Anybody know any good paradoxes?

[Goathead]

The one that always comes to my mind first is the "liar paradox":

This statement is false.

[redqueen]

1. best one ever:

Some sets, such as the set of all teacups, are not members of themselves. Other sets, such as the set of all non-teacups, are members of themselves. Call the set of all sets that are not members of themselves "R." If R is a member of itself, then by definition it must not be a member of itself. Similarly, if R is not a member of itself, then by definition it must be a member of itself.

On edit... this is called "Russell's Paradox"... To learn about this and more fun set related stuff, take a discrete math course or just google Russell's Paradox... it's fantastical!

[Commie Pinko Dirtbag]

11. I'm not aware of the exact details

But I think ol' Bertrand patched many of those holes in his Principia Mathematica. For instance, you can't assume that for every proposition f dependent on a variable x, there is a set of {x|f(x) is true}. For example, there's no "set of all sets that are not members of themselves".

In fact, there's no set X than can be called "set of all sets" either, because if there was, you could construct a set greater than that -- just say "set of all subsets of X". It's a reasoning similar to the proof for infinite number of primes.

Edit: this is a good book on the subject: http://search.barnesandnoble.com/OopBooks/OopResultsTitle.asp?WID=52981353

[redqueen]

13. Oooooh geek speak gets me so hot!

:loveya:

Yeah it's wrong, but so is the 'can't get there from here' one below... it's still fun. :)

[Richardo]

2. Bart Simpson: "You're damned if you do, and you're damned if you don't."

The 'Genius' episode. :D

[Goathead]

6. LOL classic!

That was such an early Simpson's. RDR~2 or Har Dee Har Har Get it?

[4_Legs_Good]

7. Damn! You beat me to it

Grrrrr...

david

[catzies]

3. Mine

The French are funny.
Sex is funny.
Comedy is funny.

Yet no French sex comedies are funny.

[CO Liberal]

4. Army Intelligence

:-)

[redqueen]

5. Military Intelligence

and that's an oxymoron, not a paradox... but still funny. :)

[unblock]

9. the holy roman empire was neither holy, nor roman, nor an empire. discuss.

as long as we're doing oxymorons....

[CO Liberal]

10. Chick Peas Are Neither Chicks Nor Peas. Discuss.

:-)

[unblock]

15. peanuts are neither peas nor nuts. discuss.

[unblock]

8. zeno's paradox: you can't get there from here

in order to get there, you first have to go halfway to there.
then, you have to cover half the remaining distance.

no matter how many times you advance to halfway points, there's always another halfway point before you can get there. in fact, there's an infinite number of halfway points.

so how can you get there from here?

[sui generis]

12. let's see, there's the parents

and I know many married pair'o'docs too . . .

[dean_dem]

14. If you are walking towards an object...

...and you cut you speed in half with every step, you will never actually stop, but you will also never reach the object.

My head hurts now.

[Abelman]

16. Ow

my brain hurts

[patcox2]

17. But mathematically false, no?

The infinite sum of 1/X to the N power is a finite number for any power of X greater than, what is it, 1? Does that have anything to do with it? Help, I've forgotten my calculus and I can't get up.

[Commie Pinko Dirtbag]

20. Sorta

But in this case the variable part is the exponent (sum of 1/K^n rather than sum of 1/n^K), not the base. But you're right, in both cases K has to be greater than 1 for the series to converge.

[dean_dem]

23. I think you're right, but I never took Calculus...

(Thank you, crappy VA school system). But it doesn't actually involve all that. The point is that if your speed decreases infinitely, it never actually hits zero. And the time it takes to cover a certain distance will also decrease infinitely, but you will still never actually stop.

[CO Liberal]

18. Republican Family Values

:-)

[Goathead]

19. Oh yeah, this is a good one

found it on Wikipedia:
http://en.wikipedia.org/wiki/Ship_of_Theseus

Ship of Theseus
From Wikipedia, the free encyclopedia.
The Ship of Theseus is a replacement paradox also known as Theseus's paradox.

According to Greek legend as reported by Plutarch,

"The ship wherein Theseus and the youth of Athens returned had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same."
There is also an additional question: if the replaced parts were stored in a warehouse and later used to reconstruct the ship, which—if either—would be the original ship of Theseus?

[immoderate]

21. The outline of all outlines...

Is an outline that has all other outlines listed. Where is the outline of outlines that are not in the outline of all outlines?

--IMM

[HalfManHalfBiscuit]

22. The title of Oasis' forthcoming album

"Don't Believe the Truth"

Mindblowing.

[CO Liberal]

24. Rush Limbaugh - America's Truth Detector

He finds the truth, then says the opposite.

[11 Bravo]

26. And Limbaugh is also proof of the "Equine Paradox"

which states that there are more horse's asses than there are horses.

[DelawareValleyDem]

25. A politcal one - the Alabama paradox

The Alabama paradox was the first of the apportionment paradoxes to be discovered. After the 1880 census, C. W. Seaton, chief clerk of the U. S. Census Office, computed apportionments for all House sizes between 275 and 350, and discovered that Alabama would get 8 seats with a House size of 299 but only 7 with a House size of 300. In general the term Alabama paradox refers to any apportionment scenario where increasing the total number of items would decrease one of the shares.

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

[Sporadicus]

27. Do You Not Find It Paradoxical...

...that in all of a cat's fur, there are only two holes, conveniently located where its eyes are?

...that when god(dess) created man(woman), glasses hadn't been invented - yet, look where (s)he placed our ears?

...that just enough happens in the world each day to fill every page of the daily newspaper?