws in logic and mathematics (treating time as discreet, for instance).

    #5 is a perfect example, in using a tricky little bit of logic it also contains it's undoing: Having proven by valid logical proof that he cannot be executed on a Friday, it would indeed come as a total surprise when the hangman knocked on his door the day he "knew" he was safe!

    • In other words, paradoxes only exist because of faults in the model, not faults in reality.

      That's not true. I once dated a model. Every time I tried to tell her that something was her fault, she would withold sex. Therefore, that model was never at fault. That was MY fucking reality.

    • shikha

      i thought of the same thing..!

  • Maggie

    I for one know what happens when an unstoppable force meets an immovable object.

    A.BIG.BOOM!!!!

    • I thought this too.

    • Greg

      every force has its equal and opposing force. Infinity minus infinity equals zero

      • Greg

        equals the tiniest boom in existence, but which would have the equal and opposite reaction of the biggest boom in existence. Can you say; creation?

  • fendabenda

    Somehow this list (and some of the commentary) made me think of Douglas Adams. Read his books, if you haven't already. BTW, my brain doesn't hurt, a zombie flesh eater ate it a long time ago… so now I'm just like.. happy happy joy joy!! :)

  • Astroboy

    11, and 1-5 are interesting. 6-10 are just plain stupid.

  • Lane

    Solution to #10:

    The omnipotence paradox operates on a misunderstanding of the definition of omnipotence. Omnipotence is NOT the ability to perform any conceivable action; omnipotence is simply unlimited power or “energy” — the ability to affect change.

    The true possibility or impossibility of a certain task is not determined by any level of power; that is, adding more and more power to a truly impossible task will not make it any more possible. Thus, we must consider the true possibility of creating a rock too heavy for an omnipotent being to lift.

    For a rock to be too heavy, we must conclude that such a rock could not be anything less than infinitely heavy or massive. For if said rock is finite in any way, then omnipotence immediately overrides it and it becomes completely manageable. However, an infinite rock is a logical contradiction and a true impossibility. Rocks are by very definition finite; an infinite rock is no longer truly a rock, but something else. It’s the same thing as a “married bachelor” or a “two-sided triangle”. The definitions of the objects have natural limitations, and breaching these limitations sacrifices the identity of the object. Thus, an infinitely heavy rock DOES NOT exist. It is a true impossibility.

    So no, an omnipotent being cannot create such a true impossibility. This does not stem from any particular weakness on the being’s part, but originates in the inherently limited nature of the object at hand. Omnipotence only operates in the realm of the possible and logical. Just because words can be strung together doesn’t make them any kind of tangible reality (can you smell “blue”?).

  • MAK

    I love this list! :D

  • TEX

    Several of these paradoxes have to do with looping logic – infinite self reference. An excellent book on this and interrelated subjects is Douglas Hofstadter’s “Gödel, Escher, Bach: An Eternal Golden Braid”
    If you found this list interesting – and you don’t have a headache – check it out – you’ll find it very, very interesting.

  • Cosmo312

    This is a great list, but number 1 was a slightly nerdy anti-climax. I was also expecting to see the Ship of Theseus paradox (i had to look up the official name) on here. If you have a broom, and replace the handle and brush, all the parts are different, so is is the same brush? and is a broom made from the discarded parts not the same brush?

    • That's funny, I always wondered about that, but used a band as example. Say, four musicians decide to start a band. After a while the drummer leaves and is replaced, then the bass player, then the singer. Now only the guitarist is original. After some time he quits and is also replaced by someone new. Now the band consists of 4 completely new members. Is it still the same band?

  • SNAKE!!! You created a time paradox!

    Fission Mailed

    • johnyyy

      no he did not
      he just changed the variable for an already accepted paradox.

  • joshua_the_samurai

    Brad Pit probably couldn't outrun a tortoise,

    • dandan

      hahahahaha

  • Interesting list.

    Olber's paradox isn't really too much of a paradox anymore, so I didn't bother reading it…

    But here's one:
    "Will your answer to this question not be yes?"

    • dandan

      "Will your answer to this question not be yes?"

      Maybe

  • value25

    #4. Maybe the barber can't grow facial hair.

    • David Hopkins

      Oh I see. The barber is actually an eight-year-old boy.

  • john doe
  • Will Trame

    Ouch. This list made my head hurt.

    Keep on truckin’, Listverse. Nothing like a series a conundrums with no possible or probable solution to short circuit the old grey matter.

  • mitchell

    i personally like the “pinnocio says his nose will grow” paradox myself.

  • One grain is not a "heap" of sand. It's a grain. A "heap" is nothing more than pile. Two grains of sand, one stack atop one another, would be a "stack". One grain of sand balanced on two grains would still be a stack. For a heap (a stable pile) to exist you need 4 grains of sand — three below and one on top, no balancing required.

    I've never considered problems that deal with semantics "paradoxes". If, by altering definitions, you can eliminate the paradox, then there never was a paradox. Just silly semantics.

  • Regarding the stupidity of #7:

    "…because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise."

    There are an infinite number of "points" between my nightstand and my bed, so based on that non-critically thinking illogic I should never be able to actually reach a glass of water during the night. There are also an infinite number of points between your upper and lower lip when your mouth is open, so, just going with goofy-logic, you should never be able to close your open mouth. Never mind that the infinite number of points are also proportionately infinitely small distance apart.

    • T.J.

      The logic isn't poor it's more about the conclusions you draw from it. The math is sound, but has non realistic conclusions, so we must reassess the situation.

  • mmm

    There are no paradoxes, only flaws in language.

  • Thisguy

    a truly amazing list :D

  • Breanna

    My brain!

    However, as to number six, if an animal is starving to death and there is food on either side of him, he will make a choice of his own accord in order to survive. He will go to one side and then, likely, to the other.

  • T.J.

    List should have had the 2/3 + 1/3 paradox,

    2/3 + 1/3 = 3 / 3 = 1

    1/3 = .33 (repeating forever)
    2/3 = .66 (repeating forever)
    therefore
    3/3 = .99 (repeating forever) = 1, where as we have a number that cannot be logically represented missing from the equation, .00 (repeating forever) followed by a 1, the number itself is a paradox, as we need a number after the infinite

    • the mick

      the thirds you are refering to add up to a whole number AT INFINITY.
      if that does not help you then telling you that Einstein proved that parallel lines meet at infinity is surely gonna blow your mind !!

      • SwineFlu

        the number .oo (infinitely repeating) 1 is possible, you just have your idea of infinity mixed up. Infinity means that for every possible number of zeros and then a one, you can always add one more 0. Infinity represents growth, not a number. That's why you can have a shape with an infinite number of sides.

    • johnny

      thats also another name for
      0.9999…=1
      if 0.333333…+0.66666666=1
      then 0.99999…. = 1

  • ouiareborg

    A list for trying to sound/Look smart…sad

  • some of them are quite silly and everyone can make it's own paradox. some of them have really easy solutions. there are other examples of really wicked paradoxes.

  • Ozhan

    #3 Epimenides’ Paradox
    " … if all Cretens are liars, he is also one, & if he is a liar, then all Cretens are truthful … "

    No, if he lied about all Cretens being a liar it only means there can be a number of truthfull man among them. It doesnt automaticly make *all* Cretens are truthful.

    • Ozhan

      Just like " Arnaud " said 22 hours before me :)

  • Kiroux

    Ugh! I'm probably going to sound like someone who doesn't understand the logic and therefore complains but … these types of arguments and round circle jibber jabber are exactly why I stopped taking philosophy as a subject. Most of these paradoxes are very easy to "fix" by using pure common sense or seeing that it is not a paradox to begin with. And these paradoxes are mostly created simply because the person has too much time on their hands and wants to appear somewhat intelligent to others.
    What the hell are interesting and uninteresting numbers? Numbers are only seen as interesting when the person in question finds them interesting. To someone who is not particularly drawn to mathematics or the like won't find any numbers interesting or otherwise.
    The donkey / ass paradox is also a load of bollocks. It doesn't matter which stack the donkey starts to eat since they are both of equal value. The only time it will matter is if the other stack magically disappears once the donkey decides to eat one or the other and leaves the animal wondering whether it has made the right choice. And thereby leaving it in the eternal purgatory of "what if…" (sarcasm)

  • Tom

    "If the unstoppable force met the immovable object, it would simply go around, that is what it means to be unstoppable."

    Thomas Murfitt

    Came up with that after being asked a question in gest when discussing martial arts philosphy. If you take the word unstoppable to be literal, and the word immovable to be literal, and apply to it principles of combat quoted from the earliest kung fu masters, there is no paradox, the unstoppable does not need to move the immovable when they meet. it simply needs to not be stopped. it does this by going around. this is the kind of water vs rock, soft vs hard thinking which makes up many martial systems and philosophies.

    If we replace the unstoppable with the irrestistable, then this either changes the parameters of the question (ie: they are two different properties) or it does not (they are two words for the same property).

  • dandan

    nice argument

  • Mark

    Is the answer to number one an unexplainable event?

  • Something occurred to me about the Achilles & the tortoise paradox, but not sure whether it's correct. The conclusion would only be sound if you consider two dots (conceptial dots, with no volume, no size, no shape etc) that are constantly moving at different, but constant speeds. Then yes, the distance between the two dots would become infinitely small but the faster dot would never catch up with the slower dot.
    But human being (and tortoise) do not move in a constant motion. We walk/run by taking a step, having a pause, however temporary (or in the case of the tortoise, a really long pause), before taking the next step. So essentially our movement is move, pause, move, pause etc. rather than one smooth movement. So it's perfectly logical for Achilles to catch up and overtake the tortoise, since it is possible for Achilles to move to a point before the tortoise has moved away from it.

  • Avaquizzer

    I had thought, for sure, that the Paradox of the Hilbert Hotel would be present in this article. And, perhaps for those with a little more mathematical understanding, the Banach-Tarsky Paradox.

  • Muscarius

    I studied Logic at university and several of this entries were analyzed during 1st lesson. There is nothing twisting in most of them.

  • Jose

    All I have to say is, the following statement is true: the prior statement is false.

  • #8 For each "snapshot" of time the arrow will occupy a different position, which proves thats in motion.

  • Pugiron

    LOl every one of these is false, either by misleading wording, incorect wording, or being totally fictional. there is nothing omnipotent, but if there were, the ability to create a weaknes in itself would not compel it to do so. A donkey would not be able to measyre a bale of hay other than to recognize there is enough there to eat and would not agonize of such a choice. Achilles would reach the points the tortise had been to faster than the tortise had reached them and catch up. Nothign is funnier than people of average intelligence trying to sound smarter than they are.

  • Joe blackk

    Ahhhhhh! My brain fuckin hurts! But as far as the “hanging prisoner” I don’t think it could ever be a surprise because he could be ready come noon everyday therefore it would never be a surprise…… ????? Yeah? No?

  • SAS

    No Russel's Paradox???

  • Lifeschool

    Hi there,

    Great list 7raul7 – even if you can’t remember writing it. :) Perhaps JF had a hand in some of these descriptions too – as some have mentioned already – I guess he loves this kinda thing. And so do I!

    #11 – I’ve read this over a few times and I think I get it. Of course the argument is limited itself be third-dimentional thinking (which is absolutely understandable given the author is of this physical realm and not, perhaps, an omnipotent presence observing itself). It may be easier to understand this by looking at the fifth dimention; where all ‘reality’ is basically all energy. We are dealing with kinetics and potentials – or as I like to think of it – unbound possibility. This ‘Omnipresence’ works beyond the imagination; so even if you can imagine ‘limits’ there certainly arn’t any in actuality. This ‘God’ could lift a whole planet or even a universe – because the planet and universe IS God – it’s all the same stuff (even though ‘lifting’ is also a 3rd-d concept and doesn’t exist beyond the 4th-d). On the 5th-d, ‘everything’, ‘something’ and ‘anything’, and ‘nothing’ all multi-cyclicly pop in and out of ‘existence’ – ‘everywhere’ and ALL at the same ‘time’; a bit like the static you may see on a de-tuned TV channel.

    #10 – I don’t get this paradox – where’s the duality? One grain of sand could be called a ‘heap’ because the grain itself is a ‘heap’ of layers, or a ‘heap’ of atoms, or a heap of ‘potential’. Alternatively, words used to describe anything are in themselves limited, and restrictive at best. Heap, stack, bunch, pile, – are all trying to describe something which is without description – at best it’s a work of art – at most simple it is what it IS. Even the word ‘sand’ fails to describe all this ‘IS’ness in the first place. On the 5th-d there is no ‘sand’ in as much as it’s all the same thing. On the 6th-d, there never was anything there to begin with.

    #9 – Some may find even considerably interesting numbers very uninteresting. I hate numbers personally; they’re all uninteresting to me (and that doesn’t make that fact universally interesting either). Numbers were artificially created by Man to try to fathom the workings of existence. They only ‘work’ up to the 4th-d; they ‘break’ in the 5th-d because of IPP – infinite potential possibility (e.g. when a 5 behaves like a 4, but looks like a 7, a 5, a 4 and a 0 all at the same time), – and beyond that ‘numbers’ never existed in the first place.

    #8 – It’s perhaps a bit like saying: photos/snapshots of instants do not move, therefore you cannot show movement in a photo/snapshot/instant. Even if you scalled down the ‘moments’ to untra-slow time, the object would still not appear to move because of the way it is being sampled for observation. Beyond the 4th-d, there IS no movement – that’s just another one of our cute little 3rd-d concepts – just like ‘time’ itself doesn’t exist beyond the 4th-d. From one perspecive, all 5th-d existence is happening simultaniously (which is potential rather than movement). So while the arrow is closer in reality to being completely stationary (the sub-atomic reality never moves), it is really only our brain which interpretes our hologramatical universe in this way. For example, my mind can imagine all kinds of things which my brain interprets as ‘movement’ while in actuality this physical form, this brain, and those aspects of the ‘mind’ haven’t actually moved a millimeter. But that’s how the brain sees it. In the 5th, things co-exist. In the 6th, things never existed. Another example; if I were to sit inside a car it may appear that I have ‘moved’ to my destination; while in actuality my arse has not moved an inch off that seat – I haven’t moved at all…

    #7 – I have to say… JF nails this with his ad-lib at the end. Nice one.

    #6 – Of course ass’s don’t really ‘ponder’, they just get on with it. They choose without choice. But that’s not to tackle this paradox. ‘What choice is there when there is no choice at all?’ Really the ass is stuck between doing something, anything, or doing nothing – all at the same time (does this sound familiar?) – and can’t decide. One option would be to avoid the senerio and move on. Another would be to choose ‘everything’: and if you leave an ass alone in a barn overnight – with food and water – the chances are that you would find the ass HAS eaten and drunk everything when you return. In the 5th-d, choice is an illusion. (e.g… Do you choose Chocolate ice-cream or Strawberry ice-cream? They are both ice-cream, they are both energy, they are both the same, there is no choice.) … and on the 6th-d, there never was a choice (e.g the ‘ice-cream’ never existed).

    #5 – ..so this prisoner is sitting there on a Wednesday morning thinking… “Well, it can’t a Friday, so if they don’t hang me today then it MUST be tomorrow. If they don’t hang me today I’ll KNOW it is tomorrow – so they can’t do that because I’ll know. So the only way would be to hang me today. So it’s Today!” So why did the story say the Wednesday hanging was such a surprise to this guy??

    #4 – The barber gets someone who shaves themselves to also shave HIM too.

    #3 – The term ‘all cretians are liars’ is itself a lie. If he believed he was telling the truth; he was actually lying to himself. Therefore he was a liar too.

    #2 – Double standards and retoric. The student would end up paying out money – unless a ‘win’ (by the student) in the court house also made sure that all previous bargains and bets were ruled invalid and unbinding. Otherwise the teacher would get the money.

    #1 – The postulation of a possible reality leads me to say the irresistable force would ultimately end up moving through the unmovable object. Secondly, if the irresistable force was a bullet, and the unmovable object was a solid block of titanium, then one of three things happens, deflection, absorbtion or explosion. The most likely is deflection – as most irresistable objects would bounce off unmovable ones, and simply go off in another direction.

    Bonus – I don’t quite ‘get’ this one. Not every single angle down to the nearest micron would end up with a star on the end of it, and if it did, those bodies would be so far away (and other debris would get in the way) so that the light would bearly be visible at all. Anyway, ‘space’ is only seen as ‘black’ with our 3rd-d eyes and perceptions. It’s a bit like how water looks clear in isolation but blue in consentration, or black in consentration without light. Water is neither clear, nor blue, nor black, but infused with an unlimited array of things we may suggest are ‘colours’ (95% of which lie beyond our pathetic visual spectrum), making the ‘blue’ or ‘black’ concept redundant. Science reckons ‘space’ to be a creamy kinda ‘tope’ colour (of itself), but again that’s just our eyes talking. It’s all relative on the 5th, and there is no such thing as colour by the time you get to the 6th dimentional perspective.

    Bonus Bonus: What came first, the chicken or the egg? Well, science says the nearest relative to the chicken is actually upstanding reptiles like the T-rex! So that’s what they think happened to the dinos – they just got smaller and all their teeth fell out. So lets settle the paradox. What came first? Before chickens with eggs we had reptiles with eggs, and before that we had amphibians with eggs, and before that we had fish with eggs, and before that we had mollusks (sp?) with eggs, and before that we had self dividing and replicating cells, and before that there was nothing & everything (because all of nothing is ‘everything’). So that’s an answer: nothing and everything came before the chicken AND the egg.

    Sweet dreams!

    • Mark

      "…They [numbers] only 'work' up to the 4th-d; they 'break' in the 5th-d…"

      Well, it's good that they're so useful here in the 3rd-d to provide us with all this useful technology, isn't it? :P

  • Mis

    #7: There's no paradox here. The distance between the starting point of the tortoise and the point where Achilles will catch it is exactly 11,1111…. (infinite number of 1's) feet. Until that point, it's true that the tortoise will be the first. sum[k=0..infinity](10^k) doesn't equal infinity, only 11,111… Thus the argument is only valid for that distance.

  • Mis

    sum[k=0..infinity](10^(1-k)), so 10+1+0,1+0,01+… correctly

  • Durr

    Good list, I enjoyed it- except for one thing that bothered me.
    “all Cretens are liars, he is also one, & if he is a liar, then all Cretens are truthful.”

    This is just stupid. If he is a liar then the statement that “all Cretens are liars” doesn’t mean all Cretens are truthful, it means that *not all* Cretens are liars. He can still be a liar.

  • Anaughtybear

    "So the problem with this paradox is that it is applying mathematical rules to a non-mathematical situation. This makes it invalid."

    This is otherwise known as having your head up your ass. Most of these can be either solved or simply dismissed by using common sense.

    10: There is no god, or it's a misconception that god is omnipotent. The bible is not known for historical accuracy.
    9: This is the same as the argument about what consists of a "few" items. You know what a heap of sand looks like. You don't need anyone to tell you that one grain isn't it.
    8: Yeah… it doesn't work like that.
    7: Ditto #8
    6: There is obviously no situation where an animal would starve itself to death. Send that one to Mythbusters and see how it works out for you.
    5. This guy must be Polish.
    4: This is just stupid and purposefully argumentative. He shaves himself because he's the only barber and a man. That's all you need to know. Quit bitchin'.
    3: Again, just being argumentative for the hell of it.
    2: Oh god, I so don't care anymore, but it's probable that the original agreement is ended and that it purpose of the new case.
    1: You solved that one in the description. So, why include it at all?
    Bonus: You know about sciency stuff, right. Like particles in the atmosphere that block light and all that? Okay then. Otherwise, we would all be blind from all light in the universe hitting us at all times.

    You could sit all day and make up more examples, or just accept that there are aspects of science we don't understand yet, and there are others that don't matter. In fact, some of the examples make up arbitrary rules to facilitate an argument. You might as well think about something useful instead. Cancer isn't solving itself. And yes, I realize that it's all about the philosophical pondering of the subject. I am making a separate argument for those philosophers to stop being such dumb asses.

    • Mark

      For all the haughtiness of that comment you still managed to mis-number all of your "solutions."

  • Michael Glenn

    The unstoppable force stops, and the unmovable object moves.

  • I have no name

    After reviewing this whole article, I have concluded that paradoxes only arise when morons fail to accurately describe the situations which they involve.

  • Anoonimoose

    I seriously have not loved a list as much as this one. I bookmarked it and will read it again. Thanks!

  • nameornickame

    @3000smiles, I reached that conclusion too. I think it also applies to the two dots.It would be impossible to pinpoint the point where one passed the other because the more and more accurately you measure their measurements, the less and less difference every “step” makes.

    Eventually you have to settle on a level of accuracy (in the footrace case, one step), and every movement within that level has to be ignored. So the exact position and velocity can’t be known at the same time.

    So there exists a point where you either know where Achilles’ foot is, or how fast it’s moving, but not both. If you know exactly where his foot is, your level of accuracy is so high that moving at all has no meaning any more. Once moving has any definition, you’ve lost that level of perfect accuracy.

    Maybe it’s possible for an infinitely small part of Achilles’ foot to be in two places at the same time! Interestingly enough, if this were the case, it would solve the paradox.

    As for the others… I find that listening to other people’s answers is every bit as enlightening as attempting to answer them yourself. Maybe even more so.

    I’m really disappointed the Monty Hall problem and Newcomb’s problem didn’t make the list :(

  • Are these "true" paradoxes? I thought a paradox was based purely on situation, not in wordplay..? Also, for the record, I used to come to this site all the time. But now it's so slow and clunky with all the crappy add-ons (I guess), I can barely stand to even read the lists!

  • Gav

    if an unstoppable force met an immovable object, it usually ends up in divorce court

  • macph

    my brain went for a good jog today thanks to this list. ;)

  • Chris

    JFrater, your explanation is entirely wrong.

    The paradox works physically. It's just that an infinite sum can converge to a finite value. The mathematics is being correctly applied to a physical situation. It's the non-mathematical analysis which is faulty.

  • I have one.
    Let's say I'm not normal. Maybe because I eat cupcakes with ketchup on top. Well, then i would be considered not-normal by society, but if everyone around be started eating cupcakes with ketchup on them, this would be considered normal, so those who eats cupcakes without ketchup on them would be the not-normal ones.

    This is what happens to independence. If everyone is independent, they are part of a group of independent people, making them part of a dependent society once again, so they would not be independent anymore. ^^ See?

  • Sorry for the confusion guys. My list after all but one that I sent nearly (or roughly) a year ago. No wonder I didn't immediately realize it.

  • The Bonus is actually is coolest item. It's also absolutely false.
    To say that "from the earth the sight line will end at the surface of a star" is just absurd! At what point did humans lose the ability to recognize darkness? When I look up at the night sky, I see the milky way. That is the "positive" space in my vision. There is also a great deal of blackness in the sky around, and apparently beyond, the milky way. That blackness is the "negative" space in my vision. Everyone recognizes both positive and negative space. Some may just be more aware of it than others, but no one would say that their vision stops at the last light they see.
    As to numbers? There are, indeed, no uninteresting numbers.
    I quite liked the pile of sand paradox. I liked it for a very practical reason. Last weekend I made a large Pavlova. The meringue called for 13 oz. of superfine sugar to be added to the egg whites teaspoon by teaspoon while beating.
    Do you have any idea how long it takes to make a dent in 13 oz. of superfine sugar by the teaspoonful?
    A very long time.
    The Pavlova was a great success, so it was worth all the effort. I LOVE Pavlova!

  • Yhovany

    Is it just me or do these all feel like flawed arguments. This line of reasoning only works if your treating the world like a math problem with no variable involved. Every one of these arguments can be destroyed in seconds. They all sound like a stoner sitting around going "DUDE. what if…Blah blah blah".

    So it is possible to say any idiot can figure out these paradoxes there fore they arent paradoxes and if they are paradoxes then idiots don't exist.

  • nice list.

  • darren

    * The sound of one hand clapping

    * If a tree falls in the forest and no one is there to hear it, does it still make a noise.

    hehe

    • David Hopkins

      How about, if a tree falls in a forest, and one person that was not you was around to hear it, did it make a noise?

      This scenario about the tree falling sounds about as absurd as saying that it would be victimless to shoplift if nobody, but you, knew the theft occurred, since no one would have any hard feelings. It's obviously still a wrong thing to do.

  • MmmHmm

    11 brain twisting paradoxes? Gimme a break! none of them was anywhere near a paradox

  • teh yoshi

    I was never good at these paradoxes, so I have little to offer.
    #3 – Epimenides was telling what he perceives to himself as the truth, regardless of his claim being correct or not. He wasn't lying, and of course had no intention of it. If someone believed they spotted Bigfoot, when in fact it wasn't Bigfoot, they'll still say Bigfoot exists, and they aren't purposefully lying with these claims (oh, they'll tell you about it!). To lie is to make a false statement with deliberate intent.
    However, if it so happens that Epimenides purposefully lied by calling all Cretans liars, then he truly believes at least some Cretans are honest, but does not imply ALL of them are.
    #4 – This sentence really threw me off: "It seems reasonable to imagine that the barber obeys the following rule…" Why does it seem reasonable? Maybe I'm an unreasonable man and I don't want to believe that's the case. Maybe I AM a reasonable man and believe it doesn't "seem" that way. Either way, if we say the rule is to be indeed true, and the barber is both male and the only barber in town (not ruling out that there can exist a female barber, but bear with me here), then it's also possible that he simply lives out of town, thereby making the rule null to himself. As an outsider, he can do whatever he pleases. If he shaves in his own home located outside of the town, there's no paradox.
    #5 – This sentence seals the deal: "Joyfully he retires to his cell confident that the hanging will not occur at all." It came to be a surprise to the prisoner simply because he felt full assured he WASN'T going to be hanged on either of those days. So to be hanged on any of those days will always be the opposite of what he expected, therefore surprised.
    #6 – If you want to be anal about it, we could also assume the ass (pun intended or what?) has a preference of being right- or left-hoofed, which can sway and cause imbalance to the equilibrium of the distances between the ass and the two identical haystacks, all depending on what foot it normally uses to take the first step directly forward. Either way, it's hungry, and there's food around it!

  • brian

    Fletcher needs some calculus. This paradox (#8) is a laymans confusion of trying to understand the difference between position, velocity, and acceleration. A little knowledge is a good thing.

  • John Herling

    The molecules of the irresistible force pass between those of the immovable object.

  • hank

    This is the dumbest list of paradox situations ever. Truly. The fact that they can all be proved as wrong actually removes them from being paradoxes. I particularly love all the singularities! Science words don't make folk no smarter 'n the restuvus.

  • Ralph Beatty

    The arrow paradox is a real world example Heisenberg's Uncertainty Principle. The principal posits that there are certain quantities that cannot be measured simultaneously with accuracy. If one tries to measure the speed of an object accurately, one cannot measure the object's location. Speed is defined as distance over time. If you measure something's location, it is by definition stationary. If you measure it's speed, it is moving and so the location is inaccurate. Strictly speaking, it isn't a paradox, it is a logic problem.

  • SwineFlu

    In number 11, I can think of two solutions:
    1. If the being is omnipotent then it should be able to defy logic and be able to satisfy both of the circumstances – that it cannot lift the stone and can lift the stone – in a way that is not logically comprehendable. If that answer does not satisfy you then here is another one:
    2. If the being is omnipotent then it should be able to separate the the reality into two realities, one in which it can, and one in which it cant lift the stone, which would satisfy both conditions.

    If neither of these solutions to the paradox sound reasonable to you, then there is a third possibility that you could accept:
    3. This paradox makes it impossible for omnipotent beings to exist (as if it wasn't already)

  • SwineFlu

    For #3 when he said "all cretins are liars, that means that all cretins have told at least one lie, which would make them liars. "All cretins are liars" does not specify which lie it would be. He could be a liar but still be telling the truth about that one thing.

  • Absintheus

    for the arrow paradox,,, i think that the question will lie mainly on the fact that since there are many points (or instants) in a line (as in linear time), we can never be certain of what happens from an instant to another,,, the main constriction here is the fact regarding the movement away from the instant since as it says, the movement is impossible as it is a snapshot,,, but we must recognize however that the motion occured before the snapshots of time,,, so the position change at every instant occured before you could limit the argument to "you cannot move away from the instant",,,

    for the achilles one,, i dont see the paradox here as well since what it does is slowly magnify the time until achilles reaches the tortoise,,, we are sure it will eventually reach the tortoise but the paradox "illusionizes" this by widening each infinitesimal moment where achilles is still in the process of reaching the tortoise and making it seem that it cannot,,, it's like counting from 1 to 10, but you just never reach 10, you just reach 9.9999 something and say that i seems impossible,,,

    for the hanging one,,, i think as well that there is no paradox,,, since if we have a premise that the prisoner thinks of it as that way,,, then everyday will be a surprise which validates the sentence,, the moment the prisoner accepts his conclusion, is the moment by which the paradox dissolves :P

    that's just my opinion :P

  • Jason

    Anybody heard of this one?

    The Crocodile Dilemma is an unsolvable problem in logic.[1] The premise states that a crocodile who has stolen a child promises the father that his son will be returned if and only if he can correctly predict what the crocodile will do.

    While the transaction is logically smooth (but unpredictable) if the father guesses that the child will be returned, a dilemma arises for both parties if he guesses that the child will not be returned. In the case that the crocodile decides to keep the child, he violates his terms: the father's prediction has been validated, and the child should be returned. However, in the case that the crocodile decides to give back the child, he still violates his terms, even if this decision is based on the previous result: the father's prediction has been falsified, and the child should not be returned. The question of what the crocodile should do is therefore paradoxical, and there is no justifiable solution.[2][3][4]

    The Crocodile Dilemma serves to expose some of the logical problems presented by metaknowledge. In this regard, it is similar in construction to the unexpected hanging paradox, which Richard Montague (1960) used to demonstrate that the following assumptions about knowledge are inconsistent when tested in combination:[2]

    (i) If ρ is known to be true, then ρ.

    (ii) It is known that (i).

    (iii) If ρ implies σ, and ρ is known to be true, then σ is also known to be true.

    It also bears similarities to the Liar paradox. Ancient Greek sources were the first to discuss the Crocodile Dilemma.[1]

  • jose

    The God paradox is quite well-answered here:
    http://www.jimmyakin.org/2010/03/theological-conn

    Best to all.

  • Lifeschool

    @ Christine E.K- “This is what happens to independence. If everyone is independent, they are part of a group of independent people, making them part of a dependent society once again, so they would not be independent anymore. ^^ See?”

    This is interesting as I regard myself as independent. One of my best friends is also. He grows his own food and basically operates life from his own home. Is he then among a group of independents? Yes, I suppose he is; although that would be a minority of the population. I suppose you could group a bunch of independents together – but then they don’t necessarily have to be ‘dependent’ on each other, or anything other than themselves, so they are still independents within any group. A similar group logic would be that the group ‘depends’ upon the fact that the group members are independent; but that’s just a limit of the classification method used. As soon as you/we try to put things into neat little boxes, those boxes bugger up the observation of the contents – like schrodinger’s cat.

    @ Darren “If a tree falls in the forest and no one is there to hear it, does it still make a noise?” – Logically, Yes, of course it does. Technically, No, a noise can only be called ‘a noise’ if it is heard. No hearing = no noise.

    @ Darren – The sound of one hand clapping is the sound you hear when you laugh at what a woman is wearing *SLAP!

    @ Jason – The next thing the Crocodile will do will be to consider the fathers response. If the father responds that this is what the crocodile will do then he always wins.

  • Wayne

    The problem with this list is that the top 10 are based on a singularly wild left field rule imposed on a situation that does not require it. The one about the barber — "it seems reasonable to imagine that the barber obeys the following rule" — what is that? Without that "rule" there would be no paradox — the rule exists solely for the purpose of creating the paradox. It's like saying: (Q) How does Kobe Bryant, down 5 points with less than a second left, win the game without anyone touching him or the ball? (A) New Rule: Any basket Kobe makes when down 5 points is worth 6 points. The "rule" is not valid, not anywhere close to reasonable and is there only to solve the wild "paradox." You prove this by having as your number one paradox a situation that is proven is invalid on every level of its presumptions and it's even admitted that it's only theoretical. I'd say the only real paradox is the lowest one on your list the "omnipotent" paradox.

  • Icalasari

    Here is how I define a heap, and I think it is reasonable: A heap is something with more than one piece/grain, and with each layer having at least one more piece/grain than the layer above

    This sets the minimum at three, but three does not mean it will be a heap. It could be a tower

  • keloidz

    ..nosebleed! <sniff>

  • I have come to truly hate this form of commenting.
    At first, it was just an annoyance which I thought I would become used to, and even like, enjoy maybe.
    Sadly, this is not the case.
    I can't find my own posts.
    I received an e.mail this a.m. of a post [IntenseDebate Notifications
    to me

    show details 6:19 AM (2 hours ago)

    keloidz commented on 11 Brain-Twisting Paradoxes – Listverse:

    ..nosebleed! <sniff>

    Go to comment]

    How on earth am I supposed to understand to what that is referring? Or is it just a random comment?
    My comment about the relative spaciousness of all things between atoms; that everything is more not that than there, is completely missing as far I can find…as was worded far more intelligently than above (I sort of fall short of the mark when I'm frustrated).

    Also, half the time I come to comments, there are no comments! There is a little pic of me and an arrow with the legend previous and next, but click on either and you are exactly where you are. Nowhere!

  • Jooe

    For the unstoppable object meets an irresitable force, wouldn’t the irresitable force move to the unmovable object

  • TheUltamate

    About the unstoppable force paradox:
    Let's play pretend for a while here, use our imaginations, and say we have one object that cannot, under any circumstances, be moved (without turning itself into a singularity), and another object that, under any circumstances, stop moving (without needing an infinite energy source). If these two objects were to smash into one another, assuming the impact was dead center, the irresistible object would simply rebound. While I'm not terribly well versed in physics, assuming the impact was completely elastic (let's add that little element to our imaginary land), there would be no net loss of energy, thus, the immovable object would not have moved, and the irresistible object would have never stopped.

    The Sorites' Paradox:
    This one is easy. All this one requires is a quick check to the nearest dictionary, which will define a heap as something along these lines: "a group of things placed, thrown, or lying one on another; pile." Thus, one object cannot be considered a heap as itself. Theoretically, you could break the grain of sand into a heap of atoms, which could be a heap of subatomic particles, which could be a heap of even smaller objects, etc, etc. Attempting to solve the paradox simply extends it.

    Olber's paradox:
    All this is is a astronomy question. If what we know about the universe is true, it is absolutely massive. Among that massiveness is a vast array of things that aren't stars: asteroids, planets, black holes, nebulæ, etc. The light from most stars will find itself blocked by whatever is floating about among the vast cosmos, and black holes will devour any light that gets close enough. To top it off, a star could be so far away from Earth we can't pick up the light that gets shot at us.
    Also to consider: we can see a rather limited spectrum. Some of that light may be outside our capabilities.

  • Joel

    These are my thoughts on each and every paradox.

    11) I'd start by saying omnipotence does not exist (but some believe God exists so whatever). To simplify it, think of it this way. Infinity is greater than any number in existance. Infinity is a number (it isn't, but stay with me). Therefore infinity must be greater than infinity.
    10) This isn't really a paradox. It is just pointing out the lack of technical and objective measurement for certain words.
    9) This is simply remedied by adding the stipulation that it is an interesting number in that it is the smallest number of the list of OTHERWISE uninteresting numbers (excluding it's interestingness due to it being on the list of uninteresting numbers.)
    8) To simplify: take a 3D object, say a box. Cut it in half. Cut each of the remaining rectangles parallel to the first cut. Repeat forever. Eventually you will have an infinite number of infinitly small squares. As you move along the original box, you pass over infinite number of infinitly small cross sections. Just like the arrow moves in an infinite number of time sections, each being infinitly small.
    7) A rephrasal of number 8, only a little more complicated.

    • Mark

      A number being interesting only because of one reason – despite the fact that without that reason it would be uninteresting – does not make it not not uninteresting. Your logic is very poor to non-existent.

  • Joel

    6) I wouldn't call this a paradox, this is a statement of fact (however confusing it is). I would first say the donkey would go for the first one it sees. A proponent of this paradox would have me assume he saw both at the same time. I would then say it would have a predisposition to going one way or the other due to past experiences. Again I would be told to neglect this. On and on this would go until there is literaly nothing upon which to base a desicions. Since any brain is a computer, stripping it of all means with which it would make a decision, it wouldn't be able to make one. However, this will never happen, there will always be a way for the brain to make a decision.
    5) really got me thinking. Firstly this is assuming that the exicutioner is completely logical, which humans aren't. Secondly this is working on the logic that if I haven't been hung up until this day I must be hung today, however, that is like saying wake up every day expecting to be hung, and you won't be hung, because you will be expecting it.

  • Joel

    4) This is merely a flawed assumption. The statement "He shaves all and only those men in town who do not shave themselves." isn't true, because he shaves himself. Nothing more, nothing less. It seems so much more complicated, because the assumption seems true, so it is accepted as fact, even when it is wrong.
    3) This is impossible because saying X always lies is impossible, no one always lies. If someone says I always lie, then it disproves the assumption that I always lie. Oh ho, you might say, that means he is telling the truth and therefore he always lies, creating a flaming doom-spiral of logical death. No, it just proves that sometimes he lies, and sometimes he tells the truth, not always lieing or always telling the truth. It creates a false dichotomy, where people assume he always tells the truth or always lies.

  • Joel

    2) Eauthlus is being sued because he is not trying to pay back Protagorus. All that Protagorus must prove to win is that Eauthlus is not TRYING to pay him back, him handing over the money due to a court ruling is not him TRYING to pay Protagorus back. If Eauthlus wins, then the court has decided that he is trying, and therefore he will only have to pay when he wins his first court case, which is right then and there. If Protagorus wins, the court has decided that Eauthlus isn’t trying, and should pay without winning a case, and he will probably have to double-up on the fees when he does win his first court case.
    1) I would think the unstoppable force will be re-directed, without stopping.
    BONUS) This assumes that no matter how far away you go, a star will always be visible to the naked eye. This is false. Get far enough away, and a star is no longer visible, making the night sky black.

    Sorry I had to break it into so many posts.

  • raj

    Most of these are linguistic paradoxes which means they are meaningless. Language serves as a medium through which ideas and thoughts can be shared to form a collective consciousness among humanity, and the signs and symbols, i.e. words, that make up those linguistic mediums do not possess meaning outside of both the context of which the collective agrees to apply such meaning and its relation to other agreed-upon symbols within its own linguistic parameters. The only flaw these paradoxes reveal is the inherent flaw intrinsic to all forms of language.

    • Your point is an excellent one and it ties in to what I wanted people to do with this list: find the flaws. I mentioned that in my opening paragraph.

  • theKhaled

    I really loved this list! Great work!

  • KokoClark

    The court paradox; the only ruling that would make sense and be fair, is if the judge states that both men agreed that Euathlus would not have to pay Protagoras until Euethlus won his first case. Therefore when Euathlus wins his first case( which just so happens to be with his teacher) he has to pay. There is no paradox, just silliness. Also, Protagoras would have no grounds to sue again because he will have gotten said money from the ruling in the first case and if the judgement is overturn than Protagoras would have to be paid twice for the same thing, which is unfair and unjust.

  • Jooe

    if an irresitable force met an unmovable object would the force move torwards the object?

  • Sam

    There cannot be an immovable object in a universe that has an unstoppable force or a irresistible force.
    It contradicts itself, one cannot exist if one is certain. If something is immovable, there cannot be a force that can move it.

  • Dionysus

    What I wrote beneath is true!

    What I wrote above is not true!

  • Dionysus

    Oh yeah. #11, mathematically is infinite – infinite. Just makes no sense

  • riley

    #4 he says he cant shave himself but it didnt say that there was no FEMALE barber inb that same town so she could shave him as it explicitly states there is one MALE barber leading to believe that there is a female

  • Victor

    The most Interesting Paradox in here is the Sorites one, because it shows the vague and 'undefined' terms we use today. For example, when is someone an adult? When he turns 18 years old. Okay, but does that mean that someone that is 17 years and 364 days old is less of an adult?

    If you go at 50km/hr in a school zone you are within the speed limit, but if you go at 51 km/hr you are going very fast… how? why?

  • SwineFlu

    For the unexpected hanging paradox, the problem is that his logic goes through the week backwards, but that's not the way he actually goes through it. If you go through the week forewards, there is no reason he can't get hung on monday

  • Olivier

    Guys, I haven't read any "answer" to the unstoppable force paradox. It's quite easy to be honest….
    Just imagine those forces could exist.. Let's imagine the immovable object as a middle age shield, and the unstopabble force as a sword. If you swinged the sword to the shield, the sword would just go trough the shield. The force didn't get stopped, and the shield didn't move. Easy as that.

    • SwineFlu

      The problem with that is that is that some particles of the shield would have to move to allow the shied to go through it

  • Mark

    The logic of your reply to number nine is flawed. An interesting number is one that has some characteristic or property that makes them notable or different to other numbers. Both one and Pi are interesting numbers. One because it's the smallest natural number and Pi because it's the ratio of a circle's diameter to its perimeter.

    If I gave you a set of numbers including only Pi and one, would they both be uninteresting? No, they would both still be interesting. Numbers don't wear shirts and are therefore not affected by different groupings :P

  • shakingandcrying

    wat?

  • Stacy

    The Barber Is A Girl, My Teacher Told Me This One.

  • superego

    #10 Depends on a lack of a formal definition of a heap: if a heap is defined as a conical mound of sand grains, then the point at which it is no longer a heap is when it no longer has that appearance which is subjective, on the other hand if a heap is defined as a set of sand grains (or a beard as a set of hairs) it really doesn't matter how many grains (or hairs) are in it, an empty set is still a set.

    #7 there is no paradox – the problem describes an algorithm to analyze a physical situation. Indeed the analysis itself executed in the way suggested in the "paradox" would require infinite steps. But analysis and reality are two different things.

    #6 both piles – its really a half-assed paradox. Or, the ass finds itself in a metastable state of being drawn by two equal and opposing forces – zero net force, but as soon as it is recoils from a random collision with an atom or photon, it now should find itself nearer to one of the piles and hence nonzero net force. Or, from the point of view of quantum mechanics, the ass is eating both piles until its wave function collapses to one of the piles at random when it is observed.

    #3 Is a paradox is created every time someone says "I am a liar"?

    One way to resolve this is that a "liar" is not someone who always lies, but someone who sometimes lies and sometimes tells the truth.

    But probably the intent here is to assume that if a statement is a lie then the opposite of a statement is true, in other words lie(A)=NOT A.

    So lets combine our "paradox": A=NOT A with a Boolean logic identity A= A AND A
    Substituting one of the A's, getting A=A AND NOT A, which just means A=False
    Or is it? muahahaha

    Bonus – Assuming also that the number of stars is also infinite, distributed randomly (and not making a giant sparkly "God wuz here" across the sky,) having an infinite lifetime or having an infinite amount of matter for building new ones somehow available throughout or matter constantly added/created, and no mechanism by which light would be absorbed, or for that matter that light is not quantized… then yes, it could get pretty bright.

  • R Cooke

    You kinda misstated Olber's Paradox, the paradox actually states that in a homogeneous and infinite universe we can map out shells of space i.e. hollow spheres of a given thickness and the number of stars/galaxies in each shell would be some constant (K) times the Surface area of a sphere 4*Pi*r^2 where r is the distance between the shell and the earth, now the light received at distance r from a star is some other constant q * 1/ r^2 so the light received from each shell is the number of stars * the light from each star so each shell gives off k*q*4*Pi* (r^2/r^2) since (r^2/r^2)=1 and all other values are constant then the earth receives the same amount of radiation from each shell and in an infinite universe there would be an infinite number of shells so the radiation received at earth would be a constant*infinity = infinity. This is not the case since although the universe is spatially infinite it is constrained in a temporal frame by it's age, i.e. since light travels at a finite speed and we can only see things that exist we cannot see anything from before the big bang meaning we cannot see anything at a distance greater than c*t where c is the speed of light and t is the age of the universe (around 14 billion years). This means there are a finite number of shells that contribute radiation to the area of space the earth is in hence the sky is dark. Interestingly enough this also re-enforces a relativistic view point that in arbitrary space time (such as what we exist in) each observer is the centre of their own universe and the universe will appear different to each observer, based on their velocity, acceleration and position in space time.

  • Sergio

    In the Achilles & the tortoise paradox, there's actually a clear answer:
    letas say thay this is Achilles: A; an this is the tortoise: T; and they are set like this in a field:
    A – – – – – – – – – -T; each line being 10 feet. In yhe time that Achiles runs those hundred feet, the tortoise only runs 10, our diagram continues like this:
    * – – – – – – – – – – A – T; the * being the Achilles' sstarting pint, and Achilles being on the tortoise's starting point; if achiles runs at 10 times the speed of the tortoise, our diagram continues like this:
    * – – – – – – – – – – – – A .T; being the . one footif Achilles keeps running, eventually he will overpase the tortoise, because if the tortoise keeps moving at 1/10 of Achille's speed, eventually, the distance between them would be so small, that it would be = 0, in wich case, Achilles would outrun the tortoise. People may see this as a paradox, because there will always be a space between Achiles and the tortoise, that's 1/10 of the length of the last space, but as we all know, an object moving faster at a continuous speed, will eventually outrun a slower one.

  • Hassaan

    Nice list !

    Apart from the Wannabe Paradoxes, though Not Paradoxes, yet in the Paradoxes list Paradox.

    Here's a Paradox that limits time travel :

    The Grandfather's Paradox:

    Suppose you use a time machine to travel 100 years into the past and you meet your grandfather who is still young. Now suppose you decide to shoot your grandfather for some reason, and he dies. If your grandfather was still young, never married, never had a child (your parent), then you never existed in the first place to time travel and kill your grandfather.

    • Roman

      If time travel were possible , I would not go back in time to see my grandfather, I would go back and slap Eve in the head. She is one of the reasons we are in the mess we are in. LOL

  • perfect

    hahaha… yeah, Philosophers are friggin' useless…

    • perfect

      and those who think otherwise just like to "appear" a wee bit more intelligent (if at all)

  • archangel

    I can fit an infinite number of decimals between 1 and 2 (i.e. 1.55555555555555555555555555555***, 1.55555555555555555555555555556***)… we can traverse from point 1 to point 2. We've just traversed an infinity…

  • HUgh

    For the bonus one, wouldnt it be solved by the fact what we see is not how the stars are currently? due to the speed of light, we see what the stars look like 4 million years ago, hence we are seeing only certain points, but eventually if you plot where every single star in the sky was and continue this until the end of the world, there would be no spot on that map where a star hasnt been or is….
    right?"

  • david

    #1 is easily solved:
    If we apply the unstoppable force tangentially to the immovable object, it will only spin. The object has not moved, and the force has not been stopped. The requirements of the paradox have been met.

    However, this introduces a new paradox: the immovable object is now spinning at the speed of light.

  • No 8 The Arrow Paradox. For an arrow in flight, in any instant of time, there is movement.
    Between the time the shutter of a camera has closed and when it opens again, the arrow would have moved. Just because we don't perceive it doesn't mean that there is no movement.

  • The Barbers Paradox – Is it reasonable to think that the chef of the only restaurant in town would not cook for himself when he only cooks for people in town who do not cook for themselves. I think this paradox is talking about the exception to the rule.

  • 2 The Paradox of the Court – Protagoras is right because he is the one who, in good faith, agreed to train Euathlus who seems very intelligent himself and appears, by his argument, to have exploited the "winning of the first case" condition,
    Protagoras is the one out of pocket and should be paid for his services.
    Ruling for the plaintiff :)

  • zark169

    Wow, almost all of these "paradoxes" are pretty lame. They either misapply logic/math/science, blatently ignore accepted facts, or assume certain things to be true that are end up looking really stupid under examination.

  • shikha

    for the 5 TH paradox…see if the prisonor through his arguments had concluded that none of the days will be a surprise so he wont be hanged anyday he wasn expectin the judge to knock on any day….since he was confident and not expecting wen the judge finally came he was surprised..!!..human nature..no paradox..!!!

  • Wilco

    The last one about the white sky is false, not true, based on NONSENSE.
    The sky is not white, because the stars are NOT infinite, not in our galaxy though, according to the big bang theory, there are stars as there are galaxies.
    So what we look at are stars, and the black between them is the edge of our galaxy, any other light will be diverted any way, because of the long distances, the light will bend here and there, and miss the earth.

    So there are two reasons why that is incorrect, because the other galaxies outside of our galaxy are further away from our galaxy, as stars are far away from each other, only in the same proportions. So the other galaxies are unimaginably far away, thus you can't see them, because light has it's limits too

  • Monsy Wilson

    Can God Be satan’s friend.
    Can he help satan.
    He can.

    But he didn’t. God have his own will.

    • Jay

      In the Book of Job, God and Satan do appear to be friends.

  • Colin

    Gav is correct about the bonus "paradox." We do, in fact, observe what is known in cosmology as the CMB, or "cosmic microwave background" (radiation). There are graphical representations of this in existence from very sensitive radio telescopes around the world, and you'll see that the entire night sky is indeed filled with "light" that just happens to be a) incredibly low intensity and b) outside the human-visual spectrum.

    • Jay

      Irrelevant. There should be VISUAL light everywhere.

  • Akamarured

    I found a flaw in paradox 3, you can easily correct me if i´m wrong i don´t mind
    The fact that Epimenides is lying when he says "All cretans are liars" doesn´t mean that, necessarily, every cretan tells the truth. This happens if you apply the logic,
    All cretans = X
    If one cretan is telling the truth, will epimedes be telling the truth? The answer is no. If only 1,2,3,4 …. X-1 (All cretans except Epimenides) cretans are telling the truth, the statement that "All cretans are lying" is a lie thus ending the infinite loop and paradox.
    This can be also verified with Maths and The probability Theme. Contrary Happenings (Sorry i don´t know the name for it in english :/ i literally translated it from portuguese (Acontecimentos Contrários) to english)

  • Chris

    Olbers’ paradox states that at any angle from the earth the sight line will end at the surface of a star. False. Try looking at the moon, which is not a star. Nor are any of the planets in our solar system. Stars emit light, while the other stuff doesn't. Consider also an eclipse where a non-star (the moon) blocks our view of our nearest star, the sun yielding a dark view.

  • DanielXA

    Number 3 is kinda stupid. If he says all Cretans are liars and he's a Cretan, then if he's telling the truth he is a liar. Well, that means he's lying, which means he telling the truth etc… Well anyway, it's easily solved. It's impossible for him to say all Cretans are liars and be telling the truth if he is a Cretan. Therefore, he is a liar and there are people who tell the truth and people who lie that are Cretans. That's the whole logical solution but then you could just say he was exaggerating and that not all Cretans were actually liars. Much simpler :).

  • garrett

    bonus: dark energy explains the bonus paradox … i think.. it is really hard to understand(dark energy that is)

  • Bambooi

    Number five is the man's fault don't you think?

    The guilty man just rambles and says it won't be on Friday, which is true, and then says it has to be on Thursday, but that can't happen then it won't be a surprise either. So Monday, Thuesday, and Wednesday are up for grabs.The man just has hopeful thinking.

    I think.^^

  • adrian cain

    If I state that "There are no absolutely true statements", this seems true, except that that statement itself claims to be an absolute statement of truth. Saying that "words cannot express truth", or "truth cannot be told in words", claim to be statements of truth expressed in worlds. Most paradoxes are based in the nature of the language used to express them. The language tricks you into thinking that the way it tells you to think correspondends to reality. Yet it's only ever in part at most.

  • ashish bhatt

    healp me.
    (Thanks)

  • willthespaceelf

    is heterological a heterological word?

  • Perkins

    The assertion of Olber's paradox that the night sky should be bright is actually the case. It is, however, bright in the microwave range.

  • amilynn

    The bonus paradox only works if you don't know anything about astronomy at all. If the Universe is infinitely large (which we believe it may be), then yes, there should be stars in every direction. But light travels at a finite speed, so as you look out further you are looking further back in time. The Universe itself is only like 16 billion years old, so we can only see out about that far. After a certain point, you're looking at the Universe before stars existed.

  • laji

    For sorties paradox, we can consider the heap as a shape and not a quantity.

    For the barber’s paradox, he might be going to another barber. It is so simple.

    For Epimenides paradox, we need not take Epimenides. Consider a man saying he is a liar, was he lying or telling the truth?

    The rest are more confusing.

  • Beastly

    The omnipotence paradox has a very weak argument. Any bieng who is omnipotent and chooses to limit their actions can simply choose not to do so, therefore being omnipotent. Rather pointless anyway as there is no such thing. Better to try to understand real world issues.

  • grammarnazi

    "He was, however, unaware that, by calling all Cretens liars, he had, unintentionally, called himself one, even though what he ‘meant’ was all Cretens except himself."

    Any way we can get some more commas in there?

    • Jay

      Yeah, but it don't help none no way.

  • jakob

    1 and 11 are actually the same paradox and they both fail to take into account that by definition one rules out the other.

  • ICEprototype

    smaj7 it is really easey to make a square circle

  • Jay

    Disraeli said: "All generalizations are wrong. Including this one." With that in mind, I just want to say to EVERYONE who tried to resolve one or more of these paradoxes:

    "Be-hehhhhh?" No,there won't be any Nobel Prizes in Paradox-Resolution Theory going out to any of our list members anytime soon, but that's okay. These are paradoxes and aren't meant to be resolved. The value is in the attempt and the way it opens your mind to new ways of thinking.

  • JonathanN

    I am SO confused…

  • Guest

    I just lost the GAME!!!

  • Brunelle

    well Maggie if a immovable object and a unstoppable force made a sound when they clashed then wouldnt the sound they make also be infinite, possibly, infinite sounds are silent, but is it possible for it to be silent… holy shit my brain just exploded…

  • umakemehateu

    Whenever I find myself pulling the last trashbag out of the box and then have to throw away that very same box in the last trashbag I often think to myself "How Ironic."

  • Wade

    The Bonus isn't exactly a paradox. The Universe was opaque untill it cooled down enough to stop plamsa scattering the light. If all the light in the universe was reaching us, It has been calculated that night time would be as bright as day currently is and day would be twice as bright.

    Number Seven is simply the fact that infinite sums can have finite solutions

  • dennis

    paradoxes seem to only exist if you ignore certain aspects of reality. once we remove any aspect of reality you can technically do anything. since they are in place then technically paradoxes are technically impossible (or only seem possible because we are missing a variable) in fact by nature a paradox can only exist theoretically can it not? the chicken and the egg paradox ignores evolution. (fish then amphibians then lizards then birds laid eggs long before chickens.) the "terminator paradox uses the time travel theory while ignoring the multiversal theory and technically IF you could time travel just your presence there would cause a change in the past and in theory a split in time (alternate reality) and probably screw things up immensely… though its all theory (and there are still variables I am probably missing)the very nature of a paradox is that is shouldn't exist in our reality.

  • ???§?§

    Achilles wouldn't have to transverse an infinite number of points between him and the tortoise because there are not an infinite number of points between him an the tortoise. On the smallest scales, there is a smallest length possible (currently, Planck, there could be smaller, but it suffices to say that there MUST be a smallest).

    The same goes for the arrow "paradox." Reality is pixelated on the smallest scales, it is not, as the lesser intellectual might assume, divided down into infinitesimally small segments. If this were true, then time would be the same way. And there would be an infinite amount of segments of seconds between each second and therefore, the second hand of a clock would never move because it would need to pass through an infinite amount of time segments to doso.

    • Jay

      "…it suffices to say that there MUST be a smallest…" You feel sure about that? Various people have proposed this idea with respect to both time and space, but I haven't seen anything to really suggest it's true.

  • logan

    As for the bonus…it's possible that the light from the stars within the black areas in the night sky has not reached earth yet, thus giving nothing for our brains to process other than lack of light

  • Ben

    new here… but for the first one:

    “Could an omnipotent being create a stone so heavy that even that being could not lift it?” If so, then it seems that the being could cease to be omnipotent; if not, it seems that the being was not omnipotent to begin with…."

    The keyword is "create"… he created the stone to a limit where he couldn't lift it himself, although, he could just_as_easily will to "create" a stone-lifter. and instead answer with that the omnipotent being Can lift the heavy stone, but will not see himself to Do it?

  • Brandon

    OH HEY! 2 piles of food lie equal distance from me, i guess i'll go to one and eat it then move on to the other, and oh, 1,000,000 grains of sand make a pile but when i take away about 750,000 of them it doesnt look like pile anymore so i guess its not a pile! :D Mathematicians just need to stop asking the stupid question, And start implementing common sense. wtf

  • Matt

    some of this are not paradoxs
    lets take 3 for example, you say that by calling cretens liars he is calling himself one so cretens are truthful
    analizing this under a logical reasoning (like it have been for the others) the opposite of liar is not truthful, it is not-liar which doesnt necesarily imply truthful so the endless loop breaks.

  • ManBearPigPanda

    Assume you can time travel, and that you inherited a very valuable artifact which has been passed down to your family for generations. If you take the present artifact, go back in time, and leave it in the past, will you have two when you return to the present?

  • ratattack

    10
    The Sorites’ Paradox

    the last grain is not a heap, but a grain. a singular grain cannot be a heap (which is plural)

  • mulaaks

    My head hurts…

  • David Hopkins

    I read a variation on number 5 in a math textbook. It goes like this:
    A condemned criminal is given the opportunity to make one last statement before he is executed. The truth value of the statement will determine the method by which he is executed. If the statement is true, he will be shot. If the statement is false, he will be hanged.
    The prisoner ponders for a while, then says, "I will be hanged."
    But if the executioner hangs him, his statement would become true, but a true statement requires an execution by shooting.
    On the other hand, if the prisoner is shot, his statement would become false, but a false statement means he will be hanged.
    (In the text, the executioner ends feeling he has no choice but to let the prisoner go)

  • David Hopkins

    Here are two more, both based on the paradox of halves:
    1. A light is on, but then, turns off. 30 seconds later, it turns back on. 15 seconds later, it turns back off. 7.5 seconds later it turns on. 3.75 seconds later, it turns off. 1.875 seconds later, it turns on. 0.9375 seconds later, it turns off, and so on, with the intervals of off or on always dividing in one half.
    Question. After one minute, will the light be off or on?

    2. A particle is spinning in a particle accelerator. In 30 seconds, it completes its first revolution. In 15 more seconds, it completes its second revolution. In 7.5 more seconds it completes its third revolution, and so on.
    Question: When the time elapsed is strictly greater than one minute, what happens to the particle?
    One minute of time MUST pass, but the particle couldn't still be revolving, because, given its pattern of revolution, it completes all spins possible (infinitely many) in a minute, yet it would sound pretty nonsensical for the particle to vanish into nowhere, or be in any place besides inside the accelerator.

  • Greg1987

    About #2, we are all liars, every single human being on this planet. This fact does not mean that I lie about every single thing I say. If I am a thief does that mean every object I own is stolen?

  • Greg

    Where is the time traveller's paradox? This is my all time favorite paradox…Everyone knows this one and I am sharing just for comment purposes.

    If a man travels back in time and kills his father, wouldn't he not be able to exist and, therefore, not be able to go back in time to kill his father?

    Multiple possibilities, this person could simply create a rip in space time which would end the universe entirely or simply within a certain scale, such as whatever would be affected by this, such as our planet, solar system and so on.

    In the sense of multiple Space time continuums then this person would ultimately create another timeline, and when he would re-enter his own appropriate space time coordinates; nothing would have changed. His father would still be alive, the time traveller would simply not have existed within that other "timeline" or universe.

  • raj

    it is not a brain-twister, it is creating a tornedo in my brain…
    loved it…

  • David Hopkins

    Did you know that the set of real numbers is said to be uncountable? (Look up Cantor's diagonal argument). Maybe the set of everything there is to know is also uncountable, so it literally is impossible to know everything.

  • The Bamboo Muncher

    the olber's one is easy, the reason we do not see only white is because of the length of time light takes to travel to earth…. simple

  • FilthyMove

    Wait, wut? Achilles and the Tortoise:

    Achilles runs 100 feet in say 1 second.
    Tortoise runs 10 feet in the same second
    Achilles is now 10 feet behind.
    (total 1.0 seconds)

    Achilles runs a further 10 feet in 0.1 seconds
    Tortoise runs 1 foot in 0.1 seconds.
    Achilles is now 1 foot behind
    (total 1.1 seconds)

    Achilles runs 1 foot in 0.01 seconds
    Tortoise runs 0.1 foot in 0.01 seconds
    Achilles is 0.1 foot behind
    (total 1.11 seconds)

    etc

    Or, more specifically (MATHEMATICALLY):

    X = position of the tortoise
    = 100metres + (velocity of tortoise) * time
    = 100metres + (1/10)*(velocity of achilles) * time
    So:
    X = 100metres + (10(m/s) * time)

    Y = position of Achilles
    = 0 metres + (velocity of Achilles * time)
    So:
    Y = 100(m/s) * time

    When are they at the same position?
    They are right next to each other when X = Y
    ie when:
    100*time = 100 + 10*time

    Then:
    100*time – 100 – 10*time = 0
    (10*time)(10 – 1) – 100 = 0
    10*time*9 = 100
    time = 100/90
    =>Time at which Achilles and the Tortoise will be next to each other: 1.111111111111111……. seconds and they will be 111.11111… metres from Achilles' starting point at this time.

    All I'm saying is that the problem with the paradox is nothing to do with applying mathematics to a non-mathematical situation; the fault with the statement "because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise".
    This doesn't take into account the fact that, while the gap between the two racers reduces, each consecutive time increment we are looking at also becomes smaller. So while the number of points traversed approaches infinity, the amount of time taken for each consecutive period of catch-up becomes infinitely small.

    I guess the paradox is really pointing out the fact that you can never *exactly* pinpoint a particular point in time (or space); you can always go that extra 0 .000000000000…1 second (or metre or kg) further.
    We know that Achilles *does* overtake the Tortoise, but tell me *exactly* when they are right next to each other and I'll tell you you're wrong.

    JUST WANTED TO POINT THAT OUT
    Sorry to be "that guy"…

  • Alexander

    What will happen if pinnichio says "My nose will grow"??

    • Name2

      That depends on what he believes. If he believes his nose will grow, then he’s telling the truth and his nose will not grow. If he believes it won’t grow, then he’s lying so it will grow. He will always get the opposite result of what he expects.

      So it’s just like life itself.

  • aquallogy

    Cool !

  • Robert

    @The Buridan’s ass paradox: If an ass really did encounter these piles, it would not look at the pile then look the other way… It would have to see one pile at a time and simply go to the pile it sees first, according to my logic.

  • tsj

    Very cool, but 7 is not a paradox, the amount of time it takes to cover the distance that the turtle is ahead decreases exponentially, therefore after the distance is over taken an infinite number of times you will reach the finite time that achillies overtakes the turtle. A study of limits will prove this. The math still applies.

    • Roman

      does anyone have a good recipe for turtle soup – I just caught up with the turtle.

  • thedude

    can jesus microwave a burrito so hot that even he cant eat it?

  • Suzi

    Um…You’re damned if you do, and you’re damned if you don’t.

  • Dusan Pavlicek

    JFrater's remark at the end of problem 7 (Achilles and the tortoise) doesn't really explain anything (properly) and it makes things even more confusing…

    Here's what Richard Feynman had to say about that particular problem in his Lectures on Physics:

    "A finite amount of time can be divided into an infinite number of pieces, just as a length of line can be divided into an infinite number of pieces by dividing repeatedly by two. And so, although there are an infinite number of steps (in the argument) to the point at which Achilles reaches the tortoise, it doesn't mean that there is an infinite amount of time."

  • Lewdduck

    #10 is not so much a paradox as it is a fallacy of slippery slope. For example, 1 penny is not a lot of money. 2 pennies is not a lot of money and so on. But at which point does a certain amount of pennies become a lot of money? Look it up.

  • Shakeeb Ahmed

    For the arrow/fletchers paradox: Aristotle disproved this paradox, Paramenide’s student Zeno was on the extreme of permanence and despite the fact that the arrow is said to not move at all, the fact remains that in any change one thing must be permanent which in this case, is simply the arrow. The logic presented is sanctioned by the assumption that a new arrow is presented in each progressive movement of the arrow, however, the origins of the arrow are uniform. In essence, this paradox is disproved because the same arrow travels the distance.

    • Roman

      all I can say is – To whoever says “the arrow dose not move” I am willing to do a demonstration – I shot the arrow and you get in front of it

  • Alex AK

    Epimenides’ Paradox can be resolved by including the word sometimes. So it would read all createns are liars sometimes. Thus it allows him to exclude himself from concluding that he is a liar.

  • max medlow

    the fifth one, about the hanging, can’t truly be a paradox can it? because it ends up being resolved. nonetheless, it was my favourite one :)

  • max medlow

    this is like “opposites day” that kids sometimes do. if a kid A says to kid B “jump on the spot” kid B will say “no, it is opposites day”…but then the opposite of not jumping on the spot is jumping on the spot, but the opposite of that is to not jump on the spot, and so there is a paradox…

    i am also aware that opposites day is lame, but im just saying, lol…

  • Cameron MacDonald

    If the unstoppable force hit the immovable object, then wouldn’t the unstoppable force go right through the immovable object? Then the fact that one is immovable and one is unstoppable would be correct.

  • anon

    tl;dr

  • Jason

    http://hubblesite.org/hubble_discoveries/hubble_deep_field/ This disproves the bonus one. They trained the hubble telescope on an empty region of the sky for 10 days and they were able to see galaxies 10 billion light years away

  • Katie

    My math teacher has complained several times that whenever anyone in her class get a number that is not whole as an answer, they assume it’s wrong. This is usually followed by the statement that there are many more decimals between whole numbers than whole numbers themselves, and it would follow that your answer is more likely to be a decimal than a whole number. However, my theory is that if the number of whole numbers is infinite. than there cannot be more decimals than whole.

  • Daniel

    11. Does this paradox forget the element of time? An omnipresent being has the power to limit their own powers, which simply makes them no longer omnipresent.

    10. A “heap” is not a definable measurement, it is an estimation. There is no paradox here.

    9. Unless “interesting” has some definition I’m not aware of, there is no paradox here.

    8. Yes, movement is an illusion.

    7. This one is just dumb. Any 7th grade student can explain the formula d/t=r.

  • Daniel

    Bonus: This one is just simply and totally dumb. Okay, assume the universe is infinite. But that doesn’t mean there is a perfectly unobstructed path from every star in the universe to earth.

    This list upset me, and you should be ashamed.

  • Dre

    Well Superman answered #1: They surrender

  • sophiabramos

    Name

  • jordan

    #7 Achilles and the tortoise… youre looking at the mathematical solution from the wrong point of view. when A travels 100 feet, T has traveled 10 feet. (thats a 10 to 1 ratio). Therefore A is now at T’s starting point. Now A will travel 10 feet to T’s 1 foot (10 to 1)… but at a constant speed… which means in a short finite amount of time A will have traveled another 10 feet while T only traveled another 1 foot. Thus.. A has overtaken T, but; How much time did it take? :-)

  • The Truth Fairy

    This list is fucking stupid. Only one or two of them could remotely qualify as paradoxes [the omipotence one, and perhaps the unstoppable force vs immovable object], but even still, these are just thought experiments that anyone with a reasonable IQ could easily solve.

    Most of the commenters are clearly more intelligent than the listmaker, and much more deserving of accolades.

  • Kristen

    Olber’s paradox can be cited as proof of the expanding universe theory. There are infinite planets, and therefore, it is true that there are planets in every line of sight, however, the light from the most distant planets has yet to reach us dur to expansion, so we don’t actually see them. The edge of the visible universe is called the event horizon and beyond it is everything we can’t observe from here on earth because the electromagnetic waves have not reached us yet.

  • suttercane

    Another little known mathmatical paradox: 3 men go to rent a hotel room for the night. Upon entering the hotel and speaking with the desk clerk they are informed the room will cost $30 for the night. The guys split the bill at $10 each, they pay their money and proceed to check in the room. After the desk clerk realizes he charged the gentlemen $5 to much, he gives the bellhop 5 $1 dollars bills to refund to the gentlemen for the overcharge. The bellhop goes to the guys room and informs them that they were charged $5 to much and here is their refund. Upon discussion between the men as to how they are going to evenly split 5 $1 dollar bills , they agree to each take 1 dollar back and give the remaining 2 dollars to the bellhop as a tip. Now, each guy has $9 invested in the hotel room for the night after receiving the $1 dollar back from being overcharged.. if 9×3 equals 27 and the bellhop received a $2 dollar tip…what happened to the missing dollar. Email me if you figure this out, because I’ve tried for years to figure this out and it seems that the dollar is lost by the way the story is told

    • Sam

      SPOILER ALERT: The 30 is accounted for, the guy at the desk takes 25, the bellhop takes 2, and the guests get a 3 refund. The problem starts when you mistakenly had the 27 to the 2, the 27 already contains the 2, it is the 3 the lads have u had to the 27 to get 30

  • Sam

    the pinocchio paradox has long been my fav

  • maydaylive

    there’s no such thing as “achilles and the tortoise”, it is called the tortoise and the hare, written by aesop, and re-written in its modern version by french 16th author Jean de la Fontaine under the name : le lievre et la tortue.

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

  • Richard

    Henceforth your wrong if there is an item with an infinite mass and infinite density that creates a singularity, is a black hole so it is unmovable. Therefore an object fallen into its suction would be unstoppable so what happens when an object meets a black hole you tell me.

  • Richard

    The last one is a simple explanation, sence a black hole has infinite mass and infinite density it creates a singularity. Therefore an object that is sucked into a black hole is unstoppable so what happens when the singularity and object meets thats the answer.

  • Dwarf

    These are literally retarded.

  • WhoCares

    I personally like the non-paradoxical Dunning-Kruger effect, which states that “incompetent people are also incompetent in assessing their own performance. Therefore, less competent people think their performance is competent”. In other words, stupid people try to sound smart regarding things they really have no clue about. Case in point, all the morons above this post.

  • goksMan

    great list.
    Some things are better left as they are… there are more pressing matters we should try to understand…Like solving the worlds energy crisis( and Global warming)

  • archworf

    Time is only described in segments, but cannot actually be segmented. A projectile may be said to inhabit a tunnel of time outside of created (for human use) “points”. There is no paradox, simply a failure of description. One may as well ask the temperature of an inch

  • Henry

    in regards to the omnipotent being (OB) paradox: The OB can do anything, so he can create a stone that he cannot move.. If the OB cannot move the stone, he can create a being whose only purpose is to move the stone. Thus, he remains omnipotent. Right?

    • Omar Bongo

      Wrong. If he can’t move the stone, he is ot omnipotent. If he could create a creature to move the stone, that creature would be stronger than himself, so he would not be omnipotent.

  • Curious George

    Can I post without signing up?

    • David Hopkins

      You just did.

  • Mister E

    11. The Omnipotence Paradox
    Solution 1
    The condition attached to the stone is that it should be so heavy that the omnipotent being may not move it. Thus the question is flawed because the stone would necessarily have to be infinitely large, in which case it would engulf the universe and have no end, so the concept of motion would not exist because things only move relative to other things.
    Solution 2
    The concept of infinity is misleading in this question. The omnipotent being may be infinitely strong, and the stone infinitely heavy, but one may be greater than the other. Infinite things are not necessarily equal, and this applies to rates an measurements of all sorts. Faced with this challenge, the Omnipotent being, could simply reply, “Yes, but that would take an infinite amount of time.”

    Solution 3 (Modified Solution 1)
    The omnipotent being could simply become the stone (i.e. give itself the physical attributes of an infinitely large stone). This would render the concept of motion as meaningless, without necessarily altering the omnipotent being’s abilities or omnipotence.

    10. Solution 1
    Heap is a subjective term, just like “funny” or “interesting”.
    The tallest man and the shortest man may disagree on a given heap due to its size relative the viewer.
    Alternatively, someone who lives in the desert might not call the sand in the picture a “heap” because it is so small compared to the heaps in his experience.
    Some may view the shape of the sand as being important because I could spread a million grains of sand on the ground evenly, and you would not notice any “heap” at all.
    It follows that you may not define a heap in these terms, so the premise is invalid.

    Solution 2
    The second premise is flawed. Even if “heap” can be defined as a collection of many items, there still may be an area of ambiguity as to what quantity constitutes a collection. Since the possibility must exist that there is a cut-off point, we MUST replace Premise 2 (A heap of sand minus one grain is still a heap) with the following premise: A heap of sand minus one grain is probably still a heap.
    Repeated applications of premise 2 will ensure that even if the chance is 0.1%, by the time there is only 1 grain left, the chances of that being considered a heap are miniscule.

  • Mister E

    9. The Interesting Number Paradox
    Solution 1
    The claim cannot be proven without first defining “uninteresting.” Because interest can only be a product of thought, one would have to honestly THINK about a specific number and fully comprehend it before it could be decided whether that number was interesting or not (i.e. You could show the set of numbers to a cow and, because the cow does not comprehend, you could not judge whether the cow was uninterested in any specific number or just the whole set). Unless you can prove that a mind has thought of and comprehended every natural number, you cannot prove the claim (i.e. even if the number is the smallest, one would have to know that in order to find the number interesting).

    Solution 2 (another way to think about Solution 1)
    The assumption is that the set is non-empty. Perhaps it is infinitely large. If the smallest number is interesting by virtue of the fact that it is the smallest, there must always be bigger uninteresting numbers if you wish to continue making this claim.

  • zero the zero

    in regards to paradox seven; i do not see how that is NOT a mathimatical problem. there are an infinite amount of numbers between the numbers one and two [ei. 1.01, 1.001, etc]. ill say the length of the race is a hundred feet. achilles started when the turtle was at the halfway point. before achillies can make it halfway, he must first go halfway of halfway. so 25 feet. but before that he must go 12.5. and before that 6.25. and before that 3.125. and before that 1.5624. and before that 0.78725. and so on. so if there is an infinite amount of numbers between one and two, logically and mathimatically, it is impossible to travel even one foot at any speed. so is there really such thing as motion? and time for that matter? or are they both simply inventions of man?

  • zero the zero

    Paradox ten: i do not see the complication here, a heap with 1,000,000 grains of sand is both a head and1,000,000 grains of sand. a heap with a hundred grains of sand is both a heap and hundred grains of sand. a head with two grain of sand is both a heap and… two grain of sand. obviously it must end here, for a ‘heap’, which should have been defined, cannot exist with less than a pair of what it is composed of

  • joe

    as for the bonus one, light can be bent by gravity, so even in an infinite universe the light would be attracted to other large entities and not reach earth, also not everything in space is a star, there are planets and masses of dustski

  • Tem

    for the barber paradox it says there is only 1 male barber in the town well what if there was also a female barber because it does not state it in a way that this is not possible

  • Sebastián

    Using math you can say that the barber doesn’t exist

  • Colin

    here is one for you: I owuld like to buy a hotdog for $17
    I borrow $10 dollars from john and $10 from Jack.
    so i buy the hotdog and have 3 Dollars left. I give jack and John each $1 back.
    So I owe them $9 each… So I owe $18 dollars and have 1$ in my pocket.. Where did the other dollars go???

  • Jordan

    #4…it’s not nice to call a burn victim a paradox.

  • B23RAD

    ALMOST NONE OF THESE ARE REAL PARADOXES! ALMOST ALL OF THESE TAKE TIME TO FIGURE OUT BUT CAN BE SOLVED. A PARADOX BY DEFINITION IS UNSOLVABLE AND IS AN IMPOSSIBLE CONTRADICTION.

  • p1t1o

    Anyone else think that the “answer” at the end of #11 is simply restating the paradox?

    I have also seen it posed that the very idea of this paradox implies that omnipotence is conceptually invalid – it is not a quality that any entity can have. Like saying I own infinity marbles, it just cannot be.

    As far as I remember, this was shown with fairly robust logical methods. As such, it is used by those who care (atheists etc..) as proof (or “proof” depending on who you are) that God does not exist, or at least that if there is a God, he cannot be omnipotent.

    Makes sense to me.

  • Nasser Khan

    I have the fool proof and the only correct answer there
    Is to AchIlles and TortoIes and unexpected hangIng. please help me to have It publIshed wIthout losIng my copyrIght and credIt. Thanks.

    SIncerely,
    Nasser

  • Jeerrrbbbbb

    “Could an omnipotent being create a stone so heavy that even that being could not lift it?”

    A string of words that makes no sense at all.

    There is nothing too difficult for God to do, but somethings are impossible.

    • p1t1o

      Herb, you have simply restated the problem, your “solution” makes as much sense as the original statement.

  • D.J.

    Re: paradox 3.

    The proper negation of “All Cretans are liars” is not “All Cretans tell the truth”, but rather “Some Cretans tell the truth.”

    It’s just that Epimenides is one of the liars is all.

  • Bheshaj Joshi

    Great list….
    Not sure if it is mentioned int he comments already, but I would like to mention the “Grandfather Paradox” of time travel. I think it deserves a stop on the list or perhaps a part 2 of Paradox lists.

  • john lloyd

    the shaina magdayao paradox: i feel confident that i am not insecure

  • Mickey

    The paradox involving a man as hungry as he is thirsty can be solved quite easily. The human body can survive longer without food than it can with out water. So logical thinking would be to drink first then eat.

  • Kopmel

    My head hurts!!!!! lol

  • Aiedail

    Number four- female barber, FTW

  • Someone

    I object to 10. A heap is a non-measurable object. This paradox would only works for things that cannot be measured.

  • jake

    how can a blackhole have infinite mass while we currently exist. people should stop using the word infinite so losely, because they make what they just said impossibly idiotic, if possible- but wait how would they say something impossibly idiotic if its possible to do so? i dont know any more lol i feel like a parodox now

  • mikki155

    I don’t know if someone has said this before, but what ever.

    I had a task in physics almost excact to the paradox number 7. If I compare it to Achilles and the tortoise, it would be like this: Suppose that we set Achilles postition as the “zero-position”. Then the position of the tortoise would be +100 feet, because he is 100 feet in front of Achilles. We know that both of them have a defined speed (let us say that they in this instance run at a constant speed), therefore we can express this in two respectively formulas. If we set formula one equal to formula two, we would know exactly when Achilles catches up with the tortoise.

    • mikki155

      Ops, I see now that this has been pointed out. The paradox arises when you calculate the position at a given time (for instance) for each formula separately. If you start with Achilles, you would see that he has ran a defined length after, say, 5 seconds. But the tortoise would also have gone a defined length in these 5 seconds. If we calculate further, until they are really close to each other, we could never calculate when he catches up and runs past the tortoise, because it is not possible when the formulas are calculated separately.

  • Jace

    what happens when Pinocchio says that “My nose will grow.” ?

  • Corinna

    I love this list. Nice one. Sorry if someone has already mentioned it but another good one is another paradox of Zeno. Where it is argued that in running a race, no one will ever cross the finish line. As you will begin, compete half the race, and still have half way LEFT to go between your current point and the finish line. So you run further to the next halfway point, where you then still have halfway to go between your next current point and the end. And so on for infinity, meaning you will never finish the race.

    • p1t1o

      Zeno’s paradox collapses as soon as you consider the time taken for each step as well as the distance. As the distance traveled in each segment approaches infinitely small distances, the time taken to complete each segment takes an infinitely small amount of time.

      Therefore your speed over each segment remains constant and a simple graph of distance traveled against time will show a stright line (assuming constant speed) and will cross the zero mark (the finish line) at the exact point where we would expect it to and is completely consistant with your infinitely small, infinitely fast segments.

      It is more of a thought experiment useful in considering the nature of “infinity” than a true paradox.

  • metrocop

    paradox 8 actually relates in a way to heisenberg’s uncertainty principle and planck’s constant

  • lsuttercane

    I -a paradox I would like to post that is known to me as “The paradox of the missing dollar”. Here is the premise: 3 guys go to rent a motel room for the night , the desk clerk informs them it will be $30 dollars for the night. They agree and split the cost at $10 per person. The men check into their room and 30 minutes later, the desk clerk realizes that he charged them $5 too much, he sends the bellboy up to the room with 5 -$1 dollars bills as their rebate for overpayment. The men cannot agree on how to evenly split the $5bucks, one guy suggests that they each take a dollar back and tip the bellboy $2 bucks for bringing it up to them. Now we come to premise no. 2; which leaves each one of the guys paying $9 dollars each for the room; now, if 9×3=27 and they gave the bellboy a $2 dollar tip; bringing the total to 29; where did the other dollar go??????? Please email me with suggestions; I have brain melted on this for 10 yrs., with no perceivable explanation, and even won a few bets with it…….I look forward to comments, conjucture, fallacies, and maybe even a solution.

    • p1t1o

      You said it yourself, the clerk charged them $5 too much.

      That means that the price for the rooms was $25.

      Each person is out of pocket by $9, having each paid 10 and recieved 1 back.

      3 people, $9 each, so a total expenditure of $27.

      $27 is $25 for the rooms plus the $2 tip.

      All dollars accounted for.

  • Name

    nerds

  • Lucy

    i just got mindf*cked O_o

  • Charles McDowell

    Delivery Boy Paradox

    You are the pizza delivery driver and your boss tells you your job is to deliver every pizza I make to the address I give you. Then he gives you a G.P.S. to help you reach your destination. You type in the address on the G.P.S. and it shows you on the screen where to go and how to get there. You follow that path with little belief that this device will be able to show you where to go but you try it any way. When the device said final destination, you look up expecting to see the address you want but what you see is a completely wrong house, you are actually a block away from where you want to go. You tell yourself this thing does not work, so you shut it off and try to figure it out for yourself. You start to see that you are not aware of every road, and it leads to a series of u-turns, and wrong houses. Each day again and again more wrong turns and houses, which equal’s less money for you. Then it clicks, if you can use your knowledge of the roads, plus the G.P.S. then you can eliminate most of your wrong turns. The G.P.S. will not get you to the exact location and you will still miss a turn from time to time but it always will lead you in the right direction.

    Boss=God

    Pizza=knowledge

    Address=personal happiness

    G.P.S=Balance of Science and Faith

    • p1t1o

      I think this is more of a metaphor than a paradox.

      Also, what is wrong with your GPS? Did you check God gave you the right Address? Sometimes postcodes are out of date so I’d go with the street name and number if I was you…

  • iloveparadoxes

    Some of these are not actual paradoxes.. They are fun to read however.

    Many of these items on the list combine math with languages, like the heap of sand for example.

    Languages are invented, made up, so many years ago.

    Math is discovered, by studies, observation, calculation.

    You can’t always combine the two.

    The heap of sand example again:

    a “heap” is just a word we use for multiple grains of sand. When you take a gain of sand from the heap, you will still have a heap… However, when you are at the last grain… What is left is called a single grain.

    I don’t know if there is a language out there that has no word for multiple grains, but just calls it “sand”.. then there is no paradox…

    You can’t combine math with words

    • p1t1o

      Agreed. For my statistics A-level (for the non-uk peeps: this is an exam taken at school around the age of 16-18) I had to do a study of car depreciation, the maths was easy but then I had to produce a big long essay about why the math was right and that was bl**dy awkward to write.

  • marco

    My brain hurts.

  • Listverse Einstein

    An omnipotent being can create a stone that he can not lift, for if he can not lift it, no other being can, therefor giving him no weakness.

  • Solstice

    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)”
    -Premise 1 uses standard logic. 
    -Premise 2 does not ask to be repeated. 1,000,000 – 1 = 999,999. Not 999,998, 999,997, et cetera.
    9. “proving there is no such thing as an uninteresting number”. iLol’d. 
    8. Let me introduce this person to Isaac Newton: “An object in motion…”
    7. I was going to get in-depth with this one but JFrater pointed out the logic already. In short I would explain Car 1 (Tortouise) moving at 15 mph got a headstart of 5 miles. Car 2 (Achilles) will move at 75 mph. The race is 50 miles long. Car 2 is constantly *catching up* to Car 1  because the slower car doesn’t have enough speed to ultimatly surpass or even sustain the faster car’s
    6. Is this a joke? *Looks at my two school uniforms* …..Which one should I wear!?
    5. He was ignorant to think he wouldn’t pay for his crime. Childish thinking led to his own “surprising” fate. 
    4. ” He shaves all and only those men in town who do not shave themselves.” 
    -“If the barber does not shave himself, he must abide by the rule and shave himself.” In other words whether he follows the rule or not it’s his choice to shave himself while working as a barber. 
    -“If he does shave himself, according to the rule he will not shave himself.” Purposeful hypocrisy is ignorance. But to answer the question, he doesn’t shave at the barber, he shaves at home so the rule is followed. 
    3. The only paradox here. 
    2. “Euathlus, however, claimed that if he won then by the *court’s decision* he would not have to pay Protagoras. If on the other hand Protagoras won then Euathlus would still not have won a case and therefore not be obliged to pay. The question is: which of the two men is in the right?”
    -The court has nothing to do with what two men promised each other but can have an adverse effect on Protagoras (as opposed to what he argued). Haha! The irony here is if Protagoras were to win he would get no money (Euathlus lost) and owes no money (because he won). But if he were to lose, due to legal actions (court butts in), he will HAVE TO pay Euathlus. Neither is right because both jackasses broke a promise between men (Euathlus inadvertedly because of a court being called forth). Deceit is a terrible thing. 
    1. I stand corrected. Another actual paradox. 

  • SRB

    Solution to number 7.

    The paradox implies that it will take infinite amount of time to reach the tortoise, which is false, because it is implying that reaching the 3rd point where the tortoise will take same amount of time as reaching the 2nd point or 4th point, and unless Achilles was slowing down with each time he reached the point, but never falling below tortoise speed, then it’s not maths that is at fault here, but human error. You see, in this situation we have two values that we must consider, distance and time, claiming that Achilles will never reach tortoise is claiming that he will be travelling these points forever, but in this question distance and time are related to one another, one cannot change without another not changing.

    Although here’s an interesting thought of the day, between point A and point B there are infinite amount of points, between point A and point C there are infinite amount of points as well, between point B and point C there are infinite, as well, amount of points, but these 3 distances are not equal to another. What does it mean? That we have managed to put a differing value on infinity, we have created smaller and bigger infinities, how cool is that?

    Problem with 10.

    The problem with 10 is that it’s assuming that a collection of sand is either a heap or not, the problem here is that it is not black and white, that’s why we have large heaps and small heaps. That is the solution, although 1,000,000 grains of sands – 1 is still a heap, it is a ‘smaller’ heap. The question is when does the heap no longer become a heap, but the question is also relying on subjectiveness, if we were shown a same amount of sand at two different points of lives when we would be in two different moods, and asked whether this is a heap or not, then we could claim same heap to be and not to be a heap. Therefore the answer is that at certain point a heap enters a grey area where, depending who you ask, it may or may not be called a heap.

    Number 6.

    The simple problem is that there is still a variable that can determine which stack the ass will choose, it may prefer the movement towards left than right, it’s left hemisphere might be more active at the time than right, it’s eyes might move more towards the left than right, the sole facts that one heap is one one side and other heap on the other puts a very small variable into the equation, or the fact that there are less atoms on one side than another. Not even theoretically is it true, since it’s impossible for an ass to be perfectly symmetrical which in itself will be causation of making a decision. In order to reach equilibrium, you require a force with equal value that will act in opposite direction on an object, which is impossible in real life world.

    Number 2.

    Unless he is a liar/mislead (not everyone who speaks false, lies) and NOT ALL cretans are liars. Again, it implies the black and white fallacy, the answer doesn’t have to be either 1 or 0, you can have 0.5.

    Bonus.

    The problem I see here is that the author didn’t consider the inverse square relationship of intensity and distance.

    Another problem that is necessary to understand is that this problem assumes that star emit infinite amount of photons.

    Third problem is that it’s assuming the ‘perfect vision fallacy’

    Now to debunking. If this theory was true, then it is assuming the two problems I have mentioned, therefore no matter where you stand, the intensity of the light would always remain 100%, but it is scientifically proven that the further you move from a source of light, the dimmer it becomes, why? And here comes second consideration, stars emit large numbers of light waves, not infinite, therefore the further you move away from the source, the less light waves there are per square meter, therefore less light waves reaching our eyes.

    Our eyes are also imperfect, we cannot catch hundred percent of all light waves, which is why we can’t read small fonts from large distances, even if there are some light waves reaching our eyes, they probably do so one at the time. That’s one hubble telescope had to stare at one point of space to get a clearer image of the famous hubble picture.

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  • Name

    i think a heap is anything with 2 or more grains. the point of the paradox is to show that there is no point of arbitrarily deciding what constitutes a heap, since there’s no real difference between 100000 and 99999 grains, say, or 99999 and 99998, if 100000 grains is the boundary line for a heap. but there is a big difference between 1 and 2 grains (proportionally speaking)

  • Lizardmancalcos

    11. An omnipotent being cannot lift a pebble let alone a mountian, because (s)he cannot possibly exist in the world (s)he made.
    10. If a heap is 1,000,000 grains of sand, 999,999 grains is not a heap.
    9. No number is intresting unles it means somthing. example, “1” is unintresting because it has no meaning.
    8. The same can be said about falling.
    7. The tortise wins, it’s a short race.
    6. The ass will eat both. The starving, dehidrated man must go for water first to servive. All others could flip a coin.
    5. Self fulfilling prophasy.
    4. He is only a barber when he is working. When he shaves himself he is not a barber.
    3. All cretians are liers, so is evreybody on earth. Even though they may be truthfull some of the time, or most of the time.
    2. Check mate Euathlus. Win or loose, you pay.
    1 They destroy eachother, wichever is bigger will servive. The object will brake and not move, and the force will never stop even if it breaks. I have seen it.
    BONUS. In such a forest you can see; the ground, the trunks of the trees, animals, other plants, the space between trees,ext, not just white. Space on the other hand is an infanant flat black field with an odd white tree in the far distance, now you see mostly black fields with far off (tiny) white trees in the distance.

  • Randall Sherwood

    actually the bonus is incorrect, since that we do see the night sky lit up by stars in the distance, but it is only viewable in another spectrum of light, since it is stretched, and the night sky is lit up by microwaves instead

    only nearby stars can be seen by the naked eye since light has not had to travel as far.

    • Whilst you are correct about doppler-shift being an important factor in the observation of distant phenomena, your explanation is slightly flawed. What you describe as the solution to the paradox is the cosmic microwave background which is not produced by the doppler-shift of light from distant starts.

      We are actually able to observe objects that are extremely distant regardless of this shift. This example of a paradox ceased to be such a paradox as further understanding of the nature of the universe came into being (big bang theory etc.), the paradox is now more of an illustrative thought tool.

  • Rick Haines

    So….. I’m wondering if the donkey is so smart to ponder that much and starve to death wich makes him kinda stupid or if he’s stupid enough to just randomly eat a pile wich makes him kinda smart , me , I’d just eat both piles.

  • Rick Haines

    I don’t know exactly how to phrase this so maybe someone can help me out , but it’s kinda like the universe . If the universe is infinitely expanding , what is it expanding into ? Basically there’s something on the edge or other side of everything so what’s on the end of the last item ? There can’t be a last item as there’s always something else…..did anyone understand my concept ? Lol

  • Darren

    Most of this is a play on words. Words such as ‘heap’ do not have exact definitions in all contexts. For example if 10,000 grains of sand define a heap and 9,999 do not, then there is no problem with the paradox. It is either a heap or it is not and it is easy to say which one it is. Of course from our eyes a pile of sand with 9,999 grains and a heap with 10,000 will pretty much look the same. But it is no different between measuring two pieces of string, one 0.000001mm long and another 0.000002mm long.

  • bob_sagety

    With the unstoppable force paradox the unstoppable force would go straight through the immovable object therefore is not a paradoxe

  • Simon Wilby bio

    One adjective that defines Simon Wilby is smart. He is the CEO of Smart Power, Inc. He developed ?The Smart One,? a revolutionary lithium battery powered by solar for cell phones and ?The Smart Juice? which is energy with the same principle for lap tops.

  • Dre

    With regard to the bonus paradox, the Olber’s one. We do not see all the stars in the visible galaxy from earth because 1) our atmosphere creates a kind of haze that we struggle to see the faintest of light sources through, and 2) mainly because of the sheer distance between us and these stars that are millions of light years away. I agree with the fact that if we actually could see every possible star in the Universe from Earth, we’d be blinded by a pure white sky 24/7. Yet the fact that the light from those stars occupying the black spaces we see inbetween our visible stars has to travel millions of lightyears through space dust and gas and ice etc, this light becomes obscured and lost in the gigantic voids of space.

  • pierdzimaka

    Name

  • Josh

    Here’s an interesting thought about 9:

    Premise 3: Having established that in this paradox, one grain of sand can be regarded as a heap of sand, pouring another 1,000,000 grains on top of one another would mean you have created a heap of 1,000,000 heaps.

    Premise 4: In this heap of heaps, removing one “heap” would mean it still remains a heap. Similarly to removing every grain, removing every heap would leave you with one “heap” (still one grain of sand), which you would have to accept as being 1,000,000 heaps.

    Repeat the process (i.e. now pile 1,000,000 heaps of 1,000,000 heaps on each other to make a pile of 1,000,000,000,000 heaps – still one grain of sand) infintely and you must arrive at the following conclusion…

    1 grain of sand = infinity.

  • penguinman

    Hi,
    I read the first two, are there any actual paradoxes ? or should I not bother reading them ?

    In case you are wondering,
    ‘PARADOX’ 10
    A heap can be any number of grains of sand,but I think 3 or more would be generally acceptable.
    So Don’t panic when your small heap becomes a pair of grains.

    ‘PARADOX’ 11

    Lets make a special category: The ability and will to do all things except limit ones own ability. Or, The ability to do all things including deciding not to limit ones own ability.
    Here’s a question: ‘shut up’.

  • penguin

    Nothing, because he is telling the truth.

    The nose will assume that he is referring to it growing some time in the future, which it will assume to be true (the nose can assume what is unkown because it is all-knowing)

    However if Pinocchio says, ‘My nose will grow right now’.
    The nose will not grow for the time reasonably referred to as ‘now’, then that will become a lie (in the fullness of the preceding seconds’ at which time the nose will grow in response to the lie which become apparent.

    If he says ” My nose will grow in three seconds’, the nose will then wait three seconds, and not grow, and then as the lie becomes apparent, it will grow, like the annoying little bastard it is.

  • Phehello

    The paradox about the irresistible force n immovable mass..is not 100% correct as space is infinite not finite…as even today universe is still expanding and no signs yet of slowing down…the one about stars and why we dont see just light around us..the reason is because stars a far from us.trigonometry can be used to explain this nicely.

  • Noah

    For the unstoppable force paradox, it can be partially solved with math
    since Force=Mass X Acceleration, the unstoppable force must have infinite force, similarly, the unmovable object must have infinite mass. therefore, if we rearrange the equation then it comes out to
    A = infinity/infinity
    Suck on that

  • Alex

    hmm i seem to remember seeing this exact post here: http://ow.ly/btP2o !

  • Isaac

    “What happens when an irresistible force meets an immovable object?” the most logical answer to give would be ”The Impossible will happen inevitably”
    I would like to say I think all this paradoxes refer to a part of what we are/do.
    Along time ago we decided that upon our experience of the one paradox we know which is our own life, the only possible option or the one we like to refer to as ‘the one that makes sense’ with sort of a satisfying feeling, is ONLY what we experience.
    Nonetheless why am I capable of imagining all this things and more if 99% of them will have no use or application in my experience and are not even a part of what I do? for example I can imagine myself as being able to eat wood, but it doesn’t do me any good if I suddenly crave for wood It sounds like someone decided to mess with me! What good does it make to talk about an unmovable force when I cannot say for sure if I have experienced it or not? Isn’t that sort of what we think about life? people rising from their graves is not a part of my experience but just as I cannot talk about having 30 until I get indeed to that age, I cannot talk about death ’till I’m dead. I can assume lots of things sure!! and I can even feel motivated or afraid for something that hasn’t happened and we don’t even know how it has been happening in the first place. We have a serious tendency to define our feeling called ‘being alive’ against the feeling of an experience completely unknown to us and THUS our present feels EXACTLY as we imagine that to feel like. But you and I know that I cannot seriously say for sure if I’m dead or alive! we like to feel a certain way about it! and thats exactly the feeling involved in this paradoxes. Paradoxes always involve the use and understanding of ‘infinity’ at some point. To see all paradoxes resolved, I propose starting by understanding that you can’t cut infinity in half, because, infinity assumes ”absence of parts” not ”an infinite amount of them” we are ALREADY talking about infinity in terms of ”parts” and saying that sounds like saying: an infinite amount of infinity

  • almozayaf

    The appel Paradox from TAXI tv
    http://www.youtube.com/watch?v=-U7c-9flCOs

  • gouerosp s

    Name

  • Alex

    Well what about will in place of objects? Kind of like the Dark Knight, when Joker says “this is what happens when an unstoppable force meets an immovable object”

    Will does not need to and energy or inertia to be unstoppable. Batman has a strict code to never kill anyone (the immovable object) and Joker tries his best to push his limits and get him to kill him (the unstoppable force). Batman will never kill anyone, Joker will never stopping trying to get him too. Joker keeps pushing his limits but Batman’s limits to his will are completely infinite. Joker can keep pushing but nothing will happen. Does this mean the immovable object is stronger than the unstoppable force? But Joker continually pushes and in fact keeps pushing his limits as to what Batman will do so the unstoppable force is still moving, but the immovable object still hasn’t moved.

    • Isaac

      Well what is your question? If the existence of an immovable object was not possible then we wouldn’t know about an unstoppable force either even if there was one of them present.
      But how do you define whats present now? You can’t. We have failed and will continue to do so for eternity as a species, until we understand there’s no need for definition.
      A good example: you think you are the person you see in the mirror or the one who speaks inside your head with your own voice? Take a look in the mirror and see there is no one using your mouth when you hear your voice inside your head. Now are you using your ears to listen to your voice? If you hear a voice inside your head which sounds just like when you move your mouth to talk, then you got yourself a paradox! Who is the one who needs to hear inside your head and who is the one who needs to listen? Go check out the other side of the paradox.

  • secret

    this helped my homework THANKS!!!!!!!!!!!

  • jh

    The first paradox doesn’t make sense, just because He can control what He does, doesn’t mean He will…